arXiv subjects

C. Vanderzande

Publications and source records attributed to C. Vanderzande.

11 recordsLinked to original sources

arXiv2018

The effect of memory and active forces on transition path times distributions

An analytical expression is derived for the transition path time distribution for a one-dimensional particle crossing of a parabolic barrier. Two cases are analyzed: (i) A non-Markovian process described by a generalized Langevin equation with a power-law memory kernel and (ii) a Markovian process with a noise violating the fluctuation-dissipation theorem, modeling the stochastic dynamics generated by active forces. In the case (i) we show that the anomalous dynamics strongly affecting the short time behavior of the distributions, but this happens only for very rare events not influencing the overall statistics. At long times the decay is always exponential, in disagreement with a recent study suggesting a stretched exponential decay. In the case (ii) the active forces do not substantially modify the short time behavior of the distribution, but lead to an overall decrease of the average transition path time. These findings offer some novel insights, useful for the analysis of experiments of transition path times in (bio)molecular systems.

cond-mat.stat-mech↗

arXiv2006

Criticality on networks with topology-dependent interactions

Weighted scale-free networks with topology-dependent interactions are studied. It is shown that the possible universality classes of critical behaviour, which are known to depend on topology, can also be explored by tuning the form of the interactions at fixed topology. For a model of opinion formation, simple mean field and scaling arguments show that a mapping $γ'=(γ-μ)/(1-μ)$ describes how a shift of the standard exponent $γ$ of the degree distribution can absorb the effect of degree-dependent pair interactions $J_{ij} \propto (k_ik_j)^{-μ}$, where $k_i$ stands for the degree of vertex $i$. This prediction is verified by extensive numerical investigations using the cavity method and Monte Carlo simulations. The critical temperature of the model is obtained through the Bethe-Peierls approximation and with the replica technique. The mapping can be extended to nonequilibrium models such as those describing the spreading of a disease on a network.

cond-mat.stat-mech↗

arXiv2005

Trading interactions for topology in scale-free networks

Scale-free networks with topology-dependent interactions are studied. It is shown that the universality classes of critical behavior, which conventionally depend only on topology, can also be explored by tuning the interactions. A mapping, $γ' = (γ- μ)/(1-μ)$, describes how a shift of the standard exponent $γ$ of the degree distribution $P(q)$ can absorb the effect of degree-dependent pair interactions $J_{ij} \propto (q_iq_j)^{-μ}$. Replica technique, cavity method and Monte Carlo simulation support the physical picture suggested by Landau theory for the critical exponents and by the Bethe-Peierls approximation for the critical temperature. The equivalence of topology and interaction holds for equilibrium and non-equilibrium systems, and is illustrated with interdisciplinary applications.

cond-mat.dis-nn↗

arXiv2003

Statistical mechanics of RNA folding: a lattice approach

We propose a lattice model for RNA based on a self-interacting two-tolerant trail. Self-avoidance and elements of tertiary structure are taken into account. We investigate a simple version of the model in which the native state of RNA consists of just one hairpin. Using exact arguments and Monte Carlo simulations we determine the phase diagram for this case. We show that the denaturation transition is first order and can either occur directly or through an intermediate molten phase.

cond-mat.soft↗

arXiv2002

The polymer theta-point as a knot delocalisation transition

We study numerically the tightness of prime flat knots in a model of self-attracting polymers with excluded volume. We find that these knots are localised in the high temperature swollen regime, but become delocalised in the low temperature globular phase. Precisely at the collapse transition, the knots are weakly localised. Some of our results can be interpreted in terms of the theory of polymer networks, which allows to conjecture exact exponents for the knot length probability distributions.

cond-mat.soft↗

arXiv2001

Dissipative Abelian Sandpiles and Random Walks

We show that the dissipative Abelian sandpile on a graph L can be related to a random walk on a graph which consists of L extended with a trapping site. From this relation it can be shown, using exact results and a scaling assumption, that the dissipative sandpiles' correlation length exponent νalways equals 1/d_w, where d_w is the fractal dimension of the random walker. This leads to a new understanding of the known results that ν=1/2 on any Euclidean lattice. Our result is however more general and as an example we also present exact data for finite Sierpinski gaskets which fully confirm our predictions.

