We consider the problem of an overdamped Brownian particle moving in multiscale potential with N+1 characteristic length scales: the macroscale and N separated microscales. We show that the coarse-grained dynamics is given by an overdamped Langevin equation with respect to the free energy and with a space-dependent diffusion tensor, the calculation of which requires the solution of N fully coup...

We numerically simulate a thermalization process in an energy landscape with hierarchically organized metastable states. The initial configuration is chosen to have a large energy excess relative to the thermal equilibrium value at the running temperature. We show that the initial energy surplus is dissipated in a series of intermittent bursts, or quakes, whose rate decreases as the inverse of ...

1 Probabilistic Search and Optimization for Protein Energy Landscapes 1 Amarda Shehu 1.

Many physical and chemical processes, such as folding of biopolymers, are best described as dynamics on large combinatorial energy landscapes. A concise approximate description of the dynamics is obtained by partitioning the microstates of the landscape into macrostates. Since most landscapes of interest are not tractable analytically, the probabilities of transitions between macrostates need t...

Understanding the static and even more the dynamical behavior of complex physical systems is one of the most challenging problems of current research in physics, chemistry and biology. Paradigmatic examples of condensed matter physics are spin glasses and structural glasses. More recently, in life sciences, the rapid advances in computational biology have added the exploration of the properties...

A short-ranged pairwise Morse potential is used to model colloidal clusters with planar morphologies. Potential and free energy global minima as well as rearrangement paths, obtained by basin-hopping global optimisation and discrete path sampling, are characterised. The potential and free energy landscapes are visualised using disconnectivity graphs. The short-ranged potential is found to favou...

D. A. Lidar,* D. Thirumalai, R. Elber, and R. B. Gerber Department of Physics, The Hebrew University of Jerusalem, Jerusalem 91904, Israel Department of Physical Chemistry and The Fritz Haber Center for Molecular Dynamics, The Hebrew University of Jerusalem, Jerusalem 91904, Israel Department of Chemistry and Biochemistry, Institute for Physical Science and Technology, University of Maryland, C...

We perform a comprehensive survey of the potential energy landscapes of 13-atom Morse clusters, and describe how they can be characterized and visualized. Our aim is to detail how the global features of the funnel-like surface change with the range of the potential, and to relate these changes to the dynamics of structural relaxation. We find that the landscape becomes rougher and less steep as...

To any positive number ε and any nonnegative even Schwartz function w : R → R we associate the random function u on them-torus T := R/Z defined as the real part of the random Fourier series ∑ ~ν∈Zm X~ν,ε exp(2πi~ν · ~ θ), whereX~ν,ε are complex independent Gaussian random variables with variancew(ε|~ν|). LetN denote the number of critical points of u. We describe explicitly two constantsC,C′ su...