Physical Review E

The zero-range process is a stochastic interacting particle system that is known to exhibit a condensation transition. We present a detailed analysis of this transition in the presence of quenched disorder in the particle interactions. Using rigorous probabilistic arguments, we show that disorder ch...

We show that the extension of Casimir-like forces to fluctuating fluids driven out of equilibrium can exhibit two interrelated phenomena forbidden at equilibrium: self-forces can be induced on single asymmetric objects and the action-reaction principle between two objects can be violated. These effe...

Self-propelled particles move along circles rather than along a straight line when their driving force does not coincide with their propagation direction. Examples include confined bacteria and spermatozoa, catalytically driven nanorods, active, anisotropic colloidal particles and vibrated granulate...

We investigate the collision cascade that is generated by a single moving particle in a static and homogeneous hard-sphere gas. We argue that the number of moving particles at time t grows as t^ξ and the number collisions up to time t grows as t^η , with ξ=2d∕(d+2) , η=2(d+1)∕(d+2) , ...

A segregation criterion based on the inelastic Enskog kinetic equation is derived to show the transition between the Brazil-nut effect (BNE) and the reverse Brazil-nut effect (RBNE) by varying the different parameters of the system. In contrast to previous theoretical attempts, the approach is not l...

The static structure of quasi-two-dimensional colloidal mixtures of dumbbells and spheres is studied by optical microscopy. Colloidal dumbbells, produced by aggregation of colloidal spheres, are mixed with spherical particles and confined between two parallel glass walls. The static structural prope...

The phase diagram of α -cyclodextrin/water/4-methylpyridine solutions, a system undergoing inverse melting, has been studied by differential scanning calorimetry, rheological methods, and x-ray diffraction. Two different fluid phases separated by a solid region have been observed in the high α -...

We present a quantitative theory for a relaxation function in a simple glass-forming model (binary mixture of particles with different interaction parameters). It is shown that the slowing down is caused by the competition between locally favored regions (clusters) that are long-lived but each of wh...

We consider the growth of a single fcc dendrite into an undercooled melt. Unlike most simulations of this well-studied phenomenon, we adopt an atomistic growth model that uses a kinetic Monte Carlo technique to track the free boundary. The model allows for both phase change and exchange between liqu...

A direct observation of the photochemical switching between colloidal crystals with different lattice constants in a liquid-crystal (LC) emulsion is reported. Glycerol droplets introduced in a nematic liquid crystal form two-dimensional hexagonal colloidal crystal at the nematic-air interface with a...

Human red blood cells (RBCs) exhibit vibratory motions, referred to as “flickering.” Their dynamical properties, classically attributed to thermal mechanisms, have not been fully characterized. Using detrended fluctuation analysis and multiscale entropy methods, we show that the short-term flick...

We study a statistical model describing the steady-state distribution of the fluxes in a metabolic network. The resulting model defined on continuous variables can be solved by the cavity method. In particular, analytical tractability is possible, solving the cavity equation over an ensemble of netw...

Breathing spiral waves are observed in the oscillatory chlorine dioxide-iodine-malonic acid reaction-diffusion system. The breathing develops within established patterns of multiple spiral waves after the concentration of polyvinyl alcohol in the feeding chamber of a continuously fed, unstirred reac...

We demonstrate experimental evidence of noise-induced attractor hopping in a multistable fiber laser. Multistate hopping dynamics displays complex statistical properties characterized by nontrivial scalings. When hopping is encountered between two states, the dynamics of the system is characterized ...

We investigate the spatiotemporal dynamics of a lattice of coupled chaotic maps whose coupling connections are dynamically rewired to random sites with probability p ; namely, at any instance of time, with probability p a regular link is switched to a random one. In a range of weak coupling, wher...

We show that a scaling law exists for the near-resonant dynamics of cold kicked atoms in the presence of a randomly fluctuating pulse amplitude. Analysis of a quasiclassical phase-space representation of the quantum system with noise allows a new scaling law to be deduced. The scaling law and associ...

