An unexpected type of behavior in electroconvection (EC) has been detected in nematic liquid crystals (NLCs) under the condition of comparable time scales of the director relaxation and the period of the driving ac voltage. The studied NLCs exhibit standard EC (s-EC) at the onset of the instability, except one compound in which nonstandard EC (ns-EC) has been detected. In the relevant frequency region, the threshold voltage for conductive s-EC bends down considerably, while for dielectric s-EC it bends up strongly with the decrease of the driving frequency. We show that inclusion of the flexoelectric effect into the theoretical description of conductive s-EC leads to quantitative agreement, while for dielectric s-EC a qualitative agreement is achieved. The frequency dependence of the threshold voltage for ns-EC strongly resembles that of the dielectric s-EC.

The stability and arrangements of two dust particles in a plasma are investigated in terms of the Hamiltonian of the system. It is shown that the Hamiltonian description of a non-Hamiltonian system can be used to predict qualitative features of possible equilibria in a variety of confinement potentials and can provide useful plasma diagnostics. The results compare favorably with those of simulations and are used to create experimental hypotheses. In particular, the symmetry-breaking transition of the particles as they leave the horizontal plane admits a Hamiltonian description which is used to elucidate the wake parameters.

In the present study we examine the thermodynamic consistency of lattice Boltzmann equation (LBE) models that are based on the forcing method by comparing different numerical treatments of the LBE for van der Waals fluids. The different models are applied for the calculation of bulk and interfacial thermodynamic properties at various temperatures. The effect of the interface density gradient parameter, $\kappa$, that controls surface tension, is related explicitly with the fluid characteristics, including temperature, molecular diameter, and lattice spacing, through the employment of a proper intermolecular interaction potential. A comprehensive analysis of the interfacial properties reveals some important shortcomings of the LBE methods when central finite difference schemes are employed in the directional derivative calculations and proposes a proper treatment that ensures thermodynamically consistent interfacial properties in accord with the van der Waals theory. The results are found to be in excellent quantitative agreement with exact results of the van der Waals theory preserving all the major features of the interfacial characteristics of vapor-liquid systems of different shapes and sizes.

Coupled map lattices are able to store short-term memories when an external periodic input is applied. We consider short-term memory formation in networks with both regular (nearest-neighbor) and randomly chosen connections. The regimes under which single or multiple memorized patterns are stored are studied in terms of the coupling and nonlinear parameters of the network.

We apply the iterated edge-state tracking algorithm to study the boundary between laminar and turbulent dynamics in plane Couette flow at $\mathrm{Re}=400$. Perturbations that are not strong enough to become fully turbulent or weak enough to relaminarize tend toward a hyperbolic coherent structure in state space, termed the edge state, which seems to be unique up to obvious continuous shift symmetries. The results reported here show that in cases where a fixed point has only one unstable direction, such as for the lower-branch solution in plane Couette flow, the iterated edge tracking algorithm converges to this state. They also show that the choice of initial state is not critical and that essentially arbitrary initial conditions can be used to find the edge state.

A derivation of the fluctuation-dissipation theorem for the microcanonical ensemble is presented using linear response theory. The theorem is stated as a relation between the frequency spectra of the symmetric correlation and response functions. When the system is not in the thermodynamic limit, this result can be viewed as an extension of the fluctuation-dissipation relations to a situation where dynamical fluctuations determine the response. Therefore, the relation presented here between equilibrium fluctuations and response can have a very different physical nature from the usual one in the canonical ensemble. These considerations imply that the fluctuation-dissipation theorem is not restricted to the context of the canonical ensemble, where it is usually derived. Dispersion relations and sum rules are also obtained and discussed in the present case. Although analogous to the Kramers-Kronig relations, they are not related to the frequency spectrum but to the energy dependence of the response function.

We numerically investigate force structures in the packing of fine cohesive particles using the discrete element method. By changing the particle size and therefore the van der Waals force, the effect of cohesion on the normal contact force and the total normal force, which is the sum of the normal contact forces and the van der Waals forces, is analyzed. It is shown that, with decreasing particle size, the normal contact forces become more uniform and have a narrower and more symmetric distribution, while the distributions of the total normal forces widen. Spatial correlation between the interparticle forces exists for the packing of coarse noncohesive particles. As the particle size decreases, this correlation becomes weaker for the contact forces but stronger for the total normal forces. A comparison between the effective weight of particles and the internal force structure suggests that there are differences between the particle-particle and particle-wall forces. The bimodal distribution of the effective weight indicates that there may exist two phases in the packings when cohesion is present, governed by the compressive and tensile stresses.

Surface diffusion-mediated decay of two-dimensional nanostructures is studied by means of a kinetic Monte Carlo model. We consider several possible choices for the activation energies associated with possible diffusion paths, including simple phenomenological models, as well as results provided by the embedded atom model. Numerical results show that kinetic aspects of the evolution are quite sensitive to the activation energy model chosen. In contrast, morphological aspects of the evolution exhibit a similar qualitative behavior, irrespective of the activation energy model considered. It is shown that this common behavior closely agrees with predictions from the continuous theory of surface diffusion-driven interface decay.

