arXiv subjects

Walter Nadler

Publications and source records attributed to Walter Nadler.

At least 19 recordsLinked to original sources

arXiv2008

Dynamics and Efficiency of Brownian Rotors

Brownian rotors play an important role in biological systems and in future nano-technological applications. However the mechanisms determining their dynamics, efficiency and performance remain to be characterized. Here the F0 portion of the F-ATP synthase is considered as a paradigm of a Brownian rotor. In a generic analytical model we analyze the stochastic rotation of F0-like motors as a function of the driving free energy difference and of the free energy profile the rotor is subjected to. The latter is composed of the rotor interaction with its surroundings, of the free energy of chemical transitions, and of the workload. The dynamics and mechanical efficiency of the rotor depends on the magnitude of its stochastic motion driven by the free energy energy difference and its rectification on the reaction-diffusion path. We analyze which free energy profiles provide maximum flow and how their arrangement on the underlying reaction-diffusion path affects rectification and -- by this -- the efficiency.

physics.bio-ph↗

arXiv2007

Optimizing Replica Exchange Moves For Molecular Dynamics

In this short note we sketch the statistical physics framework of the replica exchange technique when applied to molecular dynamics simulations. In particular, we draw attention to generalized move sets that allow a variety of optimizations as well as new applications of the method.

q-bio.QM↗

arXiv2007

On Dynamics and Optimal Number of Replicas in Parallel Tempering Simulations

We study the dynamics of parallel tempering simulations, also known as the replica exchange technique, which has become the method of choice for simulation of proteins and other complex systems. Recent results for the optimal choice of the control parameter discretization allow a treatment independent of the system in question. Analyzing mean first passage times across control parameter space, we find an expression for the optimal number of replicas in simulations covering a given temperature range. Our results suggest a particular protocol to optimize the number of replicas in actual simulations.

cond-mat.stat-mech↗

arXiv2007

Network Analysis of the State Space of Discrete Dynamical Systems

We study networks representing the dynamics of elementary 1-d cellular automata (CA) on finite lattices. We analyze scaling behaviors of both local and global network properties as a function of system size. The scaling of the largest node in-degree is obtained analytically for a variety of CA including rules 22, 54 and 110. We further define the \emph{path diversity} as a global network measure. The co-appearance of non-trivial scaling in both hub size and path diversity separates simple dynamics from the more complex behaviors typically found in Wolfram's Class IV and some Class III CA.

cond-mat.stat-mech↗

arXiv2007

Generalized Ensemble and Tempering Simulations: A Unified View

From the underlying Master equations we derive one-dimensional stochastic processes that describe generalized ensemble simulations as well as tempering (simulated and parallel) simulations. The representations obtained are either in the form of a one-dimensional Fokker-Planck equation or a hopping process on a one-dimensional chain. In particular, we discuss the conditions under which these representations are valid approximate Markovian descriptions of the random walk in order parameter or control parameter space. They allow a unified discussion of the stationary distribution on, as well as of the stationary flow across each space. We demonstrate that optimizing the flow is equivalent to minimizing the first passage time for crossing the space, and discuss the consequences of our results for optimizing simulations. Finally, we point out the limitations of these representations under conditions of broken ergodicity.

cond-mat.stat-mech↗

arXiv2006

Side-chain and backbone ordering in Homopolymers

In order to study the relation between backbone and side chain ordering in proteins, we have performed multicanonical simulations of deka-peptide chains with various side groups. Glu10, Gln10, Asp10, Asn10, and Lys10 were selected to cover a wide variety of possible interactions between the side chains of the monomers. All homopolymers undergo helix-coil transitions. We found that peptides with long side chains that are capable of hydrogen bonding, i.e. Glu10, and Gln10, exhibit a second transition at lower temperatures connected with side chain ordering. This occurs in gas phase as well as in solvent, although the character of the side chain structure is different in each case. However, in polymers with short side chains capable of hydrogen bonding, i.e. Asp10 and Asn10, side chain ordering takes place over a wide temperature range and exhibits no phase transition like character. Moreover, non-backbone hydrogen bonds show enhanced formation and fluctuations already at the helix-coil transition temperature, indicating competition between side chain and backbone hydrogen bond formation. Again, these results are qualitatively independent of the environment. Side chain ordering in Lys10, whose side groups are long and polar, also takes place over a wide temperature range and exhibits no phase transition like character in both environments. Reasons for the observed chain length threshold and consequences from these results for protein folding are discussed.

