The fractional Fokker-Planck equation for subdiffusion in time-dependent force fields is derived from the underlying continuous time random walk. Its limitations are discussed and it is then applied to the study of subdiffusion under the influence of a time-periodic rectangular force. As a main result, we show that such a force does not affect the universal scaling relation between the anomalous current and diffusion when applied to the biased dynamics: in the long-time limit, subdiffusion current and anomalous diffusion are immune to the driving. This is in sharp contrast with the unbiased case when the subdiffusion coefficient can be strongly enhanced, i.e., a zero-frequency response to a periodic driving is present.

The dynamics of sheared inelastic-hard-sphere systems is studied using nonequilibrium molecular-dynamics simulations and direct simulation Monte Carlo. In the molecular-dynamics simulations Lees-Edwards boundary conditions are used to impose the shear. The dimensions of the simulation box are chosen to ensure that the systems are homogeneous and that the shear is applied uniformly. Various system properties are monitored, including the one-particle velocity distribution, granular temperature, stress tensor, collision rates, and time between collisions. The one-particle velocity distribution is found to agree reasonably well with an anisotropic Gaussian distribution, with only a slight overpopulation of the high-velocity tails. The velocity distribution is strongly anisotropic, especially at lower densities and lower values of the coefficient of restitution, with the largest variance in the direction of shear. The density dependence of the compressibility factor of the sheared inelastic-hard-sphere system is quite similar to that of elastic-hard-sphere fluids. As the systems become more inelastic, the glancing collisions begin to dominate over more direct, head-on collisions. Examination of the distribution of the times between collisions indicates that the collisions experienced by the particles are strongly correlated in the highly inelastic systems. A comparison of the simulation data is made with direct Monte Carlo simulation of the Enskog equation. Results of the kinetic model of Montanero et al. [J. Fluid Mech. 389, 391 (1999)] based on the Enskog equation are also included. In general, good agreement is found for high-density, weakly inelastic systems.

Cisplatin has been known as an anticancer drug for a long time. It is therapeutically active upon binding to DNA. A double-bound cisplatin bends DNA into a localized kink. We model the elastic properties of cisplatin-DNA adducts at moderate tension $\left(<6\text{pN}\right)$. It is shown that from the mechanical point of view the action of cisplatin can be revealed by reduced persistence length. We derived two expressions for the persistence length, which apply in the linear-response and the strong-force regimes, respectively. Experimental data for DNA adducts stretched by magnetic tweezers are consistently fitted by these expressions. This allows us to estimate the degree of platination at various salt concentrations.

We performed theoretical and computational studies to determine the effect of an applied mechanical strain on the dynamic behavior of heterogeneous polymer gels undergoing the oscillatory Belousov-Zhabotinsky (BZ) reaction. In these spatially heterogeneous gels, the catalyst for the reaction is localized in specific patches within the polymer network and the BZ reaction only occurs within these catalyst-containing patches, which we refer to as BZ patches. We focused on a model for a one-dimensional system, and further assumed that the BZ reaction did not affect the degree of swelling within the gel. For gels having one and two BZ patches, we found that a tensile or compressive strain could induce transitions between the oscillatory and nonoscillatory, steady-state regimes of the system. For certain values of the BZ stoichiometric parameter $f$, these transitions could exhibit a hysteresis. In systems having two oscillating BZ patches, an applied strain could cause a switching between the in-phase and out-of-phase synchronization of the oscillations. The ability to controllably alter the dynamic behavior of BZ gels through mechanical deformations opens up the possibility of using these materials in the design of chemo-mechanical sensors.

