Kardar-Parisi-Zhang universality class and the anchored Toom interface.

We revisit the anchored Toom interface and use Kardar-Parisi-Zhang scaling theory to argue that the interface fluctuations are governed by the Airy1 process with the role of space and time interchanged. The predictions, which contain no free parameter, are numerically well confirmed for space-time statistics in the stationary state. In particular, the spatial fluctuations of the interface computed numerically agree well with those given by the GOE edge distribution of Tracy and Widom [Commun. Math. Phys. 177, 727 (1996)].

Unwinding relaxation dynamics of polymers.

The relaxation dynamics of a polymer wound around a fixed obstacle constitutes a fundamental instance of polymer with twist and torque, and it is also of relevance for DNA denaturation dynamics. We investigate it by simulations and Langevin equation analysis. The latter predicts a relaxation time scaling as a power of the polymer length times a logarithmic correction related to the equilibrium fluctuations of the winding angle. The numerical data support this result and show that at short times the winding angle decreases as a power law. This is also in agreement with the Langevin equation provided a winding-dependent friction is used, suggesting that such reduced description of the system captures the basic features of the problem.

Control of structure formation in phase-separating systems.

In this paper, we study the evolution of phase-separating binary mixtures which are subjected to alternate cooling and heating cycles. An initially homogeneous mixture is rapidly quenched to a temperature T(1)T(c). These cycles are repeated to create a domain morphology with multiple length scales, i.e., the structure factor is characterized by multiple peaks. For phase separation in d = 2 systems, we present numerical and analytical results for the emergence and growth of this multiple-scale morphology.

Unwinding dynamics of double-stranded polymers.

We consider the unwinding of two lattice polymer strands of length N that are initially wound around each other in a double-helical conformation and evolve through Rouse dynamics. The problem relates to quickly bringing a double-stranded polymer well above its melting temperature, i.e., the binding interactions between the strands are neglected, and the strands separate from each other as it is entropically favorable for them to do so. The strands unwind by rotating around each other until they separate. We find that the process proceeds from the ends inward; intermediate conformations can be characterized by a tightly wound inner part, from which loose strands are sticking out, with length l∼t(0.39). The total time needed for the two strands to unwind scales as a power of N as τ(u)∼N(2.57±0.03). We present a theoretical argument, which suggests that during this unwinding process, these loose strands are far out of equilibrium.

Elastic lattice polymers.

We study a model of "elastic" lattice polymer in which a fixed number of monomers m is hosted by a self-avoiding walk with fluctuating length l . We show that the stored length density ρm≡1-/m scales asymptotically for large m as ρm=ρ∞(1-θ/m+…) , where θ is the polymer entropic exponent, so that θ can be determined from the analysis of ρm. We perform simulations for elastic lattice polymer loops with various sizes and knots, in which we measure ρm. The resulting estimates support the hypothesis that the exponent θ is determined only by the number of prime knots and not by their type. However, if knots are present, we observe strong corrections to scaling, which help to understand how an entropic competition between knots is affected by the finite length of the chain.

Limitations of a Fokker-Planck description of nucleation.

In most nucleation theories, the dynamics of nucleation is characterized by the evolution in time of the mass of droplets, and this time evolution is described as a combination of drift and diffusion. This assumes that the mass fluctations are described by a Markovian, i.e., memoryless, stochastic process. This paper presents a method to assess in how far this assumption of Markovianity is valid. The method is employed in nucleation studies in a two-dimensional Ising model at temperature T=0.88T(c), both with spin flip dynamics and with local spin exchange dynamics. In the first case, it shows that the evolution of droplet masses might be effectively described by a Markov process on large time scales. In the latter case, however, the dynamics are far from Markovian. We argue that this is due to the presence of a locally conserved quantity.

Semiflexible filamentous composites.

Inspired by the ubiquity of composite filamentous networks in nature, we investigate models of biopolymer networks that consist of interconnected floppy and stiff filaments. Numerical simulations carried out in three dimensions allow us to explore the microscopic partitioning of stresses and strains between the stiff and floppy fractions cs and cf and reveal a nontrivial relationship between the mechanical behavior and the relative fraction of stiff polymer: when there are few stiff polymers, nonpercolated stiff "inclusions" are protected from large deformations by an encompassing floppy matrix, while at higher fractions of stiff material the stiff network is independently percolated and dominates the mechanical response.

Simulations of color development in tinted paints.

