相关论文: Carbuncles as self-similar entropy solutions
Compressing or cooling a fluid typically enhances its static interparticle correlations. However, there are notable exceptions. Isothermal compression can reduce the translational order of fluids that exhibit anomalous waterlike trends in…
Catastrophes are at the heart of many fascinating optical phenomena. The rainbow, for example, is a ray catastrophe where light rays become infinitely intense. The wave nature of light resolves the infinities of ray catastrophes while…
Stable numerical simulations for a hyperbolic system of conservation laws of relaxation type but not in divergence form are obtained by incorporating the physical entropy into the simulations. The entropy balance is utilized as an…
Liquids relax extremely slowly upon approaching the glass state. One explanation is that an entropy crisis, due to the rarefaction of available states, makes it increasingly arduous to reach equilibrium in that regime. Validating this…
The damage and fracture of materials are technologically of enormous interest due to their economic and human cost. They cover a wide range of phenomena like e.g. cracking of glass, aging of concrete, the failure of fiber networks in the…
In multicomponent systems with strong local interaction one can encounter some phenomena absent in the standard systems of statistical physics and other multicomponent systems. Namely, a system with $N$ components in the bounded volume of…
The entropy and information puzzles arising from black holes cannot be resolved if quantum gravity effects remain confined to a microscopic scale. We use concrete computations in nonperturbative string theory to argue for three kinds of…
A long-standing quantum-mechanical puzzle is whether the collapse of the wave function is a real physical process or simply an epiphenomenon. This puzzle lies at the heart of the measurement problem. One way to choose between the…
It is shown that third-order 1D nonlinear dispersion equations admit single point gradient catastrophe, described by blow-up-type similarity solutions. After blow-up, the solutions admit shock wave-type self-similar extensions. Snce such…
The infinite superpositions of random plane waves are known to be threaded with vortex line singularities which form complicated tangles and obey strict topological rules. We observe that within these structures a timelike axis appears to…
Collapse models are phenomenological models introduced to solve the measurement problem in quantum mechanics. They modify the Schr\"odinger equation by adding non-linear and stochastic terms, which induce the wavefunction collapse in space.…
The phenomenon of crumpling is common in our daily life and nature. It exhibits many interesting properties, such as ultra-tough resistance to pressure with less than 30$\%$ of volume density, power-law relation for pressure vs density, and…
We propose a new numerical approach to compute nonclassical solutions to hyperbolic conservation laws. The class of finite difference schemes presented here is fully conservative and keep nonclassical shock waves as sharp interfaces,…
Stripe-like and bubble-like patterns spontaneously form in numerous physical, chemical, and biological systems when competing long-range and short-range interactions banish uniformity. Stripe-like and the related nematic morphology are also…
The artificial viscosity approach for curing the carbuncle phenomenon (a numerical problem, also known as the shock instability) in shock-capturing methods has been recently presented and successfully tested on the first-order schemes in…
We comprehend the role of imperfections in materials consisting of interacting particles, arising from different origins on their universal features. Specifically, we report the static and dynamic responses in a cluster of Coulomb…
We discuss a theoretical approach to structural glasses as they happen in real situations. Older ideas based on `configurational entropy', on `fictive temperatures' and on Edwards' `compactivity' are sharpened and unified in an out of…
It is argued that the occurrence of disproportionately ("un-natural") large (or small) numbers, as well as deep cancellations, are comparatively natural traits of the way Nature is geared to operate in most complex systems. The idea is…
The stability of stationary solutions of first-order systems of PDE's are considered. They may include some singular geometric terms, leading to discontinuous flux and non-conservative products. Based on several examples in Fluid Mechanics,…
A large toolbox of numerical schemes for dispersive equations has been established, based on different discretization techniques such as discretizing the variation-of-constants formula (e.g., exponential integrators) or splitting the full…