Synchrony emerges in a population of oscillators interacting through in-phase couplings. We addressed a question of whether inhibitory neurons simply hinder the emergence of the synchronous activity among excitatory neurons, or facilitate it. An analysis of a simple phase model revealed that both cases may take place. Numerical simulations of the more realistic models revealed that inhibitory neurons rather facilitate rhythmic activity.

We make a numerical study of the effect that spatial perturbations have in normal Saffman-Taylor fingers driven at constant pressure gradients. We use a phase field model that allows for spatial variations in the Hele-Shaw cell. We find that, regardless of the specific way in which spatial perturbations are introduced, a lateral instability develops on the sides of the propagating Saffman-Taylor finger. Moreover, the instability exists regardless of the intensity of spatial perturbations in the cell as long as the perturbations are felt by the finger tip. If, as the finger propagates, the spatial perturbations felt by the tip change, the instability is nonperiodic. If, as the finger propagates, the spatial perturbations felt by the tip are persistent, the instability developed is periodic. In the later case, the instability is symmetrical or asymmetrical depending on the intensity of the perturbation.

Experiments and simulations from a variety of sample sizes indicated that the centrifugal force significantly affects the domain-chaos state observed in rotating Rayleigh-Bénard convection-patterns. In a large-aspect-ratio sample, we observed a hybrid state consisting of domain chaos close to the sample center, surrounded by an annulus of nearly stationary nearly radial rolls populated by occasional defects reminiscent of undulation chaos. Although the Coriolis force is responsible for domain chaos, by comparing experiment and simulation we show that the centrifugal force is responsible for the radial rolls. Furthermore, simulations of the Boussinesq equations for smaller aspect ratios neglecting the centrifugal force yielded a domain precession-frequency $f\sim {\epsilon }^{\mu }$ with $\mu \simeq 1$ as predicted by the amplitude-equation model for domain chaos, but contradicted by previous experiment. Additionally the simulations gave a domain size that was larger than in the experiment. When the centrifugal force was included in the simulation, $\mu$ and the domain size were consistent with experiment.

The axial profiles of plasma parameters for low and moderate pressures, such as the plasma potential, electron temperature, and number density, have been evaluated in magnetized inductively coupled plasma. The experimental results revealed in both cases the existence of a genuine current-free double-layer structure, separating two plasma regions with different properties. Based on the experimental results, a physical scenario for the self-assembling of the double layer is proposed. Also, the axial profile of the electron number density downstream is analyzed, emphasizing the role of neutral metastable ionization, and a simple analytical model is developed to fit the experimental data. The model allows the estimation of neutral metastable number density downstream and the recombination rate coefficient.

Seismic interferometry and the virtual-source method are related approaches for extracting the Green’s function that accounts for wave propagation between receivers by making suitable combinations of the waves recorded at these two receivers. These waves can either be excited by active, controlled, sources, or by natural incoherent sources. We compare this technique with the deconvolution of the wave field recorded at different receivers. We show that the deconvolved wave field is a solution of the same wave equation as that for the physical system, but that the deconvolved wave forms may satisfy different boundary conditions than those of the original system. We apply this deconvolution approach to the wave motion recorded at various levels in a building after an earthquake, and show how to extract the building response for different boundary conditions. Extracting the response of the system with different boundary conditions can be used to enhance, or suppress, the normal-mode response. In seismic exploration this principle can be used for the suppression of surface-related multiples.

Directed motion of topological solitons (kinks or antikinks) in the damped and ac-driven discrete sine-Gordon system is investigated. We show that if the driving field breaks certain time-space symmetries, the soliton can perform unidirectional motion. The phenomenon resembles the well known effects of ratchet transport and nonlinear harmonic mixing. Direction of the motion and its velocity depends on the shape of the ac drive. Necessary conditions for the occurrence of the effect are formulated. In comparison with the previously studied continuum case, the discrete case shows a number of new features: nonzero depinning threshold for the driving amplitude, locking to the rational fractions of the driving frequency, and diffusive ratchet motion in the case of weak intersite coupling.

This paper presents detailed experiments on persistent hole burning in photoreactive and multiple scattering media. The dependence of the hole shape and width on the sample thickness, transport mean free path, and absorption length was measured. The experimental results show good agreement with a previously reported theoretical calculation on the basis of a diffusion approximation [Phys. Rev. E 70, 046606 (2004)].

We have studied an evolutionary prisoner’s dilemma game with players located on two types of random regular graphs with a degree of 4. The analysis is focused on the effects of payoffs and noise (temperature) on the maintenance of cooperation. When varying the noise level and/or the highest payoff, the system exhibits a second-order phase transition from a mixed state of cooperators and defectors to an absorbing state where only defectors remain alive. For the random regular graph (and Bethe lattice) the behavior of the system is similar to those found previously on the square lattice with nearest neighbor interactions, although the measure of cooperation is enhanced by the absence of loops in the connectivity structure. For low noise the optimal connectivity structure is built up from randomly connected triangles.

