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Search Results (42,023)

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12 pages, 1919 KiB  
Article
Sensitivity Analysis of Numerical Coherency Model for Rock Sites
by Dongyeon Lee, Yonghee Lee, Hak-Sung Kim, Jeong-Seon Park and Duhee Park
Appl. Sci. 2025, 15(6), 2925; https://doi.org/10.3390/app15062925 - 7 Mar 2025
Abstract
Characterization of ground motion incoherency can significantly reduce the seismic load imposed on large scale infrastructures. Because of difficulties in developing an empirical coherency function from a site-specific dense array, it is seldom used in practice. A number of studies used numerical simulations [...] Read more.
Characterization of ground motion incoherency can significantly reduce the seismic load imposed on large scale infrastructures. Because of difficulties in developing an empirical coherency function from a site-specific dense array, it is seldom used in practice. A number of studies used numerical simulations to develop generic coherency models. However, they have only been developed for idealized profiles. A comprehensive parametric study evaluating the effect of various parameters influencing the calculated coherency function has not yet been performed. We utilized the measured shear wave velocity (Vs) profile at Pinyon Flat, located in California, to perform a suite of time history analyses. This site was selected because the empirical coherency function developed here has been used as a reference model for rock sites. We performed several sensitivity studies investigating the effect of both the site spatial variability and numerical analysis parameters in order to provide a guideline for developing a coherency model from numerical simulations. The outputs were compared against the empirical coherency model to better illustrate the importance of the parameters. The coefficient of variation (CV) of Vs was revealed to be the primary parameter influencing the calculated plane-wave coherency, whereas the correlation length (CL) has a secondary influence. Site-specific convergence analyses should be performed to determine the optimum numerical parameter, including the number of analyses and depth of numerical model. Considering the importance of CV and Vs, it is recommended to perform field tests to determine site-specific values to derive numerical coherency functions. Full article
(This article belongs to the Section Civil Engineering)
20 pages, 576 KiB  
Article
Model-Free Adaptive Control for Attitude Stabilization of Earth-Pointing Spacecraft Using Magnetorquers
by Fabio Celani, Mohsen Heydari and Alireza Basohbat Novinzadeh
Aerospace 2025, 12(3), 219; https://doi.org/10.3390/aerospace12030219 - 7 Mar 2025
Abstract
This paper presents an attitude stabilization algorithm for a Low Earth Orbit (LEO) Earth-pointing spacecraft using magnetorquers as the only torque actuators and employing Model-Free Adaptive Control (MFAC) as the control algorithm. MFAC is a data-driven control algorithm that relies solely on input–output [...] Read more.
This paper presents an attitude stabilization algorithm for a Low Earth Orbit (LEO) Earth-pointing spacecraft using magnetorquers as the only torque actuators and employing Model-Free Adaptive Control (MFAC) as the control algorithm. MFAC is a data-driven control algorithm that relies solely on input–output data from the plant. This paper validates the effectiveness of the proposed approach through numerical simulations in a specific case study. The simulations show that the proposed algorithm drives the spacecraft’s attitude to three-axis stabilization in the orbital frame from arbitrary initial tumbling conditions. The numerical study also shows that the proposed control algorithm outperforms a model-based Proportional–Derivative (PD) control in terms of pointing accuracy at the expense of higher energy consumption. Full article
(This article belongs to the Special Issue Spacecraft Dynamics and Control (2nd Edition))
14 pages, 264 KiB  
Opinion
The Reasonable Ineffectiveness of Mathematics in the Biological Sciences
by Seymour Garte, Perry Marshall and Stuart Kauffman
Entropy 2025, 27(3), 280; https://doi.org/10.3390/e27030280 - 7 Mar 2025
Abstract
The known laws of nature in the physical sciences are well expressed in the language of mathematics, a fact that caused Eugene Wigner to wonder at the “unreasonable effectiveness” of mathematical concepts to explain physical phenomena. The biological sciences, in contrast, have resisted [...] Read more.
The known laws of nature in the physical sciences are well expressed in the language of mathematics, a fact that caused Eugene Wigner to wonder at the “unreasonable effectiveness” of mathematical concepts to explain physical phenomena. The biological sciences, in contrast, have resisted the formulation of precise mathematical laws that model the complexity of the living world. The limits of mathematics in biology are discussed as stemming from the impossibility of constructing a deterministic “Laplacian” model and the failure of set theory to capture the creative nature of evolutionary processes in the biosphere. Indeed, biology transcends the limits of computation. This leads to a necessity of finding new formalisms to describe biological reality, with or without strictly mathematical approaches. In the former case, mathematical expressions that do not demand numerical equivalence (equations) provide useful information without exact predictions. Examples of approximations without equal signs are given. The ineffectiveness of mathematics in biology is an invitation to expand the limits of science and to see that the creativity of nature transcends mathematical formalism. Full article
(This article belongs to the Section Entropy and Biology)
25 pages, 18710 KiB  
Article
Evaluation of the Performance of Soil-Nailed Walls in Weathered Sandstones Utilizing Instrumental Data
by Anıl Yeni, Murat Ergenokon Selçuk and Ömer Ündül
Appl. Sci. 2025, 15(6), 2908; https://doi.org/10.3390/app15062908 - 7 Mar 2025
Abstract
Used for soil and weathered rocks, soil nails are rigid reinforcements positioned at certain angles on the ground to provide slope stability. A rigid reinforcement element placed in a well filled with cement grout mix after completing drilling will generate adherence stress between [...] Read more.
Used for soil and weathered rocks, soil nails are rigid reinforcements positioned at certain angles on the ground to provide slope stability. A rigid reinforcement element placed in a well filled with cement grout mix after completing drilling will generate adherence stress between the grout-mixed nail bar and soil. Due to this stress, load is transferred to the soil along the soil–grout interaction surface. In the case discussed herein, the slope at the parcel border needed to be made steeper in order to accommodate the construction of a facility in the Taşkısığı region of Sakarya province. Soil-nailed walls, which are inexpensive and suitable for weathered rocks, were needed as a support system because the slope was too steep to support itself. Support system performance was measured using two inclinometers and two soil nail pull-out tests conducted on different sections observed during and after construction. Contrary to the design-phase prediction, it was determined that the stresses started to dampen in the region closer to the slope-facing zone. Field measurement data and numerical analysis revealed that higher parameters than necessary were selected. In this context, sensitivity and parameter analyses were carried out using the Hoek–Brown constitutive model. The GSI value was re-evaluated and found to be compatible with the observation results obtained from the field performance. Since the retaining wall performance observed was higher than expected, geometric parametric analysis of the structural elements was performed; high safety coefficients were found across variations. The effects of the inclination of the slope, nail length, nail spacing, and nail slope design parameters on the safety coefficient and horizontal displacement were examined. The optimal design suggested nail lengths of 4.00 m, a spacing of 1.60 m, and slopes of 20°. It was discovered that the effect of the inclination degree of the slope on the safety coefficient was lower than expected. The results revealed that a more economical design with a similar safety factor can be obtained by shortening the lengths of the nails. Full article
(This article belongs to the Section Civil Engineering)
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Figure 1

Figure 1
<p>Location maps of the study area.</p>
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<p>A schematic related to the principles and building of the model.</p>
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<p>Various images of the study area at different stages: (<b>a</b>) boring; (<b>b</b>) pressure meter; (<b>c</b>) pull-out test equipment on a soil nail; (<b>d</b>) data logger for strain gauge reading; (<b>e</b>) pull-out test readings.</p>
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<p>Map showing the locations of boreholes (the blue boundary with a dashed area indicates the project area).</p>
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<p>Images of the sandstone in the study area: (<b>a</b>) completely weathered levels; (<b>b</b>) moderately weathered levels.</p>
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<p>Soil profile constructed according to the borehole data.</p>
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<p>Changes in physical and mechanical properties by depth.</p>
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<p>Variation in internal parameters: (<b>a</b>) angle of internal friction; (<b>b</b>) effective cohesion.</p>
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<p>Calculated horizontal displacement values from the Mohr–Coulomb model (1–1′ Section).</p>
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<p>Calculated horizontal displacement values from the Mohr–Coulomb model (2–2′ Section).</p>
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<p>Longitudinal section along the profile of the soil nail support system.</p>
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<p>A view of the soil-nailed support system after the completion of the construction phase (PT refers to pull-out test location, and IM refers to inclinometer location).</p>
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<p>Inclinometer results.</p>
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<p>Setup of the soil nail pull-out test.</p>
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<p>Soil nail pull-out test setup.</p>
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<p>Placement of strain gauge sensors on nail reinforcement via welding.</p>
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<p>Displacements in nail heads under tensile load: (<b>a</b>) PT1; (<b>b</b>) PT2.</p>
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<p>Distribution of the loads on the strain gauge sensors in the tensile test stages (<b>a</b>) PT1; (<b>b</b>) PT2.</p>
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<p>Sensitivity analyses of different degrees of weathered sandstone unit parameters: (<b>a</b>) W4–W5; (<b>b</b>) W3.</p>
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<p>Results of geometric parameter analysis using the Hoek–Brown constitutive model.</p>
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<p>Section 1–1′ HB constitutive model, preferred for geometric analysis and the inclinometer section. (<b>a</b>) Total displacement on the model; (<b>b</b>) total displacement on the wall (red denotes the (+) x direction, and blue denotes the (−) x direction).</p>
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<p>Section 2–2′ HB constitutive model, preferred for geometric analysis and the inclinometer section.</p>
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<p>Comparison of numerical analyses of Section 1−1′ and Section 2−2′ alongside actual field measurements.</p>
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<p>Horizontal displacements in the remodeled Sections 1–1′ and 2–2′.</p>
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<p>Horizontal displacement values of the inclinometer section in the remodeled Sections 1–1′ and 2–2′.</p>
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16 pages, 2125 KiB  
Article
The Use of Heterologous Antigens for Biopanning Enables the Selection of Broadly Neutralizing Nanobodies Against SARS-CoV-2
by Vazirbek S. Aripov, Anna V. Zaykovskaya, Ludmila V. Mechetina, Alexander M. Najakshin, Alexander A. Bondar, Sergey G. Arkhipov, Egor A. Mustaev, Margarita G. Ilyina, Sophia S. Borisevich, Alexander A. Ilyichev, Valentina S. Nesmeyanova, Anastasia A. Isaeva, Ekaterina A. Volosnikova, Dmitry N. Shcherbakov and Natalia V. Volkova
Antibodies 2025, 14(1), 23; https://doi.org/10.3390/antib14010023 - 7 Mar 2025
Abstract
Background: Since the emergence of SARS-CoV-2 in the human population, the virus genome has undergone numerous mutations, enabling it to enhance transmissibility and evade acquired immunity. As a result of these mutations, most monoclonal neutralizing antibodies have lost their efficacy, as they are [...] Read more.
