Using Monte Carlo simulations of the Lebwohl-Lasher model we study the director ordering in a nematic cell where the top and bottom surfaces are patterned with a lattice of $\pm 1$ point topological defects of lattice spacing $a$. As expected on general physical grounds we find that the nematic order depends on the ratio of the height of the cell $H$ to $a$. For thick cells $(H∕a\gtrsim 0.9)$ we find that the system is very well ordered and the frustration induced by the lattice of defects is relieved in a novel way by a network of half-integer defect lines which emerge from the point defects and hug the top and bottom surfaces of the cell. When $H∕a\lesssim 0.9$ the system has zero nematic order parameter and the half-integer defect lines thread through the cell joining point defects on the top and bottom surfaces. We present a simple physical argument in terms of the length of the defect lines to explain these results. To facilitate eventual comparison with experimental systems we also simulate optical textures in the presence of crossed polarizers.

The migration of a suspended vesicle in an unbounded Poiseuille flow is investigated numerically in the low Reynolds number limit. We consider the situation without viscosity contrast between the interior of the vesicle and the exterior. Using the boundary integral method we solve the corresponding hydrodynamic flow equations and track explicitly the vesicle dynamics in two dimensions. We find that the interplay between the nonlinear character of the Poiseuille flow and the vesicle deformation causes a cross-streamline migration of vesicles toward the center of the Poiseuille flow. This is in a marked contrast with a result [L. G. Leal, Annu. Rev. Fluid Mech. 12, 435 (1980)] according to which the droplet moves away from the center (provided there is no viscosity contrast between the internal and the external fluids). The migration velocity is found to increase with the local capillary number (defined by the time scale of the vesicle relaxation toward its equilibrium shape times the local shear rate), but reaches a plateau above a certain value of the capillary number. This plateau value increases with the curvature of the parabolic flow profile. We present scaling laws for the migration velocity.

We present a type of spiral vortex state that appears from a supercritical Hopf bifurcation below the linear instability of circular Couette flow in a Taylor-Couette system with rigid end plates. These spirals have been found experimentally as well as numerically as “pure” states but also coexist with “classical” spirals (or axially standing waves for smaller systems) which typically appear from linear instability in counterrotating Taylor-Couette flow. These spiral states have an axial distribution of the strongly localized amplitude in the vicinity of the rigid end plates that confine the system in the axial direction. Furthermore, they show significantly different oscillation frequencies compared to the critical spiral frequencies. Despite the localization of the amplitude near the ends, the states appear as global states with spirals that propagate either toward the middle from each end of the system or vice versa. In contrast to classical spirals, these states exhibit a spatial or a spatiotemporal reflection symmetry.

We study the aging behavior of aqueous laponite suspension, a model soft glassy material, in creep. We observe that the viscoelastic behavior is time dependent and is strongly influenced by the deformation field; the effect is known to arise due to aging and rejuvenation. We show that irrespective of the strength of the deformation field (shear stress) and age, when the imposed time scale is normalized with a dominating relaxation mode of the system, universal aging behavior is obtained, demonstrating time-stress superposition, a phenomenon that may be generic in a variety of soft materials.

Inherent structure theory is used to discover strong connections between simple characteristics of protein structure and the energy landscape of a Gō model. The potential energies and vibrational free energies of inherent structures are highly correlated, and both reflect simple measures of networks of native contacts. These connections have important consequences for models of protein dynamics and thermodynamics.

We study the conditions for extinction and survival of populations living in a patch surrounded by a hostile environment. We find analytic expressions for the steady states when population dynamics is described by diffusion and reaction is driven by compensation, depensation, or critical depensation growths. The role of initial population density is studied, and the complete bifurcation diagrams are constructed and validated numerically for the three cases studied.

In a recent paper, Marr, Müller-Linow, and Hütt [Phys. Rev. E 75, 041917 (2007)] investigate an artificial dynamic system on metabolic networks. They find a less complex time evolution of this dynamic system in real networks, compared to networks of null models. The authors argue that this suggests that metabolic network structure is a major factor behind the stability of biochemical steady states. We reanalyze the same kind of data using a dynamic system modeling actual reaction kinetics. The conclusions about stability, from our analysis, are inconsistent with those of Marr et al. We argue that this issue calls for a more detailed type of modeling.

