Search Results (8,908)

In this work, we present the semi-analytical solution for the early-time recession phase of the horizontal unconfined aquifer of finite length for steady-state initial conditions. This is a case where self-similarity arguments are not applicable. The solution is built as linear perturbations from the initial steady state. The solution is determined via a Sturm–Liouville eigenvalue problem, which should be solved numerically. On the other hand, the immediate response of the aquifer to the sudden switching off the recharge, i.e., in the earliest times, is obtained by deducing analytically the large eigenvalue asymptotic solutions of the problem. We find analytically that in this time regime, the outflow Q is given by Q = Q₀ − 1.4Q₀^5/3L^−4/3n^−2/3t^2/3, where Q₀ is the initial outflow rate, L is the length of the aquifer, n is the porosity of the formation and t is the time from the start of the recession. The stated result is very accurate for times t up to ~0.01 nL^3/2k^−1/2Q₀^−1/2, where k is the hydraulic conductivity of the formation. The analytical and quantitative relation of the presented solution with the classical recession phase asymptotic solutions derived in the past by Polubarinova (early-time solution) and Boussinesq (separable, late-time solution) is discussed in detail. The presented results can be used as a benchmark solution for modeling or numerical validation purposes. Full article

Wireless powered communication networks (WPCNs) provide a sustainable solution for energy-constrained IoT devices by enabling wireless energy transfer (WET) in the downlink and wireless information transmission (WIT) in the uplink. However, their performance is often limited by interference in uplink communication and inefficient resource allocation. To address these challenges, we propose an RSMA-aided WPCN framework, which optimizes rate-splitting factors, power allocation, and time division to enhance spectral efficiency and user fairness. To solve this non-convex joint optimization problem, we employ the simultaneous perturbation stochastic approximation (SPSA) algorithm, a gradient-free method that efficiently estimates optimal parameters with minimal function evaluations. Compared to conventional optimization techniques, SPSA provides a scalable and computationally efficient approach for real-time resource allocation in RSMA-aided WPCNs. Our simulation results demonstrate that the proposed RSMA-aided framework improves sum throughput by 12.5% and enhances fairness by 15–20% compared to conventional multiple-access schemes. These findings establish RSMA as a key enabler for next-generation WPCNs, offering a scalable, interference-resilient, and energy-efficient solution for future wireless networks. Full article

In this study, we examine the bifurcations and dynamics of a piecewise linear van der Pol equation—a model that captures self-sustained oscillations and is applied in various scientific disciplines, including electronics, neuroscience, biology, and economics. The van der Pol equation is transformed into a piecewise linear system to simplify the analysis of stability and controllability, which is particularly beneficial in engineering applications. This work explores the impact of increasing the number of linear segments on the system’s dynamics, focusing on the stability of the equilibria, phase portraits, and bifurcations. The findings reveal that while the bifurcation structure at critical values of the bifurcation parameter is complex, the topology of the piecewise linear model remains unaffected by an increase in the number of linear segments from three to four. This research contributes to our understanding of the dynamics of nonlinear systems with piecewise linear characteristics and has implications for the analysis and design of real-world systems exhibiting such behavior. Full article

Due to the complex operating environment of valves, when a fault occurs inside a valve, the vibration signal generated by the fault is easily affected by the environmental noise, making the extraction of fault features difficult. To address this problem, this paper proposes a feature extraction method based on the combination of Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN) and Fuzzy Entropy (FN). Due to the slow convergence speed and the tendency to fall into local optimal solutions of the Hippopotamus Optimization Algorithm (HO), an improved Hippopotamus Optimization (IHO) algorithm-optimized Support Vector Machine (SVM) model for valve leakage diagnosis is introduced to further enhance the accuracy of valve leakage diagnosis. The improved Hippopotamus Optimization algorithm initializes the hippopotamus population with Tent chaotic mapping, designs an adaptive weight factor, and incorporates adaptive variation perturbation. Moreover, the performance of IHO was proven to be optimal compared to HO, Particle Swarm Optimization (PSO), Grey Wolf Optimization (GWO), Whale Optimization Algorithm (WOA), and Sparrow Search Algorithm (SSA) by calculating twelve test functions. Subsequently, the IHO-SVM classification model was established and applied to valve leakage diagnosis. The prediction effects of the seven models, IHO-SVM. HO-SVM, PSO-SVM, GWO-SVM, WOA-SVM, SSA-SVM, and SVM were compared and analyzed with actual data. As a result, the comparison indicated that IHO-SVM has desirable robustness and generalization, which successfully improves the classification efficiency and the recognition rate in fault diagnosis. Full article