Background: Since the emergence of SARS-CoV-2 in the human population, the virus genome has undergone numerous mutations, enabling it to enhance transmissibility and evade acquired immunity. As a result of these mutations, most monoclonal neutralizing antibodies have lost their efficacy, as they are unable to neutralize new variants. Antibodies that neutralize a broad range of SARS-CoV-2 variants are of significant value in combating both current and potential future variants, making the identification and development of such antibodies an ongoing critical goal. This study discusses the strategy of using heterologous antigens in biopanning rounds. Methods: After four rounds of biopanning, nanobody variants were selected from a phage display library. Immunochemical methods were used to evaluate their specificity to the S protein of various SARS-CoV-2 variants, as well as to determine their competitive ability against ACE2. Viral neutralization activity was analyzed. A three-dimensional model of nanobody interaction with RBD was constructed. Results: Four nanobodies were obtained that specifically bind to the receptor-binding domain (RBD) of the SARS-CoV-2 spike glycoprotein and exhibit neutralizing activity against various SARS-CoV-2 strains. Conclusions: The study demonstrates that performing several rounds of biopanning with heterologous antigens allows the selection of nanobodies with a broad reactivity spectrum. However, the fourth round of biopanning does not lead to the identification of nanobodies with improved characteristics. Full article
(This article belongs to the Section Antibody Discovery and Engineering)
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Graphical abstract

Graphical abstract
Full article ">Figure 1
<p>Phage display scheme showing antigens, eluate, and amplicon titres for each round.</p>
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<p>Electrophoretic separation of synthesized nanobodies in 10% SDS-PAGE. Labels: M—molecular weight protein markers with the molecular weight in kDa indicated on the left (Precision Plus Protein™ Dual Xtra Prestained Protein Standards, Bio-Rad, Hercules, CA, USA); RC, SKP, KWL, PRV—purified recombinant nanobodies.</p>
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<p>Binding of ACE2 to recombinant SARS-CoV-2 S protein trimers upon inhibition of interaction by nanobodies. The 100% interaction level is considered to be the signal of direct binding between the trimer and ACE2. Notations: PRV, KWL, SKP, RC—lysates of nanobody producers; <span class="html-italic">E. coli</span> (C−)—negative control producer, lysate of cells transformed with the pET21a(−) plasmid; VHH9 (C−)—nanobody specific to HIV-1, negative control of a heterologous nanobody; iB20—broad-neutralizing human monoclonal antibody against SARS-CoV-2 [<a href="#B32-antibodies-14-00023" class="html-bibr">32</a>], positive control. One-way ANOVA showed statistically significant differences in the inhibition of ACE2 binding among nanobodies for each SARS-CoV-2 variant (Wuhan, Delta, and Omicron) with <span class="html-italic">p</span> &lt; 0.0001.</p>
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<p>Position of the KWL nanobody in the ACE2-binding domain. (<b>a</b>)—visualization of the ACE2–RBD complex (PDB ID 6VW1 [<a href="#B42-antibodies-14-00023" class="html-bibr">42</a>]); (<b>b</b>)—statistically significant KWL–RBD–Wuhan complex; (<b>c</b>)—statistically significant KWL–RBD–Delta complex; (<b>d</b>)—statistically significant KWL–RBD–Omicron complex, obtained as a result of clustering the last 100 ns of MD simulation. For better visual perception, the structure of each protein, including α-helices and β-strands, is shown in different colors. In panel (<b>a</b>), ACE2 is shown in green, in panels (<b>b</b>–<b>d</b>), the KWL nanobody is shown in purple, RBD Wuhan in blue, RBD Delta in red, and RBD Omicron in green. Hydrogen bonds, salt bridges, and π-π stacking interactions are shown as yellow, purple, and blue dashed lines, respectively.</p>
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<p>Loss of nanobody variant diversity during standard phage display procedures.</p>
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19 pages, 1581 KiB  
Article
A Structural Credit Risk Model with Jumps Based on Uncertainty Theory
by Hong Huang, Meihua Jiang, Yufu Ning and Shuai Wang
Mathematics 2025, 13(6), 897; https://doi.org/10.3390/math13060897 - 7 Mar 2025
Abstract
This study, within the framework of uncertainty theory, employs an uncertain differential equation with jumps to model the asset value process of a company, establishing a structured model of uncertain credit risk that incorporates jumps. This model is applied to the pricing of [...] Read more.
This study, within the framework of uncertainty theory, employs an uncertain differential equation with jumps to model the asset value process of a company, establishing a structured model of uncertain credit risk that incorporates jumps. This model is applied to the pricing of two types of credit derivatives, yielding pricing formulas for corporate zero-coupon bonds and Credit Default Swap (CDS). Through numerical analysis, we examine the impact of asset value volatility and jump magnitude on corporate default uncertainty, as well as the influence of jump magnitude on the pricing of zero-coupon bonds and CDS. The results indicate that an increase in volatility levels significantly enhances default uncertainty, and an expansion in the magnitude of negative jumps not only directly elevates default risk but also leads to a significant increase in the value of zero-coupon bonds and the price of CDS through a risk premium adjustment mechanism. Therefore, when assessing corporate default risk and pricing credit derivatives, the disturbance of asset value jumps must be considered a crucial factor. Full article
(This article belongs to the Special Issue Uncertainty Theory and Applications)
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Figure 1

Figure 1
<p>Pictorial representation of the proposed work.</p>
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<p>The variation in <math display="inline"><semantics> <msub> <mi mathvariant="script">M</mi> <mi>T</mi> </msub> </semantics></math> with respect to <math display="inline"><semantics> <mi>η</mi> </semantics></math>.</p>
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<p>The variation in <math display="inline"><semantics> <msub> <mi mathvariant="script">M</mi> <mi>T</mi> </msub> </semantics></math> with respect to <math display="inline"><semantics> <mi>σ</mi> </semantics></math>.</p>
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<p>The variation in <math display="inline"><semantics> <msub> <mi mathvariant="script">M</mi> <mi>T</mi> </msub> </semantics></math> with respect to <math display="inline"><semantics> <mi>μ</mi> </semantics></math>.</p>
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<p>The research approach of this section.</p>
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<p>The variation in <math display="inline"><semantics> <mrow> <mi>C</mi> <mi>S</mi> <mfenced separators="" open="(" close=")"> <mrow> <mn>0</mn> <mo>,</mo> <mi>T</mi> </mrow> </mfenced> </mrow> </semantics></math> with respect to <math display="inline"><semantics> <mi>η</mi> </semantics></math>.</p>
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<p>The variation in <math display="inline"><semantics> <mi>ω</mi> </semantics></math> with respect to <math display="inline"><semantics> <mi>η</mi> </semantics></math>.</p>
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18 pages, 7319 KiB  
Article
Parametric Aerodynamic Study of Galloping Piezoelectric Energy Harvester with Arcuate Protruding and Depressed Features
by Xiaokang Yang, Bingke Xu, Zhendong Shang, Chunyang Liu, Haichao Cai and Xiangyi Hu
Sensors 2025, 25(6), 1657; https://doi.org/10.3390/s25061657 - 7 Mar 2025
Abstract
This study explores the potential effect of a cross-sectional shape with an arcuate protruding and depressed features on the performance. The geometric configurations include two feature types (protruding and depressed), each with six distinct perimeter arrangements and three depths per arrangement, yielding thirty-six [...] Read more.
This study explores the potential effect of a cross-sectional shape with an arcuate protruding and depressed features on the performance. The geometric configurations include two feature types (protruding and depressed), each with six distinct perimeter arrangements and three depths per arrangement, yielding thirty-six different cross-sectional shapes for systematic evaluation. The aerodynamic characteristics and electrical performance are numerically analyzed, using a computational fluid dynamics model and a distributed parameter electromechanical coupling model, respectively. A smooth protruding feature on the front, top, or bottom side suppresses the electrical output; however, when located on the rear side, it significantly increases the slope of the power versus wind speed curve. Depressed features on the rear, top, or bottom side only reduce the critical wind speed and the power enhancement positively correlates with the feature depth. Compared to a square, a harvester with depressed feature on both top and bottom sides exhibits a significant jump in power at the critical wind speed, greatly improving the power. These findings provide important design guidelines for structural optimization of galloping piezoelectric energy harvesters, enabling them to match the wind energy distribution characteristics of specific regions with optimal performance. Full article
(This article belongs to the Special Issue Energy Harvesting and Self-Powered Sensors)
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Figure 1

Figure 1
<p>Schematic of the GPEH and the configuration of its cross-sectional shape.</p>
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<p>(<b>a</b>) Experimental setup; (<b>b</b>) power versus load; (<b>c</b>) power versus frequency.</p>
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<p>(<b>a</b>) Flow chart of the simulation process; (<b>b</b>) experimental and numerical results for the prototype; (<b>c</b>) comparison of results from the proposed model and the previous study by Yang [<a href="#B9-sensors-25-01657" class="html-bibr">9</a>].</p>
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<p>(<b>a</b>) Computational mesh; comparison of the results in time domain: (<b>b</b>) <span class="html-italic">C<sub>L</sub></span>, (<b>c</b>) <span class="html-italic">C<sub>D</sub></span>.</p>
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<p>Numerical coefficients versus the angle of attack for protruding and depressed features on the front and/or rear sides: (<b>a</b>) <span class="html-italic">C<sub>L</sub></span>, (<b>b</b>) <span class="html-italic">C<sub>D</sub></span>, and (<b>c</b>) <span class="html-italic">C<sub>Fy</sub></span> for the protruding feature; (<b>d</b>) <span class="html-italic">C<sub>L</sub></span>, (<b>e</b>) <span class="html-italic">C<sub>D</sub></span>, and (<b>f</b>) <span class="html-italic">C<sub>Fy</sub></span> for the depressed feature.</p>
Full article ">Figure 5 Cont.
<p>Numerical coefficients versus the angle of attack for protruding and depressed features on the front and/or rear sides: (<b>a</b>) <span class="html-italic">C<sub>L</sub></span>, (<b>b</b>) <span class="html-italic">C<sub>D</sub></span>, and (<b>c</b>) <span class="html-italic">C<sub>Fy</sub></span> for the protruding feature; (<b>d</b>) <span class="html-italic">C<sub>L</sub></span>, (<b>e</b>) <span class="html-italic">C<sub>D</sub></span>, and (<b>f</b>) <span class="html-italic">C<sub>Fy</sub></span> for the depressed feature.</p>
Full article ">Figure 6
<p>Numerical coefficients versus the angle of attack for protruding and depressed features on the top and/or bottom sides: (<b>a</b>) <span class="html-italic">C<sub>L</sub></span>, (<b>b</b>) <span class="html-italic">C<sub>D</sub></span>, and (<b>c</b>) <span class="html-italic">C<sub>Fy</sub></span> for the protruding feature; (<b>d</b>) <span class="html-italic">C<sub>L</sub></span>, (<b>e</b>) <span class="html-italic">C<sub>D</sub></span>, and (<b>f</b>) <span class="html-italic">C<sub>Fy</sub></span> for the depressed feature.</p>
Full article ">Figure 7
<p>Numerical power versus wind speed: protruding features on (<b>a</b>) the front side only, (<b>b</b>) the rear side only, and (<b>c</b>) both the front and rear sides; depressed features on (<b>d</b>) the front side only, (<b>e</b>) the rear side only, and (<b>f</b>) both the front and rear sides.</p>
Full article ">Figure 8
<p>Numerical power versus wind speed: protruding features on (<b>a</b>) the top or bottom side only, and (<b>b</b>) both the top and bottom sides; depressed features on (<b>c</b>) the top or bottom side only, and (<b>d</b>) both the top and bottom sides.</p>
Full article ">
14 pages, 1247 KiB  
Article
Effects of Discretization of Smagorinsky–Lilly Subgrid Scale Model on Large-Eddy Simulation of Stable Boundary Layers
by Jonas Banhos and Georgios Matheou
Atmosphere 2025, 16(3), 310; https://doi.org/10.3390/atmos16030310 - 7 Mar 2025
Abstract
Large-eddy simulation (LES) models are sensitive to numerical discretization because of the large fraction of resolved turbulent energy (>80%) and the strong non-linear interactions between resolved-scale fields with the turbulence subgrid scale (SGS) model. The effects of the Smagorinsky–Lilly [...] Read more.