In chaotically driven nonlinear dynamical systems, weak generalized synchrony can arise through distinct scenarios or routes in a manner similar to the onset of low-dimensional chaos or the creation of strange nonchaotic attractors in quasiperiodically driven systems. The limit sets of the dynamics ...

A key ingredient for continued expansion of nanotechnologies is the ability to create perfectly ordered arrays on a small scale with both site and size control. Self-assembly—i.e., the spontaneous formation of nanostructures—is a highly promising alternative to traditional fabrication methods. H...

Semiconductor lasers with optical feedback have chaotically pulsating output behavior. When two similar chaotic lasers are optically coupled, they can become synchronized in their optical fluctuations. Here we show that the synchronization is not only in the amplitude and in the timing of the pulses...

We demonstrate experimentally control of a chaotic system on time scales much shorter than in any previous study. Combining a multisection laser with an external Fabry-Perot etalon, the chaotic output transforms into a regular intensity self-pulsation with a frequency in the 10-GHz range. The cont...

We report that asymmetrically interacting ensembles of oscillators follow novel routes to synchrony. These routes seem to be a characteristic feature of coupling asymmetry. We show that they are unaffected by white noise except that the entrainment frequencies are shifted. The probability of occurre...

When immiscible wetting and nonwetting fluids move in parallel in a porous medium, an instability may occur at sufficiently high capillary numbers so that interfaces between the fluids initially held in place by the porous medium are mobilized. A boundary zone containing bubbles of both fluids evolv...

The time-resolved spectra of single-bubble sonoluminescence (SBSL) in sulfuric acid have been observed with a streak camera after a spectrograph. The spectral center evolves from infrared to ultraviolet gradually within a SBSL duration, which corresponds to an increase of temperature. The peak tempe...

Chemical oscillations are shown to be responsible for very low frequency modulations of a bubble oscillating nonlinearly in a high intensity ultrasound field. In the parameter space of incomplete dissociation near the onset of sonoluminescence a small bubble is shown to grow on a long time scale by ...

A simple model is proposed for the buckling and coiling instability of a viscous “fluid rope” falling on a plane. By regarding a fluid rope as a one-dimensional flow, this model accounts for only the axial and shared viscous forces. Our model successfully reproduces several experiments with no a...

We demonstrate that flows of conducting fluid along a Möbius strip and related surfaces are hydromagnetic dynamos, i.e., they can produce an exponentially growing magnetic field from an infinitesimal seed. The critical magnetic Reynolds number in one of our models is as low as about 16. Together wi...

On the basis of the fully relativistic Dirac-Fock treatment of photoionization and radiative recombination processes with regard to all multipoles of the radiative field, we have assessed the influence of nondipole effects on the radiative recombination rate coefficients. A formula for the rate coef...

The temperature equilibration rate between electrons and protons in dense hydrogen has been calculated with molecular dynamics simulations for temperatures between 10 and 600   eV and densities between 10²⁰   cm⁻³   to   10²⁴   cm⁻³ . Careful attention has been devote...

We report the observation of a strong coupling between an artificial “atom” and localized interface mode in the microwave regime. Transmittance is experimentally measured for the effective near-zero-index paired structures containing ε -negative and μ -negative materials made of composite ri...

Using soliton amplitude and phase ansatzes, a theory is proposed for searching for stationary soliton solutions to the cubic-quintic complex Ginzburg-Landau (CGL) equation. For arbitrary combinations of system parameters, our approach allows the existence of dissipative solitons together with their ...

We consider the Ising model on the Bethe lattice with aperiodic modulation of the couplings, which has been studied numerically in Phys. Rev. E 77, 041113 (2008). Here we present a relevance-irrelevance criterion and solve the critical behavior exactly for marginal aperiodic sequences. We present an...

The strong interactions between particles will make the energy within the granular materials propagate through the network of contacts and be partly dissipated. Establishing a model that can clearly classify the dissipation and dispersion effects is crucial for the understanding of the global behavi...

