arXiv subjects

Gerard T. Barkema

Publications and source records attributed to Gerard T. Barkema.

At least 37 records · Page 2Linked to original sources

arXiv2016

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. At low Wi, a polymer segment shorter than the persistence length does indeed tumble as a rigid rod. However, for higher Wi the chain does not tumble as a rigid rod, even if the polymer segment is shorter than the persistence length. In particular, from time to time the polymer segment may assume a buckled form, a phenomenon commonly known as Euler buckling. Using a bead-spring Hamiltonian model for extensible dsDNA fragments, we first analyze Euler buckling in terms of the oriented deterministic state (ODS), which is obtained as the steady-state solution of the dynamical equations by turning off the stochastic (thermal) forces at a fixed orientation of the chain. The ODS exhibits symmetry breaking at a critical Weissenberg number Wi$_{\text c}$, analogous to a pitchfork bifurcation in dynamical systems. We then follow up the analysis with simulations and demonstrate symmetry breaking in computer experiments, characterized by a unimodal to bimodal transformation of the probability distribution of the second Rouse mode with increasing Wi. Our simulations reveal that shear can cause strong deformation for a chain that is shorter than its persistence length, similar to recent experimental observations.

cond-mat.soft↗

arXiv2015

Strong long-range relaxations of structural defects in graphene simulated using a new semi-empirical potential

We present a new semi-empirical potential for graphene, which includes also an out-of-plane energy term. This novel potential is developed from density functional theory (DFT) calculations for small numbers of atoms, and can be used for configurations with millions of atoms. Our simulations show that buckling caused by typical defects such as the Stone-Wales (SW) defect extends to hundreds of nanometers. Surprisingly, this long-range relaxation lowers the defect formation energy dramatically - by a factor of $2$ or $3$ - implying that previously published DFT-calculated defect formation energies suffer from large systematic errors. We also show the applicability of the novel potential to other long-range defects including line dislocations and grain boundaries, all of which exhibit pronounced out-of-plane relaxations. We show that the energy as a function of dislocation separation diverges logarithmically for flat graphene, but converges to a constant for free standing buckled graphene. A potential in which the atoms are attracted to the 2D plane restores the logarithmic behaviour of the energy. Future simulations employing this potential will elucidate the influence of the typical long-range buckling and rippling on the physical properties of graphene.

cond-mat.mtrl-sci↗

arXiv2015

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 the specific peaks at high and low frequencies.These can be used as an independent probe of the defect density. In particular, we consider grain boundaries made of pentagon-heptagon pairs, and show that they lead to a shift of the characteristic vibrational D mode towards higher frequency; this distinguishes these line defects from the Stone-Wales point defects, which do not lead to such a shift. Our findings may be instrumental for the detection of structural lattice defects using experimental techniques that can directly measure VDOS, such as inelastic electron tunneling and inelastic neutron spectroscopy.

cond-mat.mtrl-sci↗

arXiv2015

Efficient simulation of semiflexible polymers

Using a recently developed bead-spring model for semiflexible polymers that takes into account their natural extensibility, we report an efficient algorithm to simulate the dynamics for polymers like double-stranded DNA (dsDNA) in the absence of hydrodynamic interactions. The dsDNA is modelled with one bead-spring element per basepair, and the polymer dynamics is described by the Langevin equation. The key to efficiency is that we describe the equations of motion for the polymer in terms of the amplitudes of the polymer's fluctuation modes, as opposed to the use of the physical positions of the beads. We show that, within an accuracy tolerance level of $5\%$ of several key observables, the model allows for single Langevin time steps of $\approx1.6$, 8, 16 and 16 ps for a dsDNA model-chain consisting of 64, 128, 256 and 512 basepairs (i.e., chains of 0.55, 1.11, 2.24 and 4.48 persistence lengths) respectively. Correspondingly, in one hour, a standard desktop computer can simulate 0.23, 0.56, 0.56 and 0.26 ms of these dsDNA chains respectively. We compare our results to those obtained from other methods, in particular, the (inextensible discretised) WLC model. Importantly, we demonstrate that at the same level of discretisation, i.e., when each discretisation element is one basepair long, our algorithm gains about 5-6 orders of magnitude in the size of time steps over the inextensible WLC model. Further, we show that our model can be mapped one-on-one to a discretised version of the extensible WLC model; implying that the speed-up we achieve in our model must hold equally well for the latter. We also demonstrate the use of the method by simulating efficiently the tumbling behaviour of a dsDNA segment in a shear flow.

