相关论文: Unified nonlocal rational continuum models develop…
We investigate discretization strategies for a recently introduced class of energy-based models. The model class encompasses classical port-Hamiltonian systems, generalized gradient flows, and certain systems with algebraic constraints. Our…
This paper presents a nonlinear reaction-diffusion-fluid system that simulates radiofrequency ablation within cardiac tissue. The model conveys the dynamic evolution of temperature and electric potential in both the fluid and solid regions,…
Context. Turbulent convection models in nonlinear radial stellar pulsation models rely on an extra equation for turbulent kinetic energy and fail to adequately explain mode-selection problems. Since multidimensional calculations are…
Problems with localized nonhomogeneous material properties present well-known challenges for numerical simulations. In particular, such problems may feature large differences in length scales, causing difficulties with meshing and…
In this paper, we develop a space-time upscaling framework that can be used for many challenging porous media applications without scale separation and high contrast. Our main focus is on nonlinear differential equations with multiscale…
We develop and compare several analytical approximations for the polaron problem in finite-width, non-parabolic conduction bands. The main focus of the work is an extension of the Feynman variational method to a tight-binding lattice, where…
We propose a class of nonlocal diffusion systems on time-varying domains, and fully characterize their asymptotic dynamics in the asymptotically fixed, time-periodic and unbounded cases. The kernel is not necessarily symmetric or compactly…
Extending density functional theory (DFT) to an {\it ab initio} orbital functional theory (OFT) requires new methodology for nonlocal exchange and correlation potentials. This paper describes such modifications to a standard Dirac-Slater…
Nonlocal models allow for the description of phenomena which cannot be captured by classical partial differential equations. The availability of efficient solvers is one of the main concerns for the use of nonlocal models in real world…
A nonlocal method to obtain discrete classical fields is presented. This technique relies on well-behaved matrix representations of the derivatives constructed on a non--equispaced lattice. The drawbacks of lattice theory like the fermion…
A discretization of a continuum theory with constraints or conserved quantities is called mimetic if it mirrors the conserved laws or constraints of the continuum theory at the discrete level. Such discretizations have been found useful in…
We consider a class of nonlinear Klein-Gordon equations which are Hamiltonian and are perturbations of linear dispersive equations. The unperturbed dynamical system has a bound state, a spatially localized and time periodic solution. We…
This work considers charged systems described by the modified Poisson--Nernst--Planck (PNP) equations, which incorporate ionic steric effects and the Born solvation energy for dielectric inhomogeneity. Solving the steady-state modified PNP…
Excitations of disordered systems such as glasses are of fundamental and practical interest but computationally very expensive to solve. Here we introduce a technique for modeling these excitations in an infinite disordered medium with a…
The presence and evolution of defects that appear in the manufacturing process play a vital role in the failure mechanisms of engineering materials. In particular, the collective behavior of dislocation dynamics at the mesoscale leads to…
We have recently presented an extension of the standard variational calculus to include the presence of deformed derivatives in the Lagrangian of a system of particles and in the Lagrangian density of field-theoretic models. Classical…
Using methods of kinetic theory and liquid state theory we propose a description of the non-equilibrium behavior of molecular fluids which takes into account their microscopic structure and thermodynamic properties. The present work…
We study a simple nonlocal-in-time dynamic system proposed for the effective modeling of complex diffusive regimes in heterogeneous media. We present its solutions and their commonly studied statistics such as the mean square distance. This…
Thick rods are employed in Nanotechnology to build modern electro mechanical systems. Design and optimization of such structures can be carried out by nonlocal continuum mechanics which is computationally convenient when compared to…
Recent breakthroughs in the experimental manipulation of strongly interacting atomic Rydberg gases in lattice potentials have opened a new avenue for the study of many-body phenomena. Considerable efforts are currently being undertaken to…