We investigate the nonequilibrium steady state of a one-dimensional (1D) lattice gas of dimers. The dynamics is described by a totally asymmetric exclusion process (TASEP) supplemented by attachment and detachment processes, mimicking chemical equilibrium of the 1D driven transport with the bulk reservoir. The steady-state phase diagram and current and density profiles are calculated using both a refined mean-field theory and extensive stochastic simulations. As a consequence of the on-off kinetics, a phase coexistence region arises intervening between low and high density phases such that the discontinuous transition line of the TASEP splits into two continuous ones. The results of the mean-field theory and simulations are found to coincide. We show that the physical picture obtained in the corresponding lattice gas model with monomers is robust, in the sense that the phase diagram changes quantitatively, but the topology remains unaltered. The mechanism for phase separation is identified as generic for a wide class of driven 1D lattice gases.

We show that the dominant eigenvectors of real protein structural contact matrices are highly correlated with their amino acid sequences. These results suggests that an ab initio sequence-independent profile exists for every protein structure and that this profile is highly effective in differentiating the ordering of amino acids in natural protein sequences from random sequences. This profile provides a structural code and is a key for understanding the unique behavior of protein structures. Using a lattice model, we show that there are special codable structures highly separated from random structures in the dominant eigenvector space of their structural contact matrices. As an example, we show our results provide a good explanation to the “designable principle” of protein structures.

Sustained neuronal activity can be broadly classified as either tonic firing or bursting. These two major patterns of neuronal oscillations are state dependent and may coexist. The dynamics and intracellular mechanisms of transitions between tonic firing and bursting in cortical networks remain poorly understood. Here we describe a detailed two-compartment conductance-based cortical neuron model which exhibits bistability with hysteresis between tonic firing and bursting for elevated extracellular potassium concentration. The study explains the ionic and dynamical mechanisms of burst generation and reveals the conditions underlying coexistence of two different oscillatory modes as a function of neuronal excitability.

There has been considerable recent interest in the properties of networks, such as citation networks and the worldwide web, that grow by the addition of vertices, and a number of simple solvable models of network growth have been studied. In the real world, however, many networks, including the web, not only add vertices but also lose them. Here we formulate models of the time evolution of such networks and give exact solutions for a number of cases of particular interest. For the case of net growth and so-called preferential attachment—in which newly appearing vertices attach to previously existing ones in proportion to vertex degree—we show that the resulting networks have power-law degree distributions, but with an exponent that diverges as the growth rate vanishes. We conjecture that the low exponent values observed in real-world networks are thus the result of vigorous growth in which the rate of addition of vertices far exceeds the rate of removal. Were growth to slow in the future—for instance, in a more mature future version of the web—we would expect to see exponents increase, potentially without bound.

Three-dimensional stability of stationary reaction balls is investigated in a system consisting of an autocatalysis accompanied by a slow decay of the autocatalyst. Radially stable stationary spherical structures become unstable to three-dimensional perturbations at small decay rate when the radius of the reaction ball is sufficiently large and the reactant diffuses faster than the autocatalyst. A thorough linear stability analysis and simulations in three spatial dimensions are carried out in the simplest system sustaining stationary reaction balls.

The influence of helicity on the stability of scaling regimes, on the effective diffusivity, and on the anomalous scaling of structure functions of a passive scalar advected by a Gaussian solenoidal velocity field with finite correlation time is investigated by the field theoretic renormalization group and operator-product expansion within the two-loop approximation. The influence of helicity on the scaling regimes is discussed and shown in the plane of exponents $\epsilon \text{−}\eta$, where $\epsilon$ characterizes the energy spectrum of the velocity field in the inertial range $E\propto k^{1-2\epsilon }$, and $\eta$ is related to the correlation time at the wave number $k$, which is scaled as $k^{-2+\eta }$. The restrictions given by nonzero helicity on the regions with stable fixed points that correspond to the scaling regimes are analyzed in detail. The dependence of the effective diffusivity on the helicity parameter is discussed. The anomalous exponents of the structure functions of the passive scalar field which define their anomalous scaling are calculated and it is shown that, although the separate composite operators which define them strongly depend on the helicity parameter, the resulting two-loop contributions to the critical dimensions of the structure functions are independent of helicity. Details of calculations are shown.

We present a set of electrical conductivity measurements of a mesoscopic equilibrium cluster phase in the aggregation process of charged particles induced by oppositely charged polyions. These measurements supply strong experimental evidence that correlated adsorption of polyions is driven by the counterion release. This phenomenon, known to occur in DNA-liposome mixtures in lamellar phase, i.e., when liposomes fuse together to form a sandwichlike structure encompassing DNA chains, was not previously observed in aqueous suspension of clusters of intact liposomes stuck together by polyions to form reversible aggregates. A simple statistical model of the lateral correlation of polyions at the particle surface justifies quantitatively the observed behavior of the counterion release, as shown by electrical conductivity measurements.