Large-eddy simulation (LES) models are sensitive to numerical discretization because of the large fraction of resolved turbulent energy (>80%) and the strong non-linear interactions between resolved-scale fields with the turbulence subgrid scale (SGS) model. The effects of the Smagorinsky–Lilly SGS model discretization are investigated. Three finite difference schemes are compared. Second-, fourth-, and sixth-order centered difference schemes are used to approximate the spatial derivatives of the SGS model. In the LES of homogeneous isotropic turbulence (HIT), including (non-isotropic) turbulent mixing of a passive scalar, no differences are observed with respect to the SGS model discretization. The HIT LES results are validated against a direct numerical simulation, which resolves all flow scales and does not include an SGS model. In the LES of a moderately stable atmospheric boundary layer, the LES results depend on the SGS discretization for coarse grid resolutions. The second-order scheme performs better at coarse resolutions compared to higher-order schemes. Overall, it is found that higher-order discretizations of the Smagorinsky–Lilly model are not beneficial compared to the second-order scheme. Full article
(This article belongs to the Section Atmospheric Techniques, Instruments, and Modeling)
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Figure 1

Figure 1
<p>Vertical planes of the LES initial scalar fluctuations fields. The LES initial condition is constructed using coarsened DNS data. The panels show four LES grid resolutions: (<b>a</b>) <math display="inline"><semantics> <msup> <mn>32</mn> <mn>3</mn> </msup> </semantics></math> grid, (<b>b</b>) <math display="inline"><semantics> <msup> <mn>64</mn> <mn>3</mn> </msup> </semantics></math> grid, (<b>c</b>) <math display="inline"><semantics> <msup> <mn>128</mn> <mn>3</mn> </msup> </semantics></math> grid, and (<b>d</b>) <math display="inline"><semantics> <msup> <mn>256</mn> <mn>3</mn> </msup> </semantics></math> grid. The DNS grid size is <math display="inline"><semantics> <msup> <mn>1024</mn> <mn>3</mn> </msup> </semantics></math>, which is 4 times finer than the field in panel (<b>d</b>).</p>
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<p>LES model grid configuration. A three-dimensional grid cell schematic is shown on the left. The corresponding two-dimensional configuration is shown on the right. Scalar variables and the diagonal elements of the stress tensor <math display="inline"><semantics> <mi>τ</mi> </semantics></math> are located at the grid cell centers. The velocity components (<span class="html-italic">u</span>, <span class="html-italic">v</span>, and <span class="html-italic">w</span>) and components of the SGS scalar flux (<math display="inline"><semantics> <mi>σ</mi> </semantics></math>) are located at the middle of the cell faces. The off-diagonal elements of the stress tensor are located at the middle grid cell edges in three dimensions (<b>left</b>) and at the grid cell corners in two dimensions (<b>right</b>).</p>
Full article ">Figure 3
<p>Comparison of resolved-scale TKE and scalar variance between the DNS and LES. (<b>Top row</b>) Panels (<b>a</b>–<b>d</b>) correspond to TKE and (<b>bottom row</b>) (<b>e</b>–<b>h</b>) correspond to scalar variance. Each column corresponds to a different LES grid resolution: (<b>a</b>,<b>e</b>) <math display="inline"><semantics> <msup> <mn>32</mn> <mn>3</mn> </msup> </semantics></math> grid, (<b>b</b>,<b>f</b>) <math display="inline"><semantics> <msup> <mn>64</mn> <mn>3</mn> </msup> </semantics></math> grid, (<b>c</b>,<b>g</b>) <math display="inline"><semantics> <msup> <mn>128</mn> <mn>3</mn> </msup> </semantics></math> grid, and (<b>d</b>,<b>h</b>) <math display="inline"><semantics> <msup> <mn>256</mn> <mn>3</mn> </msup> </semantics></math> grid.</p>
Full article ">Figure 4
<p>Stable boundary layer zonal velocity profiles at different LES grid resolutions and SGS term discretizations at <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>=</mo> <mn>9</mn> <mspace width="0.277778em"/> <mi mathvariant="normal">h</mi> </mrow> </semantics></math>. Each panel corresponds to a different grid resolution. Lines correspond to different orders of SGS term discretizations.</p>
Full article ">Figure 5
<p>Stable boundary layer potential temperature profiles at different LES grid resolutions and SGS term discretizations at <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>=</mo> <mn>9</mn> <mspace width="0.277778em"/> <mi mathvariant="normal">h</mi> </mrow> </semantics></math>. Each panel corresponds to a different grid resolution: (<b>a</b>) <math display="inline"><semantics> <mrow> <mo>Δ</mo> <mi>x</mi> <mo>=</mo> <mn>8</mn> <mspace width="0.277778em"/> <mi mathvariant="normal">m</mi> </mrow> </semantics></math>, (<b>b</b>) <math display="inline"><semantics> <mrow> <mo>Δ</mo> <mi>x</mi> <mo>=</mo> <mn>4</mn> <mspace width="0.277778em"/> <mi mathvariant="normal">m</mi> </mrow> </semantics></math>, and (<b>c</b>) <math display="inline"><semantics> <mrow> <mo>Δ</mo> <mi>x</mi> <mo>=</mo> <mn>2</mn> <mspace width="0.277778em"/> <mi mathvariant="normal">m</mi> </mrow> </semantics></math>. Lines correspond to different orders of SGS term discretization.</p>
Full article ">Figure 6
<p>Stable boundary layer turbulent heat flux at different LES grid resolutions and SGS term discretizations at <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>=</mo> <mn>9</mn> <mspace width="0.277778em"/> <mi mathvariant="normal">h</mi> </mrow> </semantics></math>. Each panel corresponds to a different grid resolution: (<b>a</b>) <math display="inline"><semantics> <mrow> <mo>Δ</mo> <mi>x</mi> <mo>=</mo> <mn>8</mn> <mspace width="0.277778em"/> <mi mathvariant="normal">m</mi> </mrow> </semantics></math>, (<b>b</b>) <math display="inline"><semantics> <mrow> <mo>Δ</mo> <mi>x</mi> <mo>=</mo> <mn>4</mn> <mspace width="0.277778em"/> <mi mathvariant="normal">m</mi> </mrow> </semantics></math>, and (<b>c</b>) <math display="inline"><semantics> <mrow> <mo>Δ</mo> <mi>x</mi> <mo>=</mo> <mn>2</mn> <mspace width="0.277778em"/> <mi mathvariant="normal">m</mi> </mrow> </semantics></math>. Lines correspond to different orders of SGS term discretization.</p>
Full article ">Figure 7
<p>Stable boundary layer time traces of vertically integrated TKE at different LES grid resolutions and SGS term discretizations. Each panel corresponds to a different grid resolution: (<b>a</b>) <math display="inline"><semantics> <mrow> <mo>Δ</mo> <mi>x</mi> <mo>=</mo> <mn>8</mn> <mspace width="0.277778em"/> <mi mathvariant="normal">m</mi> </mrow> </semantics></math>, (<b>b</b>) <math display="inline"><semantics> <mrow> <mo>Δ</mo> <mi>x</mi> <mo>=</mo> <mn>4</mn> <mspace width="0.277778em"/> <mi mathvariant="normal">m</mi> </mrow> </semantics></math>, and (<b>c</b>) <math display="inline"><semantics> <mrow> <mo>Δ</mo> <mi>x</mi> <mo>=</mo> <mn>2</mn> <mspace width="0.277778em"/> <mi mathvariant="normal">m</mi> </mrow> </semantics></math>. Lines correspond to different orders of SGS term discretization.</p>
Full article ">Figure 8
<p>One-dimensional compensated spectra of zonal wind for the stable boundary layer at grid resolution <math display="inline"><semantics> <mrow> <mo>Δ</mo> <mi>x</mi> <mo>=</mo> <mn>8</mn> <mspace width="0.277778em"/> <mi mathvariant="normal">m</mi> </mrow> </semantics></math> at <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>=</mo> <mn>9</mn> <mspace width="0.277778em"/> <mi mathvariant="normal">h</mi> </mrow> </semantics></math>. Each panel corresponds to a different height. Color lines correspond to different orders of the SGS term discretization, as in <a href="#atmosphere-16-00310-f007" class="html-fig">Figure 7</a>. Black line denotes slope <math display="inline"><semantics> <msup> <mi>k</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </semantics></math> for reference.</p>
Full article ">Figure 9
<p>One-dimensional compensated spectra of zonal wind for the stable boundary layer at grid resolution <math display="inline"><semantics> <mrow> <mo>Δ</mo> <mi>x</mi> <mo>=</mo> <mn>4</mn> <mspace width="0.277778em"/> <mi mathvariant="normal">m</mi> </mrow> </semantics></math> at <math display="inline"><semantics> <mrow> <mi>t</mi> <mo>=</mo> <mn>9</mn> <mspace width="0.277778em"/> <mi mathvariant="normal">h</mi> </mrow> </semantics></math>. Each panel corresponds to a different height. Color lines correspond to different orders of the SGS term discretization, as in <a href="#atmosphere-16-00310-f007" class="html-fig">Figure 7</a>. Black line denotes slope <math display="inline"><semantics> <msup> <mi>k</mi> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </semantics></math> for reference.</p>
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27 pages, 1056 KiB  
Article
Quantum Mechanical Numerical Model for Interaction of Dark Atom with Atomic Nucleus of Matter
by Timur Bikbaev, Maxim Khlopov and Andrey Mayorov
Physics 2025, 7(1), 8; https://doi.org/10.3390/physics7010008 - 7 Mar 2025
Abstract
Within the framework of the XHe hypothesis, the positive results of the DAMA/NaI and DAMA/LIBRA experiments on the direct search for dark matter particles can be explained by the annual modulation of the radiative capture of dark atoms into low-energy bound states with [...] Read more.