In pure water a hydrothermally treated zeolite Y is hydrophilic, while with the addition of an electrolyte it can no longer be soaked up spontaneously. The effective degree of hydrophobicity increases with the ion concentration, which is reflected by the increase in infiltration pressure. The pressu...

A reactive flow, the gelation of sodium acrylate (SA), was carried out in a cuboidal cavity with the top surface undergoing sinusoidal periodic motion. The instantaneous two-dimensional planar velocity fields during gelation were obtained using particle image velocimetry. The experiments were carrie...

Microbead rheology maps the fluctuations of beads immersed in soft matter to viscoelastic properties of the surrounding medium. In this paper, we present modeling extensions of the seminal results of Mason and Weitz [Phys. Rev. Lett. 74, 1250 (1995)] for a single bead and of Crocker [Phys. Rev. Let...

A detailed analysis of the structure and dynamics of the crystal-melt interface region in silicon, modeled with the Stillinger-Weber potential, is performed via molecular dynamics simulations. The focus is on the faceted (111) crystal-melt interface, but properties of the rough (100) interface are a...

The densities of states are evaluated for very short chain molecules made up of overlapping monomers, using a model which has previously been shown to produce helical structure. The results of numerical calculations are presented for tetramers and pentamers. We show that these models demonstrate beh...

Cells swell in response a hypoosmotic challenge. By converting osmotic pressure to hydrostatic pressure at the cell membrane via van’t Hoff’s law, and converting that to tension via Laplace’s law one predicts that the cell membrane should stretch and become stiff. We tested this prediction usi...

We study the statistics of the interoccurrence times between events above some threshold Q in two kinds of multifractal data sets (multiplicative random cascades and multifractal random walks) with vanishing linear correlations. We show that in both data sets the relevant quantities (probability d...

We study the conserved-mass aggregation model with mass-dependent fragmentation on random networks (RNs) and scale-free networks (SFNs) with degree distribution P(k)∼k^−γ . In the model, masses isotropically diffuse with unit rate. With rate ω , a mass m^λ is fragmented from a node with mas...

We use a semiclassical expansion as an alternative derivation of the well-known, rigorous result obtained by Hepp and Lieb for the classical limit of the spin-boson model. We also explicitly derive correction terms to the classical limit previously obtained in the context of Heisenberg equations of ...

We discuss the consequences of time reversal of the excitation parameters on the stability of a periodically driven dynamic system. The example chosen, electrohydrodynamic convection of nematics, is a well-investigated dissipative pattern-forming system, usually driven with time-periodic external el...

In a quantum ratchet accelerator system, a linearly increasing directed current can be dynamically generated without using a biased field. Generic quantum ratchet acceleration with full classical chaos [J. B. Gong and P. Brumer, Phys. Rev. Lett. 97, 240602 (2006)] constitutes a new element of quantu...

Forced turbulence combined with the effect of rotation and shear flow is studied. In a previous paper [N. Leprovost and E. J. Kim, Phys. Rev. E 78, 016301 (2008)], we considered the case where the shear and the rotation are perpendicular. Here, we consider the complementary case of parallel rotation...

An alternative drag coefficient C_d^a [=F̅ ∕(1 / 2ρU_∞²U_∞T_s)] , is proposed for an isolated bluff-body wake, where F̅ is the drag force on the body per unit length, U_∞ is the free-stream velocity, ρ is the density of fluid, and T_s is the vortex shedding p...

We investigate surface waves on the interface between a thin vapor film and a layer of liquid in the presence of a high steady heat flux. This problem arises when a metal surface heated to a high temperature is immersed into a cold liquid. The general boundary conditions, which take into account the...

Two low-dimensional magnetohydrodynamic models containing three velocity and three magnetic modes are described. One of them (nonhelical model) has zero kinetic and current helicity, while the other model (helical) has nonzero kinetic and current helicity. The velocity modes are forced in both these...

We present spectroscopic measurements in which utilized are line-intensity ratios in the near-uv to measure electron energies of several hundred eVs, which usually necessitates the use of emission in the soft x-ray region. The main intensity ratio selected is of the B   III transition 1s²2s ...

