Search Results (24)

Developing spherical sector harmonics (SSHs) benefits sound field decomposition and analysis over spherical sector regions. Although SSHs demonstrate potential in the field of spatial audio, a comprehensive investigation into their properties and performance is absent. This paper seeks to close this gap by revealing three key limitations of SSHs and exploring their performance in two aspects: sector sound field radial extrapolation and sector sound field decomposition and reconstruction. First, SSHs are not solutions to the Helmholtz equation, which is their main limitation. Then, due to the violation of the Helmholtz equation, SSHs lack the ability to conduct sound field radial extrapolation, especially for interior cases. Third, when using SSHs to decompose and reconstruct a sound field, the shifted associated Legendre polynomials and scaled exponential function in SSHs result in severe distortion around the edge of the sector region. In light of these three limitations, the future implementation of SSHs should focus on processing and analyzing the measurement sector region without any extrapolation process, and the measurement region should be larger than the target sector region. Full article

Granger causality can uncover the cause-and-effect relationships in financial networks. However, such networks can be convoluted and difficult to interpret, but the Helmholtz–Hodge–Kodaira decomposition can split them into rotational and gradient components which reveal the hierarchy of the Granger causality flow. Using Kenneth French’s business sector return time series, it is revealed that during the COVID crisis, precious metals and pharmaceutical products were causal drivers of the financial network. Moreover, the estimated Granger causality network shows a high connectivity during the crisis, which means that the research presented here can be especially useful for understanding crises in the market better by revealing the dominant drivers of crisis dynamics. Full article

The aim of the work presented in this paper was development of a thermodynamically consistent constitutive model for orthotopic metals and determination of its parameters based on standard characterisation methods used in the aerospace industry. The model was derived with additive decomposition of the strain tensor and consisted of an elastic part, derived from Helmholtz free energy, Hill’s thermodynamic potential, which controls evolution of plastic deformation, and damage orthotopic potential, which controls evolution of damage in material. Damage effects were incorporated using the continuum damage mechanics approach, with the effective stress and energy equivalence principle. Material characterisation and derivation of model parameters was conducted with standard specimens with a uniform cross-section, although a number of tests with non-uniform cross-sections were also conducted here. The tests were designed to assess the extent of damage in material over a range of plastic deformation values, where displacement was measured locally using digital image correlation. The new model was implemented as a user material subroutine in Abaqus and verified and validated against the experimental results for aerospace-grade aluminium alloy 2024-T3. Verification was conducted in a series of single element tests, designed to separately validate elasticity, plasticity and damage-related parts of the model. Validation at this stage of the development was based on comparison of the numerical results with experimental data obtained in the quasistatic characterisation tests, which illustrated the ability of the modelling approach to predict experimentally observed behaviour. A validated user material subroutine allows for efficient simulation-led design improvements of aluminium components, such as stiffened panels and the other thin-wall structures used in the aerospace industry. Full article

The use of film cooling is crucial to avoid high metal temperatures in gas turbine applications, thus ensuring a high lifetime for vanes and blades. The complex turbulent mixing process between the coolant and the main flow requires an accurate numerical prediction to correctly estimate the impact of ejection conditions on the cooling performance. Recent developments in numerical models aim at using hybrid approaches that combine high precision with low computational cost. This paper is focused on the numerical simulation of a cylindrical film cooling hole that operates at a unitary blowing ratio, with a hot gas Mach number of ${\mathit{Ma}}_m$ = 0.6, while the coolant is characterized by plenum conditions (${\mathit{Ma}}_c$ = 0). The adopted numerical approach is the Stress-Blended Eddy Simulation model (SBES), which is a blend between a Reynolds-Averaged Navier–Stokes approach and a modeled Large Eddy Simulation based on the local flow and mesh characteristics. The purpose of this paper is to investigate the ability of the hybrid model to capture the complex mixing between the coolant and the main flow. The cooling performance of the hole is quantified through the film cooling effectiveness, the Net Heat Flux Reduction (NHFR), and the discharge coefficient $C_D$ calculation. Numerical results are compared both with the experimental data obtained by the University of Karlsruhe during the EU-funded TATEF2 project and with a Scale Adaptive Simulation (SAS) run on the same computational grid. The use of ${\lambda }_2$ profiles extracted from the flow field allows for isolating the main vortical structures such as horseshoe vortices, counter-rotating vortex pairs (e.g., kidney vortices), Kelvin–Helmholtz instabilities, and hairpin vortices. Eventually, the contribution of the unsteady phenomena occurring at the hole exit section is quantified through Proper Orthogonal Decomposition (POD) and Spectral Proper Orthogonal Decomposition methods (SPOD). Full article

