arXiv subjects

B. Schmittmann

Publications and source records attributed to B. Schmittmann.

At least 37 records · Page 2Linked to original sources

arXiv2006

Towards a model for protein production rates

In the process of translation, ribosomes read the genetic code on an mRNA and assemble the corresponding polypeptide chain. The ribosomes perform discrete directed motion which is well modeled by a totally asymmetric simple exclusion process (TASEP) with open boundaries. Using Monte Carlo simulations and a simple mean-field theory, we discuss the effect of one or two ``bottlenecks'' (i.e., slow codons) on the production rate of the final protein. Confirming and extending previous work by Chou and Lakatos, we find that the location and spacing of the slow codons can affect the production rate quite dramatically. In particular, we observe a novel ``edge'' effect, i.e., an interaction of a single slow codon with the system boundary. We focus in detail on ribosome density profiles and provide a simple explanation for the length scale which controls the range of these interactions.

q-bio.BM↗

arXiv2006

A possible classification of nonequilibrium steady states

We propose a general classification of nonequilibrium steady states in terms of their stationary probability distribution and the associated probability currents. The stationary probabilities can be represented graph-theoretically as directed labelled trees; closing a single loop in such a graph leads to a representation of probability currents. This classification allows us to identify all choices of transition rates, based on a master equation, which generate the same nonequilibrium steady state. We explore the implications of this freedom, e.g., for entropy production.

cond-mat.stat-mech↗

arXiv2006

Strongly anisotropic roughness in surfaces driven by an oblique particle flux

Using field theoretic renormalization, an MBE-type growth process with an obliquely incident influx of atoms is examined. The projection of the beam on the substrate plane selects a "parallel" direction, with rotational invariance restricted to the transverse directions. Depending on the behavior of an effective anisotropic surface tension, a line of second order transitions is identified, as well as a line of potentially first order transitions, joined by a multicritical point. Near the second order transitions and the multicritical point, the surface roughness is strongly anisotropic. Four different roughness exponents are introduced and computed, describing the surface in different directions, in real or momentum space. The results presented challenge an earlier study of the multicritical point.

cond-mat.stat-mech↗

arXiv2006

Novel surface universality classes with strong anisotropy

Using renormalized field theory, we examine the dynamics of a growing surface, driven by an obliquely incident particle beam. Its projection on the reference (substrate) plane selects a ``parallel'' direction, so that the evolution equation for the surface height becomes anisotropic. The phase diagram of the model is controlled by the properties of an effective anisotropic surface tension. Our renormalization group analysis suggests the existence of a line of continuous transitions and a line of (potentially) first-order transitions, which meet at a multicritical point. The full scaling behavior for the continuous line and the multicritical point is discussed in detail. Two novel universality classes for scale-invariant surface fluctuations are found.

cond-mat.stat-mech↗

arXiv2006

Cluster growth and dynamic scaling in a two-lane driven diffusive system

Using high precision Monte Carlo simulations and a mean-field theory, we explore coarsening phenomena in a simple driven diffusive system. The model is reminiscent of vehicular traffic on a two-lane ring road. At sufficiently high density, the system develops jams (clusters) which coarsen with time. A key parameter is the passing probability, $γ$. For small values of $γ$, the growing clusters display dynamic scaling, with a growth exponent of 2/3. For larger values of $γ$, the growth exponent must be adjusted, suggesting the ordered (jammed) state is not a genuine phase but rather a finite size effect.

cond-mat.stat-mech↗

arXiv2005

Spurious phase in a model for traffic on a bridge

We present high-precision Monte Carlo data for the phase diagram of a two-species driven diffusive system, reminiscent of traffic across a narrow bridge. Earlier studies reported two phases with broken symmetry; the existence of one of these has been the subject of some debate. We show that the disputed phase disappears for sufficiently large systems and/or sufficiently low bulk mobility.

