Related papers: Thermodynamics of Third Order Phase Transition: A …
We establish a result concerning the so-called Lagrangian controllability of the Euler equation for incompressible perfect fluids in dimension 3. More precisely we consider a connected bounded domain of R^3 and two smooth contractible sets…
Previously, the Einstein equation has been described as an equation of state, general relativity as the equilibrium state of gravity, and $f({\cal R})$ gravity as a non-equilibrium one. We apply Eckart's first order thermodynamics to the…
The understanding of thermodynamic glass transition has been hindered by the lack of proper models beyond mean-field theories. Here, we propose a three-dimensional lattice glass model on a simple cubic lattice that exhibits the typical…
We solve a set of selected exercises on rotational motion requiring a mechanical and thermodynamical analysis. When non-conservative forces or thermal effects are present, a complete study must use the first law of thermodynamics together…
The well known scaling laws relating critical exponents in a second order phase transition have been generalized to the case of an arbitrarily higher order phase transition. In a higher order transition, such as one suggested for the…
We investigate the order of the topological quantum phase transition in a two dimensional quadrupolar topological insulator within a thermodynamic approach. Using numerical methods, we separate the bulk, edge and corner contributions to the…
In this paper, we consider higher order correction of the entropy and study the thermodynamical properties of recently proposed Schwarzschild-Beltrami-de Sitter black hole, which is indeed an exact solution of Einstein equation with a…
Euler's equation relates the change in angular momentum of a rigid body to the applied torque. This paper fills a gap in the literature by using Lagrangian dynamics to derive Euler's equation in terms of generalized coordinates. This is…
This is a survey highlighting several recent results concerning well/ill posedness of the Euler system of gas dynamics. Solutions of the system are identified as limits of consistent approximations generated either by physically more…
It was shown that in the canonical ensemble the simple exactly soluble statistical model of nuclei decay into nucleons, which is a limiting case of the statistical multifragmentation model, predicts the nuclear first order phase transition…
This paper investigates the stochastic 3D Euler equations on a periodic domain $\mathbb{T}^3$, driven by a $GG^*$-Wiener process $B$ of trace class: \begin{align*} \mathrm{d} u+\mathrm{div}(u\otimes u)\,\mathrm{d} t+\nabla…
Considering one-dimensional nonminimally-coupled lattice gauge theories, a class of nonlocal one-dimensional systems is presented, which exhibits a phase transition. It is shown that the transition has a latent heat, and, therefore, is a…
The effect of the external field on the weakly-discontinuous first-order phase transition is analyzed in the frame of the Landau theory. The transformation of the free energy expansion as a power series in the order parameter is suggested…
Lattice Boltzmann simulations have been very successful in simulating liquid-gas and other multi-phase fluid systems. However, the underlying second order analysis of the equation of motion has long been known to be insufficient to…
Thermodynamical properties of nuclear matter undergoing multifragmentation are studied within a simplified version of the statistical model. An exact analytical solution has been found for the grand canonical ensemble. Excluded volume…
Many frustrated spin models on three-dimensional (3D) lattices are currently being investigated, both experimentally and theoretically, and develop new types of long-range orders in their respective phase diagrams. They present…
Magnetic susceptibility, entropy and specific heat are calculated at the equilibrium points of phase transition to a phase of coexistence of ferromagnetic order and superconductivity in a new class of spin-triplet ferromagnetic…
First and second order non-equilibrium thermodynamics are studied in the context of particle creation mechanism for homogeneous and isotropic FLRW model and a general formulation of the emergent scenario is investigated. Finally, the…
Experimentalists now measure intense rotations of Lagrangian particles in turbulent flows by tracking their trajectories and Lagrangian-average velocity gradients at high Reynolds numbers. This paper formulates the dynamics of an…
In this paper we develop a geometric approach to higher order mechanics on graded bundles in both, the Lagrangian and Hamiltonian formalism, via the recently discovered weighted algebroids. We present the corresponding Tulczyjew triple for…