Dynamical critical behavior of the two-dimensional three-state Potts model.

We investigate the dynamical critical behavior of the two-dimensional three-state Potts model with single spin-flip dynamics in equilibrium. We focus on the mean-squared deviation of the magnetization M (MSD_{M}) as a function of time, as well as on the autocorrelation function of M. Our simulations reveal the existence of two crossover behaviors at times τ_{1}∼L^{z_{1}} and τ_{2}∼L^{z_{2}}, separating three dynamical regimes.

Domain Growth in Polycrystalline Graphene.

Graphene is a two-dimensional carbon allotrope which exhibits exceptional properties, making it highly suitable for a wide range of applications. Practical graphene fabrication often yields a polycrystalline structure with many inherent defects, which significantly influence its performance. In this study, we utilize a Monte Carlo approach based on the optimized Wooten, Winer and Weaire (WWW) algorithm to simulate the crystalline domain coarsening process of polycrystalline graphene.

Critical dynamical behavior of the Ising model.

We investigate the dynamical critical behavior of the two- and three-dimensional Ising models with Glauber dynamics in equilibrium. In contrast to the usual standing, we focus on the mean-squared deviation of the magnetization M, MSD_{M}, as a function of time, as well as on the autocorrelation function of M. These two functions are distinct but closely related.

Structural dynamics of polycrystalline graphene.

The exceptional properties of the two-dimensional material graphene make it attractive for multiple functional applications, whose large-area samples are typically polycrystalline. Here, we study the mechanical properties of graphene in computer simulations and connect these to the experimentally relevant mechanical properties. In particular, we study the fluctuations in the lateral dimensions of the periodic simulation cell.

Comparison of cluster algorithms for the bond-diluted Ising model.

Monte Carlo cluster algorithms are popular for their efficiency in studying the Ising model near its critical temperature. We might expect that this efficiency extends to the bond-diluted Ising model. We show, however, that this is not always the case by comparing how the correlation times τ_{w} and τ_{sw} of the Wolff and Swendsen-Wang cluster algorithms scale as a function of the system size L when applied to the two-dimensional bond-diluted Ising model.

Efficient Structural Relaxation of Polycrystalline Graphene Models.

Large samples of experimentally produced graphene are polycrystalline. For the study of this material, it helps to have realistic computer samples that are also polycrystalline. A common approach to produce such samples in computer simulations is based on the method of Wooten, Winer, and Weaire, originally introduced for the simulation of amorphous silicon.

Super slowing down in the bond-diluted Ising model.

In models in statistical physics, the dynamics often slows down tremendously near the critical point. Usually, the correlation time τ at the critical point increases with system size L in power-law fashion: τ∼L^{z}, which defines the critical dynamical exponent z. We show that this also holds for the two-dimensional bond-diluted Ising model in the regime p>p_{c}, where p is the parameter denoting the bond concentration, but with a dynamical critical exponent z(p) which shows a strong p dependence.

Approximate dynamical eigenmodes of the Ising model with local spin-exchange moves.

We establish that the Fourier modes of the magnetization serve as the dynamical eigenmodes for the two-dimensional Ising model at the critical temperature with local spin-exchange moves, i.e., Kawasaki dynamics.

Generalized Langevin equation formulation for anomalous diffusion in the Ising model at the critical temperature.

We consider the two- (2D) and three-dimensional (3D) Ising models on a square lattice at the critical temperature T_{c}, under Monte Carlo spin flip dynamics. The bulk magnetization and the magnetization of a tagged line in the 2D Ising model, and the bulk magnetization and the magnetization of a tagged plane in the 3D Ising model, exhibit anomalous diffusion. Specifically, their mean-square displacements increase as power laws in time, collectively denoted as ∼t^{c}, where c is the anomalous exponent.

Rupture of amorphous graphene via void formation.

Apart from its unique and exciting electronic properties, many sensor based applications of graphene are purely based on its mechanical and structural properties. Here, we report a numerical and analytical study of a void in amorphous (small domain polycrystalline) graphene, and we show that the energetics of the void is a balance between the line tension cost versus the increased area gain. Using the concepts of classical nucleation theory, we show that the critical radius of a void formed in amorphous graphene at constant pressure is simply the ratio of the line tension at the void and the applied pressure.

Benchmarking and refining probability-based models for nucleosome-DNA interaction.

Background: In investigations of nucleosome positioning preferences, a model that assigns an affinity to a given sequence is necessary to make predictions. One important class of models, which treats a nucleosome sequence as a Markov chain, has been applied with success when informed with experimentally measured nucleosomal sequence preferences.

Results: We find that we can also use such models as a fast approximative scheme for computationally expensive biophysical models, vastly increasing their reach.

Probing the shape of a graphene nanobubble.

Gas molecules trapped between graphene and various substrates in the form of bubbles are observed experimentally. The study of these bubbles is useful in determining the elastic and mechanical properties of graphene and adhesion energy between graphene and the substrate, and manipulating the electronic properties via strain engineering. In our numerical simulations, we use a simple description of the elastic potential and adhesion energy to show that for small gas bubbles (∼10 nm) the van der Waals pressure is in the order of 1 GPa.