We study the interaction of short laser pulses tightly focused in a tiny volume proportional to the cube of the pulse wavelength (λ³) with underdense plasma by means of real-geometry particle-in-cell simulations. Underdense plasma irradiated by relatively low-energy λ³ (and λ² ) laser pulses...

The Hamiltonian description of the self-consistent interaction between an electromagnetic plane wave and a copropagating beam of charged particles is considered. We show how the motion can be reduced to a one-dimensional Hamiltonian model (in a canonical setting) from the Vlasov-Maxwell Poisson brac...

Recently the occurrence probabilities of ground and metastable states of three-dimensional Yukawa clusters with 27 and 31 particles have been analyzed in dusty plasma experiments [D. Block , Phys. Plasmas 15, 040701 (2008)]. There it was found that, in many cases, the ground state appeared substanti...

Based on a multidimensional Riemann theta function, the Hirota bilinear method is extended to explicitly construct multiperiodic (quasiperiodic) wave solutions for the (2+1) -dimensional Bogoyavlenskii breaking soliton equation. Among these periodic waves, the one-periodic waves are well-known cnoi...

Many difficult computational problems involve the simultaneous satisfaction of multiple constraints that are individually easy to satisfy. These constraints might be derived from measurements (as in tomography or diffractive imaging), interparticle interactions (as in spin glasses), or a combination...

A particle tracking code is developed to solve a general time-fractional diffusion equation (FDE), yielding a Lagrangian framework that can track particle dynamics. Extensive simulations demonstrate the efficiency and flexibility of this simple Langevin approach. Many real problems require a vector ...

We present an efficient method to determine the Fourier-Laplace transform of the joint n-point probability distribution of a continuous-time random walk for arbitrary finite n. Additionally, we devise a recursive procedure with which it is possible to calculate the Laplace transforms of the multi point correlation functions without having to determine the joint probability distributions first. The methods are used on several examples with both independent and dependent distributions for the waiting time and the spatial step size.

The Monte Carlo wave function method or the quantum trajectory/jump approach is a powerful tool to study dissipative dynamics governed by the Markovian master equation, in particular for high-dimensional systems and when it is difficult to simulate directly. In this paper, we extend this method to the non-Markovian case described by the generalized Lindblad master equation. Two examples to illustrate the method are presented and discussed. The results show that the method can correctly reproduce the dissipative dynamics for the system. The difference between this method and the traditional Markovian jump approach and the computational efficiency of this method are also discussed.

We study dynamical phase transitions in systems with long-range interactions, using the Hamiltonian Mean Field (HMF) model as a simple example. These systems generically undergo a violent relaxation to a quasi-stationary state (QSS) before relaxing towards Boltzmann equilibrium. In the collisional regime, the out-of-equilibrium one-particle distribution function (DF) is a quasi-stationary solution of the Vlasov equation, slowly evolving in time due to finite N effects. For subcritical energy densities, we exhibit cases where the DF is well-fitted by a Tsallis q-distribution with an index q(t) slowly decreasing in time from q @ 3 (semi-ellipse) to q=1 (Boltzmann). When the index q(t) reaches an energy dependent critical value qcrit, the non-magnetized (homogeneous) phase becomes Vlasov unstable and a dynamical phase transition is triggered, leading to a magnetized (inhomogeneous) state. While Tsallis distributions play an important role in our study, we explain this dynamical phase transition by using only conventional statistical mechanics. For supercritical energy densities, we report for the first time the existence of a magnetized QSS with a very long lifetime.

We consider a generalized coagulation-decoagulation system on a one-dimensional discrete lattice with reflecting boundaries. It is known that a Bernoulli shock measure with two shock fronts might have a simple random-walk dynamics, provided that some constraints on the microscopic reaction rates of this system are fulfilled. Under these constraints the steady-state of the system can be written as a linear superposition of such shock measures. We show that the coefficients of this expansion can be calculated using the finite-dimensional representation of the quadratic algebra of the system obtained from a matrix-product approach.

