Related papers: Exact results for one dimensional fluids through f…
A new diffuse interface model for a two-phase flow of two incompressible fluids with different densities is introduced using methods from rational continuum mechanics. The model fulfills local and global dissipation inequalities and is also…
The statistical-mechanical study of the equilibrium properties of fluids, starting from the knowledge of the interparticle interaction potential, is essential to understand the role that microscopic interaction between individual particles…
The continuum equations of fluid mechanics are rederived with the intention of keeping certain mechanical and thermodynamic concepts separate. A new "mechanical" mass density is created to be used in computing inertial quantities, whereas…
As is well known, one-dimensional systems with interactions restricted to first nearest neighbors admit a full analytically exact statistical-mechanical solution. This is essentially due to the fact that the knowledge of the first…
An overview of some analytical approaches to the computation of the structural and thermodynamic properties of single component and multicomponent hard-sphere fluids is provided. For the structural properties, they yield a thermodynamically…
New exact solutions of relativistic perfect fluid hydrodynamics are described, including the first family of exact rotating solutions. The method used to search for them is an investigation of the relativistic hydrodynamical equations and…
These lecture notes present an overview of equilibrium statistical mechanics of classical fluids, with special applications to the structural and thermodynamic properties of systems made of particles interacting via the hard-sphere…
We propose new ideal hydrodynamics in the function space which describes a fluid composed of the 1+1 dimensional real scalar field in the framework of the stochastic variational method (SVM). In the derivation, the thermal equilibrium is…
We review analytical solutions of the Einstein equations which are expressed in terms of elementary functions and describe Friedmann-Lema\^itre-Robertson-Walker universes sourced by multiple (real or effective) perfect fluids with constant…
Some classical and recent results on the Euler equations governing perfect (incompressible and inviscid) fluid motion are collected and reviewed, with some small novelties scattered throughout. The perspective and emphasis will be given…
A simple, practical model for computing the equilibrium thermodynamics and structure of jellium by classical strong coupling methods is proposed. An effective pair potential and coupling constant are introduced, incorporating the ideal gas,…
In this paper, a statistical physical derivation of thermodynamically consistent fluid mechanical equations is presented for non-isothermal viscous molecular fluids. The coarse-graining process is based on (i) the adiabatic expansion of the…
Via a straightforward integration of the Einstein equations with cosmological constant, all static circularly symmetric perfect fluid 2+1 solutions are derived. The structural functions of the metric depend on the energy density, which…
Our recent result on the construction of perfect fluid equations with N=1,2 Schr\"odinger supersymmetry [Mod. Phys. Lett. A 41 (2026) 2550214] is extended to accommodate nonrelativistic conformal supersymmetries of other types. Two cases…
In this work we carry out a noncommutative analysis of several Friedmann-Robert-Walker models, coupled to different types of perfect fluids and in the presence of a cosmological constant. The classical field equations are modified, by the…
The exact statistical-mechanical solution for the equilibrium properties, both thermodynamic and structural, of one-dimensional fluids of particles interacting via the triangle-well and the ramp potentials is worked out. In contrast to…
We introduce a model of attractive penetrable spheres by adding a short range attractive square well outside a penetrable core, and we provide a detailed analysis of structural and thermodynamical properties in one dimension using the exact…
A thermodynamic analysis of weakly nonlocal non-relativistic fluids is presented under the assumption that an additional scalar field also contributes to the dynamics. The most general evolution of this field and the constitutive relations…
New, superfluid specific additive integral of motion is found. This facilitates investigation of general thermodynamic equilibrium conditions for superfluid. The analysis is performed in an extended space of thermodynamic variables…
We present a new approach to derive the connectivity properties of pairwise interacting n-body systems in thermal equilibrium. We formulate an integral equation that relates the pair connectedness to the distribution of nearest neighbors.…