Many techniques originally developed in the context of deterministic control theory have recently been applied to the quest for optimal protocols in stochastic processes. Given a system subject to environmental fluctuations, one may ask what is the best way to change its controllable parameters in time in order to maximize, on average, a certain reward function, while steering the system between two pre-assigned states. In this work, we study the problem of optimal control for a wide class of stochastic systems, inspired by a model of an energy harvester. The stochastic noise in this system is due to the mechanical vibrations, while the reward function is the average power extracted from them. We consider the case in which the electrical resistance of the harvester can be changed in time, and we exploit the tools of control theory to work out optimal solutions in a perturbative regime, close to the stationary state. Our results show that it is possible to design protocols that perform better than any possible solution with constant resistance. Full article

The problem of mathematical modeling and analysis of stochastic phenomena in population systems with competition is considered. This problem is investigated based on a discrete system of two populations modeled by the Ricker map. We study the dependence of the joint dynamic behavior on the parameters of the growth rate and competition intensity. It is shown that, due to multistability, random perturbations can transfer the population system from one attractor to another, generating stochastic P-bifurcations and transformations of synchronization modes. The effectiveness of a mathematical approach, based on the stochastic sensitivity technique and the confidence domain method, in the parametric analysis of these stochastic effects is demonstrated. For monostability zones, the phenomenon of stochastic generation of the phantom attractor is found, in which the system enters the trigger mode with alternating transitions between states of almost complete extinction of one or the other population. It is shown that the noise-induced effects are accompanied by stochastic D-bifurcations with transitions from order to chaos. Full article

The P-V and I-V curves of photovoltaic (PV) strings show multiple peaks when exposed to partial shading conditions (PSCs). The traditional maximum power point tracking (MPPT) method cannot track the global maximum power point (GMPP) due to the multi-peak characteristics, power fluctuation, and tracking speed. In this paper, a multi-peak PV MPPT method based on the honey badger algorithm (HBA) is proposed to track the GMPP in a localized shading environment. The performance of this method is also compared and analyzed with the traditional MPPT methods based on the perturbation observation (P&O) method and Particle Swarm Optimization (PSO) algorithm. The experimental results have proven that, compared with the MPPT methods based on P&O and PSO, the proposed multi-peak MPPT method based on the HBA algorithm has a faster tracking speed, higher tracking accuracy, and fewer iterations. Full article

Topology optimization (TO) is a powerful generative design tool for innovative structural design, capable of optimizing material distribution to generate structures with superior performance. However, current topology optimization algorithms mostly target a single objective and are highly dependent on the problem definition parameters, causing two critical issues: limited human controllability and solution diversity. These issues often lead to burdensome design iterations and insufficient design exploration. This paper proposes a multi-solution TO framework to address them. Human designers express their stylistic preferences for structures through sketches which are decomposed into stroke and closed-shape elements to flexibly guide each TO process. Sketch-based constraints are integrated with Fourier mapping-based length-scale control to enhance human controllability. Solution diversity is achieved by perturbing Fourier mapping frequencies and load conditions in the neural implicit TO framework. Adaptive parallel scale adjustment is incorporated to reduce the computational cost for design exploration. Using the structural design of a wheel spoke as a case study, the mechanical performance and diversity of the generated TO solutions as well as the effectiveness of human control are analyzed both qualitatively and quantitatively. The results reveal that the sketch-based constraints and length-scale control have distinct control effects on structural features and have different impacts on the mechanical performance and diversity, thereby enabling fine-grained and flexible human controllability to better balance conflicting objectives. Full article