This study systematically investigates the formation of NO_x in the thermal decomposition of N₂O, focusing on the impact of Kelvin–Helmholtz (K-H) instability in combustion environments. Using premixed CH₄ co-flow flames and an electric furnace as distinct heat sources, we explored NO_x emission dynamics under varying conditions, including reaction temperature, residence time, and N₂O dilution rates (X_N2O). Our findings demonstrate that diluting N₂O around a premixed flame increases flame length and decreases flame propagation velocity, inducing K-H instability. This instability was quantitatively characterized using Richardson and Strouhal numbers, highlighting N₂O’s role in augmenting oxygen supply within the flame and significantly altering flame dynamics. The study reveals that higher X_N2O consistently led to increased NO formation independently of nozzle exit velocity (u_jet) or co-flow rate, emphasizing the influence of N₂O concentration on NO production. In scenarios without K-H instability, particularly at lower u_jet, an exponential rise in NO₂ formation rates was observed, due to the reduced residence time of N₂O near the flame surface, limiting pyrolysis effectiveness. Conversely, at higher u_jet where K-H instability occurs, the formation rate of NO₂ drastically decreased. This suggests that K-H instability is crucial in optimizing N₂O decomposition for minimal NO_x production. Full article

Soft robotic grippers offer great advantages over traditional rigid grippers with respect to grabbing objects with irregular or fragile shapes. Shape memory polymer composites are widely used as actuators and holding elements in soft robotic grippers owing to their finite strain, high specific strength, and high driving force. In this paper, a general 3D anisotropic thermomechanical model for woven fabric-reinforced shape memory polymer composites (SMPCs) is proposed based on Helmholtz free energy decomposition and the second law of thermodynamics. Furthermore, the rule of mixtures is modified to describe the stress distribution in the SMPCs, and stress concentration factors are introduced to account for the shearing interaction between the fabric and matrix and warp yarns and weft yarns. The developed model is implemented with a user material subroutine (UMAT) to simulate the shape memory behaivors of SMPCs. The good consistency between the simulation results and experimental validated the proposed model. Furthermore, a numerical investigation of the effects of yarn orientation on the shape memory behavior of the SMPC soft gripper was also performed. Full article

Imaging through water waves will cause complex geometric distortions and motion blur, which seriously affect the correct identification of an airborne scene. The current methods main rely on high-resolution video streams or a template image, which limits their applicability in real-time observation scenarios. In this paper, a novel recovery method for the instantaneous images distorted by surface waves is proposed. The method first actively projects an adaptive and adjustable structured light pattern onto the water surface for which random fluctuation will cause the image to degrade. Then, the displacement field of the feature points in the structured light image is used to estimate the motion vector field of the corresponding sampling points in the scene image. Finally, from the perspective of fluid mechanics, the distortion-free scene image is reconstructed based on the Helmholtz-Hodge Decomposition (HHD) theory. Experimental results show that our method not only effectively reduces the distortion to the image, but also significantly outperforms state-of-the-art methods in terms of computational efficiency. Moreover, we tested the real-scene sequences of a certain length to verify the stability of the algorithm. Full article

