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From a mathematical perspective, the extraordinary properties of metamaterials are often reflected in the coefficients of the governing partial differential equations (PDEs). These coefficients may fall outside the assumptions of classical…
The capacity to predict and control bioprocesses is perhaps one of the most important objectives of biotechnology. Computational simulation is an established methodology for the design and optimization of bioprocesses, where the finite…
In the present paper we introduce a Virtual Element Method (VEM) for the approximate solution of general linear second order elliptic problems in mixed form, allowing for variable coefficients. We derive a theoretical convergence analysis…
A model of multicellular systems with several types of cells is developed from the phase field model. The model is presented as a set of partial differential equations of the field variables, each of which expresses the shape of one cell.…
The oversampling multiscale finite element method (MsFEM) is one of the most popular methods for simulating composite materials and flows in porous media which may have many scales. But the method may be inapplicable or inefficient in some…
The choice of stabilization term is a critical component of the virtual element method (VEM). However, the theory of VEM provides only asymptotic guidance for selecting the stabilization term, which ensures convergence as the mesh size…
Acoustic scattering of waves by bounded inhomogeneities in an unbounded homogeneous domain is considered. A symmetric coupled system of time-domain boundary integral equations and the second order formulation of the wave equation is…
This work is devoted to the consistent modeling of a three-phase mixture of a gas, a liquid and its vapor. Since the gas and the vapor are mis-cible, the mixture is subjected to a non-symmetric constraint on the volume. Adopting the Gibbs…
We present a new method for constructing equilibrium phase models for stellar systems, which we call the iterative method. It relies on constrained, or guided evolution, so that the equilibrium solution has a number of desired parameters…
Understanding the flow of deformable particles such as liquid drops, synthetic capsules and vesicles, and biological cells confined in a small channel is essential to a wide range of potential chemical and biomedical engineering…
In this article we propose and numerically implement a mathematical model for the simulation of three-dimensional semiconductor devices characterized by an heterogeneous material structure. The model consists of a system of nonlinearly…
Computer simulations have been employed in recent years to evaluate the configurational entropy changes in model glass-forming liquids. We consider two methods, both of which involve the calculation of the `intra-basin' entropy as a means…
In this paper, we present a study on how to develop an efficient multiscale simulation strategy for the dynamics of chemically active systems on low-dimensional supports. Such reactions are encountered in a wide variety of situations,…
Boundary element methods (BEM) are used for forward computation of bioelectromagnetic fields in multi-compartment volume conductor models. Most BEM approaches assume that each compartment is in contact with at most one external compartment.…
The state of the art in electromagnetic Finite Element Particle-in-Cell (EM-FEMPIC) has advanced significantly in the last few years. These have included understanding function spaces that must be used to represent sources and fields…
Water's phase diagram remains one of the most intricate and challenging benchmarks in molecular modeling. In this study, we compute the phase diagram of water using an Atomic Cluster Expansion (ACE) potential trained on density-functional…
In this paper, we develop the constraint energy minimizing generalized multiscale finite element method (CEM-GMsFEM) for convection-diffusion equations with inhomogeneous Dirichlet, Neumann and Robin boundary conditions, along with…
Phase diagrams are essential tools of the materials scientist, showing which phases are at equilibrium under a set of applied thermodynamic conditions. Essentially all phase diagrams today are two dimensional, typically constructed with…
Modification of coupled integral equations method (CIEM) for calculating the characteristics of the accelerating structures is presented in this paper. In earlier developed CIEM schemes the coupled integral equations are derived for the…
The development of materials science is undergoing a shift from empirical approaches to data-driven and algorithm-oriented research paradigm. The state-of-the-art platforms are confined to inorganic crystals, with limited chemical space,…