The size-based separation of electrophoresing DNA chains of varying lengths has been experimentally achieved in microfluidic obstacle arrays. The separation is actuated by the occurrence of size-dependent chain-obstacle collisions and the subsequent formation of hooked chain configurations in the array. We investigate the role played by disorder in array geometry in determining chain dynamics in the array. As a prototypical example of a disordered post array, we select a self-assembled array of magnetic colloids, wherein the degree of disorder may be varied by varying the magnetic field strength under which the array is generated. We employ Brownian dynamics simulations of chain electrophoresis in the array to compute the mobility, dispersivity, chain-obstacle collision probability, and mean chain stretch in the device, and demonstrate the link between the orientational order of the array and the resulting chain dynamics.

A series of numerical simulations of a $2\times 2$ symmetric game on a network examined whether payoff matrix noise promotes cooperation, as reported initially by Perc [New J. Phys. 8, 22 (2006)]. Agents have no memory (they offer cooperation, $C$, or defection, $D$). We assume that the network is time invariable. The effect of payoff matrix noise (PMN) is measured by a simulated payoff difference between a normal network game and a network game with PMN. The effect of PMN appears only when a local strategy adaptation is implemented (for example, a network game with imitation dynamics). The influence of PMN becomes more significant with a larger stochastic deviation, and less significant in a larger degree network. One reason for PMN’s effectiveness is the local strategy adaptation mechanism, which helps both the preservation and fixation of $C$ agents, and not that the payoff matrix noise makes a dilemma game into a Trivial (dilemma-free) game.

We study the coarsening of two-dimensional oblique stripe patterns by numerically solving potential and nonpotential anisotropic Swift-Hohenberg equations. Close to onset, all models exhibit isotropic coarsening with a single characteristic length scale growing in time as $t^{1∕2}$. Further from onset, the characteristic lengths along the preferred directions $\widehat{x}$ and $\widehat{y}$ grow with different exponents, close to 1/3 and 1/2, respectively. In this regime, one-dimensional dynamical scaling relations hold. We draw an analogy between this problem and model A in a stationary, modulated external field. For deep quenches, nonpotential effects produce a complicated dislocation dynamics that can lead to either arrested or faster-than-power-law growth, depending on the model considered. In the arrested case, small isolated domains shrink down to a finite size and fail to disappear. A comparison with available experimental results for electroconvection in nematics is presented.

We investigate both continuous (second-order) and discontinuous (first-order) transitions to macroscopic synchronization within a single class of discrete, stochastic (globally) phase-coupled oscillators. We provide analytical and numerical evidence that the continuity of the transition depends on the coupling coefficients and, in some nonuniform populations, on the degree of quenched disorder. Hence, in a relatively simple setting this class of models exhibits the qualitative behaviors characteristic of a variety of considerably more complicated models. In addition, we study the microscopic basis of synchronization above threshold and detail the counterintuitive subtleties relating measurements of time-averaged frequencies and mean-field oscillations. Most notably, we observe a state of suprathreshold partial synchronization in which time-averaged frequency measurements from individual oscillators do not correspond to the frequency of macroscopic oscillations observed in the population.

We study evolution equations which model selection and mutation within the framework of quantum mechanics. The main question is to what extent order is achieved for an ensemble of typical systems. As an indicator for mixing or purification, a quadratic entropy is used which assumes values between zero for pure states and $\left(d-1\right)∕d$ for fully mixed states. Here, $d$ is the dimension. Whereas the classical counterpart, the quasispecies dynamics, has previously been found to be predominantly mixing, the quantum quasispecies (QS) evolution surprisingly is found to be strictly purifying for all dimensions. This is also typically true for an alternative formulation (AQS) of this quantum mechanical flow. We compare this also to analogous results for the Lindblad evolution. Although the latter may be viewed as a simple linear superposition of the purifying QS and AQS evolutions, it is found to be predominantly mixing. The reason for this behavior may be explained by the fact that the two subprocesses by themselves converge to different pure states, such that the combined process is mixing. These results also apply to high-dimensional systems.

The geometrical stability of the three lattices of the cubic crystal system, viz. face-centered cubic (fcc), body-centered cubic (bcc), and simple cubic (sc), consisting of bimodal discrete hard spheres, and the transition to amorphous packing is studied. First, the random close packing (rcp) fraction of binary mixtures of amorphously packed spheres is recapitulated. Next, the packing of a binary mixture of hard spheres in randomly disordered cubic structures is analyzed, resulting in original analytical expressions for the unit cell volume and the packing fraction, and which are also valid for the other five crystal systems. The bimodal fcc lattice parameter appears to be in close agreement with empirical hard sphere data from literature, and this parameter could be used to distinguish the size mismatch effect from all other effects in distorted binary lattices of materials. Here, as a first model application, bimodal amorphous and crystalline fcc/bcc packing fractions are combined, yielding the optimum packing configuration, which depends on mixture composition and diameter ratio only. Maps of the closest packing mode are established and applied to colloidal mixtures of polydisperse spheres and to binary alloys of bcc, fcc, and hcp metals. The extensive comparison between the analytical expressions derived here and the published numerical and empirical data yields good agreement. Hence, it is seen that basic space-filling theories on “simple” noninteracting hard spheres are a valuable tool for the study of crystalline materials.

