Linear response analysis in the nonequilibrium steady state (Gaussian regime) provides two independent fluctuation-response relations. One, in the form of the symmetric matrix, manifests the departure from the equilibrium formula through the quantity so-called irreversible circulation. The other, in...

We propose an extension of the nonequilibrium invaded cluster (IC) algorithm, which reestablishes a correct scaling of fluctuations at criticality and also self-adjusts to the critical temperature. We show that by introducing a single constraint to the intrinsic quantity of the IC algorithm the temp...

We investigate a recently proposed non-Markovian random walk model characterized by loss of memories of the recent past and amnestically induced persistence. We report numerical and analytical results showing the complete phase diagram, consisting of four phases, for this system: (i) classical nonpe...

We show by resolving single-particle dynamics as a function of contact number that dynamical heterogeneity in depletion colloidal gels must have more than one structural origin. Although the magnitude of dynamical heterogeneity of weak gels with cluster structure and strong gels with string structur...

The diffusive relaxation of a colloidal fluid adsorbed in a porous medium depends on many factors, including the concentration and composition of the adsorbed colloidal fluid, the average structure of the porous matrix, and the nature of the colloid-colloid and colloid-substrate interactions. A simp...

We experimentally investigated statistical properties of side branches of quasi-two-dimensional NH₄Cl dendritic crystals. The height distributions of the side branches and their number density exhibit scale-invariant power laws. The results are in good agreement with the results of numerical simul...

KIF1A kinesins are single-headed motor proteins which move on cylindrical nanotubes called microtubules (MTs). A normal MT consists of 13 protofilaments on which the equispaced motor binding sites form a periodic array. The collective movement of the kinesins on a MT is, therefore, analogous to vehi...

Proteins acting as molecular machines can undergo cyclic internal conformational motions that are coupled to ligand binding and dissociation events. In contrast to their macroscopic counterparts, nanomachines operate in a highly fluctuating environment, which influences their operation. To bridge th...

Dynamics of molecular motors that move along linear lattices and interact with them via reversible destruction of specific lattice bonds is investigated theoretically by analyzing exactly solvable discrete-state “burnt-bridge” models. Molecular motors are viewed as diffusing particles that can a...

Active cellular transport is a fundamental mechanism for protein and vesicle delivery, cell cycle, and molecular degradation. Viruses can hijack the transport system and use it to reach the nucleus. Most transport processes consist of intermittent dynamics, where the motion of a particle, such as a ...

We show how accurate kinetic information, such as the rates of protein folding and unfolding, can be extracted from replica-exchange molecular dynamics (REMD) simulations. From the brief and continuous trajectory segments between replica exchanges, we estimate short-time propagators in conformation ...

The complex dynamics of intracellular calcium regulates cellular responses to information encoded in extracellular signals. Here we study the encoding of these external signals in the context of the Li-Rinzel model. We show that by control of biophysical parameters the information can be encoded in ...

We demonstrate the microscopic equivalent of a step-stress rheological measurement. An optical torque is applied to a birefringent wax microdisk embedded in gelatin, a highly entangled viscoelastic biopolymer, using circularly polarized laser tweezers. By increasing the laser power and measuring the...

We introduce a stochastic model of growing networks where both the number of new nodes which join the network and the number of connections vary stochastically. We provide an exact mapping between this model and the zero-range process, and calculate analytically the degree distribution for any given...

The scaling properties of spectra of real world complex networks are studied by using the wavelet transform. It is found that the spectra of networks are multifractal. According to the values of the long-range correlation exponent, the Hust exponent H , the networks can be classified into three typ...

In order to explain the empirical evidence that the dynamics of human activity may not be well modeled by Poisson processes, a model based on queuing processes was built in the literature [A. L. Barabasi, Nature (London) 435, 207 (2005)]. The main assumption behind that model is that people execute ...

We study the dynamics of unidirectionally delay-coupled nonlinear oscillators. Cascading them within a ring of fixed total propagation delay, we demonstrate simple scaling behavior of correlation properties. In fact, the correlation properties of a ring with N elements can be deduced from the auto...

In a region in phase space where there is a chaotic saddle, all initial conditions will escape from it after a transient with the exception of a set of points of zero Lebesgue measure. The action of an external noise makes all trajectories escape faster. Attempting to avoid those escapes by applying...

