The melting behavior of long, heterogeneous DNA chains is examined within the framework of the nonlinear lattice dynamics based Peyrard-Bishop-Dauxois (PBD) model. Data for the pBR322 plasmid and the complete T7 phage have been used to obtain model fits and determine parameter dependence on salt content. Melting curves predicted for the complete fd phage and the Y1 and Y2 fragments of the $\varphi \text{X}174$ phage without any adjustable parameters are in good agreement with experiment. The calculated probabilities for single base-pair opening are consistent with values obtained from imino proton exchange experiments.

We report on a theoretical study showing that the leak conductance density, $G_L$, in the squid giant axon appears to be optimal for the action potential firing frequency. More precisely, the standard assumption that the leak current is composed of chloride ions leads to the result that the experimental value for $G_L$ is very close to the optimal value in the Hodgkin-Huxley model, which minimizes the absolute refractory period of the action potential, thereby maximizing the maximum firing frequency under stimulation by sharp, brief input current spikes to one end of the axon. The measured value of $G_L$ also appears to be close to optimal for the frequency of repetitive firing caused by a constant current input to one end of the axon, especially when temperature variations are taken into account. If, by contrast, the leak current is assumed to be composed of separate voltage-independent sodium and potassium currents, then these optimizations are not observed.

We investigate the concept of a standard map for the interaction of relativistic particles and electrostatic waves of arbitrary amplitudes, under the action of external magnetic fields. The map is adequate for physical settings where waves and particles interact impulsively, and allows for a series of analytical result to be exactly obtained. Unlike the traditional form of the standard map, the present map is nonlinear in the wave amplitude and displays a series of peculiar properties. Among these properties we discuss the relation involving fixed points of the maps and accelerator regimes.

We propose a numerical method to calculate interior eigenvalues and corresponding eigenvectors for nonsymmetric matrices. Based on the subspace projection technique onto expanded Ritz subspace, it becomes possible to obtain eigenvalues and eigenvectors with sufficiently high precision. This method overcomes the difficulties of the traditional nonsymmetric Lanczos algorithm, and improves the accuracy of the obtained interior eigenvalues and eigenvectors. Using this algorithm, we investigate three-dimensional metamaterial composites consisting of positive and negative refractive index materials, and it is demonstrated that the finite-difference frequency-domain algorithm is applicable to analyze these metamaterial composites.

At low temperatures and strong friction the time evolution of the density distribution in position follows a quantum Smoluchowski equation. Recently, also higher-order contributions of quantum fluctuations to drift and diffusion coefficients have been systematically derived. As a nontrivial situation to reveal the impact of subleading quantum corrections and to demonstrate convergence properties of the perturbation series, directed transport in ratchets is studied. It is shown that the perturbation series typically has a nonmonotonous behavior. Depending on symmetry properties higher-order contributions may even compensate current reversals induced by leading quantum fluctuations. This analysis demonstrates how to consistently treat the dynamics of overdamped quantum systems at low temperatures also in numerical applications.

We study a polydisperse soft-spheres model for colloids by means of microcanonical Monte Carlo simulations. We consider a polydispersity as high as 24%. Although solidification occurs, neither a crystal nor an amorphous state are thermodynamically stable. A finite size scaling analysis reveals that in the thermodynamic limit: (a) the fluid-solid transition is rather a crystal-amorphous phase-separation, (b) such phase-separation is preceded by the dynamic glass transition, and (c) small and big particles arrange themselves in the two phases according to a complex pattern not predicted by any fractionation scenario.

The entropy of the hard-core model is analyzed subject to dimension, system size and particle density. Inspired by the exactly solvable one-dimensional case and the results from a virial expansion, we suggest a scaling relation for the two-dimensional and three-dimensional case. These relations are compared with numerical results, obtained by a modified Widom’s particle insertion method. The notion of finite size effects, relevant for atomic glass-forming systems, is discussed in the context of the present results.

We consider the Eigen quasispecies model with a dynamic environment. For an environment with sharp-peak fitness in which the most-fit sequence moves by $k$ spin-flips each period $T$ we find an asymptotic stationary state in which the quasispecies population changes regularly according to the regular environmental change. From this stationary state we estimate the maximum and the minimum mutation rates for a quasispecies to survive under the changing environment and calculate the optimum mutation rate that maximizes the population growth. Interestingly we find that the optimum mutation rate in the Eigen model is lower than that in the Crow-Kimura model, and at their optimum mutation rates the corresponding mean fitness in the eigenmodel is lower than that in the Crow-Kimura model, suggesting that the mutation process which occurs in parallel to the replication process as in the Crow-Kimura model gives an adaptive advantage under changing environment.