In a recent paper [Marr, Müller-Linow, and Hütt, Phys. Rev. E 75, 041917 (2007)], we discuss the pronounced potential of real metabolic network topologies, compared to randomized counterparts, to regularize complex binary dynamics. In the preceding Comment [Holme and Huss, Phys Rev. E77, 023901 (2008)], the authors criticize our approach and repeat our study with more realistic dynamics, where stylized reaction kinetics are implemented on sets of pairwise reactions. The authors find no dynamic difference between the reaction sets recreated from the metabolic networks and randomized counterparts. We reproduce the authors’ observation and find that their algorithm leads to a dynamical fragmentation and thus eliminates the topological information contained in the graphs. Hence, their approach cannot rule out a connection between the topology of metabolic networks and the ubiquity of steady states.

We perform orbital-free molecular dynamics simulations in the hot and dense regime for two mixtures: equimolar helium-iron and asymmetric deuterium-copper plasmas. For thermodynamic properties, we test two isobaric-isothermal mixing rules whose definitions involve either the equality of total pressures or the equality of the so-defined excess pressures of the components; the pressure and internal energy obtained by direct simulations are in very good agreement with those given by the mixing rule involving the equality of excess pressures. The viscosity of the deuterium-copper mixture is also extracted from a direct simulation and compared to the result given by a mixing rule applied to the viscosities of the pure elements. Finally, for structural properties, the effective charges given by the isobaric-isothermal mixing rule for the average atom model, used in the binary ionic mixture model, yield partial pair distribution functions in good agreement with those obtained by a direct simulation.

Dislocation kink solitons in disordered solid solutions provide an example of quasiparticles showing anomalous kinetics—i.e., the nonlinear dependence of the displacement $x$ on the time $t$, $x\sim t^{\delta }$ $(\delta <1)$. To describe the dynamic phase transition from the ordinary linear to anomalous regime, the dynamics of a quasiparticle in an energy landscape that performs a correlated random walk on the energy scale was theoretically studied. The phase diagram was characterized by the calculated temperature dependence of the threshold driving force $F_{\mathrm{th}}$ below which the average velocity of quasiparticles vanishes. The exponent $\delta$ of the kinetic equation for the anomalous phase, $x\sim t^{\delta }$, was determined by simple statistical arguments using the concepts of the “optimal fluctuation method.” The dependence of the threshold driving force $F_{\mathrm{th}}$ on the concentration of solute atoms and statistical properties of a random energy landscape relevant to disordered solid solutions was calculated. The correlations between steps of the random potential were shown to modify the concentration dependence of $F_{\mathrm{th}}$, thereby providing a qualitative explanation of experimental data on the dislocation pinning in solid solutions.

We predict that patterns with correlated surface density of atoms have statistically higher promiscuity (ability to bind stronger to an arbitrary pattern) as compared with noncorrelated patterns with the same average surface density. We suggest that this constitutes a generic design principle for highly connected proteins (hubs) in protein interaction networks. We develop an analytical theory for this effect. We show that our key predictions are generic and independent, qualitatively, on the specific form of the interatomic interaction potential, provided it has a finite range.

Circular dichroism (CD) experiments on DNA single strands $\left({\mathrm{dA}}_{\mathrm{n}}\right)$ at the ASTRID synchrotron radiation facility reveal that eight adenine (A) bases electronically couple upon $190\mathrm{nm}$ excitation. After $n=8$, the CD signal increases linearly with $n$ with a slope equal to the sum of the coupling terms. Nearest neighbor interactions account for only 24% of the CD signal whereas electronic communication is limited to nearest neighbors for two other exciton bands observed at 218 and $251\mathrm{nm}$ (i.e., dimer excited states). Electronic coupling between bases in DNA is important for nonradiative deexcitation of electronically excited states since the hazardous energy is spread over a larger spatial region.