We address the longstanding problem of recovering dynamical information from noisy acoustic emission signals arising from peeling of an adhesive tape subject to constant traction velocity. Using the phase space reconstruction procedure we demonstrate the deterministic chaotic dynamics by establishin...

We study scarring phenomena in open quantum systems. We show numerical evidence that individual resonance eigenstates of an open quantum system present localization around unstable short periodic orbits in a similar way as their closed counterparts. The structure of eigenfunctions around these class...

This paper reports the control of spatiotemporal intermittency in an electroconvective system in a nematic liquid crystal. In the spatiotemporal intermittency, an ordered structure [the defect lattice (DL)] coexists with turbulence. Control of the spatiotemporal intermittency, in which the turbulent...

We study the spatiotemporal properties of coherent states (peaks, holes, and fronts) in a bistable activator-inhibitor system that exhibits biochemical saturated autocatalysis, and in which fronts do not preserve spatial parity symmetry. Using the Gierer-Meinhardt prototype model, we find the condit...

We consider a general model of self-propelling particles interacting through a pairwise attractive force in the presence of noise and communication time delay. Previous work by Erdmann [Phys. Rev. E 71, 051904 (2005)] has shown that a large enough noise intensity will cause a translating swarm of i...

Recently, by analyzing the measurement data of Nikuradze [NACA Tech. Memo No. 1292 (1950)], it has been proposed [N. Goldenfeld, Phys. Rev. Lett. 96, 044503 (2006)] that the friction factor, f , of rough-pipe flow obeys a scaling law in the turbulent regime. Here, we provide a phenomenological scal...

Three-dimensional (3D) ac electro-osmotic (ACEO) pumps have recently been developed that are much faster and more robust than previous planar designs. The basic idea is to create a “fluid conveyor belt” by placing opposing ACEO slip velocities at different heights. Current designs involve electr...

Inertial particles advected in chaotic flows often accumulate in strange attractors. While moving in these fractal sets they usually approach each other and collide. Here we consider inertial particles aggregating upon collision. The new particles formed in this process are larger and follow the equ...

The dynamic resistance of a sphere with a general inhomogeneous slip boundary condition is analyzed in Newtonian unbounded uniform flow at low Reynolds number. The boundary condition is treated as a perturbation to a homogeneous sphere, assuming that the slip length magnitude b is much smaller tha...

An experiment on LULI 2000 laser devoted to density determination of shocked plastic from a two-dimensional monochromatic x-ray radiography is presented. A spherical quartz crystal was set to select the He-α line of vanadium at 2.382   Å and perform the image of the main target. Rear side...

The hallmark of nonlinear complexity phenomena in magnetohydrodynamic and plasma turbulence as well as all natural sciences is the appearance of intermittent fluctuating events. We introduce here a unique procedure that is both physically explicable and quantitatively accurate in deciphering the mul...

We derive an analytic formula for the lateral dynamics of solitons in a general inhomogeneous nonlinear media, and show that it can be valid over tens of diffraction lengths. In particular, we show that solitons centered at a lattice maximum can be “mathematically unstable” but “physically sta...

We investigate the critical behavior of the random-bond ±J Ising model on a square lattice at the multicritical Nishimori point in the T-p phase diagram, where T is the temperature and p is the disorder parameter ( p=1 corresponds to the pure Ising model). We perform a finite-size scaling ...

The exclusion process in which particles may jump any distance l≥1 with the probability that decays as l^−(1+σ) is studied from the coarse-grained equation for density profile in the limit when the lattice spacing goes to zero. For 1<σ<2 , the usual diffusion term of this equation is...

In two recent papers, a detailed study has been presented of the out-of-equilibrium dynamics of an infinite system of self-gravitating points initially located on a randomly perturbed lattice. In this paper, we extend the treatment of the early time phase during which strong nonlinear correlations f...

Analyzing the d -dimensional spherical model, we show that underlying saddles, defined through a map in the configuration space, play a central role in driving the phase transition. At the phase transition point the underlying saddle energy reaches its lowest value, corresponding to the trivial bou...

Numerical simulations of two-dimensional stationary dense granular flows are performed. We check that the system obeys the h_stop phenomenology. Focusing on the spatial correlations of the instantaneous velocity fluctuations of the grains, we give evidence of the existence of correlated motion over...