In simulations of phase separation kinetics, large length and time scales are involved due to the mesoscopic size of the polymer coils, and the structure formation on still larger scales of length and time. We apply a coarse-grained model of hexadecane dissolved in supercritical carbon dioxide, for which in previous work the equilibrium phase behavior has been established by Monte Carlo methods. Using parallelized simulations on a multiprocessor supercomputer, large scale molecular dynamics simulations of phase separation following pressure jumps are presented for systems containing $N=435136$ coarse-grained particles, which correspond to several millions of atoms in a box with linear dimension $447\mathrm{\AA }$. Even for large systems the phase separation can be observed up to the final, macroscopically segregated, equilibrium state. It is shown that in the segregation process the two order parameters of the system (density and concentration) are strongly coupled. The system does not follow the predicted growth law for the characteristic domain size $\mathcal{l}\left(t\right)\propto t$ in binary fluid mixtures for the range of times accessible in the simulation. Instead, it exhibits a distinctly slower growth, presumably due to the dynamic asymmetry of the constituents.

We investigate an experimentally feasible synthetic genetic network consisting of two phase repulsively coupled repressilators, which evokes multiple coexisting stable attractors with different features. We perform a bifurcation analysis to determine and classify the dynamical structure of the system. Moreover, some of the dynamical regimes found, such as inhomogeneous steady states and inhomogeneous limit cycles can further be associated with artificial cell differentiation. We also report and characterize the emergence of chaotic dynamics resulting from the intercell coupling.

The understanding of the central mechanisms favoring sex and recombination in real populations is one of the fundamental issues in evolutionary biology. Based on a previous stochastic formulation for the study of sex, here we aim to investigate the conditions under which epistasis favors the fixation of the sexual mode of reproduction in a given population. In addition, we try to identify the evolutionary forces which contribute to this process. One considers a finite population model which assumes the existence of a recombination modifier allele that can activate the recombination mechanism. We have found that sex is very little favored in a scenario of antagonistic epistasis, and this advantage only occurs in a narrow range of values of the selection coefficient $s_d$. On the other hand, synergistic epistasis favors recombination in a very broad domain. However, the major mechanism contributing to the spreading of the modifier allele depends on the range of values of $s_d$. At large $s_d$, background selection favors recombination since it increases the efficacy of selection, while at low $s_d$ Muller’s ratchet is the leading mechanism.

We study the impact of additive Gaussian noise and weak periodic forcing on the dynamics of a scale-free network of bistable overdamped oscillators. The periodic forcing is introduced to a single oscillator and therefore acts as a pacemaker trying to impose its rhythm on the whole ensemble. We show that an intermediate intensity of temporally and spatially uncorrelated noise is able to optimally assist the pacemaker in achieving this goal, thus providing evidence for stochastic resonance on weakly paced scale-free networks. Because of the inherent degree inhomogeneity of individual oscillators forming the scale-free network, the placement of the pacemaker within the network is thereby crucial. As two extremes, we consider separately the introduction of the pacemaker to the oscillator with the highest degree and to one of the oscillators having the lowest degree. In both cases the coupling strength plays a crucial role, since it determines to what extent the whole network will follow the pacemaker on the expense of a weaker correlation between the pacemaker and the units that are directly linked with the paced oscillator. Higher coupling strengths facilitate the global outreach of the pacemaker, but require higher noise intensities for the optimal response. In contrast, lower coupling strengths and comparatively low noise intensities localize the optimal response to immediate neighbors of the paced oscillator. If the pacemaker is introduced to the main hub, the transition between the locally and globally optimal responses is characterized by a double resonance that postulates the existence of an optimal coupling strength for the transmission of weak rhythmic activity across scale-free networks. We corroborate the importance of the inhomogeneous structure of scale-free networks by additionally considering regular networks of oscillators with different degrees of coupling.

We study coupled oscillator spin systems on sparse, random graphs. In particular, we examine the recent conjecture of Ichinomiya on the equivalence of a sparsely connected oscillator network with ferromagnetic interactions to a fully connected network with disordered (i.e., randomly quenched) interactions. By restricting our investigation to a Hamiltonian case we can use the techniques of equilibrium statistical mechanics to compare these two models analytically including phase diagrams and the calculation of order parameters in the ordered phase. We complete our investigation by performing some Monte Carlo simulations to compare our theoretical predictions against.

Complex networks are characterized by heterogeneous distributions of the degree of nodes, which produce a large diversification of the roles of the nodes within the network. Several centrality measures have been introduced to rank nodes based on their topological importance within a graph. Here we review and compare centrality measures based on spectral properties of graph matrices. We shall focus on PageRank (PR), eigenvector centrality (EV), and the hub and authority scores of the HITS algorithm. We derive simple relations between the measures and the (in)degree of the nodes, in some limits. We also compare the rankings obtained with different centrality measures.

