Stochastic Ornstein–Uhlenbeck Capacitors

We introduce and study a class of random capacitor systems which are both charged and discharged stochastically. A capacitor is fed by a random inflow with stationary and independent increments. Discharging occurs according to a Markovian rate which is linear in the capacitors level. The resulting capacitor dynamics are Markovian, stochastically cyclic, and regenerative. We coin these systems Lévy-charged Ornstein–Uhlenbeck capacitors. Various random quantities associated with these systems are analyzed, including: the time-to- discharge; the duration of the charging cycle; the trajectory and the peak height of the capacitor level during a charging cycle; and, the capacitors stationary equilibrium level. Furthermore, we show that there are sharp distinctions between these capacitor systems and corresponding standard Lévy-driven Ornstein–Uhlenbeck systems.     

Fluctuations for Kawasaki Dynamics

In this paper Kawasaki dynamics are considered. Lower bounds are obtained for the variance of the occupation time of a site in any dimension and for temperature above critical temperature. These lower bounds are expressed in terms of the density correlation function and hence relate the fluctuations to some phase transition quantities. At critical temperature, under a reasonable assumption of the static structure function, lower bounds for the variance of the occupation time are obtained. These lower bounds are consistent with the supposed value of the critical exponent. This paper also examines the same problem for Glauber dynamics and shows that the phase transition may not be of importance for the behavior of fluctuations.     

The Asymptotic Behavior of the Ergodic Measure of a Glauber + Kawasaki model

We consider an interacting particle system given by the Glauber + Kawasaki dynamics. It is known that this process has a reaction diffusion equation as hydrodynamic limit. The ergodicity of this process in the presence of a metastable state (double well potential) was recently proved by S. Brassesco et al. In this Letter we prove that, in the limit, as ε → 0, the expected value of each spin converges to the global minimizer of the potential. We also prove decay of correlations of the ergodic measure.AMS Subject Classification (2000). 60K35 (82C22, 82C31)This work was partially supported by CNPq     

Generation, propagation, and annihilation of metastable patterns

We study the full-time dynamics of the initial value problem, for u^ε=u^ε(x,t),

     

Enhancing the accuracy of virtual screening: molecular dynamics with quantum-refined force fields

Summary A methodology aimed at improving the accuracy of current docking–scoring procedures is proposed, and validated through detailed tests of its performance in predicting the activity of HIV-1 protease inhibitors. This methodology is based on molecular dynamics simulations using a force field whose effective charges are refined by means of a novel procedure that relies on quantum-mechanical calculations and preserves the internal consistency of the parameterization scheme.     

Development of the force field parameters for phosphoimidazole and phosphohistidine

Phosphorylation of histidine-containing proteins is a key step in the mechanism of many phosphate transfer enzymes (kinases, phosphatases) and is the first stage in a wide variety of signal transduction cascades in bacteria, yeast, higher plants, and mammals. Studies of structural and dynamical aspects of such enzymes in the phosphorylated intermediate states are important for understanding the intimate molecular mechanisms of their functioning. Such information may be obtained via molecular dynamics and/or docking simulations, but in this case appropriate force field parameters for phosphohistidine should be explicitly defined. In the present article we describe development of the GROMOS96 force field parameters for phosphoimidazole molecule--a realistic model of the phosphohistidine side chain. The parameterization is based on the results of ab initio quantum chemical calculations with subsequent refinement and testing using molecular mechanics and molecular dynamics simulations. The set of force constants and equilibrium geometry is employed to derive force field for the phosphohistidine moiety. Resulting parameters and topology are incorporated into the molecular modeling package GROMACS and used in molecular dynamics simulations of a phosphohistidine-containing protein in explicit solvent.     

Real bounds, ergodicity and negative Schwarzian for multimodal maps

We consider smooth multimodal maps which have finitely many non-flat critical points. We prove the existence of real bounds. From this we obtain a new proof for the non-existence of wandering intervals, derive extremely useful improved Koebe principles, show that high iterates have `negative Schwarzian derivative' and give results on ergodic properties of the map. One of the main complications in the proofs is that we allow to have inflection points.