cond-mat.stat-mech↗

arXiv2005

Violating conformal invariance: Two-dimensional clusters grafted to wedges, cones, and branch points of Riemann surfaces

We present simulations of 2-d site animals on square and triangular lattices in non-trivial geomeLattice animals are one of the few critical models in statistical mechanics violating conformal invariance. We present here simulations of 2-d site animals on square and triangular lattices in non-trivial geometries. The simulations are done with the newly developed PERM algorithm which gives very precise estimates of the partition sum, yielding precise values for the entropic exponent $θ$ ($Z_N \sim μ^N N^{-θ}$). In particular, we studied animals grafted to the tips of wedges with a wide range of angles $α$, to the tips of cones (wedges with the sides glued together), and to branching points of Riemann surfaces. The latter can either have $k$ sheets and no boundary, generalizing in this way cones to angles $α> 360$ degrees, or can have boundaries, generalizing wedges. We find conformal invariance behavior, $θ\sim 1/α$, only for small angles ($α\ll 2π$), while $θ\approx const -α/2π$ for $α\gg 2π$. These scalings hold both for wedges and cones. A heuristic (non-conformal) argument for the behavior at large $α$ is given, and comparison is made with critical percolation.

cond-mat.stat-mech↗

arXiv2004

Simulations of lattice animals and trees

The scaling behaviour of randomly branched polymers in a good solvent is studied in two to nine dimensions, using as microscopic models lattice animals and lattice trees on simple hypercubic lattices. As a stochastic sampling method we use a biased sequential sampling algorithm with re-sampling, similar to the pruned-enriched Rosenbluth method (PERM) used extensively for linear polymers. Essentially we start simulating percolation clusters (either site or bond), re-weigh them according to the animal (tree) ensemble, and prune or branch the further growth according to a heuristic fitness function. In contrast to previous applications of PERM, this fitness function is {\it not} the weight with which the actual configuration would contribute to the partition sum, but is closely related to it. We obtain high statistics of animals with up to several thousand sites in all dimension 2 <= d <= 9. In addition to the partition sum (number of different animals) we estimate gyration radii and numbers of perimeter sites. In all dimensions we verify the Parisi-Sourlas prediction, and we verify all exactly known critical exponents in dimensions 2, 3, 4, and >= 8. In addition, we present the hitherto most precise estimates for growth constants in d >= 3. For clusters with one site attached to an attractive surface, we verify the superuniversality of the cross-over exponent at the adsorption transition predicted by Janssen and Lyssy. Finally, we discuss the collapse of animals and trees, arguing that our present version of the algorithm is also efficient for some of the models studied in this context, but showing that it is {\it not} very efficient for the `classical' model for collapsing animals.

cond-mat.stat-mech↗

arXiv2004

Extracting Phases from Aperiodic Signals

We demonstrate by means of a simple example that the arbitrariness of defining a phase from an aperiodic signal is not just an academic problem, but is more serious and fundamental. Decomposition of the signal into components with positive phase velocities is proposed as an old solution to this new problem.

cond-mat.dis-nn↗

arXiv2004

Scaling of Star Polymers with one to 80 Arms

We present large statistics simulations of 3-dimensional star polymers with up to $f=80$ arms, and with up to 4000 monomers per arm for small values of $f$. They were done for the Domb-Joyce model on the simple cubic lattice. This is a model with soft core exclusion which allows multiple occupancy of sites but punishes each same-site pair of monomers with a Boltzmann factor $v<1$. We use this to allow all arms to be attached at the central site, and we use the `magic' value $v=0.6$ to minimize corrections to scaling. The simulations are made with a very efficient chain growth algorithm with resampling, PERM, modified to allow simultaneous growth of all arms. This allows us to measure not only the swelling (as observed from the center-to-end distances), but also the partition sum. The latter gives very precise estimates of the critical exponents $γ_f$. For completeness we made also extensive simulations of linear (unbranched) polymers which give the best estimates for the exponent $γ$.

cond-mat.soft↗

arXiv2003

Growth Algorithms for Lattice Heteropolymers at Low Temperatures

Two improved versions of the pruned-enriched-Rosenbluth method (PERM) are proposed and tested on simple models of lattice heteropolymers. Both are found to outperform not only the previous version of PERM, but also all other stochastic algorithms which have been employed on this problem, except for the core directed chain growth method (CG) of Beutler & Dill. In nearly all test cases they are faster in finding low-energy states, and in many cases they found new lowest energy states missed in previous papers. The CG method is superior to our method in some cases, but less efficient in others. On the other hand, the CG method uses heavily heuristics based on presumptions about the hydrophobic core and does not give thermodynamic properties, while the present method is a fully blind general purpose algorithm giving correct Boltzmann-Gibbs weights, and can be applied in principle to any stochastic sampling problem.

