Related papers: Fluid dynamics as intersection problem
The constraints imposed on hydrodynamics by the structure of gauge and gravitational anomalies are studied in two dimensions. By explicit integration of the consistent gravitational anomaly, we derive the equilibrium partition function at…
We consider Euler equations for potential flow of ideal incompressible fluid with a free surface and infinite depth in two dimensional geometry. Both gravity forces and surface tension are taken int account. A time-dependent conformal…
We re-derive the equations of motion of dissipative relativistic fluid dynamics from kinetic theory. In contrast to the derivation of Israel and Stewart, which considered the second moment of the Boltzmann equation to obtain equations of…
We derive and investigate several hydrodynamic formalisms that emerge from a system of classical, ultra-relativistic scalar particles self-interacting via a quartic potential. The specific form of the total cross-section enables the…
In this mostly pedagogical tutorial article a brief introduction to modern geometrical treatment of fluid dynamics and electrodynamics is provided. The main technical tool is standard theory of differential forms. In fluid dynamics, the…
An overview is presented of several diverse branches of work in the area of effectively 2D fluid equilibria which have in common that they are constrained by an infinite number of conservation laws. Broad concepts, and the enormous variety…
Arnold pointed out that the Euler equation of incompressible ideal hydrodynamics describes geodesics on the group of volume-preserving diffeomorphisms. A simple analogue is the Euler equation for a rigid body, which is the geodesic equation…
One field of fluid dynamics concerns the search for variational principles. So far, the Hamiltonian view and Riemannian geometry has been applied to find geodesics for hydrodynamic systems. Compared to Riemannian geometry sub-Riemannian…
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…
The boundary conditions at the deformable interface between two contacting fluids are derived for the general case of the large-amplitude perturbations. The interface is modeled as perturbed free boundary that evolves in time, and the…
The uncertainty relations in hydrodynamics are numerically studied. We first give a review for the formulation of the generalized uncertainty relations in the stochastic variational method (SVM), following the paper by two of the present…
Ideal fluid dynamics is studied as a relativistic field theory with particular importance on its hamiltonian structure. The Schwinger condition, whose integrated version yields the stress tensor conservation, is explicitly verified both in…
A correspondence between scalar field fluctuations and generalized fluctuations in a hydrodynamic approximation of fields is obtained. The results presented here are of interest to field-fluid correspondences and form part of theoretical…
Flows on surfaces are one of the most fundamental and classical objects in dynamical systems, and are studied from various areas (e.g. integrable systems, differential equations, fluid mechanics). Though hyperbolic flows and recurrent flows…
In this lecture note, we present several topics on relativistic hydrodynamics and its application to relativistic heavy ion collisions. In the first part we give a brief introduction to relativistic hydrodynamics in the context of heavy ion…
The potential flow of two-dimensional ideal incompressible fluid with a free surface is studied. Using the theory of conformal mappings and Hamiltonian formalism allows us to derive exact equations of surface evolution. Simple form of the…
Dipole-conserving fluids serve as examples of kinematically constrained systems that can be understood on the basis of symmetry. They are known to display various exotic features including glassylike dynamics, subdiffusive transport, and…
We consider a fermionic fluid in a non-equilibrium steady state where the fluctuation-dissipation theorem is not valid and fields conjugate to the hydrodynamic variables are explicitly required to determine response functions. We identify…
We provide a consistent statistical-mechanical treatment for describing the thermodynamics and the structure of fluids embedded in the hyperbolic plane. In particular, we derive a generalization of the virial equation relating the bulk…
A rigorous method for introducing the variational principle describing relativistic ideal hydrodynamic flows with all possible types of discontinuities (including shocks) is presented in the framework of an exact Clebsch type representation…