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To date it has not been possible to prove whether or not the three-dimensional incompressible Euler equations develop singular behaviour in finite time. Some possible singular scenarios, as for instance shock-waves, are very important from…
Motivated by cosmological applications for interacting matters, an extension of the action functional for relativistic fluids is proposed to incorporate the physics of non-adiabatic processes and chemical reactions. The former are…
This work addresses research questions arising from the application of geometrically exact beam theory in the context of fluid-structure interaction (FSI). Geometrically exact beam theory has proven to be a computationally efficient way to…
We present an algorithm for systematically reconstructing a solution of the (d+2)-dimensional vacuum Einstein equations from a (d+1)-dimensional fluid, extending the non-relativistic hydrodynamic expansion of Bredberg et al in…
A thorough account is given of the derivation of uniform semiclassical approximations to the particle and kinetic energy densities of N noninteracting bounded fermions in one dimension. The employed methodology allows the inclusion of…
In this paper, we present an analytical study, in the one space dimensional case, of the fluid dynamics system proposed in [4] to model the formation of biofilms. After showing the hyperbolicity of the system, we show that, in a open…
We derive a mathematical model for the motion of several insulating rigid bodies through an electrically conducting fluid. Starting from a universal model describing this phenomenon in generality, we elaborate (simplifying) physical…
We initiate a systematic study of intrinsic dimensional versions of classical functional inequalities which capture refined properties of the underlying objects. We focus on model spaces: Euclidean space, Hamming cube, and manifolds of…
We study the exact one electron propagator and spectral function of a solvable model of interacting electrons due to Schulz and Shastry. The solution previously found for the energies and wave functions is extended to give the spectral…
In a recent paper [Phys. Rev. E \textbf{76}, 031202 (2007)], Schmidt has proposed a Fundamental Measure Density Functional Theory for one-dimensional nonadditive hard-rod fluid mixtures and has compared its predictions for the bulk…
A remarkable feature of fluid dynamics is its relationship with classical dynamics and statistical mechanics. This has motivated in the past mathematical investigations concerning, in a special way, the "derivation" based on kinetic theory,…
We investigate the field equations in the Einstein-aether theory for static spherically symmetric spacetimes and a perfect fluid source and subsequently with the addition of a scalar field (with an exponential self-interacting potential).…
Computational fluid dynamics (CFD) has become a cornerstone of modern water engineering, providing quantitative tools for the analysis, prediction, and management of complex hydraulic systems across a wide range of spatial and temporal…
We study thermodynamic formalism of dynamical systems with non-uniform structure. Precisely, we obtain the uniqueness of equilibrium states for a family of non-uniformly expansive flows by generalizing Climenhaga-Thompson's orbit…
Using methods of kinetic theory and liquid state theory we propose a description of the non-equilibrium behavior of molecular fluids which takes into account their microscopic structure and thermodynamic properties. The present work…
The approach to a substantiation of thermodynamics is offered. A conservative system of interacting elements, which is not in equilibrium, is used as a model. This system is then split into small subsystems that are accepted as being in…
We discuss functional-integral approaches to far-from-equilibrium quantum many-body dynamics. Specific techniques considered include the two-particle-irreducible effective action and the real-time flow-equation approach. Different…
It is shown that the equilibrium Generalized Mean Spherical Model of fluid structure may be extended to nonequilibrium states with equation of state information used in equilibrium replaced by an exact condition on the two-body distribution…
This Perspective article provides an overview of some of our analytical approaches to the computation of the structural and thermodynamic properties of single-component and multicomponent hard-sphere fluids. For the structural properties,…
The observation of fluid-like behavior in nucleus-nucleus, proton-nucleus and high-multiplicity proton-proton collisions motivates systematic studies of how different measurements approach their fluid-dynamic limit. We have developed…