As a generic model system of an asymmetric binary-fluid mixture, hexadecane dissolved in carbon dioxide is considered, using a coarse-grained bead-spring model for the short polymer, and a simple spherical particle with Lennard-Jones interactions for the carbon dioxide molecules. In previous work, i...

In this work, we study the cooperative adsorption of fluids in a heterogeneous pore, in which the pore walls are composed of homogeneous substrates with chemical groups (CGs) decorating them. The adsorption caused by the homogeneous substrates alone and that by CGs do not add up to the overall adsor...

We analyze the influence of a thin polymer layer with lateral side groups on the anchoring of a nematic liquid crystal. We show that the effective anisotropic part of the anchoring energy depends on the coupling of the nematic with the polymer side groups, as well as on the coupling of the polymer s...

We consider two-dimensional dispersions of droplets of isotropic phase in a liquid with an XY -like order parameter, tilt, nematic, and hexatic symmetries being included. Strong anchoring boundary conditions are assumed. Textures for a single droplet and a pair of droplets are calculated and a univ...

The adult vasculature is comprised of three distinct compartments: the arteries, which carry blood away from the heart and display a divergent flow pattern; the capillaries, where oxygen and nutrient delivery from blood to tissues, as well as metabolic waste removal, occurs; and the veins, which car...

The properties of contact matrices ( C matrices) needed for native proteins to be the lowest-energy conformations are considered in relation to a contact energy matrix ( E matrix). The total conformational energy is assumed to consist of pairwise interaction energies between atoms or residues, eac...

When each site of a spatially extended excitable medium is independently driven by a Poisson stimulus with rate h , the interplay between creation and annihilation of excitable waves leads to an average activity F . It has recently been suggested that in the low-stimulus regime (h∼0) the respo...

A phase response curve (PRC) characterizes the signal transduction between oscillators such as neurons on a fixed network in a minimal manner, while spike-timing-dependent plasiticity (STDP) characterizes the way of rewiring networks in an activity-dependent manner. This paper demonstrates that thes...

Recently, by analyzing the measurement data of Nikuradze [NACA Tech. Memo No. 1292 (1950)], it has been proposed [N. Goldenfeld, Phys. Rev. Lett. 96, 044503 (2006)] that the friction factor, f , of rough-pipe flow obeys a scaling law in the turbulent regime. Here, we provide a phenomenological scal...

An investigation of the dynamo instability close to the threshold produced by an ABC forced flow is presented. We focus on the on-off intermittency behavior of the dynamo and the countereffect of the Lorentz force in the nonlinear stage of the dynamo. The Lorentz force drastically alters the stati...

The static and dynamic critical properties of the ferromagnetic q -state Potts models on a square lattice with q=2 and 3 are numerically studied via the nonequilibrium relaxation method. The relaxation behavior of both the order parameter and energy as well as that of the second moments are inves...

Spiral wave propagation in oscillatory media with a disk-shaped inhomogeneity is examined. Depending on the properties of the medium as well as the inhomogeneity (different frequencies in two regions), distinct spiral waves including sinklike spirals and dense-sparse spirals, are able to emerge. We ...

We study the dynamics of unidirectionally delay-coupled nonlinear oscillators. Cascading them within a ring of fixed total propagation delay, we demonstrate simple scaling behavior of correlation properties. In fact, the correlation properties of a ring with N elements can be deduced from the auto...

Experiment demonstrates the first direct transformation of a tungsten wire core to the plasma state by Joule heating during nanosecond electrical explosion in vacuum. Energy of ∼130 eV/atom was deposited into the 12 μm W wire coated by 2 μm polyimide during the first ∼10 ns . ...

Excitation of electromagnetic fields in a cavity is studied in the time domain. A signal, which excites the fields, stands in Maxwell’s equations as the electric current density given by an integrable function of coordinates and time. The problem is solved within the framework of the evolutionary ...

The effect of dissipation when due to the load of a transmission line coupled to a Josephson junction is reconsidered and evaluated by means of a simple direct procedure that supplies analytical expressions. The results are in good agreement with the ones previously reported in the literature. A sim...

A combination of reverse Monte Carlo (RMC) and computational homology is examined as a useful approach in connecting scattering experiments to mathematics for 3D morphology modeling. We develop a different method of morphology modeling from multiple two-dimensional (2D) scattering patterns of struct...