The global first passage time density of a network is the probability that a random walker released at a random site arrives at an absorbing trap at time T. We find simple expressions for the mean global first passage time T for five fractals: the d-dimensional Sierpinski gasket, T-fractal, hierarchical percolation model, Mandelbrot-Given curve and a deterministic tree. We also find an exact expression for the second moment T2 and show that the variance of the first passage time, Var(T), scales with the number of nodes within the fractal N such that Var(T) ~ N4/[`d], where [`d] is the spectral dimension.

We study geometrical properties of the complete set of solutions of the random 3-satisfiability problem. We show that even for moderate system sizes the number of clusters corresponds surprisingly well with the theoretic asymptotic prediction. We locate the freezing transition in the space of solutions which has been conjectured to be relevant in explaining the onset of computational hardness in random constraint satisfaction problems.

We calculate the relaxational dynamical critical behavior of systems of O(n||)O(n^) symmetry by renormalization group method within the minimal subtraction scheme in two loop order. The three different bicritical static universality classes previously found for such systems correspond to three different dynamical universality classes within the static borderlines. The Heisenberg and the biconical fixed point lead to strong dynamic scaling whereas in the region of stability of the decoupled fixed point weak dynamic scaling holds. Due to the neighborhood of the stability border between the strong and the weak scaling dynamic fixed point corresponding to the static biconical and the decoupled fixed point a very small dynamic transient exponent, of wvB=0.0044, is present in the dynamics for the physically important case n||=1 and n^=2 in d=3.

Molecular dynamics results are reported concerning cooperatively rearranging regions in simulated Ni0.5Zr0.5 melts down to 700 K. Emphasize is laid on discriminating between clusters of mobile atoms (CMAs) from low-frequency dynamics and the all-frequencies case, where the former characterize fluctuations and relaxations on the scale of the late #61538; regime and the #61537;-decay while the latter include, in addition, reversible high-frequency vibrations. Separation of the low-frequency part of the dynamics is carried out by low-pass filtering, exploiting the separation of time-scales below the critical temperature TC of the mode coupling theory. Low-frequency and all-frequencies dynamics merge together slightly below TC. In the low-frequency CMAs, the average size of correlated clusters of connected atoms turns out nearly one order of magnitude larger than in the all-frequencies CMAs. The low-frequency CMAs appear as local clusters propagating extreme slowly in space with characteristic time scale of s at 700 K, the scale of the #61537;-decay.

Mechanical rejuvenation and over-aging of glasses is investigated through stochastic simulations of the soft glassy rheology (SGR) model. Strain- and stress-controlled deformation cycles for a wide range of loading conditions are analyzed and compared to molecular dynamics simulations of a model polymer glass. Results indicate that deformation causes predominantly rejuvenation, whereas over-aging occurs only at very low temperatures, small strains, and for high initial energy states. Although the creep compliance in the SGR model exhibits full aging independent of applied load, large stresses in the nonlinear creep regime cause configurational changes leading to rejuvenation of the relaxation time spectrum probed after a stress cycle. During recovery, however, the rejuvenated state rapidly returns to the original aging trajectory due to collective relaxations of the internal strain.

We develop a new extended version of the mode-coupling theory (MCT) for glass transition, which incorporates activated hopping processes via the dynamical theory originally formulated to describe diffusion-jump processes in crystals. The dynamical-theory approach adapted here to glass-forming liquids treats hopping as arising from vibrational fluctuations in quasi-arrested state where particles are trapped lnside their cages, and the hopping rate is formulated in terms of the Debye-Waller factors characterizing the structure of the quasi-arrested state. The resulting expression for the hopping rate takes an activated form, and the barrier height for the hopping is "self-generated" in the sense that it is present only in those states where the dynamics exhibits a well defined plateau. It is discussed how such a hopping rate can be incorporated into MCT so that the sharp nonergodic transition predicted by the idealized version of the theory is replaced by a rapid but smooth crossover. We then show that the developed theory accounts for the breakdown of the Stokes-Einstein relation observed in a variety of fragile glass formers. It is also demonstrated that characteristic features of dynamical heterogeneities revealed by recent computer simulations are reproduced by the theory. More specifically, a substantial increase of the non-Gaussian parameter, double-peak structure in the probability distribution of particle displacements, and the presence of a growing dynamic length scale are predicted by the extended MCT developed here, which the idealized version of the theory failed to reproduce. These results of the theory are demonstrated for a model of the Lennard-Jones system, and are compared with related computer-simulation results and experimental data.