This paper extends the two-compartment granular fountain [D. van der Meer, P. Reimann, K. van der Weele, and D. Lohse, Phys. Rev. Lett. 92, 184301 (2004)] to an arbitrary number of compartments: The tendency of a granular gas to form clusters is exploited to generate spontaneous convective currents, with particles going down in the well-filled compartments and going up in the diluted ones. We focus upon the bifurcation diagram of the general $K$-compartment system, which is constructed using a dynamical flux model and which proves to agree quantitatively with results from molecular dynamics simulations.

We report on extensive molecular dynamics (MD) simulations of a model for gels in both two and three dimensions. The model consists of randomly cross-linked monomers with a concentration $p$ of cross-links above the percolation concentration so that the system is in the amorphous solid phase. As the concentration of cross-links approaches the percolation concentration, the entropic shear modulus vanishes as $G\sim {(p-p_c)}^t$ with $t\approx 1.9$ in three dimensions and $t\approx 1.3$ in two dimensions. These results hold whether or not the background fluid consisting of finite clusters is retained in the system. These results are also consistent with our previous calculations and with a conjecture of de Gennes but not with recent analytical results and another body of simulations.

The molecular dynamics during the formation of a polymer dispersed liquid crystal (PDLC) was followed by dielectric relaxation spectroscopy in the frequency range from ${10}^{-1}\text{to}2\times {10}^6\mathrm{Hz}$ and over the temperature range from $158\text{to}273\mathrm{K}$. The composite was produced by thermal polymerization induced phase separation of a mixture of triethyleneglycol dimethacrylate and the nematic liquid crystal, E7, in the proportion of 60:40 w/w. Both monomer and liquid crystal vitrify upon cooling having glass transition relaxation processes already characterized by some of us; yet E7 was previously studied in a narrower frequency range, so the present work updates its dielectric behavior. The starting mixture exhibits a rather complex dielectric spectrum due to the detection of multiple processes occurring simultaneously in the monomer and liquid crystal constituents. The PDLC formation occurs by mobility changes essentially in the liquid crystal tumbling motion, while the main relaxation of the monomer depletes upon polymerization. A low intense secondary process of E7 hardly detected in the bulk material is enhanced in both starting mixture and final composite allowing its characterization.

The dynamical behavior of molecular alignment strongly affects physical properties of nematic liquid crystals. A theoretical description can be made by a nonlinear relaxation equation of the order parameter and leads to the prediction that rather complex even chaotic orientational behavior occur. Here the influence of fluctuating shear rates on the orientational dynamics especially on chaotic solutions is discussed. With the help of phase portraits and time evolution diagrams, we investigated the influence of different fluctuation strengths on the flow aligned, isotropic, and periodic solutions. To explore the effect of fluctuations on the chaotic behavior, we calculated the largest Lyapunov exponent for different fluctuation strengths. We found in all cases that small fluctuations of the shear rate do not affect the basic features of the dynamics of tumbling nematics. Furthermore, we present an amended potential modeling the isotropic to nematic transition and discuss the equivalence and difference to the commonly used Landau–de Gennes potential. In contrast to the Landau–de Gennes potential, our potential has the advantage to restrict the order parameter to physically admissible values. In the case of extensional flow, we show that the amended potential leads for increasing extensional rate to a better agreement with experimental results.

A simple one-dimensional model is constructed for polymer motion. It exhibits the crossover from reptation to Rouse dynamics through gradually allowing hernia creation and annihilation. The model is treated by the density matrix technique which permits an accurate finite-size-scaling analysis of the behavior of long polymers.

We use a lattice Boltzmann method to study pattern formation in chemically reactive binary fluids in the regime where hydrodynamic effects are important. The coupled equations solved by the method are a Cahn-Hilliard equation, modified by the inclusion of a reactive source term, and the Navier-Stokes equations for conservation of mass and momentum. The coupling is twofold, resulting from the advection of the order parameter by the velocity field and the effect of fluid composition on pressure. We study the evolution of the system following a critical quench for a linear and for a quadratic reaction source term. Comparison is made between the high and low viscosity regimes to identify the influence of hydrodynamic flows. In both cases hydrodynamics is found to influence the pathways available for domain growth and the eventual steady states.

We report experimental and numerical results on temporal patterns of propagation failures in reaction-diffusion systems. Experiments employ the 1,4-cyclohexanedione Belousov-Zhabotinsky reaction. The propagation failures occur in the frontier region of the wave train and can profoundly affect its expansion speed. The specific rhythms observed vary from simple periodic to highly complex and possibly chaotic sequences. All but the period-1 sequences are found in the transition region between “merging” and “tracking” dynamics, which correspond to wave behavior caused by two qualitatively different types of anomalous dispersion relations.

