Related papers: Shock Reflection-Diffraction Phenomena and Multidi…
We study the spacetime obtained by superimposing two equal Aichelburg-Sexl shock waves in D dimensions traveling, head-on, in opposite directions. Considering the collision in a boosted frame, one shock becomes stronger than the other, and…
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 present work investigates the structure of fast supersonic turbulent flames typically observed as precursors to the onset of detonation. These high speed deflagrations are obtained after the interaction of a detonation wave with…
We study an inverse first-hitting problem for a one-dimensional, time-homogeneous diffusion $X(t)$ reflected between two boundaries $a$ and $b,$ which starts from a random position $\eta.$ Let $a \le S \le b$ be a given threshold, such that…
We explore rectification phenomena in a system where two-dimensional random walkers interact with a funnel-shaped ratchet under two distinct classes of reflection rules. The two classes include the angle of reflection exceeding the angle of…
Recently, the physics of aftershocks has been enriched by three new problems. We will conditionally call them dynamic, inverse, and morphological problems. Dynamic problem is to search for the cumulative effect of a round-the-world seismic…
The Maximum Energy Dissipation Principle (MEDP) for dynamics fracture, far from equilibrium, proposed by Slepyan was modified. This modification includes a decoupling between the injected and dissipated energy by adding of a time delay and…
In this paper we show for the first time the phenomenon of negative reflection in a simple mechanical structure. The latter is a grating of fixed inclusions embedded in a linear elastic matrix. Numerical analyses for out-of-plane shear…
The goal of this paper is to prove the existence and stability of shocks for viscous scalar conservation laws with space periodic flux, in the multi-dimensional case. Such a result had been proved by the first author in one space dimension,…
Refraction, traditionally viewed as a geometric event occurring at material interfaces, is now being re-examined through the lens of coherence. Recent studies in optics and photonics, including coherence tomography, Moire interference, and…
The collapse of cavities under shock is a key problem in various fields ranging from erosion of material, ignition of explosive, to sonoluminescence, etc. We study such processes using the material-point-method developed recently in the…
We are interested in nonlinear hyperbolic systems in nonconservative form arising in fluid dynamics, and, for solutions containing shock waves, we investigate the convergence of finite difference schemes applied to such systems. According…
Molecular Dynamic (MD) approach is applied to study the converging cylindrical shock waves in a dense Lennard-Jones (LJ) fluid. MD method is based on tracking of the atom motions and hence it has an fundamental advantages over hydrodynamic…
Patterns are quotidian in nature. Distinct multiscale patterns are generally a consequence of nonequilibrium dynamical processes associated with mechanical or hydrodynamic instabilities. In this thesis, I report experimental investigations…
We study the one dimensional time dependent Schr\"{o}dinger equation for a potential step with $E < V_0$. We obtain the wave is not instantaneously reflected, but for a few moment of time the wave packet penetrate into inaccessible…
Reflection equation for the scattering of lines moving in half-plane is obtained. The corresponding geometric picture is related with configurations of half-planes touching the boundary plane in 2+1 dimensions. This equation can be obtained…
The first well founded perturbation theory for classical solid systems is presented. Theoretical approaches to thermodynamic and structural properties of the hard-sphere solid provide us with the reference system. The traditional…
Extending our earlier work on Lax-type shocks of systems of conservation laws, we establish existence and stability of curved multidimensional shock fronts in the vanishing viscosity limit for general Lax- or undercompressive-type shock…
We solve (3+1)-dimensional ideal hydrodynamical equations with source terms that describe punch-through and fully stopped jets in order to compare their final away-side angular correlations in a static medium. For fully stopped jets, the…
Complex fission phenomena are studied in a unified way. Very general reflection asymmetrical equilibrium (saddle point) nuclear shapes are obtained by solving an integro-differential equation without being necessary to specify a certain…