Search Results (35)

Particle image velocimetry (PIV) flow measurements are common practice in laboratory settings in a wide variety of fields involving fluid dynamics, including biology, physics, engineering, and medicine. Dynamic fluid pressure is a notoriously difficult property to measure non-intrusively, yet its variation is a driving flow force and critical to model correctly. Techniques have been developed to estimate the pressure from velocity and velocity gradient measurements. Here, we highlight a novel application of boundary conditions when applying such pressure estimation techniques based on two-dimensional PIV data; the novel method is especially relevant to problems with complex boundary conditions. As such, it is demonstrated with PIV measurements of in vivo fish suction-feeding, which represents a challenging flow environment. Suction-feeding is a common method for capturing prey by aquatic organisms. Suction-feeding is a complex fish–fluid interaction governed by various hydrodynamic forces and the dynamic behavior of the fish (motion and forces). This study focuses on estimating the pressure within the flow field surrounding the mouth of a Bluegill sunfish (Lepomis macrochirus) during suction-feeding utilizing two-dimensional PIV measurements. High-speed imaging was used for measurements of the fish kinematics (duration and amplitude). Through the Poisson equation, the pressure field is estimated from the PIV velocity measurements. The boundary conditions for the pressure field are determined from the integral momentum equation, separately for three phases of the suction-feeding cycle. We demonstrate the utility of the technique with this case study on fish suction-feeding by quantifying the pressure field that drives the flow towards the buccal cavity, a feeding mechanism known to be dominated by pressure spatial variations over the feeding cycle. Full article

The phase transitions and switching dynamics of topological polar textures in hafnium oxide (HfO₂)-based cylindrical-shell ferroelectrics are studied using a three-dimensional (3D) phase field model based on the self-consistent solution of the time-dependent Ginzburg–Landau model and Poisson equation. The comprehensive interplays of bulk free energy, gradient energy, depolarization energy, and elastic energy are taken into account. When a cylindrical ferroelectric device is biased under the in-plane radial electric field, there is a size-controlled phase transition between the ferroelectric (FE), antiferroelectric (AFE), and paraelectric (PE) phases, depending on ferroelectric film thickness and cylindrical shell radius. For in-plane polarization textures at the equilibriums, the FE phase has a Néel-like texture with a center-type four-quad domain, the AFE phase has a monodomain texture, and the PE phase has a Bloch-like texture with a vortex four-quad domain. These polarization domain textures are resultant from energy competition and topologically protected by the geometrical confinement. The polarization dynamics from polar states towards equilibriums are analyzed considering the separated contributions of x- and y-components of polarizations that are driven by x-y in-plane electric fields. The emergent topological domains and phase transitions provide guidelines for geometrical engineering of a novel nano-structured ferroelectric device that is different from the planar one, offering new possibilities for multi-functional high-density ferroelectric memory. Full article

In this paper, we introduce the development of the Finite Difference Matrix Operators (FDMO) algorithm for solving the three-dimensional (3D) electromagnetic problem governed by the Laplace–Poisson equation. Specifically, we propose a novel approach by integrating the FDMO approach with non-uniform mesh of the 3D solution domain, optimizing computational efficiency and adaptability for complex grounding system geometries, to compute and analysis the earth potential distribution in grounding systems. The study considers two typical grid configurations—square and L-shaped of IEEE Std 80^™—as well as a real-world grounding system of high voltage substation in Vietnam. The results of potential distribution, touch, and step voltages obtained from the proposed method demonstrate high agreement with those computed using the Finite Element Method (FEM) and IEEE Std 80^™, confirming the accuracy, robustness, and practical utility of the proposed method for the grounding design of high voltage substations in power systems. Full article

A meshless, quasi-convex reproducing kernel particle framework for three-dimensional steady-state thermomechanical coupling problems is presented in this paper. A meshfree, second-order, quasi-convex reproducing kernel scheme is employed to approximate field variables for solving the linear Poisson equation and the elastic thermal stress equation in sequence. The quasi-convex reproducing kernel approximation proposed by Wang et al. to construct almost positive reproducing kernel shape functions with relaxed monomial reproducing conditions is applied to improve the positivity of the thermal matrixes in the final discreated equations. Two numerical examples are given to verify the effectiveness of the developed method. The numerical results show that the solutions obtained by the quasi-convex reproducing kernel particle method agree well with the analytical ones, with a slightly better-improved numerical accuracy than the element-free Galerkin method and the reproducing kernel particle method. The effects of different parameters, i.e., the scaling parameter, the penalty factor, and node distribution on computational accuracy and efficiency, are also investigated. Full article

