Related papers: Prediction of strong shock structure using the bim…
The state of a single-species monatomic gas from near-equilibrium to highly nonequilibrium conditions is investigated using analytical and numerical methods. Normal solutions of the Boltzmann equation for Fourier flow (uniform heat flux)…
The formation of unmagnetized electrostatic shock-like structures with a high Mach number is examined with one- and two-dimensional particle-in-cell (PIC) simulations. The structures are generated through the collision of two identical…
We revisit and derive the shock-change equations relating the dynamics of a shock wave with the partial derivatives describing the motion of a reactive fluid with general equation of state in a stream-tube with arbitrary area variation. We…
We prove a stable shock formation result for a large class of systems of quasilinear wave equations in two spatial dimensions. We give a precise description of the dynamics all the way up to the singularity. Our main theorem applies to…
In this article we propose a novel MCMC method based on deterministic transformations T: X x D --> X where X is the state-space and D is some set which may or may not be a subset of X. We refer to our new methodology as Transformation-based…
In this note, we show the existence of regular solutions to the stationary version of the Navier-Stokes system for compressible fluids with a density dependent viscosity, known as the shallow water equations. For arbitrary large forcing we…
The Gas-Kinetic Scheme (GKS), widely used in computational fluid dynamics for simulating hypersonic and other complicated flow phenomena, is extended in this work to electromagnetic problems by solving Maxwell's equations. In contrast to…
Multimodal distributions of some physics based model parameters are often encountered in engineering due to different situations such as a change in some environmental conditions, and the presence of some types of damage and nonlinearity.…
We study driven 1d lattice gas models with two types of particles and nearest neighbor hopping. We find the most general case when there is a shock solution with a product measure which has a density-profile of a step function for both…
We use the one-dimensional steady version of the equations derived in paper I to compute the structure of shock waves. The agreement with experiment is good, especially when we retain the experimental value of the Prandtl number adopted in…
Using the static-dynamic analogy, work at Bath and Bristol has uncovered the vital organizing role of the Maxwell 'energy criterion' load in the advanced post-buckling of long-thin structures which exhibit severe shell-like imperfection…
Numerical methods are developed to simulate the dynamics of atoms in a Magneto-Optic Trap (MOT), based on the fluid description of ultracold gases under laser cooling and magnetic trapping forces. With this model, equilibrium hydrostatic…
We study the shock structure and the sub-shocks formation in a binary mixture of rarefied polyatomic gases, considering the dissipation only due to the dynamic pressure. We classify the regions depending on the concentration and the Mach…
We propose a generalized extreme shock model with a possibly increasing failure threshold. While standard models assume that the crucial threshold for the system may only decrease over time, because of weakening shocks and obsolescence, we…
The scattering of electromagnetic waves by an obstacle is analyzed through a set of partial differential equations combining the Maxwell's model with the mechanics of fluids. Solitary type EM waves, having compact support, may easily be…
This paper studies the asymptotic convergence of computed dynamic models when the shock is unbounded. Most dynamic economic models lack a closed-form solution. As such, approximate solutions by numerical methods are utilized. Since the…
We provide a `user guide' to the literature of the past twenty years concerning the modeling and approximation of discontinuous solutions to nonlinear hyperbolic systems that admit small-scale dependent shock waves. We cover several classes…
We investigate exact solutions for isothermal shock problems in different one-dimensional geometries. These solutions are given as analytical expressions if possible, or are computed using standard numerical methods for solving ordinary…
For one-dimensional linear kinetic equations analytical solutions of problems about moderately strong evaporation (condensation), when frequency of collisions of molecules is constant, are received . The equation and distribution function…
A macroscopic mesoscopic, deterministic stochastic coupling strategy is proposed to accelerate the direct simulation Monte Carlo (DSMC) method for chemical reaction. First, a macroscopic synthetic equation is formulated by integrating…