arXiv subjects

Wolfhard Janke

Publications and source records attributed to Wolfhard Janke.

At least 55 records · Page 3Linked to original sources

arXiv2019

Acceptance rate is a thermodynamic function in local Monte Carlo algorithms

We study properties of Markov chain Monte Carlo simulations of classical spin models with local updates. We derive analytic expressions for the mean value of the acceptance rate of single-spin-flip algorithms for the one-dimensional Ising model. We find that for the Metropolis algorithm the average acceptance rate is a linear function of energy. We further provide numerical results for the energy dependence of the average acceptance rate for the 3- and 4-state Potts model, and the XY model in one and two spatial dimensions. In all cases, the acceptance rate is an almost linear function of the energy in the critical region. The variance of the acceptance rate is studied as a function of the specific heat. While the specific heat develops a singularity in the vicinity of a phase transition, the variance of the acceptance rate stays finite.

cond-mat.stat-mech↗

arXiv2019

Understanding nonequilibrium scaling laws governing collapse of a polymer

Recent emerging interest in experiments of single-polymer dynamics urge computational physicists to revive their understandings, particularly in the nonequilibrium context. Here we briefly discuss the currently evolving approaches of investigating the evolution dynamics of homopolymer collapse in computer simulations. Primary focus of these approaches is to understand various dynamic scaling laws related to coarsening and aging during the collapse in space dimension $d=3$, using tools popular in nonequilibrium coarsening dynamics of particle or spin systems. In addition to providing an overview of those results, we also present new preliminary data for $d=2$.

cond-mat.stat-mech↗

arXiv2019

Polymer simulation by means of tree data-structures and a parsimonious Metropolis algorithm

We show how a Monte Carlo method for generating self-avoiding walks on lattice geometries which employs a binary-tree data structure can be adapted for hard-sphere polymers with continuous degrees of freedom. Data suggests that the time per Monte Carlo move scales logarithmically with polymer size. We combine the method with a variant of the Metropolis algorithm and preserve this scaling for Lennard-Jones polymers with untruncated monomer-monomer interaction. We further show how the replica-exchange method can be adapted for the same purpose.

cond-mat.stat-mech↗

arXiv2019

Accelerating molecular dynamics simulations with population annealing

Population annealing is a powerful tool for large-scale Monte Carlo simulations. We adapt this method to molecular dynamics simulations and demonstrate its excellent accelerating effect by simulating the folding of a short peptide commonly used to gauge the performance of algorithms. The method is compared to the well established parallel tempering approach and is found to yield similar performance for the same computational resources. In contrast to other methods, however, population annealing scales to a nearly arbitrary number of parallel processors and it is thus a unique tool that enables molecular dynamics to tap into the massively parallel computing power available in supercomputers that is so much needed for a range of difficult computational problems.

physics.comp-ph↗

arXiv2019

Pearl-Necklace-Like Local Ordering Drives Polypeptide Collapse

Collapse of the polypeptide backbone is an integral part of protein folding. Using polyglycine as a probe, we explore the nonequilibrium pathways of protein collapse in water. We find that the collapse depends on the competition between hydration effects and intra-peptide interactions. Once intra-peptide van der Waal interactions dominate, the chain collapses along a nonequilibrium pathway characterized by formation of pearl-necklace-like local clusters as intermediates that eventually coagulate into a single globule. By describing this coarsening through the contact probability as a function of distance along the chain, we extract a time-dependent length scale that grows in linear fashion. The collapse dynamics is characterized by a dynamical critical exponent $z=0.5$ that is much smaller than the values of $z=1-2$ reported for non-biological polymers. This difference in the exponents is explained by the instantaneous formation of intra-chain hydrogen bonds and local ordering that may be correlated with the observed fast folding times in proteins.

physics.bio-ph↗

arXiv2019

Phase ordering kinetics of the long-range Ising model

We use an efficient method that eases the daunting task of simulating dynamics in spin systems with long-range interaction. Our Monte Carlo simulations of the long-range Ising model for the nonequilibrium phase ordering dynamics in two spatial dimensions erform significantly faster than the standard Metropolis approach and considerably more efficiently than the kinetic Monte Carlo method. Importantly, this enables us to establish agreement with the theoretical prediction for the time dependence of domain growth, in contrast to previous numerical studies. This method can easily be generalized to applications in other systems.

cond-mat.stat-mech↗

arXiv2018

Stabilization and Destabilization of Semiflexible Polymers Induced by Spherical Confinement