cond-mat.soft↗

arXiv2014

Semiflexible Polymer Dynamics with a Bead-Spring Model

We study the dynamical properties of semiflexible polymers with a recently introduced bead-spring model. We focus on double-stranded DNA. The two parameters of the model, $T^*$ and $ν$, are chosen to match its experimental force-extension curve. The bead-spring Hamiltonian is approximated in the first order by the Hessian that is quadratic in the bead positions. The eigenmodels of the Hessian provide the longitudinal (stretching) and transverse (bending) eigenmodes of the polymer, and the corresponding eigenvalues match well with the established phenomenology of semiflexible polymers. Using the longitudinal and transverse eigenmodes, we obtain analytical expressions of (i) the autocorrelation function of the end-to-end vector, (ii) the autocorrelation function of a bond (i.e., a spring, or a tangent) vector at the middle of the chain, and (iii) the mean-square displacement of a tagged bead in the middle of the chain, as sum over the contributions from the modes. We also perform simulations with the full dynamics of the model. The simulations yield numerical values of the correlation functions (i-iii) that agree very well with the analytical expressions for the linearized dynamics. We also study the mean-square displacement of the longitudinal component of the end-to-end vector that showcases strong nonlinear effects in the polymer dynamics, and we identify at least an effective $t^{7/8}$ power-law regime in its time-dependence. Nevertheless, in comparison to the full mean-square displacement of the end-to-end vector the nonlinear effects remain small at all times --- it is in this sense we state that our results demonstrate that the linearized dynamics suffices for dsDNA fragments that are shorter than or comparable to the persistence length. Our results are consistent with those of the wormlike chain (WLC) model, the commonly used descriptive tool of semiflexible polymers.

cond-mat.soft↗

arXiv2013

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. It is now possible to observe single-molecule polymer dynamics during the motion through channels with unprecedented spatial and temporal resolution. These striking experimental studies have stimulated many theoretical developments. In this short theory-experiment review, we discuss recent progress in this field with a strong focus on non-equilibrium aspects of polymer dynamics during the translocation process.

cond-mat.soft↗

arXiv2013

Universality of the triplet contact process with diffusion

The one-dimensional triplet contact process with diffusion (TCPD) model has been studied using fast multispin GPU Monte Carlo simulations. In particular, the particle density ρand the density of pairs of neighboring particles ρ_p have been monitored as a function of time. Mean field predictions for the time evolution of these observables in the critical point are ρ\sim t^{-δ} and ρ_p\sim t^{-δ_p} with δ=1/3 and δ_p=2/3. We observe that in the vicinity of the critical point of the model, the ratio ρ_p/ρtends to a constant, which shows that the one-dimensional TCPD model is not described by mean field behavior. Furthermore, our long simulations allow us to conclude that the mean field prediction of the exponent $δ$ is almost certainly not correct either. Since the crossover to the critical regime is extremely slow for the TCPD model, we are unable to pinpoint a precise value for δ, though we find as an upper bound δ< 0.32.