cond-mat.stat-mech↗

arXiv2000

Distribution of consecutive waves in the sandpile model on the Sierpinski gasket

The scaling properties of waves of topplings in the sandpile model on the Sierpinski gasket are investigated. The exponent describing the asymptotics of the distribution of last waves in an avalanche is found. Predictions for scaling exponents in the forward and backward conditional probabilites for two consecutive waves are given. All predictions were examined by numerical simulations and were found to be in reasonable agreement with the obtained data.

cond-mat.stat-mech↗

arXiv1999

Real space renormalisation for reaction-diffusion systems

The stationary state of stochastic processes such as reaction-diffusion systems can be related to the ground state of a suitably defined quantum Hamiltonian. Using this analogy, we investigate the applicability of a real space renormalisation group approach, originally developped for quantum spin systems, to interacting particle systems. We apply the technique to an exactly solvable reaction-diffusion system and to the contact process (both in $d=1$). In the former case, several exact results are recovered. For the contact process, surprisingly good estimates of critical parameters are obtained from a small-cell renormalisation.

cond-mat.stat-mech↗

arXiv1997

Sandpiles on the Sierpinski gasket

We perform extensive simulations of the sandpile model on a Sierpinski gasket. Critical exponents for waves and avalanches are determined. We extend the existing theory of waves to the present case. This leads to an exact value for the exponent $τ_w$ which describes the distribution of wave sizes: $τ_w = \ln{(9/5)}/\ln{3}$. Numerically, it is found that the number of waves in an avalanche is proportional to the number of distinct sites toppled in the avalanche. This leads to a conjecture for the exponent $τ$ that determines the distribution of avalanche sizes: $τ=1+τ_w = \ln{(27/5)}/\ln{3}$. Our predictions are in good agreement with the numerical results.

cond-mat.stat-mech↗

arXiv1995

1/f-noise in the Bak-Sneppen model

We calculate time correlation functions in the Bak-Sneppen model (Phys. Rev. Lett. {\bf 71} 4083 (1993)), a model showing self-organised criticality. For a random neighbour version of the model, analytical results are presented, while on a one dimensional lattice we give numerical results. The power spectrum of these correlation functions shows $1/f$- behaviour in both cases.

cond-mat↗

arXiv1995

Optimal self-avoiding paths in dilute random medium

By a new type of finite size scaling analysis on the square lattice, and by renormalization group calculations on hierarchical lattices we investigate the effects of dilution on optimal undirected self-avoiding paths in a random environment. The behaviour of the optimal paths remains the same as for directed paths in undiluted medium, as long as forbidden bonds are not exceeding the percolation threshold. Thus, overhanging configurations do not alter the standard self-affine directed polymer scaling regime, even above the directed threshold, when they become unavoidable. When dilution reaches the undirected threshold, the optimal path becomes fractal, with fractal dimension equal to $D_{\rm min}$, the dimension of the minimal length path on percolation cluster backbone. In this regime the optimal path energy fluctuation, $\overline{ΔE}$, can be ascribed entirely to minimal length fluctuations, and satisfies $\overline{ΔE} \propto L^ω$, with $ω=1.02 \pm 0.06$ in $2d$, $L$ being the Euclidean distance. Hierarchical lattice calculations confirm that $ω$ is also the exponent of the leading scaling correction to $\overline E \propto L^{D_{\rm min}}$. Upon approaching threshold, the probability, ${\cal R}$, that the optimal path does not stick entirely on the minimal length one, obeys ${\cal R} \sim \left( Δp\right) ^ρ$, with $ρ\sim 1.0 \pm 0.05$ on hierarchical lattices. Such behaviour could be characteristic of the crossover to fractal regime. Transfer matrix results on square lattice show that a similar full sticking does not occur for directed paths at the directed percolation threshold.

cond-mat↗