cond-mat.stat-mech↗

arXiv2003

A Growth-based Optimization Algorithm for Lattice Heteropolymers

An improved version of the pruned-enriched-Rosenbluth method (PERM) is proposed and tested on finding lowest energy states in simple models of lattice heteropolymers. It is found to outperform not only the previous version of PERM, but also all other fully blind general purpose stochastic algorithms which have been employed on this problem. In many cases it found new lowest energy states missed in previous papers. Limitations are discussed.

cond-mat.stat-mech↗

arXiv2002

Heat Conduction and Entropy Production in a One-Dimensional Hard-Particle Gas

We present large scale simulations for a one-dimensional chain of hard-point particles with alternating masses. We correct several claims in the recent literature based on much smaller simulations. Both for boundary conditions with two heat baths at different temperatures at both ends and from heat current autocorrelations in equilibrium we find heat conductivities kappa to diverge with the number N of particles. These depended very strongly on the mass ratios, and extrapolation to N -> infty resp. t -> infty is difficult due to very large finite-size and finite-time corrections. Nevertheless, our data seem compatible with a universal power law kappa ~ N^alpha with alpha approx 0.33. This suggests a relation to the Kardar-Parisi-Zhang model. We finally show that the hard-point gas with periodic boundary conditions is not chaotic in the usual sense and discuss why the system, when kept out of equilibrium, leads nevertheless to energy dissipation and entropy production.

nlin.CD↗

arXiv2002

Spin Dephasing in the Extended Strong Collision Approximation

For Markovian dynamics of field fluctuations we present here an extended strong collision approximation, thereby putting our previous strong collision approach (Phys. Rev. Lett. 83 (1999) 4215) into a systematic framework. Our new approach provides expressions for the free induction and spin echo magnetization decays that may be solved analytically or at least numerically. It is tested for the generic cases of dephasing due to an Anderson-Weiss process and due to restricted diffusion in a linear field gradient.

cond-mat.stat-mech↗

arXiv1999

Theory of Coherent and Incoherent Nuclear Spin-Dephasing in the Heart

We present an analytical theory of susceptibility induced nuclear spin dephasing in the capillary network of myocardium. Using a strong collision approach, equations are obtained for the relaxation rate of the free induction and the spin echo decay. Simulation and experimental data are well predicted by the theory. Since paramagnetic deoxyhemoglobin as the origin of nuclear spin dephasing has a higher tissue concentration in myocardium supplied by a stenotic, i. e. significantly narrowed, coronary artery, spin dephasing might serve as a diagnostic tool. Our approach can be modified for capillary networks in other tissues than myocardium and may be applied in material science.

cond-mat.soft↗

arXiv1998

A New Monte Carlo Algorithm for Protein Folding

We demonstrate that the recently proposed pruned-enriched Rosenbluth method (P. Grassberger, Phys. Rev. E 56 (1997) 3682) leads to extremely efficient algorithms for the folding of simple model proteins. We test them on several models for lattice heteropolymers, and compare to published Monte Carlo studies. In all cases our algorithms are faster than all previous ones, and in several cases we find new minimal energy states. In addition to ground states, our algorithms give estimates for the partition sum at finite temperatures.

cond-mat.stat-mech↗

arXiv1997

Testing a new Monte Carlo Algorithm for Protein Folding

We demonstrate that the recently proposed pruned-enriched Rosenbluth method PERM (P. Grassberger, Phys. Rev. E, in press (1997)) leads to extremely efficient algorithms for the folding of simple model proteins. We test it on several models for lattice heteropolymers, and compare to published Monte Carlo studies of the properties of particular sequences. In all cases our method is faster than the previous ones, and in several cases we find new minimal energy states. In addition to producing more reliable candidates for ground states, our method gives detailed information about the thermal spectrum and, thus, allows to analyze static aspects of the folding behavior of arbitrary sequences.

cond-mat.stat-mech↗

arXiv1996

Finite size scaling in neural networks

We demonstrate that the fraction of pattern sets that can be stored in single- and hidden-layer perceptrons exhibits finite size scaling. This feature allows to estimate the critical storage capacity α_c from simulations of relatively small systems. We illustrate this approach by determining α_c, together with the finite size scaling exponent ν, for storing Gaussian patterns in committee and parity machines with binary couplings and up to K=5 hidden units.

cond-mat.dis-nn↗