Various ways of implementing boundary conditions for the numerical solution of the Navier-Stokes equations by a lattice Boltzmann method are discussed. Five commonly adopted approaches are reviewed, analyzed, and compared, including local and nonlocal methods. The discussion is restricted to velocit...

We explore six classes of fractal probability laws defined on the positive half-line: Weibull, Frechét, Lévy, Hyper Pareto, Hyper Beta, and Hyper Shot Noise. Each of these classes admits a unique statistical power-law structure, and is uniquely associated with a certain operation of renormalization. All six classes turn out to be one-dimensional projections of underlying Poisson processes which, in turn, are the unique fixed points of Poissonian renormalizations. The first three classes correspond to linear Poissonian renormalizations and are intimately related to Extreme Value Theory (Weibull, Frechét) and to the Central Limit Theorem (Lévy). The other three classes correspond to nonlinear Poissonian renormalizations. Pareto's law - commonly perceived as the universal fractal probability distribution - is merely a special case of the Hyper Pareto class. PACS: 02.50.-r - Probability theory, stochastic processes, and statistics; 05.45.Df - Fractals.

We study spatial anisotropy effects on the bulk and finite-size critical behavior of the O(n) symmetric anisotropic j4 lattice model with periodic boundary conditions in a d-dimensional hypercubic geometry above, at and below Tc. The absence of two-scale factor universality is discussed for the bulk order-parameter correlation function, the bulk scattering intensity, and for several universal bulk amplitude relations. The anisotropy parameters are observable by scattering experiments at Tc. For the confined system, renormalization-group theory within the minimal subtraction scheme at fixed dimension d for 2 < d < 4 is employed. In contrast to the e = 4 - d expansion, the fixed-d finite-size approach keeps the exponential form of the order-parameter distribution function unexpanded. For the case of cubic symmetry and for n=1 our perturbation approach yields excellent agreement with the Monte Carlo (MC) data for the finite-size amplitude of the free energy of the three-dimensional Ising model at Tc by Mon [Phys. Rev. Lett. 54, 2671 (1985)]. The e expansion result is in less good agreement. Below Tc a minimum of the scaling function of the excess free energy is found. We predict a measurable dependence of this minimum on the anisotropy parameters. The relative anisotropy effect on the free energy is predicted to be significantly larger than that on the Binder cumulant. Our theory agrees quantitatively with the non-monotonic dependence of the Binder cumulant on the ferromagnetic next-nearest neighbor (NNN) coupling of the two-dimensional Ising model found by MC simulations of Selke and Shchur [J. Phys. A 38, L739 (2005)]. Our theory also predicts a non-monotonic dependence for small values of the antiferromagnetic NNN coupling and the existence of a Lifshitz point at a larger value of this coupling. The nonuniversal anisotropy effects in the finite-size scaling regime are predicted to satisfy a kind of restricted universality. The tails of the large-L behavior at T ¹ Tc violate both finite-size scaling and universality even for isotropic systems as they depend on the bare four-point coupling of the j4 theory, on the cutoff procedure, and on subleading long-range interactions.

We consider shock probes in a one-dimensional driven diffusive medium with nearest neighbor Ising interaction (KLS model). Earlier studies based on an approximate mapping of the present system to an effective zero-range process concluded that the exponents characterising the decays of several static and dynamical correlation functions of the probes depend continuously on the strength of the Ising interaction. On the contrary, our numerical simulations indicate that over a substantial range of the interaction strength, these exponents remain constant and their values are the same as in the case of no interaction (when the medium executes an ASEP). We demonstrate this by numerical studies of several dynamical correlation functions for two probes and also for a macroscopic number of probes. Our results are consistent with the expectation that the short-ranged correlations induced by the Ising interaction should not affect the large time and large distance properties of the system, implying that scaling forms remain the same as in the medium with no interactions present.

Recently we considered a stochastic discrete model which describes fronts of cells invading a wound . In the model cells can move, proliferate, and experience cell-cell adhesion. In this work we focus on a continuum description of this phenomenon by means of a generalized Cahn-Hilliard equation (GCH) with a proliferation term. As in the discrete model, there are two interesting regimes. For subcritical adhesion, there are propagating "pulled" fronts, similarly to those of Fisher-Kolmogorov equation. The problem of front velocity selection is examined, and our theoretical predictions are in a good agreement with a numerical solution of the GCH equation. For supercritical adhesion, there is a nontrivial transient behavior, where density profile exhibits a secondary peak. To analyze this regime, we investigated relaxation dynamics for the Cahn-Hilliard equation without proliferation. We found that the relaxation process exhibits self-similar behavior. The results of continuum and discrete models are in a good agreement with each other for the different regimes we analyzed.