On 10 May 2024 at 17 h:07 UTC, the simultaneous arrival of several solar coronal mass ejections (CMEs) generated the strongest geomagnetic storm of the last twenty years, with a minimum Dst = −412 nT, usually referred to as the Mother’s Day event. On 10 October 2024, the second strongest event of solar cycle 25 appeared with a Dst = −335 nT, preceded on 8 October by an event with a Dst = −153 nT. In the present work, with measurements of the vertical total electron content and with ionosonde observations from Europe, USA, and South Korea, we show that the ionization of the upper atmosphere shortly increased at the arrival of the CME for these different events, followed by a fast decrease at all latitudes. The ionization remained very low for more than a full day. While the recovery started at the beginning of the second day after the onset for both events in October, the sudden recovery in the middle of the second day on 12 May is much more unusual. The analysis of the observations at different latitudes and longitudes shows that the causes of the ionization variations during the superstorms were mainly due to strong perturbations in the ionospheric F layer, amplified by the plasmasphere’s influence on the vertical total electron content (VTEC). The erosion of the plasmasphere during these two strong events led to a plasmapause located at exceptionally low radial distances smaller than 2 Re (Earth’s radii) in the post-midnight sector and a rotating plume in the afternoon–dusk sector clearly visible in the BSPM plasmasphere model. It took several days after the storms to recover normal ionization rates. Full article

This study investigates the time-resolved aerodynamics in the cavity regions of a full-scale, high-speed, low-pressure turbine stage representative of geared turbofan engines. The turbine stage is tested in the von Karman Institute’s short-duration rotating facility at different purge rates (PR) injected through the upstream hub cavity. Spectra from the shroud and downstream hub cavity show perturbations linked to blade passing frequency and rotor speed. Asynchronous flow structures associated with ingress/egress mechanisms are observed in the rim seal of the purged cavity. At 0% PR, the ingress region extends to the entire rim seal, and pressure fluctuations are maximized. At 1% PR, the instability is suppressed and the cavity is sealed. At 0.5%, the rim-seal instability exhibits multiple peaks in the spectra, each corresponding to a state of the instability. Kelvin–Helmholtz instabilities are identified as trigger mechanisms. A novel technique based on the properties of the cross-power spectral density is developed to determine the speed and wavelength of the rotating structures, achieving higher precision than the commonly used cross-correlation method. Moreover, unlike the standard methodology, this approach allows researchers to calculate the structure characteristics for all the instability states. Spectral analysis at the turbine outlet shows that rim-seal-induced instabilities propagate into regions occupied by secondary flows. A methodology is proposed to quantify the magnitude of the induced fluctuations, showing that the interaction with secondary flows amplifies the instability at the stage outlet. Full article

Chile holds ~50% of temperate forests in the Southern Hemisphere, thus constituting a genetic–ecological heritage. However, intense anthropogenic pressures have been inducing distinct forest structural-regeneration patterns. Accordingly, we evaluated 22 soil properties at 0–5 and 5–20 cm depths in two protected sites, with similar perturbation records but contrasting post-disturbance regeneration stages: long-term secondary forest (~50 y) (SEC_FORST) (dominated by Chusquea sp.-understory) and a short-term forest after disturbance (~5 y) (FAD_IST) within a Nothofagus spp. forest to determine the potential of these soils to promote nutrient availability, water cycling, soil organic carbon (SOC) sequestration (CO₂→SOC), and microbiome. Results detected 93 correlations (r ≥ 0.80); however, no significant differences (p < 0.05) in physical or chemical properties, except for infiltration velocity (+27.97%), penetration resistance (−23%), SOC (+5.64%), and % Al saturation (+5.64%) relative to SEC_FORST, and a consistent trend of suitable values 0–5 > 5–20 cm were estimated. The SOC→CO₂ capacity reached 4.2 ± 0.5 (FAD_IST) and 2.7 ± 0.2 Mg C y⁻¹ (SEC_FORST) and only microbial abundance shifts were observed. These findings provide relevant insights on belowground resilience, evidenced by similar ecosystem services provision capacities over time, which may be influenced progressively by opportunistic Chusquea sp. Full article