The decay of the kinetic energy of a turbulent flow with time is not necessarily monotonic. This is revealed by simulations performed in the framework of discrete mechanics, where the kinetic energy can be transformed into pressure energy or vice versa; this persistent phenomenon is also observed for inviscid fluids. Different types of viscous vortex filaments generated by initial velocity conditions show that vortex stretching phenomena precede an abrupt onset of vortex bursting in high-shear regions. In all cases, the kinetic energy starts to grow by borrowing energy from the pressure before the transfer phase to the small turbulent structures. The result observed on the vortex filament is also found for the Taylor–Green vortex, which significantly differs from the previous results on this same case simulated from the Navier–Stokes equations. This disagreement is attributed to the physical model used, that of discrete mechanics, where the formulation is based on the conservation of acceleration. The reasons for this divergence are analyzed in depth; however, a spectral analysis allows finding the established laws on the decay of kinetic energy as a function of the wave number. Full article

In this paper, the hybrid Lagrangian–Eulerian solver HoPFlow is presented and evaluated against wind tunnel measurements from the New MEXICO experiment. In the paper, the distinct solvers that assemble the HoPFlow solver are presented, alongside with details on their mutual coupling and interaction. The Eulerian solver, MaPFlow, solves the compressible Navier–Stokes equations under a cell-centered finite-volume discretization scheme, while the Lagrangian solver uses numerical particles that carry mass, pressure, dilatation and vorticity as flow markers in order to represent the flow-field by following their trajectories. The velocity field is calculated with the use of the decomposition theorem introduced by Helmholtz. Computational performance is enhanced by utilizing the particle mesh (PM) methodology in order to solve the Poisson equations for the scalar potential $\varphi$ and the stream function $\overrightarrow{\psi }$. The hybrid solver is tested in 3-D unsteady simulations concerning the axial flow around the wind turbine (WT) model rotor tested in the New MEXICO experimental campaign. Simulation results are presented as integrated rotor loads, radial distribution of aerodynamic forces and moments and pressure distributions at various span-wise positions along the rotor blades. Comparison is made against experimental data and computational results produced by the pure Eulerian solver. A total of 5 PM nodes per chord length of the blade section at $75\%$ have been found to be sufficient to predict the loading at the tip region of the blade with great accuracy. Discrepancies with respect to measurements, observed at the root and middle sections of the blade, are attributed to the omission of the spinner geometry in the simulations. Full article

The aim of this paper is the accurate and efficient analysis of the surface-plasmon-mode resonances of a graphene microdisk stack in the terahertz range. By means of suitable generalized boundary conditions and Fourier series expansion, the problem is formulated in terms of sets of one-dimensional integral equations in the vector Hankel transform domain for the harmonics of the surface current densities. In virtue of the Helmholtz decomposition, the unknowns are replaced by the corresponding surface curl-free and divergence-free contributions. An approximate solution is achieved by means of the Galerkin method. The proper selection of expansion functions reconstructing the physical behavior of the surface current densities leads to a fast-converging Fredholm second-kind matrix equation, whose elements are accurately and efficiently evaluated by means of a suitable analytical procedure in the complex plane. It is shown that the surface-plasmon-mode resonance frequencies upshift by increasing the number of disks and by decreasing the distance between the disks, and that new resonances can arise for small with respect to the radius distances between the disks, resembling the dipole-mode resonances of the dielectric disk, while, for larger distances, the surface-plasmon-mode resonances can split. Full article

Numerical solutions of heterogeneous Helmholtz problems present various computational challenges, with descriptive theory remaining out of reach for many popular approaches. Robustness and scalability are key for practical and reliable solvers in large-scale applications, especially for large wave number problems. In this work, we explore the use of a GenEO-type coarse space to build a two-level additive Schwarz method applicable to highly indefinite Helmholtz problems. Through a range of numerical tests on a 2D model problem, discretised by finite elements on pollution-free meshes, we observe robust convergence, iteration counts that do not increase with the wave number, and good scalability of our approach. We further provide results showing a favourable comparison with the DtN coarse space. Our numerical study shows promise that our solver methodology can be effective for challenging heterogeneous applications. Full article