Within the framework of the XHe hypothesis, the positive results of the DAMA/NaI and DAMA/LIBRA experiments on the direct search for dark matter particles can be explained by the annual modulation of the radiative capture of dark atoms into low-energy bound states with sodium nuclei. Since this effect is not observed in other underground WIMP (weakly interacting massive particle) search experiments, it is necessary to explain these results by investigating the possibility of the existence of low-energy bound states between dark atoms and the nuclei of matter. Numerical modeling is used to solve this problem, since the study of the XHe–nucleus system is a three-body problem and leaves no possibility of an analytical solution. To understand the key properties and patterns underlying the interaction of dark atoms with the nuclei of baryonic matter, we develop the quantum mechanical description of such an interaction. In the numerical quantum mechanical model presented, takes into account the effects of quantum physics, self-consistent electromagnetic interaction, and nuclear attraction. This approach allows us to obtain a numerical model of the interaction between the dark atom and the nucleus of matter and interpret the results of direct experiments on the underground search for dark matter, within the framework of the dark atom hypothesis. Thus, in this paper, for the first time, steps are taken towards a consistent quantum mechanical description of the interaction of dark atoms, with unshielded nuclear attraction, with the nuclei of atoms of matter. The total effective interaction potential of the OHe–Na system has therefore been restored, the shape of which allows for the preservation of the integrity and stability of the dark atom, which is an essential requirement for confirming the validity of the OHe hypothesis. Full article
(This article belongs to the Special Issue Beyond the Standard Models of Physics and Cosmology: 2nd Edition)
Show Figures

Figure 1

Figure 1
<p>Hypothetical qualitative form of the effective interaction potential of XHe dark atom with the nucleus of atom of matter [<a href="#B1-physics-07-00008" class="html-bibr">1</a>]. See text for details.</p>
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<p>The eigenvalues of the helium nucleus Hamiltonian, corresponding to the first three energy levels, in the OHe dark atom potential (red solid line), along with the squared modulus of the wave functions associated with these energy levels (blue solid line). The results of the paper [<a href="#B16-physics-07-00008" class="html-bibr">16</a>] were used in the calculations.</p>
Full article ">Figure 3
<p>Interaction potentials in the OHe–Na system for fixed <math display="inline"><semantics> <msub> <mover accent="true"> <mi>R</mi> <mo>→</mo> </mover> <mi>OA</mi> </msub> </semantics></math>, including the Coulomb interaction (green dotted line) and nuclear interaction (black dotted line) between the helium nucleus and the sodium nucleus, as well as the Coulomb potential between the helium nucleus and the <math display="inline"><semantics> <msup> <mi mathvariant="normal">O</mi> <mrow> <mo>−</mo> <mo>−</mo> </mrow> </msup> </semantics></math> particle (blue dotted line). The combined total interaction potential experienced by the helium nucleus is represented by the red dotted line. The red circle shows the radius of the helium. The results of the paper [<a href="#B16-physics-07-00008" class="html-bibr">16</a>] were used in the calculations.</p>
Full article ">Figure 4
<p>The dependence of the helium ground-state energy in the polarized OHe (blue stars) on the radius vector of the sodium nucleus. The results of the paper [<a href="#B16-physics-07-00008" class="html-bibr">16</a>] were used in the calculations.</p>
Full article ">Figure 5
<p>The red solid line represents the total interaction potential of helium in the OHe–Na system for a fixed position of the sodium nucleus, <math display="inline"><semantics> <msub> <mover accent="true"> <mi>R</mi> <mo>→</mo> </mover> <mi>OA</mi> </msub> </semantics></math>. The blue solid line illustrates the squared modulus of the helium ground-state wave function within the polarized dark atom at the same fixed <math display="inline"><semantics> <msub> <mover accent="true"> <mi>R</mi> <mo>→</mo> </mover> <mi>OA</mi> </msub> </semantics></math>. Black circles denote the intersection points between the graph of the total helium potential and the squared modulus of its wave function in the ground state. The results of the paper [<a href="#B16-physics-07-00008" class="html-bibr">16</a>] were used in the calculations.</p>
Full article ">Figure 6
<p>The relationship between the dipole moment of the polarized OHe (blue stars) and the radius vector of the external sodium nucleus. The results of the paper [<a href="#B16-physics-07-00008" class="html-bibr">16</a>] were used in the calculations.</p>
Full article ">Figure 7
<p>The dependence of the dipole moment of the polarized OHe (blue stars) on the radius vector of the sodium nucleus at the moment when the dark atom undergoes repolarization. The results of the paper [<a href="#B16-physics-07-00008" class="html-bibr">16</a>] were used in the calculations.</p>
Full article ">Figure 8
<p>The squared modulus of the wave functions (blue solid line) for specific energy levels of helium in its ground state within the total interaction potential of the OHe–Na system (red solid line). These lines correspond to the particular positions of the sodium nucleus <math display="inline"><semantics> <msub> <mover accent="true"> <mi>R</mi> <mo>→</mo> </mover> <mi>OA</mi> </msub> </semantics></math>, marking the onset of the dark atom’s repolarization. The results of the paper [<a href="#B16-physics-07-00008" class="html-bibr">16</a>] were used in the calculations.</p>
Full article ">Figure 9
<p>The squared modulus of the wave functions (blue solid line) for certain ground-state energy levels of helium within the total potential of the OHe–Na system (red solid line). These are associated with the positions of the sodium nucleus <math display="inline"><semantics> <msub> <mover accent="true"> <mi>R</mi> <mo>→</mo> </mover> <mi>OA</mi> </msub> </semantics></math> at the stage when helium begins tunneling with high probability from the repolarized dark atom into the sodium nucleus. The results of the paper [<a href="#B16-physics-07-00008" class="html-bibr">16</a>] were used in the calculations.</p>
Full article ">Figure 10
<p>Various interaction potentials as functions of the distance between the helium nucleus, located within the Bohr orbit of the OHe, and the sodium: the nuclear potential in the Woods–Saxon form (black dotted line, overlapped by the blue dotted line), <math display="inline"><semantics> <msubsup> <mi>U</mi> <mi>XHe</mi> <mi mathvariant="normal">e</mi> </msubsup> </semantics></math> (green dotted line), the Stark potential (red dotted line, overlapped by the blue dotted line), and the total effective interaction potential of OHe with the sodium (blue dotted line). The black circle highlights the addition amount of the radii of the helium and sodium nuclei. The radius vector of helium is set to <math display="inline"><semantics> <mrow> <mi>r</mi> <mo>=</mo> <mo>|</mo> <mn>1.1</mn> <mo>×</mo> <msup> <mn>10</mn> <mrow> <mo>−</mo> <mn>12</mn> </mrow> </msup> <mrow> <mspace width="3.33333pt"/> <mi>cm</mi> <mo>|</mo> </mrow> </mrow> </semantics></math>. The results of the paper [<a href="#B16-physics-07-00008" class="html-bibr">16</a>] were used in the calculations.</p>
Full article ">Figure 11
<p>Various interaction potentials as functions of the separation between the helium and the sodium: the Woods–Saxon nuclear potential (black dotted line), the <math display="inline"><semantics> <msubsup> <mi>U</mi> <mi>XHe</mi> <mi mathvariant="normal">e</mi> </msubsup> </semantics></math> potential (green dotted line), the Stark potential (red dotted line), and the total effective interaction potential for the OHe–Na system (blue dotted line). The radius vector of He was set equal to <math display="inline"><semantics> <mrow> <mi>r</mi> <mo>=</mo> <mo>|</mo> <mn>1.1</mn> <mo>×</mo> <msup> <mn>10</mn> <mrow> <mo>−</mo> <mn>12</mn> </mrow> </msup> <mrow> <mspace width="3.33333pt"/> <mi>cm</mi> <mo>|</mo> </mrow> </mrow> </semantics></math> during the phase of repolarization of the OHe. The results of the paper [<a href="#B16-physics-07-00008" class="html-bibr">16</a>] were used in the calculations.</p>
Full article ">Figure 12
<p>Various interaction potentials as functions of the separation between the helium and the sodium: the Woods–Saxon nuclear potential (black dotted line, overlapped by the green dotted line), the <math display="inline"><semantics> <msubsup> <mi>U</mi> <mi>XHe</mi> <mi mathvariant="normal">e</mi> </msubsup> </semantics></math> potential (green dotted line), the Stark potential (red dotted line, overlapped by the blue dotted line), and the total effective interaction potential between OHe and the sodium (blue dotted line). The radius vector of helium was set equal to <math display="inline"><semantics> <mrow> <mi>r</mi> <mo>=</mo> <mo>|</mo> <mn>2.5</mn> <mo>×</mo> <msup> <mn>10</mn> <mrow> <mo>−</mo> <mn>12</mn> </mrow> </msup> <mrow> <mspace width="3.33333pt"/> <mi>cm</mi> <mo>|</mo> </mrow> </mrow> </semantics></math>. The results of the paper [<a href="#B16-physics-07-00008" class="html-bibr">16</a>] were used in the calculations.</p>
Full article ">Figure 13
<p>Dependence of various potentials on the separation between the helium and the sodium: the Woods–Saxon nuclear potential (black dotted line, overlapped by the green dotted line), <math display="inline"><semantics> <msubsup> <mi>U</mi> <mi>XHe</mi> <mi mathvariant="normal">e</mi> </msubsup> </semantics></math> (green dotted line), the Stark potential (red dotted line, overlapped by the blue dotted line), and the total effective interaction potential (blue dotted line). The radius vector of helium was set equal to <math display="inline"><semantics> <mrow> <mi>r</mi> <mo>=</mo> <mo>|</mo> <mn>2.5</mn> <mo>×</mo> <msup> <mn>10</mn> <mrow> <mo>−</mo> <mn>12</mn> </mrow> </msup> <mrow> <mspace width="3.33333pt"/> <mi>cm</mi> <mo>|</mo> </mrow> </mrow> </semantics></math> during the phase when the dark atom undergoes repolarization. The results of the paper [<a href="#B16-physics-07-00008" class="html-bibr">16</a>] were used in the calculations.</p>
Full article ">Figure 14
<p>The interaction potentials in the OHe–Na system for specific fixed value of <math display="inline"><semantics> <msub> <mover accent="true"> <mi>R</mi> <mo>→</mo> </mover> <mi>OA</mi> </msub> </semantics></math>, including the Coulomb interaction potential (green dotted line), nuclear interaction potential (black dotted line), and the centrifugal interaction potential (magenta solid line) between the He and the Na nucleus. Additionally, the Coulomb interaction potential between He and the <math display="inline"><semantics> <msup> <mi mathvariant="normal">O</mi> <mrow> <mo>−</mo> <mo>−</mo> </mrow> </msup> </semantics></math> is shown by blue dashed line, while the total interaction potential experienced by the He is represented by the red dotted line. The black circle shows the radius of the helium. The results of the paper [<a href="#B16-physics-07-00008" class="html-bibr">16</a>] were used in the calculations.</p>
Full article ">Figure 15
<p>Various interaction potentials relevant to the OHe–Na system: the Woods–Saxon nuclear interaction potential (black dotted line), the <math display="inline"><semantics> <msubsup> <mi>U</mi> <mrow> <mi>XHe</mi> </mrow> <mi mathvariant="normal">e</mi> </msubsup> </semantics></math> interaction potential (yellow dotted line), the Stark interaction potential (red dotted line), the centrifugal interaction potential (green dotted line), and the total effective interaction potential (blue dotted line). Potentials shown as a function of the separation distance between He in OHe and Na. The case corresponds to <math display="inline"><semantics> <mrow> <msub> <mover accent="true"> <mi>J</mi> <mo>→</mo> </mover> <mrow> <mi>OHe</mi> <mo>−</mo> <mi>Na</mi> </mrow> </msub> <mo>=</mo> <mover accent="true"> <mrow> <mn>3</mn> <mo>/</mo> <mn>2</mn> </mrow> <mo>→</mo> </mover> </mrow> </semantics></math>. See text for details. The results of the paper [<a href="#B16-physics-07-00008" class="html-bibr">16</a>] were used in the calculations.</p>
Full article ">Figure 16
<p>Various interaction potentials within the OHe–Na system, presented as functions of the separation distance between the He in OHe and Na: the Woods–Saxon nuclear interaction potential (black dotted line), the <math display="inline"><semantics> <msubsup> <mi>U</mi> <mrow> <mi>XHe</mi> </mrow> <mi mathvariant="normal">e</mi> </msubsup> </semantics></math> interaction potential (yellow dotted line), the Stark interaction potential (red dotted line), the centrifugal interaction potential (green dotted line), and the total effective interaction potential (blue dotted line). The case corresponds to <math display="inline"><semantics> <mrow> <msub> <mover accent="true"> <mi>J</mi> <mo>→</mo> </mover> <mrow> <mi>OHe</mi> <mo>−</mo> <mi>Na</mi> </mrow> </msub> <mo>=</mo> <mover accent="true"> <mn>3</mn> <mo>→</mo> </mover> </mrow> </semantics></math>. The results of the paper [<a href="#B16-physics-07-00008" class="html-bibr">16</a>] were used in the calculations.</p>
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30 pages, 17191 KiB  
Review
Review of the Near-Water Effect of Rotors in Cross-Media Vehicles
by Xingzhi Bai, Mingqing Lu, Qi Zhan, Yu Wang, Daixian Zhang, Xiao Wang and Wenhua Wu
Drones 2025, 9(3), 195; https://doi.org/10.3390/drones9030195 - 7 Mar 2025
Abstract
Cross-media vehicles, which combine the advantages of airplanes and submarines, are capable of performing complex tasks in different media and have attracted significant interest in recent years. In practice, however, cross-media rotorcrafts face numerous challenges during the cross-media transition, one of which is [...] Read more.
