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Monte Carlo methods are often employed to numerically integrate kinetic equations, such as the particle-in-cell method for the plasma kinetic equation, but these methods suffer from the introduction of counting noise to the solution. We…
Computational fluid dynamics is a direct modeling of physical laws in a discretized space. The basic physical laws include the mass, momentum and energy conservations, physically consistent transport process, and similar domain of…
This paper describes a new 2D model for the photospheric evolution of the magnetic carpet. It is the first in a series of papers working towards constructing a realistic 3D non-potential model for the interaction of small-scale solar…
Ductile damage models and cohesive laws incorporate the material plasticity entailing the growth of irrecoverable deformations even after complete failure. This unrealistic growth remains concealed until the unilateral effects arising from…
We present and analyse a micro-macro acceleration method for the Monte Carlo simulation of stochastic differential equations with separation between the (fast) time-scale of individual trajectories and the (slow) time-scale of the…
Biological tissues are complex structures composed of many elements which make light-based tissue diagnostics challenging. Over the past decades, Monte Carlo technique has been used as a fundamental and versatile approach toward modeling…
When cell sheets fold during development, their apical or basal surfaces constrict and cell shapes approach the geometric singularity in which these surfaces vanish. Here, we reveal the mechanical consequences of this geometric singularity…
The paper presents numerical simulations performed on dielectric properties of two-dimensional binary composites on eleven regular space filling tessellations. First, significant contributions of different parameters, which play an…
Discontinuities in spatial derivatives appear in a wide range of physical systems, from creased thin sheets to materials with sharp stiffness transitions. Accurately modeling these features is essential for simulation but remains…
During growth, tissue expands and deforms. Given its elastic properties, stresses emerge in an expanding and deforming tissue. Cell rearrangements can dissipate these stresses and numerous experiments confirm the viscoelastic properties of…
We use numerical simulations to investigate the behaviour of the dipole moment of the spatial distribution of different kinds of mass tracers. We select density peaks of the simulated matter distribution with mean separations of 38 and 30…
The effective, fast transport of matter through porous media is often characterized by complex dispersion effects. To describe in mathematical terms such situations, instead of a simple macroscopic equation (as in the classical Darcy's…
The electric or magnetic field of an ideal dipole is known to have a Dirac delta function at the origin. The usual textbook derivation of this delta function is rather ad hoc and cannot be used to calculate the delta-function structure for…
In the framework of a continuum theory, it is shown that the direct flexoelectric response of a finite sample essentially depends on the surface polarization energy, even in the thermodynamic limit where the body size tends to infinity. It…
Numerical modeling of electrodynamic aggregation is carried out for a random ensemble of magnetized nanodust taken as a many body system of strongly magnetized thin rods (i.e., one-dimensional static magnetic dipoles), which possess…
A computer simulation has to be fast to be helpful, if it is employed to study the behavior of a multicomponent dynamic system. This paper discusses modeling concepts and algorithmic techniques useful for creating such fast simulations.…
The kinetics of dislocations is studied with computer simulation at loadings of different intensity. It is established that the dislocations have a few different structural states. The dislocations "with the micropore" play important role…
Integral expressions are determined for the elastic displacement and stress fields due to stationary or moving dislocation loops in finite samples. These general expressions are valid for anisotropic media as well. Specifically for the…
Image acquisition techniques such as micro-computed tomography are nowadays widely available. Quantitative analysis of the resulting 3D image data enables geometric characterization of the micro-structure of materials. Stochastic geometry…
In this paper we consider a mathematical model which describes the equilibrium of two elastic rods attached to a nonlinear spring. We derive the variational formulation of the model which is in the form of an elliptic quasivariational…