Quantum heat engines employ as working agents multi-level systems instead of classical gases. We show that under some conditions quantum heat engines are equivalent to a series of reservoirs at different altitudes containing balls of various weights. A cycle consists of picking up at random a ball from one reservoir and carrying it to the next, thereby performing or absorbing some work. In particular, quantum heat engines employing as working agent two-level atoms are modeled by reservoirs containing balls of weight 0 or 1. The mechanical model helps us prove that the maximum efficiency of quantum heat engines is the Carnot efficiency. Heat pumps an negative temperatures are considered.

A discrete model exhibiting conserved dynamics with nonconserved noise involving particles of different nature, termed as linear and nonlinear, is proposed here. The morphology of the surface has been studied with different abundances of these particles. The saturated surface, slowly evolved from lower contribution of nonlinear particles to higher contribution of nonlinear particles, splits into four distinct scaling regimes with three crossover lengths. Each regime is characterized by different scaling property. It is shown that when the contribution of the nonlinear particles crosses a critical value, the surface morphology shows a linear-nonlinear `phase-transition'. The roughness exponent in nonlinear regime is well compared with that of the continuum nonlinear equation in Molecular Beam Epitaxy (MBE) class as well as MBE motivated discrete model.

We show that colloidal superstructures could be assembled in mixtures of large and small colloidal particles dispersed in a nematic liquid crystal. Using elastic interaction of small colloidal particles with the disclination lines we succeed to demonstrate how one can decorate with small particles a topological matrix of defect rings and loops formed by an array of large colloidal particles. Our simulations show that this novel concept of colloidal self-assembly in nematics could be extended down to the nanoscale particles.

A system consisting of two map-based neurons coupled through reciprocal excitatory or inhibitory chemical synapses is discussed. After a brief explanation of the basic mechanism behind generation and synchronization of bursts, parameter space is explored to determine less obvious but biologically meaningful regimes and effects. Among them, we show how excitatory synapses without any delays may induce anti-phase synchronization; that a synapse may change it character from excitatory to inhibitory and viceversa by changing its conductance, without any change in reversal potential; and that small variations in the synaptic threshold may result in drastic changes in the synchronization of spikes within bursts. Finally we show how the synchronization effects found in the two-neuron system carry over to larger networks.

We study the influence of the driving rate in the two-dimensional Oslo rice pile model. We find that the usual power-law behavior of the avalanche size distribution still holds for small avalanches, independent of the driving rate. The signature of fast driving is, however, the increase of the incidence rate of large avalanches. For larger driving rates, this increase is more prominent and spreads to smaller avalanche sizes. As a result, the mass flow due to large avalanches is increased much more than would be expected from an increase in driving rate alone. Fast driving leads to a dramatic increase in devastating avalanches, just before the continuous flow regime is reached.

We numerically study the dynamics of a discrete spring-block model introduced by Olami, Feder and Christensen (OFC) to mimic earthquakes and investigate to which extent this simple model is able to reproduce the observed spatiotemporal clustering of seismicty. Following a recently proposed method to characterize such clustering by networks of recurrent events [Geophys. Res. Lett. 33, L1304, 2006], we find that for synthetic catalogs generated by the OFC model these networks have many non-trivial statistical properties. This includes characteristic degree distributions - very similar to what has been observed for real seismicity. There are, however, also significant differences between the OFC model and earthquake catalogs indicating that this simple model is insufficient to account for certain aspects of the spatiotemporal clustering of seismicity.

This article reports on a joint theoretical and experimental study of the Pauli quantum-mechanical stress tensor Tab(x,y) for open two-dimensional chaotic billiards. In the case of a finite current flow through the system the interior wave function is expressed as y = u+iv. With the assumption that u and v are Gaussian random fields we derive analytic expressions for the statistical distributions for the quantum stress tensor components Tab. The Gaussian random field model is tested for a Sinai billiard with two opposite leads by analyzing the scattering wave functions obtained numerically from the corresponding Schrödinger equation. Two-dimensional quantum billiards may be emulated from planar microwave analogues. Hence we report on microwave measurements for an open 2D cavity and how the quantum stress tensor analogue is extracted from the recorded electric field. The agreement with the theoretical predictions for the distributions for Tab(x,y) is quite satisfactory for small net currents. However, a distinct difference between experiments and theory is observed at higher net flow, which could be explained using a Gaussian random field, where the net current was taken into account by an additional plane wave with a preferential direction and amplitude.

