Related papers: Carbuncles as self-similar entropy solutions
Gibbs paradox in the context of statistical mechanics addresses the issue of additivity of entropy of mixing gases. The usual discussion attributes the paradoxical situation to classical distinguishability of identical particles and credits…
Several examples are used to illustrate how we deal cavalierly with infinities and unphysical systems in physics. Upon examining these examples in the context of infinities from Cantor's theory of transfinite numbers, the only known…
Three classes of higher-order nonlinear parabolic hyperbolic, and nonlinear dispersion equations are shown to admit exact blow-up or compacton solutions, which are induced by elliptic equations with non-Lipschitz nonlinearities. Variational…
It has become increasingly apparent that a number of perplexing issues associated with the interpretation of quantum mechanics are more easily resolved once the notion of retrocausality is introduced. The aim here is to list and discuss…
A theory of structure is formulated for systems of many structureless classical particles with stable local interactions in Euclidean space. Such systems are shown to have their structure in thermodynamic equilibrium determined exactly by a…
In this work we investigate the presence of lump-like solutions in models described by a single real scalar field. We take advantage of a procedure recently used to describe explicit analytical solutions and we study several distinct…
In diffraction catastrophes such as the rainbow the wave nature of light resolves ray singularities and draws delicate interference patterns. In quantum catastrophes such as the black hole the quantum nature of light resolves wave…
Particle suspensions are ubiquitous in our daily life, but are not well understood due to their complexity. During the last twenty years, various simulation methods have been developed in order to model these systems. Due to varying…
The first junction conditions of spherically symmetric bubbles are solved for some cases, and whereby analytic models to the Einstein field equations are constructed. The effects of bubbles on the spacetime structure are studied and it is…
Cavitation is a general phenomenon of the fluid flows with obstacles. It appears in the cooling conduits of the fast nuclear engines. A model of this phenomenon using the theory of Laplace and a common non-convex energy for the liquid and…
Superconducting cosmic string may admit shock-like discontinuities of the current when the latter is spacelike ("magnetic" regime), while no shock at timelike current ("electric" regime) was discovered in numerical simulations. We find that…
We consider the numerical approximation of a system of partial differential equations involving a nonlinear Schr\"odinger equation coupled with a hyperbolic conservation law. This system arises in models for the interaction of short and…
We study black holes for the linear hyperbolic equations describing the wave propagation in the moving medium. Such black holes are called artificial since the Lorentz metric associated with the hyperbolic equation does not necessary…
We review some recent advances in black hole thermodynamics, including statistical mechanical origins of black hole entropy and its leading order corrections, from the viewpoints of various quantum gravity theories. We then examine the…
Students of quantum mechanics encounter discrete quantum numbers in a somewhat incoherent and bewildering number of ways. For each physical system studied, quantum numbers seem to be introduced in its own specific way, some enumerating from…
We describe a new class of nonequilibrium quantum many-body phenomena in the form of networks of caustics that dominate the many-body wavefunction in the semiclassical regime following a sudden quench. It includes the light cone-like…
While traditional approaches to prevent the carbuncle phenomenon in gas dynamics simulations increase the viscosity on entropy and shear waves near shocks, it was quite recently suggested to instead decrease the viscosity on the acoustic…
Discrete numerical methods with finite time-steps represent a practical technique to solve initial-value problems involving nonlinear differential equations. These methods seem particularly useful to the study of chaos since no analytical…
Bringing gravity into a quantum-mechanical framework is likely the most profound remaining problem in fundamental physics. The "unitarity crisis" for black hole evolution appears to be a key facet of this problem, whose resolution will…
In spherical symmetry compelling numerical evidence suggests that in general relativity solutions near the threshold of black hole formation exhibit critical behavior. One aspect of this is that threshold solutions themselves are…