Nonparaxial propagation of the vector vortex light beams in free space was investigated theoretically. Propagation-induced polarization changes in vector light beams with different spatial intensity distributions were analyzed. It is shown that the hybrid vector Bessel modes with polarization-OAM (orbital angular momentum) entanglement are the exact solutions of the vector Helmholtz equation. Decomposition of arbitrary vector beams in the initial plane z = 0 into these polarization-invariant beams with phase and polarization singularities was used to analyze the evolution of the polarization of light within the framework of the 2 × 2 coherency matrix formalism. It is shown that the 2D degree of polarization decreases with distance if the incident vector beam is not the modal solution. The close relationship of the degree of polarization with the quantum-mechanical purity parameter is emphasized. Full article

Wave-based acoustics simulation methods such as finite element method (FEM) are reliable computer simulation tools for predicting acoustics in architectural spaces. Nevertheless, their application to practical room acoustics design is difficult because of their high computational costs. Therefore, we propose herein a parallel wave-based acoustics simulation method using dissipation-free and dispersion-optimized explicit time-domain FEM (TD-FEM) for simulating room acoustics at large-scale scenes. It can model sound absorbers with locally reacting frequency-dependent impedance boundary conditions (BCs). The method can use domain decomposition method (DDM)-based parallel computing to compute acoustics in large rooms at kilohertz frequencies. After validation studies of the proposed method via impedance tube and small cubic room problems including frequency-dependent impedance BCs of two porous type sound absorbers and a Helmholtz type sound absorber, the efficiency of the method against two implicit TD-FEMs was assessed. Faster computations and equivalent accuracy were achieved. Finally, acoustics simulation of an auditorium of 2271 ${\mathrm{m}}^3$ presenting a problem size of about 150,000,000 degrees of freedom demonstrated the practicality of the DDM-based parallel solver. Using 512 CPU cores on a parallel computer system, the proposed parallel solver can compute impulse responses with 3 s time length, including frequency components up to 3 kHz within 9000 s. Full article

In this treatment of random dynamical systems, we consider the existence—and identification—of conditional independencies at nonequilibrium steady-state. These independencies underwrite a particular partition of states, in which internal states are statistically secluded from external states by blanket states. The existence of such partitions has interesting implications for the information geometry of internal states. In brief, this geometry can be read as a physics of sentience, where internal states look as if they are inferring external states. However, the existence of such partitions—and the functional form of the underlying densities—have yet to be established. Here, using the Lorenz system as the basis of stochastic chaos, we leverage the Helmholtz decomposition—and polynomial expansions—to parameterise the steady-state density in terms of surprisal or self-information. We then show how Markov blankets can be identified—using the accompanying Hessian—to characterise the coupling between internal and external states in terms of a generalised synchrony or synchronisation of chaos. We conclude by suggesting that this kind of synchronisation may provide a mathematical basis for an elemental form of (autonomous or active) sentience in biology. Full article

In this work, we investigate analytically the solutions of a nonlinear div-curl system with fractional derivatives of the Riemann–Liouville or Caputo types. To this end, the fractional-order vector operators of divergence, curl and gradient are identified as components of the fractional Dirac operator in quaternionic form. As one of the most important results of this manuscript, we derive general solutions of some non-homogeneous div-curl systems that consider the presence of fractional-order derivatives of the Riemann–Liouville or Caputo types. A fractional analogous to the Teodorescu transform is presented in this work, and we employ some properties of its component operators, developed in this work to establish a generalization of the Helmholtz decomposition theorem in fractional space. Additionally, right inverses of the fractional-order curl, divergence and gradient vector operators are obtained using Riemann–Liouville and Caputo fractional operators. Finally, some consequences of these results are provided as applications at the end of this work. Full article