We derive expressions for determination of the stress and the elastic constants in systems composed of particles interacting via noncentral two-body potentials as thermal averages of products of first and second partial derivatives of the interparticle potentials and components of the interparticle separation vectors. These results are adapted to hard potentials, where the stress and the elastic constants are expressed as thermal averages of the components of normals to contact surfaces between the particles and components of vectors separating their centers. The averages require knowledge of the simultaneous contact probabilities of two pairs of particles. We apply the expressions to particles for which a contact function can be defined, and demonstrate the feasibility of the method by computing the stress and the elastic constants of a two-dimensional system of hard ellipses using Monte Carlo simulations.

Segregation patterns formed by time-periodic flow of polydisperse granular material (varying in particle size) in quasi-two-dimensional (quasi-2D) tumblers capture the symmetries of Poincaré sections, stroboscopic maps of the underlying flow, derived from a continuum model which contains no information about particle properties. We study this phenomenon experimentally by varying the concentration of small particles in a bidisperse mixture in quasi-2D tumblers with square and pentagonal cross sections. By coupling experiments with an analysis of periodic points, we explain the connection between the segregation patterns and the dynamics of the underlying flow. Analysis of the eigenvectors and unstable manifolds of hyperbolic points shows that lobes of segregated small particles stretch from hyperbolic points toward corners of the tumbler, demonstrating the connection between regions of chaotic flow and the shape of the segregation patterns. Furthermore, unstable manifolds map the shape of lobes of segregated particles. The techniques developed here can also be applied to nonpolygonal tumblers such as elliptical tumblers, as well as to circular tumblers with time-periodic forcing.

The $n$-alkanes ${\mathrm{C}}_{12}{\mathrm{H}}_{26}$, ${\mathrm{C}}_{14}{\mathrm{H}}_{30}$, and ${\mathrm{C}}_{16}{\mathrm{H}}_{34}$ have been imbibed and solidified in mesoporous Vycor glass with a mean pore diameter of $10\mathrm{nm}$. The samples have been investigated by x-ray diffractometry and calorimetric measurements. The structures and phase sequences have been determined. Apart from a reduction and the hysteresis of the melting-freezing transition, pore-confined C12 reproduces the liquid-triclinic phase sequence of the bulk material, but for C16 an orthorhombic rotator mesophase appears that in the bulk state is absent for C16 but well known from odd-numbered alkanes of similar length. In pore-confined C14 this phase shows up on cooling but not on heating.

Electroporation, in which electric pulses create transient pores in the cell membrane, is an important technique for drug and DNA delivery. Electroporation kinetics is mathematically described by an advection-diffusion boundary value problem. This study uses singular perturbation to derive a reduced description of the pore creation transient in the form of a single integrodifferential equation for the transmembrane voltage $V\left(t\right)$. The number of pores and the distribution of their radii are computed from $V\left(t\right)$. The analysis contains two nonstandard features: the use of the voltage deviation to peel away the strong exponential dependence of pore creation upon the transmembrane potential, and the autonomous approximation of the pore evolution. Comparing the predictions of the reduced equation with the simulations of the original problem demonstrates that this analysis allows one to predict with good accuracy the number and distribution of pores as a function of the electric pulse strength.

Gap junctions between excitatory neurons are shown to disrupt the persistent state. The asynchronous state of the network loses stability via a Hopf bifurcation and then the active state is destroyed via a homoclinic bifurcation with a stationary state. A partial differential equation (PDE) is developed to analyze the Hopf and the homoclinic bifurcations. The simplified dynamics are compared to a biophysical model where similar behavior is observed. In the low noise case, the dynamics of the PDE is shown to be very complicated and includes possible chaotic behavior. The onset of synchrony is studied by the application of averaging to obtain a simple criterion for destabilization of the asynchronous persistent state.

We study a possible electrostatic mechanism underlying the compaction of DNA inside the nuclei of eucaryotes: the tail-bridging effect between nucleosomes, the fundamental DNA packaging units of the chromatin complex. As a simple model of the nucleosome we introduce the eight-tail colloid, a charged sphere with eight oppositely charged, flexible, grafted chains that represent the terminal histone tails. We show that our complexes attract each other via the formation of chain bridges and contrast this to the effect of attraction via charge patches. We demonstrate that the attraction between eight-tail colloids can be tuned by changing the fraction of charged monomers on the tails. This suggests a physical mechanism of chromatin compaction where the degree of DNA condensation is controlled via biochemical means, namely the acetylation and deacetylation of lysines in the histone tails.

We study the failure properties of fiber bundles with a finite lower cutoff of the strength disorder varying the range of interaction between the limiting cases of completely global and completely local load sharing. Computer simulations revealed that at any range of load redistribution there exists a critical cutoff strength where the macroscopic response of the bundle becomes perfectly brittle, i.e., linearly elastic behavior is obtained up to global failure, which occurs catastrophically after the breaking of a small number of fibers. As an extension of recent mean field studies [Phys. Rev. Lett. 95, 125501 (2005)], we demonstrate that approaching the critical cutoff, the size distribution of bursts of breaking fibers shows a crossover to a universal power law form with an exponent $3∕2$ independent of the range of interaction.