In this paper we report and analyze complex spatiotemporal dynamics recorded in electroconvection in the nematic liquid crystal I52, driven by an ac voltage slightly above the onset value. The instability mechanism creating the pattern is an oscillatory (Hopf) instability, giving rise to two pairs of counterpropagating rolls traveling in oblique directions relative to the unperturbed director axis. If a system of nonlinear partial differential equations shows the same set of unstable modes, the pattern above the onset is represented in a weakly nonlinear analysis as a superposition of the traveling rolls in terms of wave envelopes varying slowly in space and time. Motivated by this procedure, we extract slowly varying envelopes from the space-time data of the pattern, using a four-wave demodulation based on Fourier analysis. In order to characterize the spatiotemporal dynamics, we apply a variety of diagnostic methods to the envelopes, including the calculation of mean intensities and correlation lengths, global and local Karhunen-Loève decompositions in Fourier space and physical space, the location of holes, the identification of coherent vertical structures, and estimates of Lyapunov exponents. The results of this analysis provide strong evidence that our pattern exhibits extensive spatiotemporal chaos. One of its main characteristics is the presence of coherent structures of low and high intensities extended in the vertical (parallel to the director) direction.

To reveal the relation between network structures found in two-dimensional biological systems, such as protoplasmic tube networks in the plasmodium of true slime mold, and spatiotemporal oscillation patterns emerged on the networks, we constructed coupled phase oscillators on weighted planar networks and investigated their dynamics. Results showed that the distribution of edge weights in the networks strongly affects (i) the propensity for global synchronization and (ii) emerging ratios of oscillation patterns, such as traveling and concentric waves, even if the total weight is fixed. In-phase locking, traveling wave, and concentric wave patterns were, respectively, observed most frequently in uniformly weighted, center weighted treelike, and periphery weighted ring-shaped networks. Controlling the global spatiotemporal patterns with the weight distribution given by the local weighting (coupling) rules might be useful in biological network systems including the plasmodial networks and neural networks in the brain.

Oscillations are ubiquitous phenomena in biological systems. Conventional models of biological periodic oscillations usually invoke interconnecting transcriptional feedback loops. Some specific proteins function as transcription factors, which in turn negatively regulate the expression of the genes that encode these “clock proteins.” These loops may lead to rhythmic changes in gene expression in a cell. In the case of multicellular tissue, collective oscillation is often due to the synchronization of these cells, which manifest themselves as autonomous oscillators. In contrast, we propose here a different scenario for the occurrence of collective oscillation in a group of nonoscillatory cells. Neither periodic external stimulation nor pacemaker cells with intrinsically oscillator are included in the present system. By adopting a spatially inhomogeneous active factor, we observe and analyze a coupling-induced oscillation, inherent to the phenomenon of wave propagation due to intracellular communication.

By a means of a method based on the reductive perturbation method, we show that the amplitude of waves on the nonlinear electrical transmission lines (NLTLs) is described by the cubic-quintic complex Ginzburg-Landau (CGL) equation. Then, we revisit analytically and numerically the processes of modulational instability (MI). The evolution of dissipative modulated waves through the network is also examined, and we show that solitonlike excitations can be induced by MI. Analytical results, illustrating the nature of MI of plane-wave solution, are also found to be in good agreement with numerical findings.

We study in further detail particle models displaying a boundary-induced absorbing state phase transition [Deloubrière and van Wijland Phys. Rev. E 65, 046104 (2002) and Barato and Hinrichsen, Phys. Rev. Lett. 100, 165701 (2008)]. These are one-dimensional systems consisting of a single site (the boundary) where creation and annihilation of particles occur, and a bulk where particles move diffusively. We study different versions of these models and confirm that, except for one exactly solvable bosonic variant exhibiting a discontinuous transition and trivial exponents, all the others display nontrivial behavior, with critical exponents differing from their mean-field values, representing a universality class. Finally, the relation of these systems with a $\left(0+1\right)$-dimensional non-Markovian process is discussed.