This paper generalizes the efficient matrix decomposition method for solving the finite-difference (FD) discretized three-dimensional (3D) Poisson’s equation using symmetric 27-point, 4th-order accurate stencils to adapt more boundary conditions (BCs), i.e., Dirichlet, Neumann, and Periodic BCs. It employs equivalent Dirichlet nodes to streamline source term computation due to BCs. A generalized eigenvalue formulation is presented to accommodate the flexible 4th-order stencil weights. The proposed method significantly enhances computational speed by reducing the 3D problem to a set of independent 1D problems. As compared to the typical matrix inversion technique, it results in a speed-up ratio proportional to $n^4$, where $n$ is the number of nodes along one side of the cubic domain. Accuracy is validated using Gaussian and sinusoidal source fields, showing 4th-order convergence for Dirichlet and Periodic boundaries, and 2nd-order convergence for Neumann boundaries due to extrapolation limitations—though with lower errors than traditional 2nd-order schemes. The method is also applied to vortex-in-cell flow simulations, demonstrating its capability to handle outer boundaries efficiently and its compatibility with immersed boundary techniques for internal solid obstacles. Full article

In this study, we introduce an innovative approach for addressing fractional partial differential equations (fPDEs) by combining Monte Carlo-based physics-informed neural networks (PINNs) with the cuckoo search (CS) optimization algorithm, termed PINN-CS. There is a further enhancement in the application of quasi-Monte Carlo assessment that comes with high efficiency and computational solutions to estimates of fractional derivatives. By employing structured sampling nodes comparable to techniques used in finite difference approaches on staggered or irregular grids, the proposed PINN-CS minimizes storage and computation costs while maintaining high precision in estimating solutions. This is supported by numerous numerical simulations to analyze various high-dimensional phenomena in various environments, comprising two-dimensional space-fractional Poisson equations, two-dimensional time-space fractional diffusion equations, and three-dimensional fractional Bloch–Torrey equations. The results demonstrate that PINN-CS achieves superior numerical accuracy and computational efficiency compared to traditional fPINN and Monte Carlo fPINN methods. Furthermore, the extended use to problem areas with irregular geometries and difficult-to-define boundary conditions makes the method immensely practical. This research thus lays a foundation for more adaptive and accurate use of hybrid techniques in the development of the fractional differential equations and in computing science and engineering. Full article

This paper investigates the electromagnetic fields being scattered by a metal spherical object in a vacuum environment, providing a numerical implementation of the obtained analytical results. A time-harmonic magnetic dipole source, far enough, emits the incident field at low frequencies, oriented arbitrarily in the three-dimensional space. The aim is to find a detailed solution to the scattering problem at spherical coordinates, which is useful for data inversion. Based on the theory of low frequencies, the Maxwell-type problem is transformed into Laplace’s or Poisson’s interconnected equations, accompanied by the proper boundary conditions on the perfectly conducting sphere and the radiation conditions at infinity, which are solved gradually. Broadly, the static and the first three dynamic terms are sufficient, while the terms of a higher order are negligible, which is confirmed by the field graphical representation. Full article

To describe stationary physical systems, well-known boundary problems for shielded Poisson and Sophie Germain equations are used. The obtained shielded harmonic and biharmonic systems are approximated using the finite element method and fictitiously continued. The resulting problems are solved using the developed method of iterative extensions. To expedite the convergence of this method, the relationships between physical quantities on the extension of systems and additional parameters of the iterative method are employed. The formulations of sufficient convergence conditions for the iterative process utilize interdisciplinary connections with functional analysis, applying discrete analogs of the principles of function extensions while preserving norm and class. In the algorithmic implementation of the iterative extensions method, automation is applied to control the selection of the optimal iterative parameter value during information processing. In accordance with the fictitious domain methodology, solvable problems from domains with a complex geometry are reduced to problems in a rectangle in the two-dimensional case and in a rectangular parallelepiped in the three-dimensional case. But now, in the problems being solved, the minimization of the error of the iterative processes is carried out with a norm stronger than the energy norm. Then, all relative errors are estimated from above in the used norms by terms of infinitely decreasing geometric progressions. A generalization of the developed methodology to boundary value problems for polyharmonic equations is possible. Full article