cond-mat.stat-mech↗

arXiv2005

Exact dynamics of a reaction-diffusion model with spatially alternating rates

We present the exact solution for the full dynamics of a nonequilibrium spin chain and its dual reaction-diffusion model, for arbitrary initial conditions. The spin chain is driven out of equilibrium by coupling alternating spins to two thermal baths at different temperatures. In the reaction-diffusion model, this translates into spatially alternating rates for particle creation and annihilation, and even negative ``temperatures'' have a perfectly natural interpretation. Observables of interest include the magnetization, the particle density, and all correlation functions for both models. Two generic types of time-dependence are found: if both temperatures are positive, the magnetization, density and correlation functions decay exponentially to their steady-state values. In contrast, if one of the temperatures is negative, damped oscillations are observed in all quantities. They can be traced to a subtle competition of pair creation and annihilation on the two sublattices. We comment on the limitations of mean-field theory and propose an experimental realization of our model in certain conjugated polymers and linear chain compounds.

cond-mat.stat-mech↗

arXiv2005

Steady States of a Nonequilibrium Lattice Gas

We present a Monte Carlo study of a lattice gas driven out of equilibrium by a local hopping bias. Sites can be empty or occupied by one of two types of particles, which are distinguished by their response to the hopping bias. All particles interact via excluded volume and a nearest-neighbor attractive force. The main result is a phase diagram with three phases: a homogeneous phase, and two distinct ordered phases. Continuous boundaries separate the homogeneous phase from the ordered phases, and a first-order line separates the two ordered phases. The three lines merge in a nonequilibrium bicritical point.

cond-mat.stat-mech↗

arXiv2005

Will jams get worse when slow cars move over?

Motivated by an analogy with traffic, we simulate two species of particles (`vehicles'), moving stochastically in opposite directions on a two-lane ring road. Each species prefers one lane over the other, controlled by a parameter $0 \leq b \leq 1$ such that $b=0$ corresponds to random lane choice and $b=1$ to perfect `laning'. We find that the system displays one large cluster (`jam') whose size increases with $b$, contrary to intuition. Even more remarkably, the lane `charge' (a measure for the number of particles in their preferred lane) exhibits a region of negative response: even though vehicles experience a stronger preference for the `right' lane, more of them find themselves in the `wrong' one! For $b$ very close to 1, a sharp transition restores a homogeneous state. Various characteristics of the system are computed analytically, in good agreement with simulation data.

cond-mat.stat-mech↗

arXiv2005

Gas permeation through a polymer network

We study the diffusion of gas molecules through a two-dimensional network of polymers with the help of Monte Carlo simulations. The polymers are modeled as non-interacting random walks on the bonds of a two-dimensional square lattice, while the gas particles occupy the lattice cells. When a particle attempts to jump to a nearest-neighbor empty cell, it has to overcome an energy barrier which is determined by the number of polymer segments on the bond separating the two cells. We investigate the gas current $J$ as a function of the mean segment density $ρ$, the polymer length $\ell$ and the probability $q^{m}$ for hopping across $m$ segments. Whereas $J$ decreases monotonically with $ρ$ for fixed $\ell$, its behavior for fixed $ρ$ and increasing $\ell$ depends strongly on $q$. For small, non-zero $q$, $J$ appears to increase slowly with $\ell$. In contrast, for $q=0$, it is dominated by the underlying percolation problem and can be non-monotonic. We provide heuristic arguments to put these interesting phenomena into context.

cond-mat.soft↗

arXiv2004

Complete Solution of the Kinetics in a Far-from-equilibrium Ising Chain

The one-dimensional Ising model is easily generalized to a \textit{genuinely nonequilibrium} system by coupling alternating spins to two thermal baths at different temperatures. Here, we investigate the full time dependence of this system. In particular, we obtain the evolution of the magnetisation, starting with arbitrary initial conditions. For slightly less general initial conditions, we compute the time dependence of all correlation functions, and so, the probability distribution. Novel properties, such as oscillatory decays into the steady state, are presented. Finally, we comment on the relationship to a reaction-diffusion model with pair annihilation and creation.

cond-mat.stat-mech↗

arXiv2004

Driven Diffusive Systems: How Steady States Depend on Dynamics

In contrast to equilibrium systems, non-equilibrium steady states depend explicitly on the underlying dynamics. Using Monte Carlo simulations with Metropolis, Glauber and heat bath rates, we illustrate this expectation for an Ising lattice gas, driven far from equilibrium by an `electric' field. While heat bath and Glauber rates generate essentially identical data for structure factors and two-point correlations, Metropolis rates give noticeably weaker correlations, as if the `effective' temperature were higher in the latter case. We also measure energy histograms and define a simple ratio which is exactly known and closely related to the Boltzmann factor for the equilibrium case. For the driven system, the ratio probes a thermodynamic derivative which is found to be dependent on dynamics.

