arXiv subjects

Sergio Curilef

Publications and source records attributed to Sergio Curilef.

7 recordsLinked to original sources

arXiv2020

Solving equations of motion by using Monte Carlo Metropolis: Novel method via Random Paths and Maximum Caliber Principle

A permanent challenge in physics and other disciplines is to solve partial differential equations, thereby a beneficial investigation is to continue searching for new procedures to do it. In this Letter, a novel Monte-Carlo Metropolis framework is presented for solving the equations of motion in Lagrangian systems. The implementation lies in sampling the paths space with a probability functional obtained by using the maximum caliber principle. The methodology was applied to the free particle and the harmonic oscillator problems, where the numerically-averaged path obtained from the Monte-Carlo simulation converges to the analytical solution from classical mechanics, in an analogous way with a canonical system where energy is minimized by sampling the state space and computing the average state for each system. Thus, we expect that this procedure can be general enough to solve other differential equations in physics and to be a useful tool to calculate the time-dependent properties of dynamical systems in order to understand the non-equilibrium behavior of statistical mechanical systems.

physics.comp-ph↗

arXiv2015

Novel Dynamics and Thermodynamics in systems with long range interactions

Systems with long range interactions display some anomalies when its dynamics and thermodynamics are studied below certain conditions. Among these anomalies are the quasi- stationary states, which are exacerbated because of special initial conditions that are used here. We present in this letter a new Hamiltonian whose potential is inspired in the two-dipole interaction. An analytical solution is obtained for the equilibrium in the canonical ensemble that is coincident with the one obtained from computational simulations. However, results from this model presents a kind of nonequivalence of ensembles in long-living states before arriving to equilibrium. Thus, a complete characterization is made for the nonequilibrium through molecular dynamics. In which, novel quasi-stationary states are observed due to the long range interactions.

cond-mat.stat-mech↗

arXiv2007

On the statistical physics of metastable and non-equilibrium stationary states

The optimization problems defining meta-stable or stationary equilibrium are explored. The Gibbs scheme is modified aiming to describe the statistical properties of a class of non-equilibrium and metastable states. The system is assumed to maximize the usual definition of the Entropy, subject to the standard constant energy and norm restrictions, plus additional constraints. The central assumption is that the existence of the considered metastable state is determined by the action of this additional dynamical constraint, that blocks the evolution of the system up to its maximum Entropy state, thus maintaining it in the metastable or stationary configuration. After requiring from the statistical description to be valid for the combination of two nearly independent subsystems, it follows that the eigenvalues of the constraint operators C should have the restricted homogeneous form C(p{i})=p{i}^{q}, in terms of the eigenvalues of the density matrix p{i}, where q is a fixed real number. Therefore, the distribution of the eigenvalues of the constraint function have the Tsallis structure. This conclusion suggests the interpretation of the q parameter as reflecting the homogeneous dependence of the constraint determining the metastable state on the density matrix. An application to the plasma experiments of Huang and Driscoll is expected to be considered elsewhere in order to compare the results with Tsallis scheme and the minimal Enstrophy one.

cond-mat.stat-mech↗

arXiv2006

Trapped and Bound Classical States of an Electric Dipole in Magnetic Field

In the present work, we study the classical behavior of an electric dipole in presence of an external uniform magnetic field. We derive equations and constants of motion from the Lagrangian formulation. We obtain an infinitely periodic effective potential that describes a rotational motion. The problem is not directly separable in relative and center of mass variables; even though, we are able to write the energy of the system as a function of an only term, the relative variable. We define another constant of motion, which couples the relative with the center of mass variables. We describe conditions for bound states of the dipole. In addition, we discuss the problem in the approximation of small oscillations. Finally, we explore the existence of a possible family of trapped states in a region of the space where there are no classical turning points.

physics.class-ph↗

arXiv2004

Mean Field in Long-Range Ferromagnets and Periodic Boundary Conditions

Periodic boundary conditions are applied to a ferromagnetic spin lattice. A symmetrical lattice and its contributions all over space are being used. Results, for the Ising model with ferromagnetic interaction that decays as a $1/r^{D+ν}$ law, are discussed in the mean field approximation

cond-mat.stat-mech↗

arXiv2004

On exact summations in long-range interactions

In this work, simple exact results are presented for summations in two-particle potential with long-range interactions. Polygamma function is used to evaluate summations. Results are found when a periodic media is consider. Periodic boundary conditions are applied by symmetric repetitions of a central cell. Contributions over all space are used in the problem. The potential depends strongly on the size of the system; however, forces are convergents anywhere.

nlin.SI↗

arXiv1999

Critical Temperature and Nonextensivity in Long-range Interacting Lennard-Jones-like Fluids

Molecular dynamic simulations for systems with $D=2,3$ Lennard-Jones-like interactions are studied. In the model, we assume that, at long distances, the two-body attractive potential decays as $r^{-α}$. Thermodynamic extensivity (nonextensivity) is observed for $α> D$ ($0\leq α\leq D$). Particular attention is payed to the liquid-gas critical point located, in the temperature-pressure plane, at ($T_c,P_c$). ($T_c,P_c$) are, in the $N\to \infty$ limit ($N\equiv$ number of molecules), {\em finite} for $α> D$ and {\em diverge} for $α\leq D$ (as $(α- D)^{-1}$ for $α/D \to 1 + 0$). However, the variables $T_c^* \equiv T_c/N^*$ and $P_c^* \equiv P_c/N^*$ with $N^* \equiv [N^{1-α/D} -1]/[1-α/D]$ remain {\em finite for all} $α$. Thus, the extensive and nonextensive regions become unified, as recently conjectured. These results should be useful for discussing gravitation and some special fluids

cond-mat↗