Integer linear programs (ILPs) and mixed integer programs (MIPs) often have multiple distinct optimal solutions, yet the widely used Gurobi optimization solver returns certain solutions at disproportionately high frequencies. This behavior is disadvantageous, as, in fields such as biomedicine, the identification and analysis of distinct optima yields valuable domain-specific insights that inform future research directions. In the present work, we introduce MORSE (Multiple Optima via Random Sampling and careful choice of the parameter Epsilon), a randomized, parallelizable algorithm to efficiently generate multiple optima for ILPs. MORSE maps multiplicative perturbations to the coefficients in an instance’s objective function, generating a modified instance that retains an optimum of the original problem. We formalize and prove the above claim in some practical conditions. Furthermore, we prove that for 0/1 selection problems, MORSE finds each distinct optimum with equal probability. We evaluate MORSE using two measures; the number of distinct optima found in r independent runs, and the diversity of the list (with repetitions) of solutions by average pairwise Hamming distance and Shannon entropy. Using these metrics, we provide empirical results demonstrating that MORSE outperforms the Gurobi method and unweighted variations of the MORSE method on a set of 20 Mixed Integer Programming Library (MIPLIB) instances and on a combinatorial optimization problem in cancer genomics. Full article

Background/Objectives: Traditional fusion leads to a loss of spine mobility across the fused vertebrae. Vertebral body tethering (VBT) was developed with the goal of increasing flexibility and maintaining some spinal mobility. However, it is not known if the additional mobility leads to significant functional improvement. This prospective motion analysis study evaluates functional outcomes, specifically gait stability, in pre-operative, post-fusion, and post-VBT patients by using postural perturbations on a treadmill. Methods: Overall, 79 subjects underwent a computer-controlled treadmill study with postural perturbations, which simulated trips and slips. The subjects were harnessed for safety. Overall, 21 subjects were healthy controls, 18 patients were at least one-year post-VBT, 15 patients were at least one-year post-fusion, and 25 were pre-operative scoliosis patients. Subject weight, height, and treadmill acceleration were recorded and used to determine anteroposterior single (ASSTs, PSSTs) and multiple (AMSTs, PMSTs) stepping thresholds to describe the maximum torque a patient could withstand before failing to recover from the simulated trip. Independent t-tests were run to compare groups under the advice of a master statistician with expertise in orthopedic surgery. Results: Pre-operative scoliosis patients had lower PSSTs than healthy controls (uncorrected p = 0.036). No significant differences were observed between pre-operative and post-operative groups for both fusion and VBT. There was no significant difference in ASST, AMST, or PMST between any of the groups. Conclusions: The lower PSST in pre-operative scoliosis patients compared to healthy controls may reflect impaired reactive balance and potentially increased fall risk. Interestingly, there was no significant difference in reactive balance measures between pre-operative and post-operative scoliosis patients or between post-fusion and post-VBT patients. Full article

Using a tumor-immune growth model, we investigate how immunotherapy affects its dynamical characteristics. Specifically, we extend the prey–predator model of tumor cells and immune cells by including periodic immunotherapy, the nonlinear damping of cancer cells, and the dynamics of a healthy cell population, and investigate the effects of the model parameters. The ideal value of immunotherapy, which promotes the growth of immune (and healthy) cells while contributing to the elimination or control of the cancer cells, is determined by using Fisher information as a measure of variability throughout our study. Full article

In spite of its unbroken PT symmetry, the popular imaginary cubic oscillator Hamiltonian $H^{\left(IC\right)}=p^2+\mathrm{i}{x}^3$ does not satisfy all of the necessary postulates of quantum mechanics. This failure is due to the “intrinsic exceptional point” (IEP) features of $H^{\left(IC\right)}$ and, in particular, to the phenomenon of a high-energy asymptotic parallelization of its bound-state-mimicking eigenvectors. In this paper, it is argued that the operator $H^{\left(IC\right)}$ (and the like) can only be interpreted as a manifestly unphysical, singular IEP limit of a hypothetical one-parametric family of certain standard quantum Hamiltonians. For explanation, ample use is made of perturbation theory and of multiple analogies between IEPs and conventional Kato’s exceptional points. Full article