Efficient simulation of semiflexible polymers with stiff bonds.

We investigate the simulation of stiff (extensible) and rigid (inextensible) semiflexible polymers in solution. In particular, we focus on polymers represented as chains of beads, interconnected by bonds with a low to zero extensibility, and significant persistence in the bond orientations along the chain, whose dynamical behavior is described by the Langevin equation. We review the derivation of the pseudopotential needed for rigid bonds.

Dynamics of a double-stranded DNA segment in a shear flow.

We study the dynamics of a double-stranded DNA (dsDNA) segment, as a semiflexible polymer, in a shear flow, the strength of which is customarily expressed in terms of the dimensionless Weissenberg number Wi. Polymer chains in shear flows are well known to undergo tumbling motion. When the chain lengths are much smaller than the persistence length, one expects a (semiflexible) chain to tumble as a rigid rod.

Probing Crystallinity of Graphene Samples via the Vibrational Density of States.

The purity of graphene samples is of crucial importance for their experimental and practical use. In this regard, the detection of the defects is of direct relevance. Here, we show that structural defects in graphene samples give rise to clear signals in the vibrational density of states (VDOS) at specific peaks at high and low frequencies.

DFT+U studies of Cu doping and p-type compensation in crystalline and amorphous ZnS.

Zinc sulfide is an excellent candidate for the development of a p-type transparent conducting material that has great demands in solar energy and optoelectronic applications. Doping with Cu is one potential way to make ZnS p-type while preserving its optical transparency for the solar spectrum; however, this is limited by the extremely low solubility of Cu in ZnS and charge compensation mechanisms that eliminate the p-type characteristics. These mechanisms are different in crystalline (c-ZnS) and amorphous structures (a-ZnS), leading to different tendencies of doping Cu in these two ZnS phases, as well as the feasibility to form the p-type material.

Through the eye of the needle: recent advances in understanding biopolymer translocation.

In recent years polymer translocation, i.e., transport of polymeric molecules through nanometer-sized pores and channels embedded in membranes, has witnessed strong advances.

On the stability of fractal globules.

The fractal globule, a self-similar compact polymer conformation where the chain is spatially segregated on all length scales, has been proposed to result from a sudden polymer collapse. This state has gained renewed interest as one of the prime candidates for the non-entangled states of DNA molecules inside cell nuclei. Here, we present Monte Carlo simulations of collapsing polymers.

Structural modes of a polymer in the repton model.

Using extensive computer simulations, the behavior of the structural modes-more precisely, the eigenmodes of a phantom Rouse polymer-are characterized for a polymer in the three-dimensional repton model and are used to study the polymer dynamics at time scales well before the tube renewal. Although these modes are not the eigenmodes for a polymer in the repton model, we show that numerically the modes maintain a high degree of statistical independence. The correlations in the mode amplitudes decay exponentially with (p∕N)(2)A(t), in which p is the mode number, N is the polymer length, and A(t) is a single function shared by all modes.

Rouse modes of self-avoiding flexible polymers.

Using a lattice-based Monte Carlo code for simulating self-avoiding flexible polymers in three dimensions in the absence of explicit hydrodynamics, we study their Rouse modes. For self-avoiding polymers, the Rouse modes are not expected to be statistically independent; nevertheless, we demonstrate that numerically these modes maintain a high degree of statistical independence. Based on high-precision simulation data we put forward an approximate analytical expression for the mode amplitude correlation functions for long polymers.

Simulations of two-dimensional unbiased polymer translocation using the bond fluctuation model.

We use the bond fluctuation model (BFM) to study the pore-blockade times of a translocating polymer of length N in two dimensions, in the absence of external forces on the polymer (i.e., unbiased translocation) and hydrodynamic interactions (i.

Linear model for fast background subtraction in oligonucleotide microarrays.

Background: One important preprocessing step in the analysis of microarray data is background subtraction. In high-density oligonucleotide arrays this is recognized as a crucial step for the global performance of the data analysis from raw intensities to expression values.

Results: We propose here an algorithm for background estimation based on a model in which the cost function is quadratic in a set of fitting parameters such that minimization can be performed through linear algebra.

Amplitude and frequency spectra of thermal fluctuations of a translocating RNA molecule.

Using a combination of theory and computer simulations, we study the translocation of an RNA molecule, pulled through a solid-state nanopore by an optical tweezer, as a method for determining its secondary structure. The resolution with which the elements of the secondary structure can be determined is limited by thermal fluctuations. We present a detailed study of these thermal fluctuations, including the frequency spectrum, and show that these rule out single-nucleotide resolution under the experimental conditions which we simulated.

Non-equilibrium dynamics of single polymer adsorption to solid surfaces.

The adsorption of polymers to surfaces is crucial for understanding many fundamental processes in nature. Recent experimental studies indicate that the adsorption dynamics is dominated by non-equilibrium effects. We investigate the adsorption of a single polymer of length N to a planar solid surface in the absence of hydrodynamic interactions.