Statistical properties of coupled dynamic-stochastic systems are studied within a combination of the maximum information principle and the superstatistical approach. The conditions at which the Shannon entropy functional leads to power-law statistics are investigated. It is demonstrated that, from a quite general point of view, the power-law dependencies may appear as a consequence of “global” constraints restricting both the dynamic phase space and the stochastic fluctuations. As a result, at sufficiently long observation times the dynamic counterpart is driven into a nonequilibrium steady state whose deviation from the usual exponential statistics is given by the distance from the conventional equilibrium.

Statistical fluctuations in the eigenvalues of the scattering, impedance, and admittance matrices of two-port wave-chaotic systems are studied experimentally using a chaotic microwave cavity. These fluctuations are universal in that their properties are dependent only upon the degree of loss in the cavity. We remove the direct processes introduced by the nonideally coupled driving ports through a matrix normalization process that involves the radiation-impedance matrix of the two driving ports. We find good agreement between the experimentally obtained marginal probability density functions (PDFs) of the eigenvalues of the normalized impedance, admittance, and scattering matrix and those from random matrix theory (RMT). We also experimentally study the evolution of the joint PDF of the eigenphases of the normalized scattering matrix as a function of loss. Experimental agreement with the theory by Brouwer and Beenakker for the joint PDF of the magnitude of the eigenvalues of the normalized scattering matrix is also shown.

It has been recently proposed that some natural phenomena, such as sunspot occurrence, can be represented by a modulated Markov jitter, which is a high-frequency Markov signal multiplied by a long-term component. The two parameters of this model can be estimated using a nonlinear method based on absolute derivatives. This analysis is applied here to a different physical system: the temperature time series measured during air avalanches in the vertical access pit of an underground quarry. The thermal fluctuations associated with these turbulent flows, driven by the external temperature forcing, actually appear as another practical realization of a modulated Markov jitter. One parameter of the model provides the lifetime of the temperature fluctuations, which can be estimated as a function of time and position. The obtained lifetime is of the order of 10 to $25\min$, and is remarkably constant in time for each sensor, independently of the amplitude of the forcing. Furthermore, a significant and persistent spatial structure is observed, revealing a long-term intrinsic organization of the turbulent air flows in the pit. Such a stable spatial organization may reflect a general feature of turbulent phenomena.

We demonstrate that kinematic simulation (KS) of three-dimensional homogeneous turbulence produces fluid element pair statistics in agreement with the predictions of L F. Richardson [Proc. R. Soc. London, Ser. A 110, 709 (1926)] even though KS lacks explicit modeling of turbulent sweeping of small eddies by large ones. This scaling is most clearly evident in the turbulent diffusivity’s dependence on rms pair separation and, to a lesser extent, on the pair’s travel time statistics. It is also shown that kinematic simulation generates a probability density function of pair separation which is in good agreement with recent theory [S. Goto and J. C. Vassilicos, New J. Phys. 6, 65 (2004)] and with the scaling of the rms pair separation predicted by L. F. Richardson [Proc. R. Soc. London, Ser. A 110, 709 (1926)]. Finally, the statistical persistence hypothesis (SPH) is formulated mathematically and its validity tested in KS. This formulation introduces the concept of stagnation point velocities and relates these to fluid accelerations. The scaling of accelerations found in kinematic simulation supports the SPH, even though KS does not generate a Kolmogorov scaling for the acceleration variance (except for a specific case and a limited range of outer to inner length-scale ratios). An argument is then presented that suggests that the stagnation points in homogeneous isotropic turbulence are on average long-lived.

Our experiment shows that external focusing strongly influences the plasma density and the diameter of femtosecond Ti-sapphire laser filaments generated in air. The control of plasma filament parameters is suitable for many applications such as remote spectroscopy, laser induced electrical discharge, and femtosecond laser material interactions. The measurements of the filament showed the plasma density increases from ${10}^{15}{\mathrm{cm}}^{-3}\text{to}2\times {10}^{18}{\mathrm{cm}}^{-3}$ when the focal length decreases from $380\mathrm{cm}\text{to}10\mathrm{cm}$ while the diameter of the plasma column varies from $30\mu \mathrm{m}\text{to}90\mu \mathrm{m}$. The experimental results are in good qualitative agreement with the results of numerical simulations.

Optical Bragg acceleration structures are waveguides with a vacuum core and dielectric layers as a cladding, designed to guide laser light at the speed-of-light TM mode and accelerate charged particles. In this study, we analyze the electromagnetic forces exerted on the dielectric layers of a planar structure by both the guided laser light and the wake-field of moving charges. The distribution of the volume force densities, as well as the surface force densities, in the interfaces between the layers as a result of the laser propagation is given, and analytic scaling laws for the maximal values are obtained. Separation of the wake-field into the structure’s eigenmodes is essential in order to determine the different contributions of the wake-field to the total impulse that acts on the structure. It is shown that the impact of the wake-field on the structure results almost entirely from the fundamental TM mode. While the total force on the dielectric layers may be significantly stronger than the gravitational force, we show that for typical structures, the pressures that develop are orders of magnitude below the damage threshold.