The effects of stochastic perturbations in a nonlinear $\alpha \Omega$-dynamo model are investigated. By using transformation of variables we identify a “slow” variable that determines the global evolution of the non-normal $\alpha \Omega$-dynamo system in the subcritical case. We apply an adiabatic elimination procedure to derive a closed stochastic differential equation for the slow variable for which the dynamics is determined along one of the eigenvectors of the full system. We derive the corresponding Fokker-Planck equation and show that the generation of a large scale magnetic field can be regarded as a first-order phase transition. We show that the an advantage of the reduced system is that we have explicit expressions for both the stochastic and deterministic potentials. We also obtain the stationary solution of the Fokker-Planck equation and show that an increase in the intensity of the multiplicative noise leads to qualitative changes in the stationary probability density function. The latter can be interpreted as a noise-induced phase transition. By a numerical simulation of the stochastic galactic dynamo model, we show that the qualitative behavior of the “empirical” stationary pdf of the slow variable is accurately predicted by the stationary pdf of the reduced system.

We propose a discrete lattice version of the Fokker-Planck kinetic equation in close analogy with the lattice-Boltzmann scheme. Our work extends an earlier one-dimensional formulation to arbitrary spatial dimension $D$. A generalized Hermite-Gauss procedure is used to construct a discretized kinetic equation and a Chapman-Enskog expansion is applied to adapt the scheme so as to correctly reproduce the macroscopic continuum equations. The linear stability of the algorithm with respect to the finite time step $\Delta t$ is characterized by the eigenvalues of the collision matrix. A heuristic second-order algorithm in $\Delta t$ is applied to investigate the time evolution of the distribution function of simple model systems, and compared to known analytical solutions. Preliminary investigations of sedimenting Brownian particles subjected to an orthogonal centrifugal force illustrate the numerical efficiency of the Lattice-Fokker-Planck algorithm to simulate nontrivial situations. Interactions between Brownian particles may be accounted for by adding a standard Bhatnagar-Gross-Krook collision operator to the discretized Fokker-Planck kernel.

Linearly sloped or “ramp” potentials belong to a class of core-softened models which possess a liquid-liquid critical point (LLCP) in addition to the usual liquid-gas critical point. Furthermore, they exhibit thermodynamic anomalies in their density and compressibility, the nature of which may be akin to those occurring in water. Previous simulation studies of ramp potentials have focused on just one functional form, for which the LLCP is thermodynamically stable. In this work we construct a series of ramp potentials, which interpolate between this previously studied form and a ramp-based approximation to the Lennard-Jones (LJ) potential. By means of Monte Carlo simulation, we locate the LLCP, the first order high density liquid (HDL)–low density liquid (LDL) coexistence line, and the line of density maxima for a selection of potentials in the series. We observe that as the LJ limit is approached, the LLCP becomes metastable with respect to freezing into a hexagonal close packed crystalline solid. The qualitative nature of the phase behavior in this regime shows a remarkable resemblance to that seen in simulation studies of accurate water models. Specifically, the density of the liquid phase exceeds that of the solid; the gradient of the metastable LDL-HDL line is negative in the pressure $\left(p\right)$-temperature $\left(T\right)$ plane; while the line of density maxima in the $p\text{−}T$ plane has a shape similar to that seen in water and extends into the stable liquid region of the phase diagram. As such, our results lend weight to the “second critical point” hypothesis as an explanation for the anomalous behavior of water.

Minimal energy shapes of closed, elastic shells with 12 pentagonal disclinations introduced in otherwise hexagonally coordinated crystalline lattice are studied. The geometry and the total energy of shells are studied as a function of the elastic properties of the material they are made of. Particular emphasis is put on the buckling transition of the shells, that is, a strong preference of the shell shapes to “buckle out” in spatial regions close to the pentagonal disclinations for a certain range of the elastic parameters of the problem. The transition effectively increases the mean square aspherity of shapes, making them look more like an icosahedron rather than a sphere, which is a preferred shape prior to the onset of the transition. The properties of the buckling transition are studied in cases when (i) the total volume enclosed by the elastic shell has to be fixed and when (ii) there is an internal pressure acting on the shell. This may be related to the maturation process in nonenveloped dsDNA viruses, where the insertion of the genetic material in a preformed protein shell (viral coating) may effectively impose the fixed volume and/or pressure constraint. Several scenarios that may explain the experimentally observed feature of mature viruses being more aspherical (facetted) from their immature precursors are discussed, and predictions for the elastic properties of viral coatings are obtained on the basis of the presented studies.

We discuss how the diffusive dynamics of a conserved order parameter should be numerically treated when impenetrable wall surfaces are present and interact with the degrees of freedom characterized by the order parameter. We derive the discretization scheme for the dynamics, paying particular attention to the conservation of the order parameter in the strict numerical sense. The discretized chemical potential, or the functional derivative of the free energy, contains a surface contribution inversely proportional to the grid spacing $\mathrm{\Delta }z$, which was proposed heuristically in a recent paper of Henderson and Clarke [Macromol. Theory Simul. 14, 435 (2005)]. Although apparently that surface contribution diverges in the continuum limit $\mathrm{\Delta }z\to 0$, we can show, by an analytic argument and numerical calculations, that this divergence does not yield any anomalies, and that our discretization scheme is well defined in this limit. We also discuss the correspondence of our treatment to the model proposed by Puri and Binder [Phys. Rev. A 46, R4487 (1992)] extensively used for the present problem.