相关论文: The Golden Ratio and Hydrodynamics
It is shown that for a liquid in any connected vessels system, it is not possible to fulfill simultaneously Pascal's principle, mass conservation, and energy conservation. The viscosity has to necessarily be taken into account to understand…
Why is ``worthless'' fiat money generally accepted as payment for goods and services? In equilibrium theory, the value of money is generally not determined: the number of equations is one less than the number of unknowns, so only relative…
Many have wondered how mathematics, which appears to be the result of both human creativity and human discovery, can possibly exhibit the degree of success and seemingly-universal applicability to quantifying the physical world as…
We study the hydrodynamic limits of the simple exclusion processes and the zero range processes on crystal lattices. For a periodic realization of crystal lattice, we derive the hydrodynamic limit for the exclusion processes and the zero…
Stochastic thermodynamics is formulated for variables that are odd under time reversal. The invariance under spatial rotation of the collision rates due to the isotropy of the heat bath is shown to be a crucial ingredient. An alternative…
We report an experimental evidence of a global bifurcation on a highly turbulent von Karman flow. The mean flow presents multiple solutions: the canonical symmetric solution becomes marginally unstable towards a flow which breaks the basic…
Hydrodynamics provides a concise but powerful description of long-time and long-distance physics of correlated systems out of thermodynamic equilibrium. Here we construct hydrodynamic equations for nonrelativistic particles with a…
Quantum mechanical wave functions have phases. These phases either initial or acquired during time evolution usually do not enter the final expressions for observable physical quantities. Nevertheless in many cases the observable physical…
A hydrodynamic formulation of the evolution of large-scale structure in the Universe is presented. It relies on the spatially coarse-grained description of the dynamical evolution of a many-body gravitating system. Because of the assumed…
Two identical particles driven by the same steady force through a viscous fluid may move relative to one another due to hydrodynamic interactions. The presence or absence of this relative translation has a profound effect on the dynamics of…
We solve a set of selected exercises on rotational motion requiring a mechanical and thermodynamical analysis. When non-conservative forces or thermal effects are present, a complete study must use the first law of thermodynamics together…
Relativistic dissipative hydrodynamics including hydrodynamic fluctuations is formulated by putting an emphasis on non-linearity and causality. As a consequence of causality, dissipative currents become dynamical variables and noises…
We consider a simple model of an internally driven self-rotating object; a rotor, confined to two dimensions by a thin film of low Reynolds number fluid. We undertake a detailed study of the hydrodynamic interactions between a pair of…
Topological defects are an essential part of the structure and dynamics of all liquid crystals, and they are particularly important in experiments and simulations on active liquid crystals. In a recent paper, Vromans and Giomi [Soft Matter,…
There has been a recent tendency to apply Schroedinger's wave equation to macroscopic domains, from Bose-Einstein condensates in neutron stars to planetary orbits. In these applications a hydrodynamical interpretation, involving vortices in…
The interaction of electrical fields and liquids can lead to phenomena that defies intuition. Some famous examples can be found in Electrohydrodynamics as Taylor cones, whipping jets or non-coalescing drops. A less famous example is the…
The thermodynamic formalism for dynamical systems with many degrees of freedom is extended to deal with time averages and fluctuations of some macroscopic quantity along typical orbits, and applied to coupled map lattices exhibiting phase…
Invariant integrability criterion for the equations of hydrodynamical type is found. This criterion is written in the form of vanishing for some tensor which is derived from the velocities matrix of hydrodynamical equations.
Copulas are widely used in financial economics as well as in other areas of applied mathematics. Yet, there is much arbitrariness in their choice. The author proposes "a natural copula" concept, which minimizes Wasserstein distance between…
Hydrodynamics is a general theoretical framework for describing the long-time large-distance behaviors of various macroscopic physical systems, with its equations based on conservation laws such as energy-momentum conservation and charge…