Video fusion aims to synthesize video footage from different sources into a unified, coherent output. It plays a key role in areas such as video editing and special effects production. The challenge is to ensure the quality and naturalness of synthetic video, especially when dealing with footage of different sources and qualities. Researchers continue to strive to optimize algorithms to adapt to a variety of complex application scenarios and improve the effectiveness and applicability of video fusion. We introduce an algorithm based on a convolution pyramid and propose a 3D video fusion algorithm that looks for the potential function closest to the gradient field in the least square sense. The 3D Poisson equation is solved to realize seamless video editing. This algorithm uses a multi-scale method and wavelet transform to approximate linear time. Through numerical optimization, a small core is designed to deal with large target filters, and multi-scale transformation analysis and synthesis are realized. In terms of seamless video fusion, it shows better performance than existing algorithms. Compared with editing multiple 2D images into video after Poisson fusion, the video quality produced by this method is very close, and the computing speed of the video fusion is improved to a certain extent. Full article

The finite element simulation is a valid way for the rapid development of the root-cutting mechanism for hydroponic Chinese kale. The stem of the hydroponic Chinese kale was simplified as a transverse isotropic elastic body, and axial compression, three-point bending, and shear tests were performed. The ANSYS/LS-DYNA19.2 software was adopted for stem shear simulation, and the regression equation of the maximum simulated shear force was established. The optimized mechanical parameters were determined by minimizing the deviation between the maximum shear force obtained from the simulation and test. The three-dimensional scanning method was employed to establish the geometric model of the hydroponic Chinese kale stem. The cutting finite element simulation model and test platform were constructed. Displacement, deformation, and force measured from simulation and test were compared. Through measurement and simulation calibration, an axial elastic modulus of 6.22 MPa, axial Poisson’s ratio of 0.46, radial elastic modulus of 3.56 MPa, radial Poisson’s ratio of 0.44, radial shear modulus of 0.8 MPa, and a failure strain of 0.08 were determined. During the cutting simulation and test, the resulting maximum displacement deviations of the marking points on the end of the stem were 0.68 mm along the X-axis and 2.83 mm along the Y-axis, while the maximum deviations of the cutting and clamping force were 0.49 N and 0.77 N, respectively. The deformation and force variation laws of the kale stem in the cutting simulation and test process were basically consistent. It showed that the mechanical parameters calibrated by the simulation were accurate and effective, and the stem cutting simulation results with the finite element method were in good agreement with that of the cutting test. The study provided a reference for the rapid optimization design of the root-cutting mechanism for hydroponic Chinese kale harvest. Full article

Cell migration in a biological medium towards a blood vessel is modeled, as a random process, sucessively inside an annulus (two-dimensional domain) and an annular cylinder (three-dimensional domain). The conditional probability function u for the cell moving inside such domains (tissue) fulfills by assumption a diffusion–advection equation that is subject to a Dirichlet boundary condition on the outer boundary and a Robin boundary condition on the inner boundary. The mean first-passage time (MFPT) function determined by u estimates the average time for the travelling cell to reach various interesting targets. The MFPT function fulfills a Poisson equation inside a domain with suitable boundary conditions, which give rise to various mathematical problems. The main novelty of this study is the characterization of such an MFPT function inside an annulus and an annular cylinder, which is subject to a Robin boundary condition on the inner boundary and a Dirichlet boundary condition on the outer one, and these are integral functions whose densities are the solution of an inhomogeneous system of linear integral equations. Full article

