arXiv subjects

I. Santamaria-Holek

Publications and source records attributed to I. Santamaria-Holek.

25 records · Page 2Linked to original sources

arXiv2006

Mesoscopic constitutive relations for dilute polymer solutions

A novel approach to the dynamics of dilute solutions of polymer molecules under flow conditions is proposed by applying the rules of mesoscopic nonequilibrium thermodynamics (MNET). The probability density describing the state of the system is taken to be a function of the position and velocity of the molecules, and on a local vector parameter accounting for its deformation. This function obeys a generalized Fokker-Planck equation, obtained by calculating the entropy production of the system, and identifying the corresponding probability currents in terms of generalized forces. In simple form, this coarse-grained description allows one to derive hydrodynamic equations where molecular deformation and diffusion effects are coupled. A class of non-linear constitutive relations for the pressure tensor are obtained. Particular models are considered and compared with experiments.

cond-mat.stat-mech↗

arXiv2005

A Nonequilibrium Thermodynamic Approach to Generalized Statistics for Brownian Motion

We analyze the dynamics of a Brownian gas in contact with a heat bath in which large temperature fluctuations occur. There are two distinct time scales present, one describes the decay of the fluctuations in the temperature and the other one is associated with the establishment of local equilibrium. Although the gas has reached local equilibrium, there exist large fluctuations in an intensive parameter (temperature) which break the thermodynamic equilibrium with the heat bath. Thus the decay of the fluctuations in the intensive parameter is larger than the characteristic time for the establishment of local equilibrium. We show that the dynamics of such large and intensive fluctuations may be described by adopting a nonequilibrium thermodynamics approach with an adequate formulation of local equilibrium. A coarsening procedure is then used to contract the space of mesoscopic variables needed to describe the dynamics of the gas and the extensive character of the description is lost. This procedure allows us to derive an effective Maxwell-Boltzmann factor (EMBF) for the Brownian gas, as has been recently proposed in the literature. Furthermore, we use this local equilibrium distribution and an entropy functional to derive a nonequilibrium probability distribution and a hydrodynamic description for the Brownian gas which contains fluctuating transport coefficients. The ensuing description is nonextensive and our analysis shows that the coarse-graining procedure is responsible for the nonextensivity property.

cond-mat.stat-mech↗

arXiv2005

Kinetics of growth process controlled by mass-convective fluctuations and finite-size curvature effects

In this study, a comprehensive view of a model crystal formation in a complex fluctuating medium is presented. The model incorporates Gaussian curvature effects at the crystal boundary as well as the possibility for superdiffusive motion near the crystal surface. A special emphasis is put on the finite-size effect of the building blocks (macroions, or the aggregates of macroions) constituting the crystal. From it an integrated static-dynamic picture of the crystal formation in terms of mesoscopic nonequilibrium thermodynamics (MNET), and with inclusion of the physically sound effects mentioned, emerges. Its quantitative measure appears to be the overall diffusion function of the formation which contains both finite-size curvature-inducing effects as well as a time-dependent superdiffusive part. A quite remarkable agreement with experiments, mostly those concerning investigations of dynamic growth layer of (poly)crystaline aggregation, exemplified by non-Kossel crystals and biomolecular spherulites, has been achieved.

cond-mat.soft↗

arXiv2004

Mesoscopic thermodynamics of stationary states

A thermodynamics for systems at a stationary states is formulated. It is based upon the assumption of the existence of local equilibrium in phase space which enables one to interpret the probability density ans its conjugated nonequilibrium chemical potential as a mesoscopic thermodynamic variables. The probability current is obtained from the entropy production related to the probability diffusion process and leads to the formulation of the Fokker-Planck equation. For the case of a gas of Brownian particles under steady flow in the dilute and concentrated regimes we derive nonequilibrium equations of state.

cond-mat.stat-mech↗

arXiv2003

Local quasi-equilibrium description of slow relaxation systems

We present a dynamical description of slow relaxation processes based on the extension of Onsager's fluctuation theory to systems in local quasi-equilibrium. A non-Markovian Fokker-Planck equation for the conditional probability density is derived and from it we obtain the relaxation equation for the moments. We show that the fluctuation-dissipation theorem can be formulated in terms of the temperature of the system at local quasi-equilibrium. Our theory may be applied to a wide variety of systems undergoing slow relaxation. We discuss in particular slow dynamics in glassy systems and Brownian motion in a granular gas.

cond-mat.stat-mech↗

arXiv2003

Slow dynamics and local quasi-equilibrium. Relaxation in supercooled colloidal systems

We present a Fokker-Planck description of supercooled colloidal systems exhibiting slow relaxation dynamics. By assuming the existence of a local quasi-equilibrium state during the relaxation of the system, we derive a non-Markovian Fokker-Planck equation for the non-stationary conditional probability. A generalized Stokes-Einstein relation containing the temperature of the system instead of the temperature of the bath is obtained. Our results explain experiments showing that the diffusion coefficient is not proportional to the inverse of the effective viscosity at frequencies related to the diffusion time scale.

cond-mat↗

arXiv2003

Memory effects in nonlinear transport: kinetic equations and ratchet devices

We present a new method to derive kinetic equations for systems undergoing non-linear transport in the presence of memory effects. In the framework of mesoscopic nonequilibrium thermodynamics, we derive a generalized Fokker-Planck equation incorporating memory effects through time-dependent coefficients. As applications, we first discuss the non-Markovian dynamics of anomalous diffusion in a potential, analyzing the validity of the fluctuation-dissipation theorem. In a second application, we propose a new ratchet mechanism in which the periodic driving acting on the particle is induced by the Onsager coupling of the diffusion current with an oscillating thermodynamic force.

cond-mat.stat-mech↗