Spherical confinement can act either stabilizing or destabilizing on the collapsed state of a semi-flexible polymer. General free-energy arguments suggest that the order of the unconstrained collapse transition is the distinguishing factor: First order implies stabilization, second order causes destabilization. We confirm this conjecture by Monte Carlo simulations of a coarse-grained model for semiflexible polymers whose chain stiffness tunes the transition order. The resulting physical picture is potentially relevant for other systems under strong confinement such as proteins and DNA.

cond-mat.soft↗

arXiv2018

The Droplet Formation-Dissolution Transition in Different Ensembles: Finite-Size Scaling from Two Perspectives

The formation and dissolution of a droplet is an important mechanism related to various nucleation phenomena. Here, we address the droplet formation-dissolution transition in a two-dimensional Lennard-Jones gas to demonstrate a consistent finite-size scaling approach from two perspectives using orthogonal control parameters. For the canonical ensemble, this means that we fix the temperature while varying the density and vice versa. Using specialised parallel multicanonical methods for both cases, we confirm analytical predictions at fixed temperature (rigorously only proven for lattice systems) and corresponding scaling predictions from expansions at fixed density. Importantly, our methodological approach provides us with reference quantities from the grand canonical ensemble that enter the analytical predictions. Our orthogonal finite-size scaling setup can be exploited for theoretical and experimental investigations of general nucleation phenomena - if one identifies the corresponding reference ensemble and adapts the theory accordingly. In this case, our numerical approach can be readily translated to the corresponding ensembles and thereby proves very useful for numerical studies of equilibrium droplet formation, in general.

physics.comp-ph↗

arXiv2018

Dissipative Dynamics of a Single Polymer in Solution: A Lowe-Andersen Approach

We study the equilibrium dynamics of a single polymer chain under good solvent condition. Special emphasis is laid on varying the drag force experienced by the chain while it moves. To this end we model the solvent in a mesoscopic manner by employing the Lowe-Andersen approach of dissipative particle dynamics which is known to reproduce hydrodynamic effects. Our approach captures the correct static behavior in equilibrium. Regarding the dynamics, we investigate the scaling of the self-diffusion coefficient $D$ with respect to the length of the polymer $N$, yielding results that are compatible with the Zimm scaling $D \sim N^{-3/5}$.

cond-mat.soft↗

arXiv2018

Finite-size scaling of Monte Carlo simulations for the fcc Ising antiferromagnet: Effects of the low-temperature phase degeneracy

The Ising antiferromagnet on a face-centered cubic (fcc) lattice with nearest-neighbor interaction only is well known to exhibit a macroscopic (exponential in the system size $L$) ground-state degeneracy. With increasing temperature, this degeneracy is expected to be lifted and the model undergoes a first-order phase transition. For a model with an exponential degeneracy in the whole low-temperature phase, it was recently found that the finite-size scaling behavior is governed by leading correction terms $\sim L^{-2}$ instead of $\sim L^{-3}$ as usual. To test the conjecture that such a transmuted behavior may effectively persist also for the fcc antiferromagnet up to some crossover system size, we have performed parallel multicanonical Monte Carlo simulations for lattices of linear size $L \le 18$ with periodic boundary conditions and determined various inverse pseudo phase transition temperatures, as well as the extremal values of the specific heat and the energetic Binder parameter. We indeed find that, for the simulated lattice sizes, the conjectured transmuted finite-size scaling ansatz fits the data better than the standard ansatz. On this basis, we extrapolate for the transition temperature an estimate of $T_0 = 1.735047(46)$.

cond-mat.stat-mech↗

arXiv2018

Dynamic Greedy Algorithms for the Edwards-Anderson Model

To provide a novel tool for the investigation of the energy landscape of the Edwards-Anderson spin-glass model we introduce an algorithm that allows an efficient execution of a greedy optimization based on data from a previously performed optimization for a similar configuration. As an application we show how the technique can be used to perform higher-order greedy optimizations and simulated annealing searches with improved performance.

cond-mat.dis-nn↗

arXiv2018

Distribution of metastable states of Ising spin glasses

Local minima also known as inherent structures are expected to play an essential role for the behavior of spin glasses. Here, we propose techniques to efficiently sample these configurations in Monte Carlo simulations. For the Sherrington-Kirkpatrick and the three-dimensional Edwards-Anderson model their spectra are determined and compared to analytical results.