cond-mat.stat-mech↗

arXiv2013

Dynamical Eigenmodes of a Polymerized Membrane

We study the bead-spring model for a polymerized phantom membrane in the overdamped limit, which is the two-dimensional generalization of the well-known Rouse model for polymers. We derive the {\it exact} eigenmodes of the membrane dynamics (the "Rouse modes"). This allows us to obtain exact analytical expressions for virtually any equilibrium or dynamical quantity for the membrane. As examples we determine the radius of gyration, the mean square displacement of a tagged bead, and the autocorrelation function of the difference vector between two tagged beads. Interestingly, even in the presence of tensile forces of any magnitude the Rouse modes remain the exact eigenmodes for the membrane. With stronger forces the membrane becomes essentially flat, and does not get the opportunity to intersect itself; in such a situation our analysis provides a useful and exactly soluble approach to the dynamics for a realistic model flat membrane under tension.

cond-mat.soft↗

arXiv2013

Dynamical Eigenmodes of Star and Tadpole Polymers

The dynamics of phantom bead-spring chains with the topology of a symmetric star with $f$ arms and tadpoles ($f=3$, a special case) is studied, in the overdamped limit. In the simplified case where the hydrodynamic radius of the central monomer is $f$ times as heavy as the other beads, we determine their dynamical eigenmodes exactly, along the lines of the Rouse modes for linear bead-spring chains. These eigenmodes allow full analytical calculations of virtually any dynamical quantity. As examples we determine the radius of gyration, the mean square displacement of a tagged monomer, and, for star polymers, the autocorrelation function of the vector that spans from the center of the star to a bead on one of the arms.

cond-mat.soft↗

arXiv2012

A model for the dynamics of extensible semiflexible polymers

We present a model for semiflexible polymers in Hamiltonian formulation which interpolates between a Rouse chain and worm-like chain. Both models are realized as limits for the parameters. The model parameters can also be chosen to match the experimental force-extension curve for double-stranded DNA. Near the ground state of the Hamiltonian, the eigenvalues for the longitudinal (stretching) and the transversal (bending) modes of a chain with N springs, indexed by p, scale as lambda_lp ~ (p/N)^2 and lambda_tp ~ p^2(p-1)^2/N^4 respectively for small p. We also show that the associated decay times tau_p ~ (N/p)^4 will not be observed if they exceed the orientational time scale tau_r ~ N^3 for an equally-long rigid rod, as the driven decay is then washed out by diffusive motion.

cond-mat.soft↗

arXiv2012

SAWdoubler: a program for counting self-avoiding walks

This article presents SAWdoubler, a package for counting the total number Z(N) of self-avoiding walks (SAWs) on a regular lattice by the length-doubling method, of which the basic concept has been published previously by us. We discuss an algorithm for the creation of all SAWs of length N, efficient storage of these SAWs in a tree data structure, and an algorithm for the computation of correction terms to the count Z(2N) for SAWs of double length, removing all combinations of two intersecting single-length SAWs. We present an efficient numbering of the lattice sites that enables exploitation of symmetry and leads to a smaller tree data structure; this numbering is by increasing Euclidean distance from the origin of the lattice. Furthermore, we show how the computation can be parallelised by distributing the iterations of the main loop of the algorithm over the cores of a multicore architecture. Experimental results on the 3D cubic lattice demonstrate that Z(28) can be computed on a dual-core PC in only 1 hour and 40 minutes, with a speedup of 1.56 compared to the single-core computation and with a gain by using symmetry of a factor of 26. We present results for memory use and show how the computation is made to fit in 4 Gbyte RAM. It is easy to extend the SAWdoubler software to other lattices; it is publicly available under the GNU LGPL license.

cond-mat.stat-mech↗

arXiv2011

Saturation of front propagation in a reaction-diffusion process describing plasma damage in porous low-k materials

We propose a three-component reaction-diffusion system yielding an asymptotic logarithmic time-dependence for a moving interface. This is naturally related to a Stefan-problem for which both one-sided Dirichlet-type and von Neumann-type boundary conditions are considered. We integrate the dependence of the interface motion on diffusion and reaction parameters and we observe a change from transport behavior and interface motion \sim t^1/2 to logarithmic behavior \sim ln t as a function of time. We apply our theoretical findings to the propagation of carbon depletion in porous dielectrics exposed to a low temperature plasma. This diffusion saturation is reached after about 1 minute in typical experimental situations of plasma damage in microelectronic fabrication. We predict the general dependencies on porosity and reaction rates.

