Related papers: Thermodynamic formalism for contracting Lorenz flo…
The classical Lorentz reciprocal theorem (LRT) was originally derived for slow viscous flows of incompressible Newtonian fluids under the isothermal condition. In the present work, we extend the LRT from simple to complex fluids with open…
In the framework of irreversible thermodynamics, we study autonomous systems of reaction-diffusion equations to show how the entropy and free energy of an open and irreversible reactor depend on concentrations. To do this, we find a…
We define a natural extension of pluriclosed flow aiming at constructing solutions of the Hull-Strominger system. We give several geometric formulations of this flow, which yield a series of a priori estimates for the flow and also for the…
Isothermal compressible two-phase flows with and without phase transition are modeled, employing Darcy's and/or Forchheimer's law for the velocity field. It is shown that the resulting systems are thermodynamically consistent in the sense…
A wide spectrum of electrokinetic studies is modelled as isothermal ones to expedite analysis even when such conditions may be extremely difficult to realize in practice. As a clear and novel departure from this trend, we address the case…
Lyapunov's theorem provides a fundamental characterization of the stability of dynamical systems. This paper presents a categorical framework for Lyapunov theory, generalizing stability analysis with Lyapunov functions categorically. Core…
Let $M$ be a closed manifold and consider the Hamiltonian flow associated to an autonomous Tonelli Hamiltonian $H:T^*M\rightarrow \mathbb R$ and a twisted symplectic form. In this paper we study the existence of contractible periodic orbits…
The current study formulates a convective model of the Lorenz type near the temperature of maximum density. The existence of this temperature actualizes water dynamics in temperate lakes. There is a conceptual interest what this feature…
In this article we review the perfect-fluid hydrodynamics with spin framework proposed recently. This framework generalises the standard relativistic hydrodynamics framework to include spin degrees of freedom and provides a natural method…
We study solutions of the relativistic hydrodynamical equations, which describe spherical or cylindrical expansion of ideal fluid. We derived approximate solutions involving two arbitrary functions, which describe asymptotic behavior of…
In 2007, Ye \& Zhang introduced a version of local topological entropy. Since their entropy function is, as we show under mild conditions, constant for topologically transitive dynamical systems, we propose to adjust the notion in a way…
We develop a complete description of the class of conformal relativistic dissipative fluids of divergence form, following the formalism carried out by Geroch, Lindblom and Pennisi. This type of theories is fully described in terms of…
We investigate the fully developed flow between two parallel plates and the film flow over a plate in an electrically conducting fluid under the action of a parallel Lorentz force. Exact analytical solutions are derived for velocity, flow…
We study the dynamics of compressible fluids in rotating heterogeneous porous media. The fluid flow is of {F}orchheimer-type and is subject to a mixed mass and volumetric flux boundary condition. The governing equations are reduced to a…
The complex potentials representing flows around a vertical plate semi-submerged in a uniform stream are derived in analytical forms by the reduction method. They are composed from the regular solution and a weak singular eigen solution.…
Let $\{T^t\}$ be a smooth flow with positive speed and positive topological entropy on a compact smooth three dimensional manifold, and let $\mu$ be an ergodic measure of maximal entropy. We show that either $\{T^t\}$ is Bernoulli, or…
The Eulerian system of dynamic equations for the ideal fluid is closed but incomplete. The complete system of dynamic equations arises after appending Lin constraints which describe motion of fluid particles in a given velocity field. The…
The recent developments in fluid/gravity correspondence give a new impulse to the study of fluid dynamics of supersymmetric theories. In that respect, the entropy current formalism requires some modifications in order to be adapted to…
Dynamics of relativistic outflows along the rotation axis of a Kerr black hole is investigated using a simple model that takes into account the relativistic tidal force of the central source as well as the Lorentz force due to the…
We formulate a relativistic hydrodynamic theory for fluids with spin and intrinsic dilation charges. Using an entropy-current analysis, we derive constitutive relations featuring a bulk viscosity and a dilation conductivity governing the…