cond-mat.dis-nn↗

arXiv2018

Approximate ground states of the random-field Potts model from graph cuts

While the ground-state problem for the random-field Ising model is polynomial, and can be solved using a number of well-known algorithms for maximum flow or graph cut, the analogue random-field Potts model corresponds to a multi-terminal flow problem that is known to be NP hard. Hence an efficient exact algorithm is very unlikely to exist. As we show here, it is nevertheless possible to use an embedding of binary degrees of freedom into the Potts spins in combination with graph-cut methods to solve the corresponding ground-state problem approximately in polynomial time. We benchmark this heuristic algorithm using a set of quasi-exact ground states found for small systems from long parallel tempering runs. For not too large number $q$ of Potts states, the method based on graph cuts finds the same solutions in a fraction of the time. We employ the new technique to analyze the breakup length of the random-field Potts model in two dimensions.

cond-mat.dis-nn↗

arXiv2018

From particle condensation to polymer aggregation

We draw an analogy between droplet formation in dilute particle and polymer systems. Our arguments are based on finite-size scaling results from studies of a two-dimensional lattice gas to three-dimensional bead-spring polymers. To set the results in perspective, we compare with in part rigorous theoretical scaling laws for canonical condensation in a supersaturated gas at fixed temperature, and derive corresponding scaling predictions for an undercooled gas at fixed density. The latter allows one to efficiently employ parallel multicanonical simulations and to reach previously not accessible scaling regimes. While the asymptotic scaling can not be observed for the comparably small polymer system sizes, they demonstrate an intermediate scaling regime also observable for particle condensation. Altogether, our extensive results from computer simulations provide clear evidence for the close analogy between particle condensation and polymer aggregation in dilute systems.

cond-mat.stat-mech↗

arXiv2018

Percolation thresholds and fractal dimensions for square and cubic lattices with long-range correlated defects

We study long-range power-law correlated disorder on square and cubic lattices. In particular, we present high-precision results for the percolation thresholds and the fractal dimension of the largest clusters as function of the correlation strength. The correlations are generated using a discrete version of the Fourier filtering method. We consider two different metrics to set the length scales over which the correlations decay, showing that the percolation thresholds are highly sensitive to such system details. By contrast, we verify that the fractal dimension $d_{\rm f}$ is a universal quantity and unaffected by the choice of metric. We also show that for weak correlations, its value coincides with that for the uncorrelated system. In two dimensions we observe a clear increase of the fractal dimension with increasing correlation strength, approaching $d_{\rm f}\rightarrow 2$. The onset of this change does not seem to be determined by the extended Harris criterion.

cond-mat.stat-mech↗

arXiv2017

Scaling laws during collapse of a homopolymer: Lattice versus off-lattice

We present comparative results from simulations of a lattice and an off-lattice model of a homopolymer, in the context of kinetics of the collapse transition. Scaling laws related to the collapse time, cluster coarsening and aging behavior are compared. Although in both models the cluster growth is independent of temperature, the related exponents turn out to be different. Conversely, the aging and associated scaling properties are found to be universal, with the nonequilibrium autocorrelation exponent obeying a recently derived bound.

cond-mat.stat-mech↗

arXiv2017

GPU accelerated population annealing algorithm

Population annealing is a promising recent approach for Monte Carlo simulations in statistical physics, in particular for the simulation of systems with complex free-energy landscapes. It is a hybrid method, combining importance sampling through Markov chains with elements of sequential Monte Carlo in the form of population control. While it appears to provide algorithmic capabilities for the simulation of such systems that are roughly comparable to those of more established approaches such as parallel tempering, it is intrinsically much more suitable for massively parallel computing. Here, we tap into this structural advantage and present a highly optimized implementation of the population annealing algorithm on GPUs that promises speed-ups of several orders of magnitude as compared to a serial implementation on CPUs. While the sample code is for simulations of the 2D ferromagnetic Ising model, it should be easily adapted for simulations of other spin models, including disordered systems. Our code includes implementations of some advanced algorithmic features that have only recently been suggested, namely the automatic adaptation of temperature steps and a multi-histogram analysis of the data at different temperatures.

physics.comp-ph↗

arXiv2017

Polymer Adsorption on Curved Surfaces

The conformational behavior of a coarse-grained finite polymer chain near an attractive spherical surface was investigated by means of multicanonical Monte Carlo computer simulations. In a detailed analysis of canonical equilibrium data over a wide range of sphere radius and temperature, we have constructed entire phase diagrams both for non-grafted and end-grafted polymers. For the identification of the conformational phases, we have calculated several energetic and structural observables such as gyration tensor based shape parameters and their fluctuations by canonical statistical analysis. Despite the simplicity of our model, it qualitatively represents in the considered parameter range real systems that are studied in experiments. The work dicussed here could have experimental implications from protein-ligand interactions to designing nano smart materials.

cond-mat.soft↗