Related papers: Simple demonstration of different types of couplin…
Multiscale problems are computationally costly to solve by direct simulation because the smallest scales must be represented over a domain determined by the largest scales of the problem. We have developed and analyzed new numerical methods…
Consider a fluid flowing through a junction between two pipes with different sections. Its evolution is described by the 2D or 3D Euler equations, whose analytical theory is far from complete and whose numerical treatment may be rather…
The relationship between thermal light and coherent pulses is of fundamental and practical interest. We now know that thermal light cannot be represented as a statistical mixture of single pulses. In this paper we ask whether or not thermal…
The zero-temperature and finite-temperature thermodynamics of two-component Fermi gases with finite-range attractive interaction suffer from fermion sign problem, which seems like an insurmountable problem in exact numerical simulations. In…
Engineering strong interactions between quantum systems is essential for many phenomena of quantum physics and technology. Typically, strong coupling relies on short-range forces or on placing the systems in high-quality electromagnetic…
Composite systems, where couplings are of two types, a combination of strong dilute and weak dense couplings of Ising spins, are examined through the replica method. The dilute and dense parts are considered to have independent canonical…
With the advent of high-level programming languages capable of quickly rendering three-dimensional simulations, the inclusion of computers as a learning tool in the classroom has become more prevalent. Although work has begun to study the…
The one-dimensional harmonic oscillator in a box problem is used to introduce the concept of a mixed-mode shell-model scheme. The method combines low-lying ``pure mode'' states of a system to achieve a better description in situations where…
Deterministic simulations of the rate equations governing cluster dynamics in materials are limited by the number of equations to integrate. Stochastic simulations are limited by the high frequency of certain events. We propose a coupling…
A set of traveling wave solution to convection-reaction-diffusion equation is studied by means of methods of local nonlinear analysis and numerical simulation. It is shown the existence of compactly supported solutions as well as solitary…
Continuum equations are ubiquitous in physical modelling of elastic, viscous, and viscoelastic systems. The equations of continuum mechanics take nontrivial forms on curved surfaces. Although the curved surface formulation of the continuum…
Molecular dynamics simulations are used to model the thermal properties of a fluid containing solid nanoparticles (nanofluid). The flexibility of molecular simulation allows us to consider the effects of particle mass, particle-particle and…
A vibrational model of heat conduction in liquids with soft pairwise interactions is applied to estimate the thermal conductivity coefficient of strongly coupled Yukawa fluids. A reasonable agreement with the available data from numerical…
We describe the mathematical theory of diffusion and heat transport with a view to including some of the main directions of recent research. The linear heat equation is the basic mathematical model that has been thoroughly studied in the…
Many suspensions contain particles with complex shapes that are affected not only by hydrodynamics, but also by thermal fluctuations, internal kinematic constraints and other long-range non-hydrodynamic interactions. Modeling these systems…
Controlling the spectral response of thermal emitters has become increasingly important for a range of energy and sensing applications. Conventional approaches to achieving arbitrary spectrum selectivity in photonic systems have entailed…
We considered the propagation of nonlinear shallow water waves in a narrow channel presenting a fork. We aimed at computing the coupling conditions for a 1D effective model, using 2D simulations and an analysis based on the conservation…
Multiscale and multiphysics applications are now commonplace, and many researchers focus on combining existing models to construct combined multiscale models. Here we present a concise review of multiscale applications and their source…
The pairing correlations in hot nuclei $^{162}$Dy are investigated in terms of the thermodynamical properties by covariant density functional theory. The heat capacities $C_V$ are evaluated in the canonical ensemble theory and the paring…
Coupled problems with various combinations of multiple physics, scales, and domains are found in numerous areas of science and engineering. A key challenge in the formulation and implementation of corresponding coupled numerical models is…