Existing continuum models for reactive transport in porous media tend to overestimate the extent of solute mixing and mixing-controlled reactions because the continuum models treat both the mechanical and diffusive mixings as an effective Fickian process. Recently, we have proposed a phenomenological Langevin model for flow and transport in porous media [A. M. Tartakovsky, D. M. Tartakovsky, and P. Meakin, Phys. Rev. Lett. 101, 044502 (2008)]. In the Langevin model, the fluid flow in a porous continuum is governed by a combination of a Langevin equation and a continuity equation. Pore-scale velocity fluctuations, the source of mechanical dispersion, are represented by the white noise. The advective velocity (the solution of the Langevin flow equation) causes the mechanical dispersion of a solute. Molecular diffusion and sub-pore-scale Taylor-type dispersion are modeled by an effective stochastic advection-diffusion equation. Here, we propose a method for parameterization of the model for a synthetic porous medium, and we use the model to simulate multicomponent reactive transport in the porous medium. The detailed comparison of the results of the Langevin model with pore-scale and continuum (Darcy) simulations shows that: (1) for a wide range of Peclet numbers the Langevin model predicts the mass of reaction product more accurately than the Darcy model; (2) for small Peclet numbers predictions of both the Langevin and the Darcy models agree well with a prediction of the pore-scale model; and (3) the accuracy of the Langevin and Darcy model deteriorates with the increasing Peclet number but the accuracy of the Langevin model decreases more slowly than the accuracy of the Darcy model. These results show that the separate treatment of advective and diffusive mixing in the stochastic transport model is more accurate than the classical advection-dispersion theory, which uses a single effective diffusion coefficient (the dispersion coefficient) to describe both types of mixing.

Recently, Han and Heary [Phys. Rev. Lett. 99, 236808 (2007)] proposed an approach to steady-state quantum transport through mesoscopic structures, which maps the nonequilibrium problem onto a family of auxiliary quantum impurity systems subject to imaginary voltages. We employ continuous-time quantum Monte-Carlo solvers to calculate accurate imaginary time data for the auxiliary models. The spectral function is obtained from a maximum entropy analytical continuation in both Matsubara frequency and complexified voltage. To enable the analytical continuation we construct a kernel which is compatible with the analytical structure of the theory. While it remains a formidable task to extract reliable spectral functions from this unbiased procedure, particularly for large voltages, our results indicate that the method in principle yields results in agreement with those obtained by other methods.

By appealing to renewal theory we determine the equations that the mean exit time of a continuous-time random walk with drift satisfies both when the present coincides with a jump instant or when it does not. Particular attention is paid to the corrections ensuing from the non-Markovian nature of the process. We show that when drift and jumps have the same sign the relevant integral equations can be solved in closed form. The case when holding times have the classical Erlang distribution is considered in detail.

In a well-stirred system undergoing chemical reactions, fluctuations in the reaction propensities are approximately captured by the corresponding chemical Langevin equation. Within this context, we discuss in this work how the Kramers escape theory can be used to predict rare events in chemical reactions. As an example, we apply our approach to a recently proposed model on cell proliferation with relevance to skin cancer [P. B. Warren, Phys. Rev. E 80, 030903 (2009)]. In particular, we provide an analytical explanation for the form of the exponential exponent observed in the onset rate of uncontrolled cell proliferation.

The butterfly Pierella luna (Nymphalidae) shows an intriguing rainbow iridescence effect: the forewings of the male, when illuminated along the axis from the body to the wing tip, decompose a white light beam as a diffraction grating would do. Violet light, however, emerges along a grazing angle, near the wing surface, while the other colors, from blue to red, exit respectively at angles progressively closer to the direction perpendicular to the wing plane. This sequence is the reverse of the usual decomposition of light by a grating with a periodicity parallel to the wing surface. It is shown that this effect is produced by a macroscopic deformation of the entire scale, which curls in such a way that it forms a “vertical” grating, perpendicular to the wing surface, and functions in transmission instead of reflection.

It is shown numerically that the deviatoric stress tensor is second-order accurate in the bulk Bhatnagar-Gross-Krook lattice Boltzmann (LB) method. In an earlier work [T. Krüger et al., Phys. Rev. E 79, 46704 (2009)], we have already predicted the second-order convergence. However, numerical simulations using a duct flow were not fully in line with this prediction. In particular, the convergence rate of the stress tensor was observed to depend on the LB boundary condition. In the present paper, we examine a pure bulk system, the decaying Taylor-Green vortex flow. Our prediction on the second-order accuracy of the stress tensor is unambiguously evidenced via these studies.

