arXiv subjects
Publications and source records attributed to A. Perez-Madrid.
We propose a method to analyze the dynamics of systems exhibiting slow relaxation which is based on mesoscopic non-equilibrium thermodynamics. The method allows us to obtain kinetic equations of the Fokker-Planck type for the probability functional and their corresponding Langevin equations. Our results are compared with the ones obtained by other authors.
We present a general formalism able to derive the kinetic equations of polymer dynamics. It is based on the application of nonequilibrium thermodynamics to analyze the irreversible processes taking place in the conformational space of the macromolecules. The Smoluchowski equation results from the analysis of the underlying diffusion process in that space within the scheme of nonequilibrium thermodynamics. We apply the method to different situations, concerning flexible, semiflexible and rod-like polymers and to the case of more concentrated solutions in which interactions become important.
We show that a magnetic dipole in a shear flow under the action of an oscillating magnetic field displays stochastic resonance in the linear response regime. To this end, we compute the classical quantifiers of stochastic resonance, i.e. the signal to noise ratio, the escape time distribution, and the mean first passage time. We also discuss limitations and role of the linear response theory in its applications to the theory of stochastic resonance.
We show a new mechanism to extract energy from non-equilibrium fluctuations typical of periodically driven non-Hermitian systems. The transduction of energy between the driving force and the system is revealed by an \emph{anomalous} behavior of the susceptibility, leading to a diminution of the dissipated power and consequently to an improvement of the transport properties. The general framework is illustrated by the analysis of some relevant cases.
We discuss the effect of an homogeneous flow in the aggregation process of colloidal magnetic particles at moderate concentration. Situations in which the presence of flow acts in favor of the chaining process: particles assemble into chains larger than the ones emerging in the absence of flow, under the only influence of an externnaly imposed field, have been analyzed. The results we obtain follow from the analysis of the pair correlation function which, owing to the potencial character of the flow we consider, can be interpreted in terms of a Boltzmann-like stationary distribution function. To render the influence of the flow on the resulting structures explicit, we study the particular cases of axisymmetric and planar elongational flows.
We discuss inertial effects in systems outside equilibrium within the framework of non-equilibrium thermodynamics. By introducing a Gibbs equation in which the entropy depends on the probability density, we are able to describe a system of Brownian particles immersed in a heat bath in both inertial and diffusion regimes. In the former, a relaxation equation for the diffusion current is obtained whereas in the latter we recover Fick's law. Our approach, which uses the elements of the theory of internal degrees of freedom, constitutes the mesoscopic version of a previous analysis which takes into account the kinetic energy of diffusion.
We introduce a new scheme to analyze the kinetics of homogeneous nucleation in terms of a global order parameter. Our approach is based on the application of the internal degrees of freedom formalism to derive a kinetic equation of the Kramers type formulated for a global reaction coordinate. We provide explicit expressions for the quantities and coefficients involved in the process, suitable for simulation. In addition, our picture recovers in the quasi-stationary case the transition rate obtained from the method of reactive flux. The equation we present may provide a link between theoretical approaches to homogeneous nucleation (generally formulated in terms of a kinetic equation of the Fokker-Planck type) and simulations (which mostly employ linear response theory). In this context, our scheme provides a theoretical framework to interpret and extend the results obtained in recent simulations.
We present a new approach to analyze homogeneous nucleation based on non-equilibrium thermodynamics. The starting point is the formulation of a Gibbs equation for the variations of the entropy of the system, whose state is characterized by an internal coordinate or degree of freedom. By applying the method of non-equilibrium thermodynamics we then obtain the entropy production corresponding to a diffusion process in the internal space. The linear laws together with the continuity equation lead to a kinetic equation of the Fokker-Planck type. By choosing properly the degree of freedom we are able to obtain a new kinetic equation for a global crystallization order parameter (used in recent simulations), and also we recover some of the existing equations. The consistency of the scheme we propose is proved in the quasi-stationary case. Finally, we also outline the way in which our formalism could be extended to more general situations.
We propose a new mechanism to increase the reactions ratesin multistable autocatalytic systems. The mechanism is based upon the possibility for the enhancement of the response of the system due to the cooperative behavior between the noise and an external periodic modulation. In order to illustrate this feature we compute the reaction velocities for the particular case of the Sel'Kov model, showing that they increase significantly when the periodic modulation is introduced. This behavior originates from the existence of a minimum in the mean first passage time, one of the signatures of stochastic resonance.
We propose a method to analytically show the possibility for the appearance of a maximum in the signal-to-noise ratio in nonpotential systems. We apply our results to the FitzHugh-Nagumo model under a periodic external forcing, showing that the model exhibits stochastic resonance. The procedure that we follow is based on the reduction to a one-dimensional dynamics in the adiabatic limit, and in the topology of the phase space of the systems under study. Its application to other nonpotential systems is also discussed.
We have studied the relaxation and transport properties of a ferrofluid in an elongational flow. These properties are influenced by the bistable nature of the potential energy. Bistability comes from the irrotational character of the flow together with the symmetry of the dipoles. Additionally, the presence of a constant magnetic field destroys the symmetry of the potential energy magnetizing the system. We have shown that at a moderate temperature, compared to the height of the energy barrier, the viscosity decreases with respect to the value it would have if the potential were stable. This phenomenon is known as the 'negative viscosity' effect. Thermal motion induces jumps of the magnetic moment between the two stable states of the system leading to the aforementioned lowered dissipation effect.
The methods of non-equilibrium thermodynamics of systems with an interface have been applied to the study of thermionic emission processes in abrupt semiconductor junctions, including the effects of surface states . Our analysis covers different situations of interest, concerning unipolar and bipolar systems, either degenerate or not, with or without interface states and under steady and non-steady conditions. In this way, a complete phenomenological modelling of thermionic emission-interface states processes has been proposed, overcoming some of the inherent limititations of the currently existing models.
By considering an ensemble of Brownian particles suspended in a heat bath as a thermodynamic system with an internal degree of freedom it is possible to obtain the Fokker-Planck equation for Brownian motion in a temperature gradient, by applying the scheme of non-equilibrium thermodynamics. We recover explicitely the equations derived in particular by Zubarev and Bashkirov using statistical mechanical and kinetic methods. In addition when the temperature gradient does not have an externally imposed magnitude we obtain the differential equation for the temperature field, which is coupled to the Fokker-Planck equation.
We show that a dispersion of monodomain ferromagnetic particles in a solid phase exhibits stochastic resonance when a driven linearly polarized magnetic field is applied. By using an adiabatic approach, we calculate the power spectrum, the distribution of residence times and the mean first passage time. The behavior of these quantities is similar to their corresponding ones in other systems in which stochastic resonance has also been observed.