On basis of numerical simulation it is found a novel type of dissipative solitons in passive mode-locked fiber lasers with anomalous frequency dispersion. These solitons have a powerful pedestal with a periodical structure. They can be multistable: with the same laser parameters the pedestals can have different structures. The single solitons with an asymmetric pedestal demonstrate bistability: there exist two stable states with right and left spectral-spatial asymmetries for which the single soliton velocities are different.

We propose a method of analysis of dynamical networks based on a recent measure of Granger causality between time series, based on kernel methods. The generalization of kernel Granger causality to the multivariate case, here presented, shares the following features with the bivariate measures: (i) the nonlinearity of the regression model can be controlled by choosing the kernel function and (ii) the problem of false-causalities, arising as the complexity of the model increases, is addressed by a selection strategy of the eigenvectors of a reduced Gram matrix whose range represents the additional features due to the second time series. Moreover, there is no {\it a priori} assumption that the network must be a directed acyclic graph. We apply the proposed approach to a network of chaotic maps and to a simulated genetic regulatory network: it is shown that the underlying topology of the network can be reconstructed from time series of node's dynamics, provided that a sufficient number of samples is available. Considering a linear dynamical network, built by preferential attachment scheme, we show that for limited data use of bivariate Granger causality is a better choice w.r.t methods using $L1$ minimization. Finally we consider real expression data from HeLa cells, 94 genes and 48 time points. The analysis of static correlations between genes reveals two modules corresponding to well known transcription factors; Granger analysis puts in evidence nineteen causal relationships, all involving genes related to tumor development. \pacs{05.45.Xt , 87.18.Vf}

Finite-amplitude gravity water waves in Bragg resonance with a periodic one-dimensional topography are studied numerically using exact equations of motion for ideal potential free-surface flows. Spontaneous formation of highly nonlinear localized structures is observed in the numerical experiments. These coherent structures consisting of several nearly standing extreme waves are similar in many aspects to the Bragg solitons previously known in nonlinear optics.

In this work, we use a dissipative particle dynamics (DPD)-based model for two-phase flows to simulate the breakup of liquid nanocylinders. Rayleigh’s criterion, which states that liquid cylinders are unstable to disturbances with a wavelength longer than their circumference, is shown to be valid even at the nanolevel in agreement with prior molecular dynamics simulations. It is shown that satellite drops are not observed at the nanolevel because of the significant role played by thermal fluctuations which leads to a symmetric breakup of the neck joining the two main drops. We show that the global rupture time follows predictions from linear stability theory and the dynamics near the breakup point agree well with the theoretical predictions which state that breakup is accelerated due to thermal fluctuations.

Loose packings of spheres with bidisperse or lognormal distributions are generated by random sequential deposition. Porosity, conductivity and permeability are determined. Porosities correspond to loose packings, but they follow the usual trends for bidisperse packings. Conductivity and permeability follow power laws as functions of the porosity of the packings. Several other quantities such as the classical Kozeny constant are successfully represented as functions of porosity. Some dimensionless representations gather the numerical data on curves valid for all particle distributions. Finally, comparisons with experimental data are satisfactory.

We study the potential and plasma density variations around a solid object in a plasma flow, emphasizing supersonic flows. These objects can be dust grains, for instance. Conducting as well as insulating materials are considered. In a streaming plasma, a dust grain develops an electric dipole moment which varies systematically with the relative plasma flow. The strength and direction of this dipole moment depends critically on the material. The net charge together with the electric dipole associated with the dust grains gives rise to electric fields which affects the trajectories of nearby charged particles. The perturbation of ion orbits in streaming plasmas can give rise to a focusing of ions in the wake region facing away from the plasma flow. We study the parameter dependence of this ion focus. Our simulations are carried out in two spatial dimensions by a Particle-in-Cell code, treating ions and electrons as individual particles.