Communities are clusters of nodes with a higher than average density of internal connections. Their detection is of great relevance to better understand the structure and hierarchies present in a network. Modularity has become a standard tool in the area of community detection, providing at the same time a way to evaluate partitions and, by maximizing it, a method to find communities. In this work, we study the modularity from a combinatorial point of view. Our analysis (as the modularity definition) relies on the use of the configurational model, a technique that given a graph produces a series of randomized copies keeping the degree sequence invariant. We develop an approach that enumerates the null model partitions and can be used to calculate the probability distribution function of the modularity. Our theory allows for a deep inquiry of several interesting features characterizing modularity such as its resolution limit and the statistics of the partitions that maximize it. Additionally, the study of the probability of extremes of the modularity in the random graph partitions opens the way for a definition of the statistical significance of network partitions.

We study the scaling of three-dimensional crack roughness using large-scale beam lattice systems. Our results for prenotched samples indicate that the crack surface is statistically isotropic, with the implication that experimental findings of anisotropy of fracture surface roughness in directions parallel and perpendicular to crack propagation is not due to the scalar or vectorial elasticity of the model. In contrast to scalar fuse lattices, beam lattice systems do not exhibit anomalous scaling or an extra dependence of roughness on system size. The local and global roughness exponents (${\zeta }_{loc}$ and $\zeta$, respectively) are equal to each other, and the three-dimensional crack roughness exponent is estimated to be ${\zeta }_{loc}=\zeta =0.48\pm 0.03$. This closely matches the roughness exponent observed outside the fracture process zone. The probability density distribution $p\left[\Delta h\left(\ell \right)\right]$ of the height differences $\Delta h\left(\ell \right)=\left[h\left(x+\ell \right)-h\left(x\right)\right]$ of the crack profile follows a Gaussian distribution, in agreement with experimental results.

We consider convection in a horizontally magnetized viscous fluid layer in the gravitational field heated from below with a vertical temperature gradient. Following Rayleigh-Bénard scenario and using a general magnetohydrodynamic approach, we obtain a simple set of four ordinary differential equations. In addition to the usual three-dimensional Lorenz model a new variable describes the profile of the induced magnetic field. We show that nonperiodic oscillations are influenced by anisotropic magnetic forces resulting not only in an additional viscosity but also substantially modifying nonlinear forcing of the system. On the other hand, this can stabilize convective motion of the flow. However, for certain values of the model parameters we have identified a deterministic intermittent behavior of the system resulting from bifurcation. In this way, we have identified here a basic mechanism of intermittent release of energy bursts, which is frequently observed in space and laboratory plasmas. Hence, we propose this model as a useful tool for the analysis of intermittent behavior of various environments, including convection in planets and stars. Therefore, we hope that our simple but still a more general nonlinear model could shed light on the nature of hydromagnetic convection.

The intrinsic stochasticity of gene expression can lead to large variations in protein levels across a population of cells. To explain this variability, different sources of messenger RNA (mRNA) fluctuations (“Poisson” and “telegraph” processes) have been proposed in stochastic models of gene expression. Both Poisson and telegraph scenario models explain experimental observations of noise in protein levels in terms of “bursts” of protein expression. Correspondingly, there is considerable interest in establishing relations between burst and steady-state protein distributions for general stochastic models of gene expression. In this work, we address this issue by considering a mapping between stochastic models of gene expression and problems of interest in queueing theory. By applying a general theorem from queueing theory, Little’s Law, we derive exact relations which connect burst and steady-state distribution means for models with arbitrary waiting-time distributions for arrival and degradation of mRNAs and proteins. The derived relations have implications for approaches to quantify the degree of transcriptional bursting and hence to discriminate between different sources of intrinsic noise in gene expression. To illustrate this, we consider a model for regulation of protein expression bursts by small RNAs. For a broad range of parameters, we derive analytical expressions (validated by stochastic simulations) for the mean protein levels as the levels of regulatory small RNAs are varied. The results obtained show that the degree of transcriptional bursting can, in principle, be determined from changes in mean steady-state protein levels for general stochastic models of gene expression.

We study the distribution of the minimum free energy (MFE) for the Turner model of pseudoknot free RNA secondary structures over ensembles of random RNA sequences. In particular, we are interested in those rare and intermediate events of unexpected low MFEs. Generalized ensemble Markov-chain Monte Carlo methods allow us to explore the rare-event tail of the MFE distribution down to probabilities such as ${10}^{-70}$ and to study the relationship between the sequence entropy and structural properties for sequence ensembles with fixed MFEs. Entropic and structural properties of those ensembles are compared with natural RNA of the same reduced MFE ($z$ score).