We investigate the cascading failure on weighted complex networks by adopting a local weighted flow redistribution rule, where the weight of an edge is $(k_i{k}_j{)}^{\theta }$ with $k_i$ and $k_j$ being the degrees of the nodes connected by the edge. Assume that a failed edge leads only to a redistribution of the flow passing through it to its neighboring edges. We found that the weighted complex network reaches the strongest robustness level when the weight parameter $\theta =1$, where the robustness is quantified by a transition from normal state to collapse. We determined that this is a universal phenomenon for all typical network models, such as small-world and scale-free networks. We then confirm by theoretical predictions this universal robustness characteristic observed in simulations. We furthermore explore the statistical characteristics of the avalanche size of a network, thus obtaining a power-law avalanche size distribution together with a tunable exponent by varying $\theta$. Our findings have great generality for characterizing cascading-failure-induced disasters in nature.

Feedback control is applied to change conditions of a noise-induced transition in a nonlinear second order dynamic system. The mathematical model used in the analysis is a system of two-component equations describing operation of a semiconductor–gas-discharge image converter. The control algorithm is proposed using the speed-gradient method for a linearized model system. It is found by computer simulations that, under conditions when the noise is effective in determining the destructive dynamics of the system without control, the role of noise can be essentially suppressed by a proper feedback control. The control efficiency depends on the amplitude of control signal in a nonmonotonic way, thus demonstrating a resonancelike regularity. Application of the proposed control method can be useful in solving other problems, such as providing survival of endangered species in ecology, improving stability of lasers, etc.

Departing from the classical Buckley-Leverett theory for two-phase immiscible flows in porous media, a reduced evolution equation for the water-oil displacement front is formulated and studied numerically. The reduced model successfully reproduces the basic features of the finger-forming dynamics observed in recent direct numerical simulations.

Two-temperature, two-mass quasiequilibrium plasmas may occur in electron-ion plasmas, nuclear-matter, as well as in electron-hole condensed-matter systems. Dense two-temperature hydrogen plasmas straddle the difficult partially degenerate regime of electron densities and temperatures which are important in astrophysics, in inertial-confinement fusion research, and other areas of warm dense-matter physics. Results from quantum Monte Carlo (QMC) are used to benchmark the procedures used in classical molecular-dynamics simulations and hypernetted chain (HNC) and classical-map HNC (CHNC) methods to derive electron-electron and electron-proton pair-distribution functions. Where QMC is not available, we used Kohn-Sham results as the reference calculation. Then, nonequilibrium molecular dynamics for two-temperature, two-mass plasmas are used to obtain pair distribution functions without specifying the interspecies cross temperature. Using these results, the correct HNC and CHNC procedures for the evaluation of pair-distribution functions in two-temperature two-mass two-component charged fluids are established and results for a mass ratio of 1:5, typical of electron-hole fluids, are presented.

We present a general numerical scheme for the practical implementation of statistical moment closures suitable for modeling complex, large-scale, nonlinear systems. Building on recently developed equation-free methods, this approach numerically integrates the closure dynamics, the equations of which may not even be available in closed form. Although closure dynamics introduce statistical assumptions of unknown validity, they can have significant computational advantages as they typically have fewer degrees of freedom and may be much less stiff than the original detailed model. The numerical closure approach can in principle be applied to a wide class of nonlinear problems, including strongly coupled systems (either deterministic or stochastic) for which there may be no scale separation. We demonstrate the equation-free approach for implementing entropy-based Eyink-Levermore closures on a nonlinear stochastic partial differential equation.

Liquid crystals are intriguing electrically responsive soft matter systems. We report previously unexplored field-induced changes in the structures of some frustrated liquid crystal phases and describe them theoretically. Specifically, we have discovered using resonant x-ray scattering that the four-layer intermediate smectic phase can undergo either a transition to the ferrielectric (three-layer) phase or to the ferroelectric phase, depending on temperature. Our studies of intermediate phases using electric fields offer a way to test theories that describe ferroelectricity in self-assembling fluids.

The structure of hard rod-disk mixtures is studied using Monte Carlo simulations and integral equation theory, for a range of densities in the isotropic phase. By extension of methods used in single component fluids, the pair correlation functions of the molecules are calculated and comparisons between simulation and integral equation theory, using a number of different closure relations, are made. Comparison is also made for thermodynamic data and phase behavior.