cond-mat.stat-mech↗

arXiv2003

A nonequilibrium lattice gas of two species: Monte Carlo investigations

We present the phase diagram of a far from equilibrium system, mapped by Monte Carlo simulation. The model is a lattice gas of two species of particles and holes. The two species are biased to hop in opposite directions and interact via excluded volume and nearest neighbor attractions. Three phases are found as a function of temperature and charge density.

cond-mat.stat-mech↗

arXiv2003

Watching a drunkard for ten nights: A study of distributions of variances

For any physical observable in statistical systems, the most frequently studied quantities are its average and standard deviation. Yet, its full distribution often carries extremely interesting information and can be invoked to put any surprising properties of the individual moments into perspective. As an example, we consider a problem concerning simple random walks which was posed in a recent text. When a drunk is observed over L nights, taking N steps per night, and the number of steps to the right is recorded for each night, an average and a variance based on these data can be computed. When the variance is used to estimate p, the probability for the drunk to step right, complex values for p are frequently found. To put such obviously nonsensical results into context, we study the full probability distribution for the variance of the data string. We discuss the connection of our results to the problem of data binning and provide two other brief examples to demonstrate the importance of full distributions.

cond-mat↗

arXiv2003

Effects of differential mobility on biased diffusion of two species

Using simulations and a simple mean-field theory, we investigate jamming transitions in a two-species lattice gas under non-equilibrium steady-state conditions. The two types of particles diffuse with different mobilities on a square lattice, subject to an excluded volume constraint and biased in opposite directions. Varying filling fraction, differential mobility, and drive, we map out the phase diagram, identifying first order and continuous transitions between a free-flowing disordered and a spatially inhomogeneous jammed phase. Ordered structures are observed to drift, with a characteristic velocity, in the direction of the more mobile species.

cond-mat.stat-mech↗

arXiv2003

High temperature expansion for a driven bilayer system

Based directly on the microscopic lattice dynamics, a simple high temperature expansion can be devised for non-equilibrium steady states. We apply this technique to investigate the disordered phase and the phase diagram for a driven bilayer lattice gas at half filling. Our approximation captures the phases first observed in simulations, provides estimates for the transition lines, and allows us to compute signature observables of non-equilibrium dynamics, namely, particle and energy currents. Its focus on non-universal quantities offers a useful analytic complement to field-theoretic approaches.

cond-mat.stat-mech↗

arXiv2002

Stationary correlations for a far-from-equilibrium spin chain

A kinetic one-dimensional Ising model on a ring evolves according to a generalization of Glauber rates, such that spins at even (odd) lattice sites experience a temperature $T_{e}$ ($T_{o}$). Detailed balance is violated so that the spin chain settles into a non-equilibrium stationary state, characterized by multiple interactions of increasing range and spin order. We derive the equations of motion for arbitrary correlation functions and solve them to obtain an exact representation of the steady state. Two nontrivial amplitudes reflect the sublattice symmetries; otherwise, correlations decay exponentially, modulo the periodicity of the ring. In the long chain limit, they factorize into products of two-point functions, in precise analogy to the equilibrium Ising chain. The exact solution confirms the expectation, based on simulations and renormalization group arguments, that the long-time, long-distance behavior of this two-temperature model is Ising-like, in spite of the apparent complexity of the stationary distribution.

cond-mat.stat-mech↗

arXiv2002

Non-equilibrium stationary state of a two-temperature spin chain

A kinetic one-dimensional Ising model is coupled to two heat baths, such that spins at even (odd) lattice sites experience a temperature $T_{e}$ ($% T_{o}$). Spin flips occur with Glauber-type rates generalised to the case of two temperatures. Driven by the temperature differential, the spin chain settles into a non-equilibrium steady state which corresponds to the stationary solution of a master equation. We construct a perturbation expansion of this master equation in terms of the temperature difference and compute explicitly the first two corrections to the equilibrium Boltzmann distribution. The key result is the emergence of additional spin operators in the steady state, increasing in spatial range and order of spin products. We comment on the violation of detailed balance and entropy production in the steady state.

cond-mat.stat-mech↗