We present a numerical study of the impact energy decay in a composite granular chain containing two heavy and one light sections. We observe a marked crossover in the power-law behavior of the impact-energy decay. The average reflection frequency first increases with a decreasing acceleration, and arrives at its maximum at “crossing” time then decays almost exponentially. The analysis demonstrates that this phenomenon is related to the structural transition from compression to dilation state in both heavy-particle sections. The further calculations suggest the dependence relation of the power-law exponent $\left({\gamma }_{cb}\right)$ in compression state on the mass ratio $(m_2∕m_1)$ and the Hertz law exponent $\left(n\right)$ of the composite granular chain ${\gamma }_{cb}\sim (\frac{m_2}{m_1}{)}^{1∕(n+1)}$.

Within the Monte Carlo formalism supplemented by the modified Newton-Raphson optimization technique, we investigated structural and dynamical properties of two-dimensional binary clusters confined in an external hard-wall potential. Two species of differently charged classical particles, interacting through the repulsive Coulomb force are confined in the cluster. Subtle changes in the energy landscape and the stable cluster configurations are investigated as a function of the total number of particles and the relative number of each of the two particle species. The excitation spectrum and the normal modes corresponding to the ground-state configuration of the system are discussed, and the lowest nonzero eigenfrequency as a measure of the stability of the cluster is analyzed. The influence of the particle mass on the eigenfrequencies and eigenmodes are studied, i.e., we study a binary system of particles with different charge and different mass. Several unique features distinct from a monodisperse system are obtained.

We study water-in-oil microemulsions, in particular dispersions of water droplets coated with a monolayer of the anionic surfactant AOT in a continuous phase of $n$-decane. Upon addition of the amphiphilic triblock copolymer PEO(polyethylenoxide)-PI(polyisoprene)-PEO, a transient network is formed. At constant droplet size we vary the polymer concentration and there is clear evidence for an increasing crosslinking of the droplets from structural investigations with small-angle x-ray scattering. The dynamics of concentration fluctuations consisting of the translational diffusion of the droplets and the relaxation of the network are monitored with photon correlation spectroscopy. We mainly focus on the variation of the dynamic behavior as a function of the number of polymer molecules per droplet and the droplet volume fraction, which may be taken as a measure for the interdroplet distance. With increasing polymer content the dynamics of the system slows down and three different relaxation processes may be distinguished. We discuss the origin of the different relaxation modes. In particular, it turns out that the intermediate relaxation mode may be suppressed by index matching the oil matrix and the PI block and that it is effectively slowed down by an additional loading of the emulsion droplets with polyethylene glycol of increasing molecular weight.

We investigate the dynamic behavior upon lateral compression of two mixed films made with one of the two semifluorinated alkanes $\mathrm{F}\left({\mathrm{CF}}_2{)}_8\right({\mathrm{CH}}_2{)}_{18}\mathrm{H}$ and $\mathrm{F}\left({\mathrm{CF}}_2{)}_{10}\right({\mathrm{CH}}_2{)}_{10}\mathrm{H}$ and the natural $\alpha$-helix alamethicin peptide. Surface pressure, surface potential versus molecular area isotherms, and grazing-incidence x-ray diffraction were applied to characterize this system. We show that both mixed films demix vertically to form two asymmetric flat bilayers where the lower layer is made of alamethicin and the upper layer is made of semifluorinated molecules. The structure matching of the semifluorinated alkanes (where the hydrophilic group is missing) with a suitable organization of the underlying alamethicin monolayer allows for a continuous compression of the upper semifluorinated layers while the density of the lower alamethicin monolayer remains constant. Comparing data of the two studied mixed films enables us to evaluate the effect of chain length on the in-plane organization of the molecules and on the electric properties of the upper layers.

The velocity of domain walls caused by a symmetry-breaking instability is experimentally investigated for the case of electroconvection in a nematic liquid crystal. It turns out that the velocity increases linearly with the distance from the bifurcation creating the domains. This scaling behavior does not agree with the drift pitchfork bifurcation. It has, however, been predicted by a minimal model describing our scenario.

