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We offer an insight into our mathematical endeavors, which aim to advance the foundational understanding of energy systems in a broad context, encompassing facets such as charge transport, energy storage, markets, and collective behavior.…
We develop a unified continuum modeling framework for viscous fluids and hyperelastic solids using the Gibbs free energy as the thermodynamic potential. This framework naturally leads to a pressure primitive variable formulation for the…
Fluid discontinuities, such as shock fronts and vortex sheets, can reflect waves and become unstable to corrugation. Analytical calculations of these phenomena are tractable in the simplest cases only, while their numerical simulations are…
A crystal plasticity theory was developed for use in simulations of dynamic loading at high pressures and strain rates. At pressures of the order of the bulk modulus, compressions o(100%) may be induced. At strain rates o(10^9)/s or higher,…
We report a new theory of dissipative forces acting between colliding viscoelastic bodies. The impact velocity is assumed not to be large, to avoid plastic deformations and fragmentation at the impact. The bodies may be of an arbitrary…
A wide and critical comparison of the capability of Method of Characteristics, Explicit Path-Conservative Finite Volume Method and Semi-Implicit Staggered Finite Volume Method is presented and discussed, in terms of accuracy and efficiency.…
The output of molecular dynamics simulations is high-dimensional, and the degrees of freedom among the atoms are related in intricate ways. Therefore, a variety of analysis frameworks have been introduced in order to distill complex motions…
Mathematical models and computer algorithms are developed to calculate dynamic stress concentration and fracture wave propagation in a reinforced composite sheet. The composite consists of a regular system alternating extensible fibers and…
Exact one-dimensional solutions to the equations of fluid dynamics are derived in the large-Pr and small-Pr limits (where Pr is the Prandtl number). The solutions are analogous to the Pr = 3/4 solution discovered by Becker and analytically…
Numerical algorithms for solving problems of mathematical physics on modern parallel computers employ various domain decomposition techniques. Domain decomposition schemes are developed here to solve numerically initial/boundary value…
The Lattice Boltzmann Method (LBM), e.g. in [ 1] and [2 ], can be interpreted as an alternative method for the numerical solution of partial differential equations. Consequently, although the LBM is usually applied to solve fluid flows, the…
Soft porous materials, such as biological tissues and soils, are exposed to periodic deformations in a variety of natural and industrial contexts. The detailed flow and mechanics of these deformations have not yet been systematically…
We have presented some practical consequences on the molecular-dynamics simulations arising from the numerical algorithm published recently in paper Int. J. Mod. Phys. C 16, 413 (2005). The algorithm is not a finite-difference method and…
We are interested in a class of numerical schemes for the optimization of nonlinear hyperbolic partial differential equations. We present continuous and discretized relaxation schemes for scalar, one-- conservation laws. We present…
A fundamental challenge in computer analysis of power flow is the rigorous understanding of the impact of different loading levels on the solutions of the power flow equation. This letter presents a comprehensive study of possible numerical…
In this work, we provide a solution to the problem of computing collision stress in particle-tracking simulations. First, a formulation for the collision stress between particles is derived as an extension of the virial stress formula to…
Grip, walk, crawl, and jump. Soft robots are integrated functional structures composed of compliant mechanisms, whose activity spans various industrial applications such as surgery, healthcare, surveillance, and even planetary exploration.…
Although for the most part classical, the topic of electrostatics finds to this day new applications. In this review we highlight several theoretical results on electrostatics, chosen to both illustrate general principles, and for their…
The steady-state of a generalized coagulation-decoagulation model on a one-dimensional lattice with reflecting boundaries is studied using a matrix-product approach. It is shown that the quadratic algebra of the model has a four-dimensional…
This short communication develops a new numerical procedure suitable for a large class of ordinary differential equation systems found in models in physics and engineering. The main numerical procedure is analogous to those concerning the…