Cross-media vehicles, which combine the advantages of airplanes and submarines, are capable of performing complex tasks in different media and have attracted significant interest in recent years. In practice, however, cross-media rotorcrafts face numerous challenges during the cross-media transition, one of which is the complex mixed air–water flows induced by their rotors operating in close proximity to the water surface. These flows can result in aerodynamic penalties and structural damage to the rotors. The interactions between a water surface and a rotor wake bring about potential risks of cross-media locomotion, which is known as the near-water effect of rotors. Given that the distinctions between the near-water effect and the ground effect of rotors are not yet widely understood, this study details the discovery of the near-water effect and provides a comprehensive review of the evolutionary development of the near-water effect, tracing its understanding from the ground effect to the influence of droplets through aerodynamic modeling, numerical simulations, and near-water experimental studies. Furthermore, open problems and challenges associated with the near-water effect are discussed, including flow field measurements and numerical simulation approaches. Additionally, potential applications of the near-water effect for the development of cross-media rotorcraft are also described, which are valuable for aerodynamic design and cross-media control. Full article
Show Figures

Figure 1

Figure 1
<p>Representative cross-media vehicles (CMVs): (<b>a</b>) multi-rotored [<a href="#B12-drones-09-00195" class="html-bibr">12</a>]; (<b>b</b>) fixed-winged [<a href="#B7-drones-09-00195" class="html-bibr">7</a>]; (<b>c</b>) hybrid-winged [<a href="#B9-drones-09-00195" class="html-bibr">9</a>]; (<b>d</b>) bioinspired [<a href="#B11-drones-09-00195" class="html-bibr">11</a>]; and (<b>e</b>) hydrofoil [<a href="#B13-drones-09-00195" class="html-bibr">13</a>] vehicles.</p>
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<p>Typical water exit modes for multi-rotor and fixed-wing CMVs [<a href="#B16-drones-09-00195" class="html-bibr">16</a>].</p>
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<p>(<b>a</b>) Schematic of near–water effect; (<b>b</b>) mixed air–water flows induced by rotor [<a href="#B17-drones-09-00195" class="html-bibr">17</a>].</p>
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<p>Image sequence showing the mini-CMV breaching the water surface [<a href="#B27-drones-09-00195" class="html-bibr">27</a>].</p>
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<p>(<b>a</b>) Tested <span class="html-italic">D</span> = 0.56 m and <span class="html-italic">D</span> = 0.25 m commercial rotor blades; (<b>b</b>) mixed air–water flows induced by rotor at <span class="html-italic">z</span>/<span class="html-italic">R</span> = 0.4 [<a href="#B17-drones-09-00195" class="html-bibr">17</a>].</p>
Full article ">Figure 6
<p>Aerodynamic performance affected by near-water effect [<a href="#B17-drones-09-00195" class="html-bibr">17</a>]: (<b>a</b>) thrust coefficient of <span class="html-italic">D</span> = 0.56 m blade; (<b>b</b>) torque coefficient of <span class="html-italic">D</span> = 0.56 m blade; (<b>c</b>) thrust coefficient of <span class="html-italic">D</span> = 0.25 m blade; (<b>d</b>) thrust versus power of <span class="html-italic">D</span> = 0.56 m blade under NEW, IGE, and OGE states at <span class="html-italic">z</span>/<span class="html-italic">R</span> = 0.1; (<b>e</b>) thrust fluctuation caused by droplets of <span class="html-italic">D</span> = 0.56 m blade at <span class="html-italic">z</span>/<span class="html-italic">R</span> = 0.3; (<b>f</b>) structural damage caused by droplets on lower wing of <span class="html-italic">D</span> = 0.56 m blade.</p>
Full article ">Figure 7
<p>(<b>a</b>) Test platform; (<b>b</b>) rotor speed characteristic with height under the NWE at different throttle settings; (<b>c</b>) thrust characteristic with height under the NWE at different throttle settings; (<b>d</b>) comparison of rotor thrust under IGE vs. NWE [<a href="#B29-drones-09-00195" class="html-bibr">29</a>].</p>
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<p>(<b>a</b>) Image of rotor in transition (top: at low throttle, bottom: at high throttle); (<b>b</b>) the variance of the Transition Index as the rotor enters or exits the water at various throttle settings; (<b>c</b>) RPM versus throttle at various heights between fully-in-air and fully-in-water results [<a href="#B30-drones-09-00195" class="html-bibr">30</a>].</p>
Full article ">Figure 9
<p>Sequence diagram of cross-media locomotion [<a href="#B31-drones-09-00195" class="html-bibr">31</a>]. (<b>a</b>) t<sub>1</sub>=1.82 s; (<b>b</b>) t<sub>2</sub>=3.47 s; (<b>c</b>) t<sub>c</sub>=4.84 s; (<b>d</b>) t<sub>4</sub>=5.82 s; (<b>e</b>) t<sub>6</sub>=7.00 s.</p>
Full article ">Figure 10
<p>(<b>a</b>) Tilting ducted fan CMV; (<b>b</b>) rotor thrust characteristics under NWE and OGE conditions [<a href="#B32-drones-09-00195" class="html-bibr">32</a>].</p>
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<p>Comparison of experimental results (OGE vs. NWE) [<a href="#B34-drones-09-00195" class="html-bibr">34</a>]: (<b>a</b>) thrust; (<b>b</b>) power.</p>
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<p>Schematic of typical depression modes [<a href="#B35-drones-09-00195" class="html-bibr">35</a>] (the green arrows show the approximate trajectory of air, the red curve shows the approximate trajectory of the droplets entering the rotor disk): (<b>a</b>) dimpling; (<b>b</b>) splashing; (<b>c</b>) penetrating.</p>
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<p>Comparison of experimental results (OGE vs. NWE): (<b>a</b>) thrust characteristic of <span class="html-italic">D</span> = 1.3 m ducted fan under OGE, IGE, and NWE states [<a href="#B44-drones-09-00195" class="html-bibr">44</a>]; (<b>b</b>) spatial streamlines under NWE state [<a href="#B44-drones-09-00195" class="html-bibr">44</a>]; (<b>c</b>) thrust characteristic of <span class="html-italic">D</span> = 0.15 m ducted fan [<a href="#B45-drones-09-00195" class="html-bibr">45</a>]; (<b>d</b>) diagram of velocity vector [<a href="#B45-drones-09-00195" class="html-bibr">45</a>].</p>
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<p>Water surface shape: (<b>a</b>) simulation result for <span class="html-italic">D</span> = 1.3 m ducted fan [<a href="#B44-drones-09-00195" class="html-bibr">44</a>]; (<b>b</b>) simulation result for 0.15 m diameter ducted fan [<a href="#B45-drones-09-00195" class="html-bibr">45</a>]; (<b>c</b>) experimental result for <span class="html-italic">D</span> = 0.07 m ducted fan [<a href="#B35-drones-09-00195" class="html-bibr">35</a>].</p>
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<p>Velocity contour map and aerodynamic characteristics [<a href="#B47-drones-09-00195" class="html-bibr">47</a>]: (<b>a</b>) thrust coefficient at different rotor heights; (<b>b</b>) torque coefficient at different rotor heights; (<b>c</b>) the velocity magnitude field under the IGE state; (<b>d</b>) the velocity magnitude field under the NWE state.</p>
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<p>Time-averaged velocity field measured via PIV at different rotor heights off the water surface [<a href="#B35-drones-09-00195" class="html-bibr">35</a>] (arrows represent streamlines): (<b>a</b>) <span class="html-italic">z</span>/<span class="html-italic">R</span> = 0.5; (<b>b</b>) <span class="html-italic">z</span>/<span class="html-italic">R</span> = 0.2; (<b>c</b>) <span class="html-italic">z</span>/<span class="html-italic">R</span> = 0.1.</p>
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<p>Droplets generated by interface instability at low rotor speeds [<a href="#B35-drones-09-00195" class="html-bibr">35</a>]: (<b>a</b>) crown formation; (<b>b</b>) finger structure.</p>
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<p>Flow field through a hovering rotor under IGE (the left column in each subgraph) or FSE (the right column in each subgraph) conditions. Plots show sectional contours of dimensionless vorticity. The dark blue solid line represents the free surface at the end, while the black dashed line represents the free surface at the initial state [<a href="#B49-drones-09-00195" class="html-bibr">49</a>].</p>
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<p>Comparison of the normalized rotor thrust vs. dimensionless rotor-plane distance between the two proximity conditions. The black solid line represents the fitted curve under the IGE, while the red one represents the fitted curve under the FSE. <span class="html-italic">γ</span> represents dimensionless rotor height [<a href="#B49-drones-09-00195" class="html-bibr">49</a>].</p>
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<p>Experimental results [<a href="#B50-drones-09-00195" class="html-bibr">50</a>]: (<b>a</b>) thrust curve; (<b>b</b>) change in water surface.</p>
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<p>Simulation results [<a href="#B51-drones-09-00195" class="html-bibr">51</a>]: (<b>a</b>) trajectory tracking in the second simulation; (<b>b</b>) forces involved in the vehicle displacement.</p>
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<p>Optical interference caused by droplets and splashing.</p>
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<p>The effect of splash-reflected light outside the laser sheet on the cross-correlation calculations: (<b>a</b>) raw image; (<b>b</b>) cross-correlation results.</p>
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<p>Schematic of potential fountain effect as part of near-water effect for multi-rotor CMVs.</p>
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<p>Mixed air–water flows induced by multi-rotor system and thrust characteristics at <span class="html-italic">n</span> = 6600 r/min and <span class="html-italic">z/R</span> = 0.5.</p>
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<p>The water film remaining on the blade.</p>
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17 pages, 7744 KiB  
Article
An Equivalent Modeling Method for Electromagnetic Radiation of PWM Fans with Multiple Radiation Sources
by Jinsheng Yang, Xuan Zhao, Jingxuan Xia, Wei Zhang, Pingan Du and Baolin Nie
Appl. Sci. 2025, 15(6), 2887; https://doi.org/10.3390/app15062887 - 7 Mar 2025
Abstract
Axial flow fans, used for heat dissipation in electronic equipment, may generate significant electromagnetic interference during PWM speed regulation. Due to its multiple radiation sources and relatively smaller size compared to the equipment, the radiation prediction model for equipment-level EMC analysis often involves [...] Read more.