Monte Carlo simulations have been used to investigate how several thermodynamic and kinetic factors affect the distribution of pigments, when a water-based pigment dispersion is added to a solvent-borne paint. Our model contains three types of lattice particles: water, pigment and organic solvent, with short-ranged interactions. These particles move through biased diffusion, with a species-dependent mobility. Moreover, to mimic the crosslinking of the resin, the mobility of the solvent particles decreases in time. Also, the water of the pigment dispersion evaporates slowly. First, we study which conditions yield the desired equilibrium phase behavior, with homogeneously distributed pigment. Next, we study how kinetics can prevent the system to reach equilibrium. We present examples in which these kinetic processes prevent dispersion in spite of favorable equilibrium conditions, as well as examples in which a homogeneous distribution is reached against unfavorable equilibrium conditions.

Frequency-dependent stiffening of semiflexible networks: a dynamical nonaffine to affine transition.

By combining the force-extension relation of single semiflexible polymers with a Langevin equation to capture the dissipative dynamics of chains moving through a viscous medium we study the dynamical response of cross-linked biopolymer materials. We find that at low frequencies the network deformations are highly nonaffine, and show a low plateau in the modulus. At higher frequencies, this nonaffinity decreases while the elastic modulus increases. With increasing frequency, more and more nonaffine network relaxation modes are suppressed, resulting in a stiffening. This effect is fundamentally different from the high-frequency stiffening due to the single-filament relaxation modes [F. Gittes and F. C. MacKintosh, Phys. Rev. E 58, R1241 (1998)], not only in terms of its mechanism but also in its resultant scaling: G'(ω) ∼ ω(α) with α > 3/4. This may determine nonlinear material properties at low, physiologically relevant frequencies.

Non-Markovian dynamics of clusters during nucleation.

Most theories of homogeneous nucleation are based on a Fokker-Planck-like description of the behavior of the mass of clusters. Here we will show that these approaches are incomplete for a large class of nucleating systems, as they assume the effective dynamics of the clusters to be Markovian, i.e., memoryless. We characterize these non-Markovian dynamics and show how this influences the dynamics of clusters during nucleation. Our results are validated by simulations of a three-dimensional Ising model with locally conserved magnetization.

Monte Carlo study of multiply crosslinked semiflexible polymer networks.

We present a method to generate realistic, three-dimensional networks of crosslinked semiflexible polymers. The free energy of these networks is obtained from the force-extension characteristics of the individual polymers and their persistent directionality through the crosslinks. A Monte Carlo scheme is employed to obtain isotropic, homogeneous networks that minimize the free energy and for which all of the relevant parameters can be varied: the persistence length and the contour length as well as the crosslinking length may be chosen at will. We also provide an initial survey of the mechanical properties of our networks subjected to shear strains, showing them to display the expected nonlinear stiffening behavior. Also, a key role for nonaffinity and its relation to order in the network is uncovered.

Universality class of the pair contact process with diffusion.

The pair contact process with diffusion (PCPD) is studied with a standard Monte Carlo approach and with simulations at fixed densities. A standard analysis of the simulation results, based on the particle densities or on the pair densities, yields inconsistent estimates for the critical exponents. However, if a well-chosen linear combination of the particle and pair densities is used, leading corrections can be suppressed, and consistent estimates for the independent critical exponents delta=0.16(2) , beta=0.28(2) , and z=1.58 are obtained. Since these estimates are also consistent with their values in directed percolation (DP), we conclude that the PCPD falls in the same universality class as DP.

Modeling background intensity in DNA microarrays.

DNA microarrays are devices that are able, in principle, to detect and quantify the presence of specific nucleic acid sequences in complex biological mixtures. The measurement consists in detecting fluorescence signals from several spots on the microarray surface onto which different probe sequences are grafted. One of the problems of the data analysis is that the signal contains a noisy background component due to nonspecific binding. We present a physical model for background estimation in Affymetrix Genechips. It combines two different approaches. The first is based on the sequence composition, specifically its sequence-dependent hybridization affinity. The second is based on the strong correlation of intensities from locations which are the physical neighbors of a specific spot on the chip. Both effects are incorporated in a background estimator which contains 24 free parameters, fixed by minimization on a training data set. In all data analyzed the sequence-specific parameters, obtained by minimization, are found to strongly correlate with empirically determined stacking free energies for RNA-DNA hybridization in solution. Moreover, there is an overall agreement with experimental background data and we show that the physics-based model that we propose performs on average better than purely statistical approaches for background calculations. The model thus provides an interesting alternative method for background subtraction schemes in Affymetrix Genechips.

Unbiased computation of transition times by pathway recombination.

In many systems, the time scales of the microscopic dynamics and macroscopic dynamics of interest are separated by many orders of magnitude. Examples abound, for instance, nucleation, protein folding, and chemical reactions. For these systems, direct simulation of phase space trajectories does not efficiently determine most physical quantities of interest. The past decade has seen the advent of methods circumventing brute force simulation. For most dynamical quantities, these methods all share the drawback of systematical errors. We present a novel method for generating ensembles of phase space trajectories. By sampling small pieces of these trajectories in different phase space domains and piecing them together in a smart way using equilibrium properties, we obtain physical quantities such as transition times. This method does not have any systematical error and is very efficient; the computational effort to calculate the first passage time across a free energy barrier does not increase with the height of the barrier. The strength of the method is shown in the Ising model. Accurate measurements of nucleation times span almost ten orders of magnitude and reveal corrections to classical nucleation theory.