We present a study of the effect of decoupled azimuthal and zenithal weak anchoring on the transition between $\mathrm{C}1$ and $\mathrm{C}2$ chevron structures in smectic-$C$ liquid crystals. We consider temperatures below the $\text{Sm}A\text{-Sm}C$ transition and assume that the value of the smectic cone angle can be regarded as constant through the cell. By standard Euler-Lagrange minimization of the total energy we obtain a simple analytical expression for the equilibrium director twist angle in the $\mathrm{C}1$ and $\mathrm{C}2$ chevron states. Using this analytical form, we are able to compare the total energies of the $\mathrm{C}1$ and $\mathrm{C}2$ chevrons, and determine the globally stable chevron profile. We show that the $\mathrm{C}2$ state is preferred when the azimuthal anchoring strength is relatively large, while $\mathrm{C}1$ chevrons will dominate for strong zenithal anchoring.

We investigate the role of inhomogeneities in zero-range processes in condensation dynamics. We consider the dynamics of balls hopping between nodes of a network with one node of degree $k_1$ much higher than a typical degree $k$, and find that the condensation is triggered by the inhomogeneity and that it depends on the ratio $k_1∕k$. Although, on the average, the condensate takes an extensive number of balls, its occupation can oscillate in a wide range. We show that in systems with strong inhomogeneity, the typical melting time of the condensate grows exponentially with the number of balls.

Bispectral analysis, recently introduced as a technique for revealing time-phase relationships, is extended to make use of wavelets rather than Fourier analysis. It is thus able to encompass instantaneous phase-time dependence for the case of two or more coupled nonlinear oscillators. The method is demonstrated and evaluated by use of test signals from a pair of coupled Poincaré oscillators. It promises to be useful in a wide range of scientific contexts for studies of interacting oscillators whose basic frequencies are significantly time variable.

The propagation of compressional MHD waves is studied for an externally driven system. It is assumed that the combined action of the external sources and sinks of the entropy results in the harmonic oscillation of the entropy (and temperature) in the system. It is found that with the appropriate resonant conditions fast and slow waves get amplified due to the phenomenon of parametric resonance. In addition, it is shown that the considered waves are mutually coupled as a consequence of the nonequilibrium state of the background medium. The coupling is strongest when the plasma $\beta \approx 1$. The proposed formalism is sufficiently general and can be applied to many dynamical systems, both under terrestrial and astrophysical conditions.

In a recent paper, Altschuler and Pérez-Garrido [Phys. Rev. E 76, 016705 (2007)] have presented a four-dimensional polytope with 80 vertices. We demonstrate how this polytope can be derived from the regular four-dimensional 600-cell with 120 vertices if two orthogonal positive disclinations are created. Some related polytopes are also described.

We study a lattice model for the spreading of fluid films, which are a few molecular layers thick, in narrow channels with inert lateral walls. We focus on systems connected to two particle reservoirs at different chemical potentials, considering an attractive substrate potential at the bottom, confining sidewalls, and hard-core repulsive fluid-fluid interactions. Using kinetic Monte Carlo simulations we find a diffusive behavior. The corresponding diffusion coefficient depends on the density and is bounded from below by the free one-dimensional diffusion coefficient, valid for an inert bottom wall. These numerical results are rationalized within the corresponding continuum limit.

We explore a model of a random relaxation shot noise system in which (i) the shot inflow is a general Poisson point process, with possibly infinite Poissonian rates; and (ii) the exponential relaxations governing the shot decay are randomized. This system model is applicable to physical environments polluted by radioactive contamination of heterogeneous types. The statistics of random relaxation shot noise systems are analyzed quantitatively and comprehensively: stationary structure, correlation structure, process distribution, fractality and asymptotic fractality, and the display—both separately and simultaneously—of the Noah and Joseph effects. Results are obtained explicitly and in closed form, and facilitate the design of tractable shot noise systems with unique features.

The domain dynamics of magnetization obeying the time-dependent Ginzburg-Landau equation driven by a dichotomous Markov noise is discussed. The system with various domain sizes in the early stage temporally evolves following an annihilation of neighboring domain walls, where each domain wall moves diffusively. Three statistics on the domain size, i.e., average domain size, the ensemble average of the domain size distribution function, and the spatial power spectrum of the magnetization, are evaluated to characterize the domain wall annihilation process. A phenomenological evolution equation for the domain-size distribution function is constructed by simplifying the annihilation process of the domain wall appropriately, and the underlying mechanism of those statistics is investigated.

The predator-prey-type ecosystem is investigated, taking into account the time-delay effect of the prey population on the predator population, as well as random variations in the birth rate of the preys and the death rate of the predators. The stochastic averaging procedure is applied to obtain the probability distributions of the predator and prey populations at the state of statistical stationarity. It is found that two system parameters, quantifying the effects of prey self-competition and the time delay, respectively, play the most important roles. Results are also obtained from Monte Carlo simulations to compare with the analytical results.