We investigate transport mechanism of a small hydrophobic solute molecule across two types of fluid interfaces, (i) an interface between two immiscible liquids and (ii) a surfactant-covered liquid-liquid interface. These systems are modeled by coarse-grained molecular dynamics simulations. It is demonstrated that dynamics of the solute molecule near the interface significantly deviates from Markovian Brownian motion. Specifically, the correlation time of the random force acting on the solute strongly depends on the distance between the solute and the interface and increases by two orders of magnitude within a very narrow (less than 1 nm wide) region near the interface. The slow fluctuations of the random force in this narrow region are caused by capillary waves. The region location and width are determined by interface protrusions caused by attraction between the solute and the hydrophobic phase. We use results of molecular dynamics simulations to develop a stochastic model for the coupled solute-interface dynamics and estimate the rate of the solute transport across the interface. The observed phenomenon appears to be a general feature of mass transport across fluid or flexible membranes. The coupling between the solute transport and the interface fluctuations is the strongest in areas corresponding to large free energy gradient or near a free energy barrier for the solute transport. This suggests a strong influence of the coupled solute-interface dynamics on the rate of mass transfer across interfaces.

Using phase field method, effects of the surface tension anisotropy on sidebranching and sidebranch evolution are investigated to study the deterministic sidebranching mechanism in solute dendritic growth. The results show that, the dendrite in the scaled profile for different surface tension anisotropy have the self-affine primary dendritic trunk but with different sidebranches, and the non-monotonic behavior of the concentration distribution along the interface near the dendritic tip is the significant characteristic of the sidebranch development.

Capillary forces have been measured by Atomic Force Microscopy in the plate-sphere setup between gold, borosilicate glass, GeSbTe, titanium, and UV irradiated amorphous titanium-dioxide surfaces. The force measurements were performed as a function of surface roughness in the range 0.2 - 15 nm rms, and relative humidity ranging between 2 and 40 2 1suggests the persistence of a nanometers thick adsorbed water layer that acts as a capillary bridge between contacting surfaces. Moreover, we found a significantly different scaling behavior of the force with rms roughness for materials with different hydrophilicity as compared to gold-gold surfaces.

Monte Carlo simulations of the Asakura-Oosawa (AO) model for colloid-polymer mixtures confined between two parallel repulsive structureless walls are presented and analyzed in the light of current theories on capillary condensation and interface localization transitions. Choosing a polymer-to-colloid size ratio of q=0.8 and studying ultrathin films in the range of D=3 to D=10 colloid diameters thickness, grand canonical Monte Carlo methods are used; phase transitions are analyzed via finite size scaling, as in previous work on bulk systems and under confinement between identical types of walls. Unlike the latter work, inequivalent walls are used here: while the left wall has a hard-core repulsion for both polymers and colloids, at the right wall an additional square-well repulsion of variable strength acting only on the colloids is present. We study how the phase separation into colloid-rich and colloid-poor phases occurring already in the bulk is modified by such a confinement. When the asymmetry of the wall-colloid interaction increases, the character of the transition smoothly changes from capillary condensation-type to interface localization-type. For very thin films (i.e. for D=3) and a suitable choice of the wall-colloid interactions, evidence is found that the critical behavior falls in the universality class of the two-dimensional Ising model. Otherwise, we observe crossover scaling between different universality classes (namely, the crossover from the three-dimensional to the two-dimensional Ising model universality class). The colloid and polymer density profiles across the film in the various phases are discussed, as well as the correlation of interfacial fluctuations in the direction parallel to the confining walls. The broadening of the interface between the coexisting colloid-rich and polymer-rich phases (located parallel to the confining walls) is understood in terms of capillary wave fluctuations. The experimental observability of all these phenomena is briefly discussed.

