Related papers: High order derivatives of Boltzmann microcanonical…
In this paper an approach is outlined. With this approach some explicit algorithms can be applied to solve the initial value problem of $n-$dimensional damped oscillators. This approach is based upon following structure: for any…
We develop a geometric foundation of microcanonical thermodynamics in which entropy and its derivatives are determined from the geometry of phase space, rather than being introduced through an a priori ensemble postulate. Once the minimal…
A scheme for calculating corrections to all orders to the entropy of any thermodynamic system due to statistical fluctuations around equilibrium has been developed. It is then applied to the BTZ black hole, AdS-Schwarzschild black Hole and…
A multiscale theory of interacting continuum mechanics and thermodynamics of mixtures of fluids, electrodynamics, polarization and magnetization is proposed. The mechanical (reversible) part of the theory is constructed in a purely…
Physical quantities obtained from the microcanonical entropy surfaces of classical spin systems show typical features of phase transitions already in finite systems. It is demonstrated that the singular behaviour of the microcanonically…
This article is devoted to derivation of the Laplace transforms of the derivatives with respect to parameters of certain special functions, namely, the Mittag-Leffler type, Wright and Le Roy type functions. These formulas show…
We propose a stochastic dynamics to be associated to a deterministic motion defined by a set of first order differential equation. The transitions that defined the stochastic dynamics are unidirectional and the rates are equal to the…
The two-fluid Maxwell system couples frictionless electron and ion fluids via Maxwell's equations. When the frequencies of light waves, Langmuir waves, and single-particle cyclotron motion are scaled to be asymptotically large, the…
We present a new derivation of the momentum exchange method to compute the flow force and torque on a submerged body in lattice Boltzmann methods. Our derivation does not depend on a particular implementation of the boundary conditions at…
In systems with detailed balance, the stationary distribution and the equilibrium distribution are identical, creating a clear connection between energetic and entropic quantities. Many driven systems violate detailed balance and still pose…
Dissipative Lagrangians and Hamiltonians having Coulomb, viscous and quadratic damping,together with gravitational and elastic terms are presented for a formalism that preserves the Hamiltonian as a constant of the motion. Their derivations…
A general discussion is made concerning the ways in which one can get signatures about a possible liquid-gas phase transition in nuclear matter. Microcanonical temperature, heat capacity and second order derivative of the entropy versus…
A computational study of higher-order derivative ratios on a time interval leading to the enstrophy peak is presented in the case of the 3D Taylor-Green vortex, a benchmark problem in the simulation of turbulent flows. The main finding is…
The most rigorous physical description of non-equilibrium gas dynamics is rooted in the numerical solution of the Boltzmann equation. Yet, the large number of degrees of freedom and the wide range of both spatial and temporal scales render…
The article presents the conservative dynamics of gravitationally interacting two-point-mass systems up to the eight order in the inverse power of the velocity of light, i.e.\ 4th post-Newtonian (4PN) order, and up to quadratic order in…
In this contribution we extend the Taylor expansion method proposed previously by one of us and establish equivalent partial differential equations of DDH lattice Boltzmann scheme at an arbitrary order of accuracy. We derive formally the…
We consider hydrodynamics with non conserved number of particles and show that it can be modeled with effective fluid Lagrangians which explicitly depend on the velocity potentials. For such theories, the {}``shift symetry''…
Fluctuations of conserved charges in a grand canonical ensemble can be calculated as derivatives of the free energy with respect to the respective chemical potential. They are directly related to experimentally available observables that…
We obtain macroscopic adiabatic thermodynamic transformations by space-time scalings of a microscopic Hamiltonian dynamics subject to random collisions with the environment. The microscopic dynamics is given by a chain of oscillators…
We present a set of uniform polynomial equations that provides multidimensional on-lattice higher-order models of the lattice Boltzmann theory, while keeping compact the number of discrete velocities. As examples, we explicitly derive two-…