cond-mat.stat-mech↗

arXiv2011

Exact enumeration of self-avoiding walks

A prototypical problem on which techniques for exact enumeration are tested and compared is the enumeration of self-avoiding walks. Here, we show an advance in the methodology of enumeration, making the process thousands or millions of times faster. This allowed us to enumerate self-avoiding walks on the simple cubic lattice up to a length of 36 steps.

math-ph↗

arXiv2011

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's 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 $(p/N)^2A(t)$, in which $p$ is the mode number, $N$ is the polymer length and $A(t)$ is a single function shared by all modes. In time, the quantity $A(t)$ causes an exponential decay for the mode amplitude correlation functions for times $<1$; a stretched exponential with an exponent 1/2 between times 1 and $τ_R\sim N^2$, the time-scale for diffusion of tagged reptons along the contour of the polymer; and again an exponential decay for times $t>τ_R$. Having assumed statistical independence and the validity of a single function $A(t)$ for all modes, we compute the temporal behavior of three structural quantities: the vectorial distance between the positions of the middle monomer and the center-of-mass, the end-to-end vector, and the vector connecting two nearby reptons around the middle of the polymer. Furthermore, we study the mean-squared displacement of the center-of-mass and the middle repton, and their relation with the temporal behavior of the modes.

cond-mat.soft↗

arXiv2010

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 c_s and c_f, and reveal a non-trivial relationship between the mechanical behavior and the relative fraction of stiff polymer: when there are few stiff polymers, non-percolated 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.

q-bio.BM↗

arXiv2010

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 $ρ_m = 1 - /m$ scales asymptotically for large $m$ as $ρ_m=ρ_\infty(1-θ/m + ...)$, where $θ$ is the polymer entropic exponent, so that $θ$ can be determined from the analysis of $ρ_m$. We perform simulations for elastic lattice polymer loops with various sizes and knots, in which we measure $ρ_m$. 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.

cond-mat.stat-mech↗

arXiv2010

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.e., the polymer is a Rouse polymer), through a narrow pore. Earlier studies using the BFM concluded that the pore-blockade time scales with polymer length as $τ_d \sim N^β$, with $β=1+2ν$, whereas some recent studies with different polymer models produce results consistent with $β=2+ν$, originally predicted by us. Here $ν$ is the Flory exponent of the polymer; $ν=0.75$ in 2D. In this paper we show that for the BFM if the simulations are extended to longer polymers, the purported scaling $τ_d \sim N^{1+2ν}$ ceases to hold. We characterize the finite-size effects, and study the mobility of individual monomers in the BFM. In particular, we find that in the BFM, in the vicinity of the pore the individual monomeric mobilities are heavily suppressed in the direction perpendicular to the membrane. After a modification of the BFM which counters this suppression (but possibly introduces other artifacts in the dynamics), the apparent exponent $β$ increases significantly. Our conclusion is that BFM simulations do not rule out our theoretical prediction for unbiased translocation, namely $β=2+ν$.

cond-mat.soft↗

arXiv2009

Linear model for fast background subtraction in oligonucleotide microarrays

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. 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. The model incorporates two effects: 1) Correlated intensities between neighboring features in the chip and 2) sequence-dependent affinities for non-specific hybridization fitted by an extended nearest-neighbor model. The algorithm has been tested on 360 GeneChips from publicly available data of recent expression experiments. The algorithm is fast and accurate. Strong correlations between the fitted values for different experiments as well as between the free-energy parameters and their counterparts in aqueous solution indicate that the model captures a significant part of the underlying physical chemistry.

q-bio.QM↗