We analyze the molecular dynamics heterogeneity of the liquid crystal 4-n-octyl-4'-cyanobiphenyl (8CB) nanoconfined in porous silicon. We show that the temperature dependence of the dynamic correlation length xwall, which measures the distance over which a memory of the interfacial slowing-down of the molecular dynamics persists, is closely related to the growth of the short-range static order arising from quenched random fields. More generally, this result may also shed some light onto the connection between static and dynamic heterogeneities in a wide class of condensed and soft matter systems.

Langmuir monolayers of chiral liquid crystals on the surface of water exhibit orientational waves with complex spatiotemporal patterns. These patterns arise from a collective precession of the mesogenic molecules, driven by the evaporation of water through the monolayer. We investigate the behavior of these orientational waves around topological defects in the molecular orientation. Through Brewster angle microscopy, we find that the waves form a reversing spiral pattern, which rotates about the central vortex. With increasing relative humidity, the rotation slows and then stops. We model the system theoretically, and show that predicted patterns are in good agreement with the experiments.

Extensive Brownian dynamics simulations of conformational changes accompanying the overcharging of a dendrimer by an oppositely charged long linear polyelectrolyte (LPE) have been carried out. The simulated results have been compared with the predictions of the Nguen and Shklovskii correlation theory (Physica A 293, 324 (2001)) for impenetrable charged spherical macroion. Dendrimer overcharging is caused by the spatial correlations between excess of the LPE charges adsorbed onto its surface. The LPE-length dependence of the corresponding correlation energy is in agreement with the theoretical predictions. Maximum of the LPE adsorption occurs at some critical LPE length , and the first order phase transition from completely coiled conformation to the conformation with tails takes place. The phase transition is accompanied by the drastic increase in the relative fluctuations of the polyelectrolyte size. Upon increasing the linear-chain length above , the one-long-tail conformation becomes energetically preferable; the exchange time between the long-tail conformation and the short-tails conformation is very large.

The linking and writhing numbers are key quantities when characterizing the structure of a piece of supercoiled DNA. Defined as double integrals over the shape of the double-helix, these numbers are not always straightforward to compute, though a simplified formula was established in a theorem by Fuller (1978). We examine the range of applicability of this widely-used simplified formula, and show that it cannot be employed for plectonemic DNA. We show that inapplicability is due to a hypothesis of Fuller theorem that is not met. The hypothesis seems to have been overlooked in many works.

Feedback connections and noise are ubiquitous features of neuronal networks, and affect in a determinant way the patterns of neural activity. Here we study how the subthreshold dynamics of a neuron interacts with time-delayed feedback and noise. We use a Hodgkin-Huxley-type model of a thermoreceptor neuron, and assume the feedback to be linear, corresponding effectively to a recurrent electrical connection via gap junctions. This type of feedback can model electrical autapses, which connect the terminal fibers of a neuron's axon with dendrites from the same neuron. Thus the delay in the feedback loop is due basically to axonal propagation time. We chose model parameters for which the neuron displays, in the absence of feedback and noise, only subthreshold oscillations. These oscillations, however, take the neuron close to the firing threshold, such that small perturbations can drive it above the level for generation of action potentials. The resulting interplay between weak delayed feedback, noise, and the subthreshold intrinsic activity is nontrivial. For negative feedback, depending on the delay, the firing rate can be lower than in the noise-free situation. This is due to the fact that noise inhibits feedback-induced spikes by driving the neuronal oscillations away from the firing threshold. For positive feedback, there are regions of delay values where the noise-induced spikes are inhibited by the feedback; in this case it is the feedback that drives the neuronal oscillations away from the threshold. Our study contributes to a better understanding of the role of electrical self-connections, in the presence of noise and subthreshold activity.