Axial flow fans, used for heat dissipation in electronic equipment, may generate significant electromagnetic interference during PWM speed regulation. Due to its multiple radiation sources and relatively smaller size compared to the equipment, the radiation prediction model for equipment-level EMC analysis often involves a huge number of grids, which leads to computational difficulties and inefficiencies, and thus an equivalent modeling method for the electromagnetic radiation of PWM fan is presented. First, a detailed field-circuit coupling model of the radiation from winding and driving circuits is established using the time-domain finite-integral method with non-uniform grids. Then, a near-field hexahedron is defined to surround the fan, and the electromagnetic field of all its surfaces is derived based on the Huygens principle and calculated. Finally, the hexahedron encapsulating all radiation sources within the fan can be used in a higher level simulation as replicable and reusable equivalent sources. The proposed method is validated by a numerical example and actual measurements and applied to predict the radiation emissions within an electronic enclosure. The results show that the equivalent model can reduce 81.4% computation time and maintain good consistency in comparison to the detailed field-circuit coupling model. Full article
(This article belongs to the Section Electrical, Electronics and Communications Engineering)
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<p>Electronic enclosure with axial flow fans for heat dissipation.</p>
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<p>Paths of conducted interference.</p>
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<p>Multiple electromagnetic radiation sources inside the fan.</p>
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<p>Three-dimensional detailed model of fan radiation calculation.</p>
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<p>PCB 3D model. (<b>a</b>) Power input network; (<b>b</b>) inverter circuit output network.</p>
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<p>Three-dimensional detailed model of fan radiation calculation.</p>
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<p>Modeling of axial flow fan external drive circuit.</p>
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<p>Detailed model using non-uniform grid technique.</p>
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<p>Schematic diagram of equivalent modeling of near-far field of fan radiation.</p>
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<p>Computational domain of the equivalent model.</p>
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<p>Electric field distribution for two models. (<b>a</b>) Calculated by detailed model; (<b>b</b>) calculated by equivalent model.</p>
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<p>Comparison of electric field intensity at the monitoring point.</p>
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<p>Measurement configuration.</p>
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<p>Layout for radiation emission measurements.</p>
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<p>Detailed model of the radiation emission of the fan.</p>
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<p>Conduction current measurement for DC lines. (<b>a</b>) Conduction current measurement; (<b>b</b>) current measurement results.</p>
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<p>Comparison of the measured results with the results of the two computational models.</p>
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<p>Axial flow fan installed inside the enclosure.</p>
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<p>Comparison of electric field distribution inside an electronic enclosure in top view. (<b>a</b>) Calculated by detailed model; (<b>b</b>) calculated by equivalent model.</p>
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<p>Comparison of electric field intensity at the monitoring point.</p>
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27 pages, 13326 KiB  
Article
Observations of the Microphysics and Type of Wintertime Mixed-Phase Precipitation, and Instrument Comparisons at Sorel, Quebec, Canada
by Faisal S. Boudala, Mathieu Lachapelle, George A. Isaac, Jason A. Milbrandt, Daniel Michelson, Robert Reed and Stephen Holden
Remote Sens. 2025, 17(6), 945; https://doi.org/10.3390/rs17060945 - 7 Mar 2025
Viewed by 81
Abstract
Winter mixed-phase precipitation (P) impacts transportation, electric power grids, and homes. Forecasting winter precipitation such as freezing precipitation (ZP), freezing rain (ZR), freezing drizzle (ZL), ice pellets (IPs), and the snow (S) and rain (R) boundary remains challenging due to the complex cloud [...] Read more.
Winter mixed-phase precipitation (P) impacts transportation, electric power grids, and homes. Forecasting winter precipitation such as freezing precipitation (ZP), freezing rain (ZR), freezing drizzle (ZL), ice pellets (IPs), and the snow (S) and rain (R) boundary remains challenging due to the complex cloud microphysical and dynamical processes involved, which are difficult to predict with the current numerical weather prediction (NWP) models. Understanding these processes based on observations is crucial for improving NWP models. To aid this effort, Environment and Climate Change Canada deployed specialized instruments such as the Vaisala FD71P and OTT PARSIVEL disdrometers, which measure P type (PT), particle size distributions, and fall velocity (V). The liquid water content (LWC) and mean mass-weighted diameter (Dm) were derived based on the PARSIVEL data during ZP events. Additionally, a Micro Rain Radar (MRR) and an OTT Pluvio2 P gauge were used as part of the Winter Precipitation Type Research Multi-Scale Experiment (WINTRE-MIX) field campaign at Sorel, Quebec. The dataset included manual measurements of the snow water equivalent (SWE), PT, and radiosonde profiles. The analysis revealed that the FD71P and PARSIVEL instruments generally agreed in detecting P and snow events. However, FD71P tended to overestimate ZR and underestimate IPs, while PARSIVEL showed superior detection of R, ZR, and S. Conversely, the FD71P performed better in identifying ZL. These discrepancies may stem from uncertainties in the velocity–diameter (V-D) relationship used to diagnose ZR and IPs. Observations from the MRR, radiosondes, and surface data linked ZR and IP events to melting layers (MLs). IP events were associated with colder surface temperatures (Ts) compared to ZP events. Most ZR and ZL occurrences were characterized by light P with low LWC and specific intensity and Dm thresholds. Additionally, snow events were more common at warmer T compared to liquid P under low surface relative humidity conditions. The Pluvio2 gauge significantly underestimated snowfall compared to the optical probes and manual measurements. However, snowfall estimates derived from PARSIVEL data, adjusted for snow density to account for riming effects, closely matched measurements from the FD71P and manual observations. Full article
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<p>ECCC observation site at Sorel, Quebec, Canada located at 46.04°N, 73.11°W. The map is derived from Google Earth.</p>
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<p>ECCC instrumentation platform at the Sorel site. Views towards the east (<b>a</b>) and south (<b>b</b>).</p>
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<p>Observation of T and RH (<b>a</b>), wind speed (WXT520) (<b>b</b>), and precipitation type (PT) based on the FD71P and PARSIVEL (<b>c</b>). In panel (<b>c</b>), the symbols represent no precipitation (C), snow (S), snow pellets (SPs), ice pellets (IPs), snow grains (SGs), ice crystals (ICs), rain (R), freezing rain (ZR), freezing drizzle (ZL), PT is not identified (un), and R+L+S (RLS).</p>
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<p>Frequency distributions of PT reported based on FD71 and PARSIVEL compared to the manual-based observations. The symbols represent no precipitation (C), snow (S), snow pellets (SPs), ice pellets (IPs), snow grains (SGs), ice crystals (ICs), rain (R), freezing rain (ZR), freezing drizzle (ZL), PT is not identified (UN), and R+L+S (RLS).</p>
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<p>Time series of human- and instrument-based PT (<b>a</b>); RH and T (<b>b</b>); precipitation intensity (Rate) based on FD71P (P), the mean particle (<math display="inline"><semantics> <mrow> <msub> <mrow> <mi mathvariant="normal">V</mi> </mrow> <mrow> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">n</mi> </mrow> </msub> </mrow> </semantics></math>) size and fall velocity (<math display="inline"><semantics> <mrow> <msub> <mrow> <mi mathvariant="normal">D</mi> </mrow> <mrow> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">n</mi> </mrow> </msub> </mrow> </semantics></math>) (<b>c</b>); and precipitation particle spectra based on the PARSIVEL disdrometer (<b>d</b>).</p>
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<p>Time series of liquid water content (LWC) (<b>a</b>), equivalent radar reflectivity factor (<math display="inline"><semantics> <mrow> <msub> <mrow> <mi mathvariant="normal">Z</mi> </mrow> <mrow> <mi mathvariant="normal">e</mi> </mrow> </msub> <mo>)</mo> </mrow> </semantics></math> (<b>b</b>), and fall velocity (<math display="inline"><semantics> <mrow> <mi mathvariant="normal">V</mi> </mrow> </semantics></math>) (<b>c</b>) based on MRR. Time series of the human- and instrument-based precipitation type (PT) (<b>d</b>).</p>
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<p>Vertical profiles of (T) (<b>a</b>) and RH (<b>b</b>), observed using a radiosonde in March.</p>
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<p>Time series of human- and instrument-based PT (<b>a</b>); RH and T (<b>b</b>); precipitation intensity (Rate) based on FD71P (P), the mean particle (<math display="inline"><semantics> <mrow> <msub> <mrow> <mi mathvariant="normal">V</mi> </mrow> <mrow> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">n</mi> </mrow> </msub> </mrow> </semantics></math>) size and fall velocity (<math display="inline"><semantics> <mrow> <msub> <mrow> <mi mathvariant="normal">D</mi> </mrow> <mrow> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">n</mi> </mrow> </msub> </mrow> </semantics></math>) (<b>c</b>); and precipitation particle spectra based on the PARSIVEL disdrometer (<b>d</b>) for 22 February 2022.</p>
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<p>Time series of liquid water content (LWC) (<b>a</b>), equivalent radar reflectivity factor (<math display="inline"><semantics> <mrow> <msub> <mrow> <mi mathvariant="normal">Z</mi> </mrow> <mrow> <mi mathvariant="normal">e</mi> </mrow> </msub> </mrow> </semantics></math>) (<b>b</b>), and fall velocity (V) (<b>c</b>) based on MRR. Time series of the human- and instrument-based precipitation type (PT) (<b>d</b>) for 23 February 2022.</p>
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<p>Vertical profiles of (T) (<b>a</b>) and RH (<b>b</b>), observed using a radiosonde for 23 February 2022, case. (46.03°N, 73.11°W).</p>
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<p>Velocity and size relationship particle distribution (<math display="inline"><semantics> <mrow> <msub> <mrow> <mi mathvariant="normal">N</mi> </mrow> <mrow> <mi mathvariant="normal">d</mi> <mo>,</mo> <mi mathvariant="normal">v</mi> </mrow> </msub> </mrow> </semantics></math>); mean <math display="inline"><semantics> <mrow> <mo>(</mo> <msub> <mrow> <mi mathvariant="normal">V</mi> </mrow> <mrow> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">n</mi> </mrow> </msub> <mo>)</mo> </mrow> </semantics></math> and ± standard deviation (±SD); empirical velocity and size relationship based on [<a href="#B40-remotesensing-17-00945" class="html-bibr">40</a>] (G&amp;K) for rain, hail stone (HS) based on [<a href="#B44-remotesensing-17-00945" class="html-bibr">44</a>] (HS-M); solid sphere density of snow (<math display="inline"><semantics> <mrow> <msub> <mrow> <mi mathvariant="sans-serif">ρ</mi> </mrow> <mrow> <mi>s</mi> </mrow> </msub> </mrow> </semantics></math>) 0.91 g cm<sup>−3</sup> (Ssp <math display="inline"><semantics> <mrow> <msub> <mrow> <mi mathvariant="sans-serif">ρ</mi> </mrow> <mrow> <mi>s</mi> </mrow> </msub> </mrow> </semantics></math> = 0.91) and 0.35 g cm<sup>−3</sup> (Ssp <math display="inline"><semantics> <mrow> <msub> <mrow> <mi mathvariant="sans-serif">ρ</mi> </mrow> <mrow> <mi>s</mi> </mrow> </msub> </mrow> </semantics></math> = 0.35) based on [<a href="#B41-remotesensing-17-00945" class="html-bibr">41</a>] (HW); lump graupel of medium density based on [<a href="#B43-remotesensing-17-00945" class="html-bibr">43</a>] (GRL-midden-LH); and fresh hailstone [<a href="#B42-remotesensing-17-00945" class="html-bibr">42</a>] (HS-KH)). The dates, times, and observed precipitation types are also displayed. The precipitation types are represented as freezing rain (ZR) (<b>a</b>), snow (S) (<b>b</b>), ice pellets (IP) (<b>d</b>,<b>e</b>), and rain (R) (<b>c</b>,<b>f</b>).</p>
