Asymptotically exponential hitting times and metastability: a pathwise approach without reversibility

We study the hitting times of Markov processes to target set $G$, starting from a reference configuration $x_0$ or its basin of attraction. The configuration $x_0$ can correspond to the bottom of a (meta)stable well, while the target $G$ could be either a set of saddle (exit) points of the well, or a set of further (meta)stable configurations. Three types of results are reported: (1) A general theory is developed, based on the path-wise approach to metastability, which has three important attributes. First, it is general in that it does not assume reversibility of the process, does not focus only on hitting times to rare events and does not assume a particular starting measure. Second, it relies only on the natural hypothesis that the mean hitting time to $G$ is asymptotically longer than the mean recurrence time to $x_0$ or $G$. Third, despite its mathematical simplicity, the approach yields precise and explicit bounds on the corrections to exponentiality. (2) We compare and relate different metastability conditions proposed in the literature so to eliminate potential sources of confusion. This is specially relevant for evolutions of infinite-volume systems, whose treatment depends on whether and how relevant parameters (temperature, fields) are adjusted. (3) We introduce the notion of early asymptotic exponential behavior to control time scales asymptotically smaller than the mean-time scale. This control is particularly relevant for systems with unbounded state space where nucleations leading to exit from metastability can happen anywhere in the volume. We provide natural sufficient conditions on recurrence times for this early exponentiality to hold and show that it leads to estimations of probability density functions

Shaken Dynamics: An Easy Way to Parallel Markov Chain Monte Carlo

We define a class of Markovian parallel dynamics for spin systems on arbitrary graphs with nearest neighbor interaction described by a Hamiltonian function H(sigma). These dynamics turn out to be reversible and their stationary measure is explicitly determined. Convergence to equilibrium and relation of the stationary measure to the usual Gibbs measure are discussed when the dynamics is defined on Z(2). Further it is shown how these dynamics can be used to define natively parallel algorithms to face problems in the context of combinatorial optimization

Ideal gas approximation for a two-dimensional rarefied gas under Kawasaki dynamics

Article / Letter to editorMathematisch Instituu

Water-Peptide Site-Specific Interactions: A Structural Study on the Hydration of Glutathione

AbstractWater-peptide interactions play an important role in determining peptide structure and function. Nevertheless, a microscopic description of these interactions is still incomplete. In this study we have investigated at the atomic scale length the interaction between water and the tripeptide glutathione. The rationale behind this work, based on the combination between a neutron diffraction experiment and a computer simulation, is twofold. It extends previous studies on amino acids, addressing issues such as the perturbation of the water network brought by a larger biomolecule in solution. In addition, and more importantly, it seeks a possible link between the atomic length scale description of the glutathione-water interaction with the specific biological functionality of glutathione, an important intracellular antioxidant. Results indicate a rather weak hydrogen bond between the thiol (-SH) group of cysteine and its first neighbor water molecule. This -SH group serves as a proton donor, is responsible for the biological activity of glutathione, and it is involved in the formation of glutathione disulfide, the oxidized form of glutathione. Moreover, the hydration shell of the chemically identical carboxylate group on the glutamic acid residue and on the glycine residue shows an intriguing different spatial location of water molecules and coordination numbers around the two CO2− groups

Springback effect and structural features during the drying of silica aerogels tracked by in-situ synchrotron X-ray scattering

The springback effect during ambient pressure drying of aerogels is an interesting structural phenomenon, consisting of a severe shrinkage followed by almost complete re-expansion. The drying of gels causes shrinkage, whereas re-expansion is believed to be linked to repelling forces on the nanoscale. A multi-scale structural characterization of this significant volume change is key in controlling aerogel processing and properties. In this work, hydrophobic, monolithic silica aerogels with high specific surface areas were synthesized by modification with trimethylchlorosilane and ambient pressure drying. Here, we report a multi-method approach focusing on in-situ X-ray scattering to observe alterations of the nanostructured material during the drying of surface-modified and unmodified silica gels. Both show a porous fractal nanostructure, which partially collapses during drying and only recovers in surface-modified samples during the springback effect. Distinct changes of the X-ray scattering data were reproducibly associated with the shrinkage, re-expansion and drying of the gel network. Our findings may contribute to tailor aerogels with specific functionality, as the springback effect has a direct influence on properties (e.g., porosity, pore size distribution), which is directly affected by the degree of re-expansion