Physical-chemistry-based analysis of affymetrix microarray data.

We analyze publicly available data on Affymetrix microarray spike-in experiments on the human HGU133 chipset in which sequences are added in solution at known concentrations. The spike-in set contains sequences of bacterial, human, and artificial origin. Our analysis is based on a recently introduced molecular-based model (Carlon, E.; Heim, T. Physica A 2006, 362, 433) that takes into account both probe-target hybridization and target-target partial hybridization in solution. The hybridization free energies are obtained from the nearest-neighbor model with experimentally determined parameters. The molecular-based model suggests a rescaling that should result in a "collapse" of the data at different concentrations into a single universal curve. We indeed find such a collapse, with the same parameters as obtained previously for the older HGU95 chip set. The quality of the collapse varies according to the probe set considered. Artificial sequences, chosen by Affymetrix to be as different as possible from any other human genome sequence, generally show a much better collapse and thus a better agreement with the model than all other sequences. This suggests that the observed deviations from the predicted collapse are related to the choice of probes or have a biological origin rather than being a problem with the proposed model.

Comment on "Solving the riddle of the bright mismatches: labeling and effective binding in oligonucleotide arrays".

In a recent paper [Phys. Rev. E 68, 011906 (2003)], Naef and Magnasco suggested that the "bright" mismatches observed in Affymetrix microarray experiments are caused by the fluorescent molecules used to label RNA target sequences, which would impede target-probe hybridization. Their conclusion is based on the observation of "unexpected" asymmetries in the affinities obtained by fitting microarray data from publicly available experiments. We point out here that the observed asymmetry is due to the inequivalence of RNA and DNA, and that the reported affinities are consistent with stacking free energies obtained from melting experiments of unlabeled nucleic acids in solution. The conclusion of Naef and Magnasco is therefore based on an unjustified assumption.

Spinodal decomposition via surface diffusion in polymer mixtures.

We present experimental results for spinodal decomposition in polymer mixtures of gelatin and dextran. The domain growth law is found to be consistent with t 1/4 growth over extended time regimes. Similar results are obtained from lattice simulations of a polymer mixture. This slow growth arises due to the suppression of the bulk mobility of polymers. In that case, spinodal decomposition is driven by the diffusive transport of material along domain interfaces, which gives rise to a t 1/4 growth law.

Phase separation driven by surface diffusion: a Monte Carlo study.

We propose a kinetic Ising model to study phase separation driven by surface diffusion. This model is referred to as Model S, and consists of the usual Kawasaki spin-exchange kinetics (Model B) in conjunction with a kinetic constraint. We use multispin coding techniques to develop fast algorithms for Monte Carlo simulations of Models B and S. We use these algorithms to study the late stages of pattern dynamics in these systems, and compare properties of the evolution morphologies, e.g., growth laws, domain distribution functions, and spatial and temporal correlation functions.

Nucleation times in the two-dimensional Ising model.

We consider the distribution of nucleation times in systems with Brownian type dynamics, as described by classical nucleation theory. This is studied for a prototype system: the two-dimensional Ising model with spin-flip dynamics in an external magnetic field. Direct simulation results for the nucleation times, spanning more than four orders of magnitude, are compared with theoretical predictions. In contrast to usual treatments we determine size-dependent droplet free energies and effective transition rates for growth and shrinkage directly from our simulations. The free energies so determined are well described by the classical Becker-Do ring expression, provided one uses an effective surface tension that exceeds the macroscopic surface tension by up to 20%. Within this framework there is good agreement between simulation results and theoretical predictions for the mean nucleation time. In addition we consider the short-time behavior of the nucleation probability after an initial quench into the metastable state. We present theoretical estimates and show that these too agree well with simulation results.

Activated sampling in complex materials at finite temperature: the properly obeying probability activation-relaxation technique.

While the dynamics of many complex systems is dominated by activated events, there are very few simulation methods that take advantage of this fact. Most of these procedures are restricted to relatively simple systems or, as with the activation-relaxation technique (ART), sample the conformation space efficiently at the cost of a correct thermodynamical description. We present here an extension of ART, the properly obeying probability ART (POP-ART), that obeys detailed balance and samples correctly the thermodynamic ensemble. Testing POP-ART on two model systems, a vacancy and an interstitial in crystalline silicon, we show that this method recovers the proper thermodynamical weights associated with the various accessible states and is significantly faster than molecular dynamics in the simulations of a vacancy below 700 K.