As shown recently, it is possible to create, on a vibrating fluid interface, mobile emitters of Faraday waves [Y. Couder, S. Protière, E. Fort, and A. Boudaoud, Nature 437, 208 (2005)]. They are formed of droplets bouncing at a subharmonic frequency which couple to the surface waves they emit. The droplet and its wave form a spontaneously propagative structure called a “walker.” In the present paper we investigate the large variety of orbital motions exhibited by two interacting walkers having different sizes and velocities. The various resulting orbits which can be circular, oscillating, epicycloidal, or “paired walkers” are defined and characterized. They are shown to result from the wave-mediated interaction of walkers. Their relation to the orbits of other localized dissipative structures is discussed.

From the periodicity of regional climate change to sustained oscillations in living cells, the transition between stationary and oscillatory behavior is often through a Hopf bifurcation. When a parameter slowly passes or ramps through a Hopf bifurcation there is a delayed transition to sustained oscillations and an associated memory effect where onset is dependent on the initial state of the system. Most theoretical studies of the delay and memory effect assume constant ramp speeds, overlooking the problem of slow parameter acceleration or deacceleration through the Hopf bifurcation. Using both numerical and analytic methods, we show that slow nonlinear ramps can significantly increase or decrease the onset threshold, changing profoundly our understanding of the associated memory effect. We found that slow parameter acceleration increases the threshold, whereas slow deacceleration decreases the threshold. The theory is applied to the formation of pacemakers in the unstirred Belousov-Zhabotinsky reaction and the onset of elliptic bursting in the context of nerve membrane excitability. We show that our results generalize to all systems where slow passage through a Hopf bifurcation is the underlying mechanism for onset.

For oscillating time series, the prediction is often focused on the turning points. In order to predict the turning point magnitudes and times it is proposed to form the state space reconstruction only from the turning points and modify the local (nearest-neighbor) model accordingly. The model on turning points gives optimal predictions at a lower dimensional state space than the optimal local model applied directly on the oscillating time series and is thus computationally more efficient. Simulations on different oscillating nonlinear systems showed that it gives better predictions of turning points and this is confirmed also for the time series of annual sunspots and total stress in a plastic deformation experiment.

We have numerically investigated the axisymmetric motion of a finite-sized nearly occluding air bubble through a shear-thinning Casson fluid flowing in blood vessels of circular cross section. The numerical solution entails solving a two-layer fluid model—a cell-free layer and a non-Newtonian core together with the gas bubble. This problem is of interest to the field of rheology and for gas embolism studies in health sciences. The numerical method is based on a modified front-tracking method. The viscosity expression in the Casson model for blood (bulk fluid) includes the hematocrit [the volume fraction of red blood cells (RBCs)] as an explicit parameter. Three different flow Reynolds numbers, ${\mathrm{Re}}_{\mathrm{app}}={\rho }_l{U}_{\max }d∕{\mu }_{\mathrm{app}}$, in the neighborhood of 0.2, 2, and 200 are investigated. Here, ${\rho }_l$ is the density of blood, $U_{\max }$ is the centerline velocity of the inlet Casson profile, $d$ is the diameter of the vessel, and ${\mu }_{\mathrm{app}}$ is the apparent viscosity of whole blood. Three different hematocrits have also been considered: 0.45, 0.4, and 0.335. The vessel sizes considered correspond to small arteries, and small and large arterioles in normal humans. The degree of bubble occlusion is characterized by the ratio of bubble to vessel radius (aspect ratio), $\lambda$, in the range $0.9⩽\lambda ⩽1.05$. For arteriolar flow, where relevant, the Fahraeus-Lindqvist effects are taken into account. Both horizontal and vertical vessel geometries have been investigated. Many significant insights are revealed by our study: (i) bubble motion causes large temporal and spatial gradients of shear stress at the “endothelial cell” (EC) surface lining the blood vessel wall as the bubble approaches the cell, moves over it, and passes it by; (ii) rapid reversals occur in the sign of the shear stress (+ → − → +) imparted to the cell surface during bubble motion; (iii) large shear stress gradients together with sign reversals are ascribable to the development of a recirculation vortex at the rear of the bubble; (iv) computed magnitudes of shear stress gradients coupled with their sign reversals may correspond to levels that cause injury to the cell by membrane disruption through impulsive compression and stretching; and (v) for the vessel sizes and flow rates investigated, gravitational effects are negligible.

A variational principle governing the dynamics of a vortex filament in unbounded incompressible inviscid fluid flow was suggested by Rasetti and Regge [Physica A 80, 217 (1975)]. This variational principle holds in the approximation taking into account the logarithmically large terms, on the order of $\ln (L∕a)$, $L$ and $a$ being the length and the cross-section radius of the filament, respectively. In this approximation, the Hamiltonian is a function of $L$. Accordingly, the filament length $L$ is constant in the course of motion. In this paper, a variational principle is obtained that takes into account also the terms on the order of unity. A characteristic feature of the more precise theory is the evolution of the filament length. The variational principle of the vortex filament dynamics is derived from the variational principle for the arbitrary vortex motion of an incompressible inviscid fluid found recently.

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 changes the critical exponent in the interaction strength below which a condensation transition may occur. The local critical densities may exhibit large fluctuations, and their distribution shows an interesting crossover from exponential to algebraic behavior.