A fast pollutant dispersion model for urban canopies is developed by coupling mean wind profiles to a parameterisation of turbulent diffusion and solving the time-dependent advection–diffusion equation. The performance of a simplified, coarse-grained representation of the velocity field is investigated. Spatially averaged mean wind profiles within local averaging regions or repeating units are predicted by solving the three-dimensional Poisson equation for a set of discrete vortex sheets. For each averaging region, the turbulent diffusion is parameterised in terms of the mean wind profile using empirical constants derived from large-eddy simulation (LES). Nearly identical results are obtained whether the turbulent fluctuations are specified explicitly or an effective diffusivity is used in their place: either version of the fast dispersion model shows much better agreement with LES than does the Gaussian plume model (e.g., the normalized mean square error inside the canopy is several times smaller). Passive scalar statistics for a regular cubic building array show improved agreement with LES when wind profiles vary in the horizontal. The current implementation is around 50 times faster than LES. With its combination of computational efficiency and moderate accuracy, the fast model may be suitable for time-critical applications such as emergency dispersion modelling. Full article

Auxetic textiles are emerging as an enticing option for many advanced applications due to their unique deformation behavior under tensile loading. This study reports the geometrical analysis of three-dimensional (3D) auxetic woven structures based on semi-empirical equations. The 3D woven fabric was developed with a special geometrical arrangement of warp (multi-filament polyester), binding (polyester-wrapped polyurethane), and weft yarns (polyester-wrapped polyurethane) to achieve an auxetic effect. The auxetic geometry, the unit cell resembling a re-entrant hexagon, was modeled at the micro-level in terms of the yarn’s parameters. The geometrical model was used to establish a relationship between the Poisson’s ratio (PR) and the tensile strain when it was stretched along the warp direction. For validation of the model, the experimental results of the developed woven fabrics were correlated with the calculated results from the geometrical analysis. It was found that the calculated results were in good agreement with the experimental results. After experimental validation, the model was used to calculate and discuss critical parameters that affect the auxetic behavior of the structure. Thus, geometrical analysis is believed to be helpful in predicting the auxetic behavior of 3D woven fabrics with different structural parameters. Full article

This article investigates the size dependent on piezoelectrically layered perforated nanobeams embedded in an elastic foundation considering the material Poisson’s ratio and the flexoelectricity effects. The composite beam is composed of a regularly squared cut-out elastic core with two piezoelectric face sheet layers. An analytical geometrical model is adopted to obtain the equivalent geometrical variables of the perforated core. To capture the Poisson’s ratio effect, the three-dimensional continuum mechanics adopted to express the kinematics are kinetics relations in the framework of the Euler–Bernoulli beam theory (EBBT). The nonlocal strain gradient theory is utilized to incorporate the size-dependent electromechanical effects. The Hamilton principle is applied to derive the nonclassical electromechanical dynamic equation of motion with flexoelectricity impact. A closed form solution for resonant frequencies is obtained. Numerical results explored the impacts of geometrical and material characteristics on the nonclassical electromechanical behavior of nanobeams. Obtained results revealed the significant effects of the mechanical, electrical, and elastic foundation parameters on the dynamic behavior of piezoelectric composite nanobeams. The developed procedure and the obtained results are helpful for many industrial purposes and engineering applications, such as micro/nano-electromechanical systems (MEMS) and NEMS. Full article

Mean wind profiles within a unit-aspect-ratio street canyon have been estimated by solving the three-dimensional Poisson equation for a set of discrete vortex sheets. The validity of this approach, which assumes inviscid vortex dynamics away from boundaries and a small nonlinear contribution to the growth of turbulent fluctuations, is tested for a series of idealised and realistic flows. In this paper, the effects of urban geometry on accuracy are examined with neutral flow over shallow, deep, asymmetric and realistic canyons, while thermal effects are investigated for a single street canyon and both bottom cooling and heating. The estimated mean profiles of the streamwise and spanwise velocity components show good agreement with reference profiles obtained from the large-eddy simulation: the canyon-averaged errors (e.g., normalised absolute errors around 1%) are of the same order of magnitude as those for the unit-aspect-ratio street canyon. It is argued that the approach generalises to more realistic flows because strong spatial localisation of the vorticity field is preserved. This work may be applied to high-resolution modelling of winds and pollutants, for which mean wind profiles are required, and fast statistical modelling, for which physically-based estimates can serve as initial guesses or substitutes for analytical models. Full article