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<p>Composite two-dimensional histograms. 2D density plots of 1 min averaged ZP (<b>a</b>), and solid precipitation (S, IP, IC, and SG) (<b>b</b>) events plotted against T and RH.</p>
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<p>Liquid fraction calculated based on the observed temperature intervals and precipitation type.</p>
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<p>Liquid precipitation intensity measured using FD71P and Pluvio2 (<b>a</b>), PARSIVEL and Pluvio2 (<b>b</b>), PARSIVEL and FD71P (<b>c</b>), and calculated PARSIVEL (<math display="inline"><semantics> <mrow> <msub> <mrow> <mi mathvariant="normal">P</mi> </mrow> <mrow> <mi mathvariant="normal">p</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">r</mi> <mi mathvariant="normal">s</mi> <mi mathvariant="normal">c</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">l</mi> </mrow> </msub> <mo>)</mo> </mrow> </semantics></math> and FD71P (<b>d</b>). The best fit lines, equations, and statistical <span class="html-italic">p</span> values (<math display="inline"><semantics> <mrow> <msub> <mrow> <mi mathvariant="normal">P</mi> </mrow> <mrow> <mi mathvariant="normal">v</mi> </mrow> </msub> <mo>)</mo> </mrow> </semantics></math> are also given.</p>
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<p>Solid precipitation intensity measured using FD71P and Pluvio2 (<b>a</b>), PARSIVEL and Pluvio2 (<b>b</b>), PARSIVEL and FD71P (<b>c</b>), and modified PARSIVEL (<math display="inline"><semantics> <mrow> <msub> <mrow> <mi mathvariant="normal">P</mi> </mrow> <mrow> <mi mathvariant="normal">p</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">r</mi> <mi mathvariant="normal">s</mi> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">o</mi> <mi mathvariant="normal">d</mi> </mrow> </msub> <mo>)</mo> </mrow> </semantics></math> and FD71P (<b>d</b>). The best fit lines, equations, and statistical <span class="html-italic">p</span> values (<math display="inline"><semantics> <mrow> <msub> <mrow> <mi mathvariant="normal">P</mi> </mrow> <mrow> <mi mathvariant="normal">v</mi> </mrow> </msub> <mo>)</mo> </mrow> </semantics></math> are also given.</p>
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<p>2D frequency distribution of ZR and ZL as a function temperature and precipitation intensity (P) (<b>a</b>,<b>c</b>), P and <math display="inline"><semantics> <mrow> <msub> <mrow> <mi mathvariant="normal">D</mi> </mrow> <mrow> <mi mathvariant="normal">m</mi> </mrow> </msub> </mrow> </semantics></math> (<b>b</b>,<b>d</b>), and temperature and <math display="inline"><semantics> <mrow> <msub> <mrow> <mi mathvariant="normal">D</mi> </mrow> <mrow> <mi mathvariant="normal">m</mi> </mrow> </msub> </mrow> </semantics></math> (<b>e</b>,<b>f</b>).</p>
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<p>2D frequency distribution of T and LWC in freezing precipitation.</p>
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<p>Ten-minute averaged observed LWC plotted against the precipitation intensity during ZR events (<b>a</b>). Best fit lines based on [<a href="#B53-remotesensing-17-00945" class="html-bibr">53</a>] (Best-1949), [<a href="#B54-remotesensing-17-00945" class="html-bibr">54</a>] (MP-1948), in this study (LWC<sub>fit</sub>(P)) and the statistical p values (<math display="inline"><semantics> <mrow> <msub> <mrow> <mi mathvariant="normal">P</mi> </mrow> <mrow> <mi mathvariant="normal">v</mi> </mrow> </msub> <mo>)</mo> </mrow> </semantics></math> are also shown. LWC, parameterized as a function of precipitation (<math display="inline"><semantics> <mrow> <msub> <mrow> <mi mathvariant="normal">P</mi> </mrow> <mrow> <mi mathvariant="normal">r</mi> </mrow> </msub> </mrow> </semantics></math>) and the mean mass-weighted diameter (<math display="inline"><semantics> <mrow> <msub> <mrow> <mi mathvariant="normal">D</mi> </mrow> <mrow> <mi mathvariant="normal">m</mi> </mrow> </msub> <mo>)</mo> </mrow> </semantics></math>, plotted against the observed LWC (<math display="inline"><semantics> <mrow> <mi mathvariant="normal">L</mi> <mi mathvariant="normal">W</mi> <msub> <mrow> <mi mathvariant="normal">C</mi> </mrow> <mrow> <mi mathvariant="normal">o</mi> <mi mathvariant="normal">b</mi> <mi mathvariant="normal">s</mi> </mrow> </msub> </mrow> </semantics></math>) (<b>b</b>).</p>
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20 pages, 2732 KiB  
Article
Throughput of Buffer with Dependent Service Times
by Andrzej Chydzinski
Appl. Syst. Innov. 2025, 8(2), 34; https://doi.org/10.3390/asi8020034 - 7 Mar 2025
Viewed by 18
Abstract
We study the throughput and losses of a buffer with stochastically dependent service times. Such dependence occurs not only in packet buffers within TCP/IP networks but also in many other queuing systems. We conduct a comprehensive, time-dependent analysis, which includes deriving formulae for [...] Read more.
We study the throughput and losses of a buffer with stochastically dependent service times. Such dependence occurs not only in packet buffers within TCP/IP networks but also in many other queuing systems. We conduct a comprehensive, time-dependent analysis, which includes deriving formulae for the count of packets processed and lost over an arbitrary period, the temporary intensity of output traffic, the temporary intensity of packet losses, buffer throughput, and loss probability. The model considered enables mimicking any packet interarrival time distribution, service time distribution, and correlation between service times. The analytical findings are accompanied by numerical computations that demonstrate the influence of various factors on buffer throughput and losses. These results are also verified through simulations. Full article
(This article belongs to the Section Applied Mathematics)
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<p>Packet buffer with stochastically dependent packet sizes and service times.</p>
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<p>Correlation of two consecutive transmission times, <math display="inline"><semantics> <msub> <mi>ρ</mi> <mn>1</mn> </msub> </semantics></math>, versus parameter <span class="html-italic">a</span>.</p>
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<p>Coefficient of variation, <span class="html-italic">C</span>, for the time between packets versus parameter <span class="html-italic">b</span>.</p>
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<p>Output traffic intensity in time for four different values of <math display="inline"><semantics> <msub> <mi>ρ</mi> <mn>1</mn> </msub> </semantics></math>. <math display="inline"><semantics> <mrow> <mi>N</mi> <mo>(</mo> <mn>0</mn> <mo>)</mo> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>C</mi> <mo>=</mo> <mn>4</mn> </mrow> </semantics></math> in every case.</p>
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<p>Output traffic intensity in time for four different values of <math display="inline"><semantics> <msub> <mi>ρ</mi> <mn>1</mn> </msub> </semantics></math>. <math display="inline"><semantics> <mrow> <mi>N</mi> <mo>(</mo> <mn>0</mn> <mo>)</mo> <mo>=</mo> <mi>K</mi> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>C</mi> <mo>=</mo> <mn>4</mn> </mrow> </semantics></math> in every case.</p>
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<p>Output traffic intensity over a long time for four different values of <math display="inline"><semantics> <msub> <mi>ρ</mi> <mn>1</mn> </msub> </semantics></math>. <math display="inline"><semantics> <mrow> <mi>N</mi> <mo>(</mo> <mn>0</mn> <mo>)</mo> <mo>=</mo> <mi>K</mi> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>C</mi> <mo>=</mo> <mn>4</mn> </mrow> </semantics></math> in every case.</p>
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<p>Output traffic intensity in time for four different values of <span class="html-italic">C</span>. <math display="inline"><semantics> <mrow> <mi>N</mi> <mo>(</mo> <mn>0</mn> <mo>)</mo> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>ρ</mi> <mn>1</mn> </msub> <mo>=</mo> <mn>0.4</mn> </mrow> </semantics></math> in every case.</p>
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<p>Output traffic intensity in time for four different values of <span class="html-italic">C</span>. <math display="inline"><semantics> <mrow> <mi>N</mi> <mo>(</mo> <mn>0</mn> <mo>)</mo> <mo>=</mo> <mi>K</mi> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>ρ</mi> <mn>1</mn> </msub> <mo>=</mo> <mn>0.4</mn> </mrow> </semantics></math> in every case.</p>
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<p>Output traffic intensity over a long time for four different values of <span class="html-italic">C</span>. <math display="inline"><semantics> <mrow> <mi>N</mi> <mo>(</mo> <mn>0</mn> <mo>)</mo> <mo>=</mo> <mi>K</mi> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>ρ</mi> <mn>1</mn> </msub> <mo>=</mo> <mn>0.4</mn> </mrow> </semantics></math> in every case.</p>
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<p>Loss intensity in time for three different initial buffer occupancies, <span class="html-italic">n</span>. <math display="inline"><semantics> <mrow> <msub> <mi>ρ</mi> <mn>1</mn> </msub> <mo>=</mo> <mn>0.4</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>C</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math> in every case.</p>
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<p>Loss intensity in time for three different initial buffer occupancies, <span class="html-italic">n</span>. <math display="inline"><semantics> <mrow> <msub> <mi>ρ</mi> <mn>1</mn> </msub> <mo>=</mo> <mn>0.1</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>C</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math> in every case.</p>
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<p>Stationary throughput versus <span class="html-italic">C</span> and <math display="inline"><semantics> <msub> <mi>ρ</mi> <mn>1</mn> </msub> </semantics></math>.</p>
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<p>Stationary throughput versus <span class="html-italic">C</span> for four different values of <math display="inline"><semantics> <msub> <mi>ρ</mi> <mn>1</mn> </msub> </semantics></math>.</p>
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<p>Stationary throughput versus <math display="inline"><semantics> <msub> <mi>ρ</mi> <mn>1</mn> </msub> </semantics></math> for four different values of <span class="html-italic">C</span>.</p>
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<p>Stationary loss probability versus <span class="html-italic">C</span> and <math display="inline"><semantics> <msub> <mi>ρ</mi> <mn>1</mn> </msub> </semantics></math>.</p>
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<p>Stationary throughput <span class="html-italic">T</span> versus buffer size <span class="html-italic">K</span> for five different values of <math display="inline"><semantics> <msub> <mi>ρ</mi> <mn>1</mn> </msub> </semantics></math>. <math display="inline"><semantics> <mrow> <mi>C</mi> <mo>=</mo> <mn>4</mn> </mrow> </semantics></math>.</p>
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<p>Stationary throughput <span class="html-italic">T</span> versus buffer size <span class="html-italic">K</span>, for four different values of traffic intensity. <math display="inline"><semantics> <mrow> <mi>C</mi> <mo>=</mo> <mn>4</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>ρ</mi> <mn>1</mn> </msub> <mo>=</mo> <mn>0.2</mn> </mrow> </semantics></math>.</p>
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20 pages, 3687 KiB  
Article
Towards a Comprehensive Framework for Made-to-Measure Alginate Scaffolds for Tissue Engineering Using Numerical Simulation
by Alexander Bäumchen, Johnn Majd Balsters, Beate-Sophie Nenninger, Stefan Diebels, Heiko Zimmermann, Michael Roland and Michael M. Gepp
Gels 2025, 11(3), 185; https://doi.org/10.3390/gels11030185 - 7 Mar 2025
Viewed by 141
Abstract
Alginate hydrogels are integral to many cell-based models in tissue engineering and regenerative medicine. As a natural biomaterial, the properties of alginates can vary and be widely adjusted through the gelation process, making them versatile additives or bulk materials for scaffolds, microcarriers or [...] Read more.