We study dynamic phenomena in a large social network of nearly 3 ×104 individuals who interact in the large virtual world of the Massive Multiplayer Online Role Playing Game (MMORPG). On the basis of a database received from the on-line game server, we examine the structure of the friendship network and human dynamics. To investigate the relation between networks of acquaintances in virtual and real worlds, we carried out a survey among the players. We show that even though the virtual network did not develop as a growing graph of an underlying network of social acquaintances in the real world, it influences it. Furthermore we find very interesting scaling laws concerning human dynamics. Our research shows how long people are interested in a single task and how much time they devote to it. Surprisingly exponent values in both cases are close to minus one. We calculate the activity of individuals, i.e. the relative time daily devoted to interactions with others in the artificial society. Our research shows that the distribution of activity is not uniform, is highly correlated with the degree of the node and that such human activity has a significant influence on dynamic phenomena, e.g. epidemic spreading and rumor propagation, in complex networks. We find that spreading is accelerated (an epidemic) or decelerated (a rumor) as a result of super-spreaders' various behavior.

We study the scaling of two-dimensional crack roughness using large scale beam lattice systems. Our results indicate that the crack roughness obtained using beam lattice systems does not exhibit anomalous scaling in sharp contrast to the simulation results obtained using scalar fuse lattices. The local and global roughness exponents (zloc and z, respectively) are equal to each other, and the two-dimensional crack roughness exponent is estimated to be zloc = z = 0.64 0.02. Removal of overhangs (jumps) in the crack profiles eliminates even the minute differences between the local and global roughness exponents. Furthermore, removing these jumps in the crack profile completely eliminates the multiscaling observed in other studies. We find that the probability density distribution p[Dh(l)] of the height differences Dh(l) = [h(x+l) - h(x)] of the crack profile obtained after removing the jumps in the profiles follows a Gaussian distribution even for small window sizes (l).

A simplified version of the stochastic Fermi-Ulam model is investigated in order to elucidate the effect of a class of rare low-velocity events on the velocity diffusion process and consequently Fermi acceleration. The relative fraction of these events, for sufficiently large times, decreases monotonically with increasing variance of the magnitude of the particle velocity. However, a treatment of the diffusion problem which totally neglects these events, gives rise to a glaring inconsistency associated with the mean value of the magnitude of the velocity in the ensemble. We propose a general scheme for treating the diffusion process in velocity space, which succeeds in capturing the effect of the low-velocity events on the diffusion, providing a consistent description of the acceleration process. The present study exemplifies the influence of low-probability events on the transport properties of time-dependent billiards.

Periodic stripe patterns which form when an electric field is applied to a thin nematic liquid crystal layer with a very low conductivity are discussed. In this case, the dielectric electroconvection mode persists down to very low frequencies of the driving voltage. A Lifschitz point, i.e. a transition from normal to oblique rolls, is detected in the dielectric regime. A crossover from electroconvection to flexoelectric domains occurs for extremely low frequencies of about 0.1 Hz. The crossover scenario yields pattern morphologies characteristic for both mechanisms, i.e. electroconvection and flexoelectric domains, which appear consecutively within one period of the driving voltage. A theoretical description of the onset characteristics of dielectric convection, which is based on an extended model including flexoelectricity, is also presented.

We investigate and clarify the notion of locality as it pertains to the cascades of two-dimensional turbulence. The mathematical framework underlying our analysis is the infinite system of balance equations that govern the generalized unfused structure functions, first introduced by L'vov and Procaccia. As a point of departure we use a revised version of the system of hypotheses that was proposed by Frisch for three-dimensional turbulence. We show that both the enstrophy cascade and the inverse energy cascade are local in the sense of non-perturbative statistical locality. We also investigate the stability conditions for both cascades. We have shown that statistical stability with respect to forcing applies unconditionally for the inverse energy cascade. For the enstrophy cascade, statistical stability requires large-scale dissipation and a vanishing downscale energy dissipation. A careful discussion of the subtle notion of locality is given at the end of the paper.