Related papers: Shock Reflection-Diffraction, von Neumann's Conjec…
The problem of collisionless shocks is posed as the problem of understanding how in a completely collisionless streaming high-temperature plasma shocks can develop at all, forming discontinuous transition layers of thickness much less than…
Shock waves are supersonic disturbances propagating in a fluid and giving rise to dissipation and drag. Weak shocks, i.e., those of small amplitude, can be well described within the hydrodynamic approximation. On the other hand, strong…
In the first half of the paper we consider interaction between the small amplitude travelling waves ("sound") and the shock waves in the transmission line containing both nonlinear capacitors and nonlinear inductors. We calculate the…
A Neumann problem for a wave equation perturbed by viscous terms with small parameters is considered. The interaction of waves with the diffusion effects caused by a higher-order derivative with small coefficient {\epsilon}, is…
We consider large-scale dynamics of non-equilibrium dense soliton gas for the Korteweg-de Vries (KdV) equation in the special "condensate" limit. We prove that in this limit the integro-differential kinetic equation for the spectral density…
Boltzmann's equation provides a microscopic model for the evolution of dilute classical gases. A fundamental problem in mathematical physics is to rigorously derive Boltzmann's equation starting from Newton's laws. In the 1970s, Oscar…
In the recent years, mater-wave interferometry has attracted growing attention due to its unique suitability for high-precision measurements and study of fundamental aspects of quantum theory. Diffraction and interference of matter waves…
Asymptotic decay laws for planar and nonplanar shock waves and the first order associated discontinuities that catch up with the shock from behind are obtained using four different approximation methods. The singular surface theory is used…
The KdV-Burgers equation is a canonical model describing the interplay between nonlinearity, viscosity and dispersion, and it admits viscous-dispersive shocks as traveling wave solutions. In this paper, we establish an $L^2$-contraction…
The addition of higher order asymptotic corrections to the Korteweg-de Vries equation results in the extended Korteweg-de Vries equation. These higher order terms destabilise the dispersive shock wave solution, also termed an undular bore…
The shock wave instability induced when interacting with a small waviness on an interface was investigated analytically and numerically. The perturbation to the shock was phenomenologically treated assuming this as the consequence of the…
The question of whether a singularity can form in an initially regular flow, described by the 3D incompressible Navier-Stokes (NS) equations, is a fundamental problem in mathematical physics. The NS regularity problem is super-critical,…
In this paper a theory of reflective X-ray multilayer structures with a graded (slowly varying) period based on the coupled waves method and quasi-classical asymptotic expansions is reported. A number of exact solutions of the coupled wave…
Plastic deformation is widely regarded as an intrinsically dissipative phenomenon and its theoretical description is largely phenomenological. We argue instead that plasticity possesses a non-dissipative, symmetry determined backbone:…
This experimental study addresses the re-initiation mechanism of detonation waves following the Mach reflection of a shock-flame complex. The detonation diffraction around a cylinder is used to reproducibly generate the shock-flame complex…
To characterize the Neumann problem for nonlinear Fokker-Planck equations, we investigate distribution dependent reflecting SDEs (DDRSDEs) in a domain. We first prove the well-posedness and establish functional inequalities for reflecting…
Undular bores, or dispersive shock waves, are non-stationary waves propagating as oscillatory transitions between two basic states, in which the oscillatory structure gradually expands and grows in amplitude with distance travelled. We…
Suppose that a plane wave is incident onto an impenetrable grating profile of Dirichlet or Impedance type or a penetrable grating. The grating interface is assumed to be given by a Lipschitz function in two dimensions. We derive stability…
Consider an exterior problem of the three-dimensional elastic wave equation, which models the scattering of a time-harmonic plane wave by a rigid obstacle. The scattering problem is reformulated into a boundary value problem by introducing…
Accurate and efficient prediction of three-dimensional (3D) fields in wave interactions with large, complex-shaped objects is essential for applications in electromagnetic computation, computer graphics, optical metrology, and freeform…