Measurements of the L-shell emission of highly charged gold ions were made under controlled laboratory conditions using the SuperEBIT electron beam ion trap, allowing detailed spectral observations of lines from Fe-like Au53+ through Ne-like Au69+. Using atomic data from the Flexible Atomic Code, we have identified strong 3d5/2® 2p3/2 emission features that can be used to diagnose the charge state distribution in high energy density plasmas, such as those found in the laser entrance hole of hot hohlraum radiation sources. We provide collisional-radiative calculations of the average ion charge áZ ñ as a function of temperature and density, which can be used to relate charge state distributions inferred from 3d5/2® 2p3/2 emission features to plasma conditions, and investigate the effects of plasma density on calculated L-shell Au emission spectra.

The exponential splitting of the classical evolution operator yields symplectic integrators if the canonical Hamiltonian is separable. Similar splitting of the non-canonical evolution operator for a charged particle in a magnetic field produces exact energy conserving algorithms. The latter algorithms evaluate the magnetic field directly with no need of a vector potential and are more stable with far less phase errors than symplectic integrators. For a combined electric and magnetic field, these algorithms from splitting the non-cannonical evolution operator are neither fully symplectic nor exactly energy conserving, yet they behave exactly like symplectic algorithms in having qualitatively correct trajectories and bounded periodic energy errors. This work shows that exponential splitting algorithms of any order for solving particle trajectories in a general electric and magnetic field can be systematically derived by use of the angular momentum operator of quantum mechanics. The use of operator analysis in this work fully comprehends the intertwining interaction between electric and magnetic forces and make possible the derivation of highly non-trivial integrators.

The soliton interaction is investigated based on solving the higher-order nonlinear Schrödinger equation with the effects of third-order dispersion, self-steepening and stimulated Raman scattering. By using Hirota's bilinear method, the analytic one-, two- and three-soliton solutions of this model are obtained. According to those solutions, of physical and optical interests, relevant properties and features are illustrated. The results of this paper will be of certain value to the study on signal amplification and pulse compression.

The evolution of the domain wall is reduced to the dynamics of the membrane. The rigorous construction of curved membranes in the real scalar field models with domain wall solutions is presented. An example of the curved membrane is discussed in details. The curved domain wall solutions are constructed.

The aim of the paper is to show that splitting of a waveguide leads to fission of bulk solitons in solids. We study the dynamics of a longitudinal bulk solitary wave in a delaminated, symmetric layered elastic bar. First, we consider a two-layered bar and assume that there is a perfect interface when x < 0 and complete debonding (splitting) when x > 0, where the axis Ox is directed along the bar. We derive the so-called Doubly Dispersive Equation (DDE) for a long nonlinear longitudinal bulk wave propagating in an elastic bar of rectangular cross section. We formulate the problem for a delaminated two-layered bar in terms of the DDE with piecewise constant coefficients, subject to continuity of longitudinal displacement and normal stress across the "jump" at x = 0. We find the weakly nonlinear solution to the problem and consider the case of an incident solitary wave. The solution describes both the reflected and transmitted waves in the far field, as well as the diffraction in the near field (in the vicinity of the jump). We generalize the solution to the case of a symmetric n-layered bar. We show that delamination can lead to the fission of an incident solitary wave, and obtain explicit formulae for the number, amplitudes, velocities and positions of the secondary solitary waves propagating in each layer of the split waveguide. We establish that generally there is a higher-order reflected wave even when the leading order reflected wave is absent.

In non-ideal gas lattice Boltzmann (LB) models, obtaining the correct form of the pressure tensor is essential in determining many of the statistical mechanical properties such as the surface tension and the density profile. Here we outline a general approach for calculating the pressure tensor in LB models with interactions beyond the nearest neighbors. The statistical mechanical properties calculated from such a pressure tensor are shown to agree very well with those measured from numerical experiments. Comparisons with alternative theories are also made.

The Bell-Evans-Polanyi principle that is valid for a chemical reaction that proceeds along the reaction coordinate over the transition state is extended to molecular dynamics trajectories that in general do not cross the dividing surface between the initial and the final local minima at the exact transition state. Our molecular dynamics Bell-Evans-Polanyi principle states that low energy molecular dynamics trajectories are more likely to cross into the basin of attraction of a low energy local minimum than high energy trajectories. In the context of global optimization schemes based on molecular dynamics our molecular dynamics Bell-Evans-Polanyi principle implies that using trajectories that have an energy that is only somewhat higher than the energy necessary to overcome the barriers lead fastest to the global minimum of funnel like energy landscapes.