10,270 research outputs found
Chaos in spin glasses revealed through thermal boundary conditions
We study the fragility of spin glasses to small temperature perturbations
numerically using population annealing Monte Carlo. We apply thermal boundary
conditions to a three-dimensional Edwards-Anderson Ising spin glass. In thermal
boundary conditions all eight combinations of periodic versus antiperiodic
boundary conditions in the three spatial directions are present, each appearing
in the ensemble with its respective statistical weight determined by its free
energy. We show that temperature chaos is revealed in the statistics of
crossings in the free energy for different boundary conditions. By studying the
energy difference between boundary conditions at free-energy crossings, we
determine the domain-wall fractal dimension. Similarly, by studying the number
of crossings, we determine the chaos exponent. Our results also show that
computational hardness in spin glasses and the presence of chaos are closely
related.Comment: 4 pages, 4 figure
Importance Sampling for Multiscale Diffusions
We construct importance sampling schemes for stochastic differential
equations with small noise and fast oscillating coefficients. Standard Monte
Carlo methods perform poorly for these problems in the small noise limit. With
multiscale processes there are additional complications, and indeed the
straightforward adaptation of methods for standard small noise diffusions will
not produce efficient schemes. Using the subsolution approach we construct
schemes and identify conditions under which the schemes will be asymptotically
optimal. Examples and simulation results are provided
Large Deviations and Importance Sampling for Systems of Slow-Fast Motion
In this paper we develop the large deviations principle and a rigorous
mathematical framework for asymptotically efficient importance sampling schemes
for general, fully dependent systems of stochastic differential equations of
slow and fast motion with small noise in the slow component. We assume
periodicity with respect to the fast component. Depending on the interaction of
the fast scale with the smallness of the noise, we get different behavior. We
examine how one range of interaction differs from the other one both for the
large deviations and for the importance sampling. We use the large deviations
results to identify asymptotically optimal importance sampling schemes in each
case. Standard Monte Carlo schemes perform poorly in the small noise limit. In
the presence of multiscale aspects one faces additional difficulties and
straightforward adaptation of importance sampling schemes for standard small
noise diffusions will not produce efficient schemes. It turns out that one has
to consider the so called cell problem from the homogenization theory for
Hamilton-Jacobi-Bellman equations in order to guarantee asymptotic optimality.
We use stochastic control arguments.Comment: More detailed proofs. Differences from the published version are
editorial and typographica
Duality Between Relaxation and First Passage in Reversible Markov Dynamics: Rugged Energy Landscapes Disentangled
Relaxation and first passage processes are the pillars of kinetics in
condensed matter, polymeric and single-molecule systems. Yet, an explicit
connection between relaxation and first passage time-scales so far remained
elusive. Here we prove a duality between them in the form of an interlacing of
spectra. In the basic form the duality holds for reversible Markov processes to
effectively one-dimensional targets. The exploration of a triple-well potential
is analyzed to demonstrate how the duality allows for an intuitive
understanding of first passage trajectories in terms of relaxational
eigenmodes. More generally, we provide a comprehensive explanation of the full
statistics of reactive trajectories in rugged potentials, incl. the so-called
`few-encounter limit'. Our results are required for explaining quantitatively
the occurrence of diseases triggered by protein misfolding.Comment: 17 pages, 5 figure
The Activation-Relaxation Technique : ART nouveau and kinetic ART
The evolution of many systems is dominated by rare activated events that occur on timescale ranging from nanoseconds to the hour or more. For such systems, simulations must leave aside the full thermal description to focus specifically on mechanisms that generate a configurational change. We present here the activation relaxation technique (ART), an open-ended saddle point search algorithm, and a series of recent improvements to ART nouveau and kinetic ART, an ART-based on-the-fly off-lattice self-learning kinetic Monte Carlo method
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