Related papers: Propagation of a Three-dimensional Weak Shock Fron…
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…
The paper considers one-dimensional flows of polytropic (calorically ideal) gas. These flows include three cases of gas dynamics: plain one-dimensional flows (one-dimensional space), radially symmetric flows in two-dimensional space and…
Assuming Newton's law of cooling, the propagation and structure of isothermal acoustic shocks are studied under four different viscosity laws. Employing both analytical and numerical methods, 1D traveling wave solutions for the velocity and…
Motivated by many applications (geophysical flows, general relativity), we attempt to set the foundations for a study of entropy solutions to nonlinear hyperbolic conservation laws posed on a (Riemannian or Lorentzian) manifold. The flux of…
We study the one-dimensional Riemann problem for a hyperbolic system of three conservation laws of Temple class. This systems it is a simplification of a recently propose system of five conservations laws by Bouchut and Boyaval that model…
The physical quantities in a gas should vary continuously across a shock. However, the physics inherent in the compressible Euler equations is insufficient to describe the width or structure of the shock. We demonstrate the existence of…
We investigate the dynamics and the pathways of the collapse of a single, semiflexible polymer in a poor solvent via 3-D Brownian Dynamics simulations. Earlier work indicates that the condensation of semiflexible polymers generically…
Mechanical metamaterials can be designed to exhibit unique mechanical properties, including tunable auxetic behavior as well as multi-stability, which arise from the geometry and configuration of the constituent building blocks.…
We study 3D chaotic dynamics through an analysis of transport in a granular flow in a half-full spherical tumbler rotated sequentially about two orthogonal axes (a bi-axial "blinking" tumbler). The flow is essentially quasi-2D in any…
Ideal systems of equations such as Euler and MHD may develop singular structures like shocks, vortex/current sheets. Among these, vortical singularities arise due to vortex stretching which can lead to unbounded growth of enstrophy.…
The transport of deformable particles through porous media underlies a wealth of applications ranging from filtration to oil recovery to the transport and spreading of biological agents. Using direct numerical simulations, we analyze the…
Astrophysical fluids under the influence of magnetic fields are often subjected to single-fluid or two-fluid approximations. In the case of weakly ionized plasmas however, this can be inappropriate due to distinct responses from the…
Symmetries and conservation laws are studied for a generalized Westervelt equation which is a nonlinear partial differential equation modelling the propagation of sound waves in a compressible medium. This nonlinear wave equation is widely…
This paper studies the stability and large-time behavior of the three-dimensional (3-D) Boltzmann equation near shock profiles. We prove the nonlinear stability of the composite wave consisting of two shock profiles under general…
We study a particular deformation of the potential KdV model (pKdV) and construct the quasi-conservation laws by a direct method. The charge densities, differing from their integrable counterpart with homogeneous degree terms, exhibit mixed…
For nonlinear hyperbolic systems of conservation laws in one space variable, we establish the existence of nonclassical entropy solutions exhibiting nonlinear interactions between shock waves with strong strength. The proposed theory is…
We study the two-dimensional structural stability of shock waves in a compressible isentropic inviscid elastic fluid in the sense of the local-in-time existence and uniqueness of discontinuous shock front solutions of the equations of…
The gravity-driven spreading of one fluid in contact with another fluid is of key importance to a range of topics. To describe these phenomena, the two-layer shallow-water equations is commonly employed. When one layer is significantly…
We propose a transport theory for the kinetic evolution of solar-wind electrons in the heliosphere. We derive a gyro-averaged kinetic transport equation that accounts for the spherical expansion of the solar wind and the geometry of the…
We present a new third-order, semi-discrete, central method for approximating solutions to multi-dimensional systems of hyperbolic conservation laws, convection-diffusion equations, and related problems. Our method is a high-order extension…