Alginate hydrogels are integral to many cell-based models in tissue engineering and regenerative medicine. As a natural biomaterial, the properties of alginates can vary and be widely adjusted through the gelation process, making them versatile additives or bulk materials for scaffolds, microcarriers or encapsulation matrices in tissue engineering and regenerative medicine. The requirements for alginates used in biomedical applications differ significantly from those for technical applications. Particularly, the generation of novel niches for stem cells requires reliable and predictable properties of the resulting hydrogel. Ultra-high viscosity (UHV) alginates possess alginates with special physicochemical properties, and thus far, numerical simulations for the gelation process are currently lacking but highly relevant for future designs of stem cell niches and cell-based models. In this article, the gelation of UHV alginates is studied using a microscopic approach for disc- and sphere-shaped hydrogels. Based on the collected data, a multiphase continuum model was implemented to describe the cross-linking process of UHV alginate polysaccharides. The model utilizes four coupled kinetic equations based on mixture theory, which are solved using finite element software. A good agreement between simulation results and experimental data was found, establishing a foundation for future refinements in the development of an interactive tool for cell biologists and material scientists. Full article
(This article belongs to the Special Issue Recent Research on Alginate Hydrogels in Bioengineering Applications)
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Graphical abstract

Graphical abstract
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<p>Time-lapse sequence of alginate gelation with different concentrations of cross-linking agents. (<b>a</b>) 10 mM BaCl<sub>2</sub> solution, (<b>b</b>) 20 mM BaCl<sub>2</sub> solution and (<b>c</b>) 40 mM BaCl<sub>2</sub> solution. The gelation kinetics of the alginate are derived from the course of the traveling gelled/liquid interface. Due to low contrast, dashed white lines are used to indicate segments of the gelled/liquid interface. Scale bar indicates 1000 μm. Images are enhanced using a bandpass filter in ImageJ.</p>
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<p>Analysis of the gelation process of alginate discs. (<b>a</b>) Gelation kinetics analyzed by the decreasing diameter of the gelation front. The kinetics of gelation depend strongly on the applied cross-linker concentration: the higher the BaCl<sub>2</sub> concentration, the faster the overall gelation of the alginate droplet. (<b>b</b>) Velocity of the gelation front of alginates. Doubling the cross-linker concentration leads to a linear increase in gelation velocity. The velocity of gelation in this work is defined as the reduction of the ungelled core and is negative. Data are expressed as mean value ± standard deviation (n = 5 gelation experiments). Standard deviation in (<b>a</b>) is shown as a ribbon for visualization purposes.</p>
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<p>Analysis of the alginate gelation process of alginate spheres (beads, microcarriers). Gelation kinetics were analyzed by the decreasing diameter of the gelation front. The kinetics of gelation depend strongly on the applied cross-linker concentration: the higher the BaCl<sub>2</sub> concentration, the faster the overall gelation of the alginate droplet. (<b>a</b>) Single gelation experiments using 10 mM BaCl<sub>2</sub> solution; (<b>b</b>) single gelation experiments using 20 mM BaCl<sub>2</sub> solution; (<b>c</b>) single gelation experiments using 40 mM BaCl<sub>2</sub> solution; (<b>d</b>) the velocity of gelation front of alginates from (<b>a</b>) to (<b>c</b>) extracted by linear curve fitting. The velocity of gelation in this work is defined as the reduction of the ungelled core and is negative. Doubling the cross-linker concentration leads to a linear increase in gelation velocity. Data colors in (<b>a</b>–<b>c</b>) refer to different gelation experiments. Data in (<b>d</b>) are expressed as mean values ± standard deviation (n = 5 gelation experiments).</p>
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<p>Alginate micro-layer formation during gelation. (<b>a</b>) <b>Top</b>: Microscopic image of the formed layer at the outer border of the alginate disc; scale bar: 200 µm. Inset: Lower magnification of the area indicated by the black dashed line. Black arrow: Line scan of intensity in the graph. <b>Bottom</b>: The graph illustrates the data from the line scan of intensity. (<b>b</b>) Schematic illustration of layer formation in alginate disc-like hydrogels (adapted from [<a href="#B52-gels-11-00185" class="html-bibr">52</a>]; created with BioRender.com).</p>
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<p>Time-lapse of alginate gelation simulation with different concentration boundary conditions of the cross-linking agent. The left half of each time point shows the visualization of the numerical model, while the right half shows the microscopic image of one experimental replicate. (<b>a</b>) 10 mM BaCl<sub>2</sub> solution, (<b>b</b>) 20 mM BaCl<sub>2</sub> solution and (<b>c</b>) 40 mM BaCl<sub>2</sub> solution. Brighter areas indicate a higher amount of the ongoing gelling reaction. Scale bar indicates 1000 µm.</p>
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<p>Comparison of experimental data (solid line) and numerical modeling (dotted lines).</p>
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<p>Setup and principle of observing the gelation process. (<b>a</b>) A thin disc-like volume of alginate is poured into a dish and covered by a thin silicone spacer for gelation with different BaCl<sub>2</sub> solutions. This process can be observed using phase contrast microscopy, and a concentric decrease in the traveling liquid/gelled interface can be tracked and used for the quantification of the gelation process. (<b>b</b>) Schematic drawing at two different time points of alginate gelation. The disc-like volume of alginate is surrounded by the BaCl<sub>2</sub> cross-linker solutions and, consequently, barium (and chloride) ions diffuse into the alginate sol, triggering the gelation that can be tracked by the traveling liquid/gelled interface over time. The diameters of the circular interfaces decrease over time and disappear after the complete gelation of the alginate discs. (<b>b</b>) generated with BioRender.com.</p>
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<p>(<b>a</b>) Representative volume filled with the free polymer, barium ions and cross-linked polymer (and water). (<b>b</b>) Macroscopic domain and RVE as a magnification of a spatial point. The mass of constituent φ<sup>α</sup> inside the RVE changes due to the flux over the boundary and the mass exchange. Created with BioRender.com.</p>
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24 pages, 1543 KiB  
Article
Stochastic Up-Scaling of Discrete Fine-Scale Models Using Bayesian Updating
by Muhammad Sadiq Sarfaraz, Bojana V. Rosić and Hermann G. Matthies
Computation 2025, 13(3), 68; https://doi.org/10.3390/computation13030068 - 7 Mar 2025
Viewed by 188
Abstract
In this work, we present an up-scaling framework in a multi-scale setting to calibrate a stochastic material model. In particular with regard to application of the proposed method, we employ Bayesian updating to identify the probability distribution of continuum-based coarse-scale model parameters from [...] Read more.
In this work, we present an up-scaling framework in a multi-scale setting to calibrate a stochastic material model. In particular with regard to application of the proposed method, we employ Bayesian updating to identify the probability distribution of continuum-based coarse-scale model parameters from fine-scale measurements, which is discrete and also inherently random (aleatory uncertainty) in nature. Owing to the completely dissimilar nature of models for the involved scales, the energy is used as the essential medium (i.e., the predictions of the coarse-scale model and measurements from the fine-scale model) of communication between them. This task is realized computationally using a generalized version of the Kalman filter, employing a functional approximation of the involved parameters. The approximations are obtained in a non-intrusive manner and are discussed in detail especially for the fine-scale measurements. The demonstrated numerical examples show the utility and generality of the presented approach in terms of obtaining calibrated coarse-scale models as reasonably accurate approximations of fine-scale ones and greater freedom to select widely different models on both scales, respectively. Full article
(This article belongs to the Special Issue Synergy between Multiphysics/Multiscale Modeling and Machine Learning)
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Figure 1

Figure 1
<p>Loading cases: (Load I) hydrostatic compression, (Load II) bi-axial tension–compression.</p>
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<p>Deformation approximation for the two-phase material in the truss element [<a href="#B82-computation-13-00068" class="html-bibr">82</a>].</p>
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<p>Inclusion and matrix interface (<b>left</b>) and its FEM discretization with interface elements shown in red (<b>right</b>) [<a href="#B80-computation-13-00068" class="html-bibr">80</a>].</p>
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<p>Fine-scale realizations for different numbers of particles: <math display="inline"><semantics> <mrow> <mo>[</mo> <mn>5</mn> <mo>,</mo> <mn>10</mn> <mo>,</mo> <mn>25</mn> <mo>,</mo> <mn>50</mn> <mo>]</mo> </mrow> </semantics></math> embedded in the matrix phase.</p>
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<p>Prior and posterior PDF for bulk <span class="html-italic">K</span> and shear <span class="html-italic">G</span> moduli on coarse-scale model, using one fine-scale realization.</p>
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<p>Coarse-scale prior and posterior predicted energy PDFs for load cases: (I,II), using one fine-scale realization.</p>
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<p>Fine-scale energy PDFs for load cases (I,II) for different numbers of particles.</p>
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<p>Coarse-scale prior and posterior PDF for <span class="html-italic">K</span> and <span class="html-italic">G</span> using fine scale with different numbers of particles.</p>
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<p>Coarse-scale posterior predicted energy comparison with fine-scale measurements with different numbers of particles for load cases (I,II).</p>
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<p>Correlation between prior and posterior (up-scaled) coarse-scale <span class="html-italic">K</span> and <span class="html-italic">G</span> considering all fine-scale particle cases.</p>
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<p>Correlation between energies from load cases I and II using coarse-scale prior and up-scaled <span class="html-italic">K</span> and <span class="html-italic">G</span> considering all fine-scale particle cases.</p>
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