相关论文: Hydrodynamic Singularities
This Living Review updates a previous version which its itself an update of a review article. Numerical exploration of the properties of singularities could, in principle, yield detailed understanding of their nature in physically realistic…
We establish several quantitative results about singular Ricci flows, including estimates on the curvature and volume, and the set of singular times.
When speaking of unsolved problems in physics, this is surprising at first glance to discuss the case of fluid mechanics. However, there are many deep open questions that come with the theory of fluid mechanics. In this paper, we discuss…
The process of interaction between nonlinear waves on a free surface of a nonconducting fluid in a strong tangential electric field is simulated numerically (effects of the force of gravity and capillarity are neglected). It is shown that…
We present a discussion on some physical aspects of gravitational collapse which is based on a list of questions related to relevant issues in the study of that phenomenon. Providing answers to those questions we bring out the role played…
Recent theoretical developments in hydrodynamics of particles with spin 1/2 are briefly reviewed.
The relativistic hydrodynamical equations are being examined with the aim of extracting the quantum-mechanical equations (the relativistic Klein-Gordon equation and the Schr\"odinger equation in the non-relativistic limit). In both cases it…
Quantum fluid (or hydrodynamic) models provide an attractive alternative for the modeling and simulation of the electron dynamics in nano-scale objects. Compared to more standard approaches, such as density functional theory or phase-space…
A certain class of integrable hydrodynamic type systems with three independent and N dependent variables is considered. We choose the existence of a pseudopotential as a criterion of integrability. It turns out that the class of integrable…
We consider fundamental physical constants which are among a few of the most important pieces of information we have learned about Nature after its intensive centuries-long studies. We discuss their multifunctional role in modern physics…
These are notes based on lectures given at the 2021 summer school on Fundamental Problems in Statistical Physics XV. Their purpose is to give a very brief introduction to Generalized Hydrodynamics, which provides a description of the large…
Cell motility in viscous fluids is ubiquitous and affects many biological processes, including reproduction, infection, and the marine life ecosystem. Here we review the biophysical and mechanical principles of locomotion at the small…
These lectures present results and problems on the characterization of structurally stable dynamics. We will shed light those which do not seem to depend on the regularity class (holomorphic or differentiable). Furthermore, we will present…
Liquids flow, making them remarkably distinct from solids and close to gases. At the same time, interactions in liquids are strong as in solids. The combination of these two properties is believed to be the ultimate obstacle to constructing…
Event-by-event hydrodynamics (or hydrodynamics with fluctuating initial conditions) has been developed in the past few years. Here we discuss how it may help to understand the various structures observed in two-particle correlations.
Optical singularities, which are positions within an electromagnetic field where certain field parameters become undefined, hold significant potential for applications in areas such as super-resolution microscopy, sensing, and…
We propose a generalization of equations of quantum mechanics in the hydrodynamic form by introducing the terms taking into account the diffusion velocity at zero and finite temperatures and the density energy of diffusion pressure of the…
We investigate the behavior of a one-dimensional diatomic fluid under a shock wave excitation. We find that the properties of the resulting shock wave are in striking contrast with those predicted by hydrodynamic and kinetic approaches,…
This paper is an attempt to classify finite-time singularities of PDEs. Most of the problems considered describe free-surface flows, which are easily observed experimentally. We consider problems where the singularity occurs at a point, and…
Short introduction to exotic differential structures on manifolds is given. The possible physical context of this mathematical curiosity is discussed. The topic is very interesting although speculative.