We study extremal statistics and return intervals in stationary long-range correlated sequences for which the underlying probability density function is bounded and uniform. The extremal statistics we consider (e.g., maximum relative to minimum) are such that the reference point from which the maximum is measured is itself a random quantity. We analytically calculate the limiting distributions for independent and identically distributed random variables, and use these as a reference point for correlated cases. The distributions are different from that of the maximum itself (i.e., a Weibull distribution), reflecting the fact that the distribution of the reference point either dominates over or convolves with the distribution of the maximum. The functional form of the limiting distributions is unaffected by correlations, although the convergence is slower. We show that our findings can be directly generalized to a wide class of stochastic processes. We also analyze return interval distributions, and compare them to recent conjectures of their functional form.

We investigate the kinetics of irreversible reaction $nA+mB\to 0$. When $nA$ particles and $mB$ particles encounter on the same site, the reaction takes place. We classify the reaction into two classes, the symmetric and the asymmetric reactions. The symmetric reaction means both $nA+mB\to 0$ and $mA+nB\to 0$, while the asymmetric reaction means only $nA+mB\to 0$ for a given $\left(n,m\right)$ pair. The kinetics of the reaction follows the fluctuation-dominated kinetics of $A+B\to 0$ for $N<N_c$, where $N_c$ is the crossover $N\left(=n+m\right)$. For $N\ge N_c$, the kinetics follows a mean-field rate equation. For the asymmetric reaction, it was shown that $N_c$ is 5. We numerically show that the reaction symmetry changes $N_c$ in one dimension. We investigate the asymptotic scaling behaviors of density and various lengths characterizing the spatial organization of particles such as domain length and interparticle distance. Lengths exhibit much clear crossover to the mean-field region at the expected $N_c$ of each reaction. From the scaling behavior of density and lengths, we show $N_c=4$ for the symmetric reaction in one dimension. Therefore the symmetry in the reaction changes the upper critical dimension, which implies that the kinetics cannot be described by a single theory.

Motivated by a recent experimental study on the interaction between colloidal particles in a confined nematic liquid crystal [M. Vilfan, N. Osterman, M. Čopič, M. Ravnik, S. Žumer, J. Kotar, D. Babič, and I. Poberaj, Phys. Rev. Lett. 101, 237801 (2008)], we discuss in an analytical manner how the interaction potential $U$ between spherical colloidal particles in a confined nematic cell behaves as a function of the interparticle distance $r$. We show that the short-range potential follows a power law $U\left(r\right)\sim r^{-5}$ as expected from the quadrupolar nature of the interaction, while the long-range potential is dominated by an exponential function $U\left(r\right)\sim \sqrt{d/r}\text{exp}\left(-2\pi r/d\right)$, where $d$ is the cell thickness. These two regimes are interchanged at $r/d\simeq 0.8$. This behavior of $U\left(r\right)$ is in a good semiquantitative agreement with the experimental finding.

The crystalline structures in thin films of polystyrene-$b$-poly(ethylene oxide) (PS-$b$-PEO) diblock copolymers were studied in dependence on the degree of supercooling. Atomic force microscopy showed that the crystalline domains (lamellae) consist of grains, which are macroscopic at low and intermediate degrees of supercooling, but of submicrometer size for strong supercooling. Using grazing-incidence wide-angle x-ray scattering, we could determine the grain orientation distribution function which shows that the chain stems are perpendicular to the lamellae at low supercooling, but tilted at intermediate and strong supercooling. These results suggest that, at intermediate and strong supercooling, the crystalline PEO lamellae do not grow homogeneously, but by the formation of small crystallites at the growth front.

Shannon entropy $H$ and genome order index $S$ are used in segmenting DNA sequences. Zhang et al. [Phys. Rev. E 72, 041917 (2005)] found that the two schemes are equivalent when a DNA sequence is converted to a binary sequence of S (strong H bond) and W (weak H bond). They left the mathematical proof to mathematicians who are interested in this issue. In this paper, a possible mathematical explanation is given. Moreover, we find that Chargaff parity rule 2 is the necessary condition of the equivalence, and the equivalence disappears when a DNA sequence is regarded as a four-symbol sequence. At last, we propose that $S-2^{-H}$ may be related to species evolution.

Molecular chirality frustrates the two-dimensional assembly of filamentous molecules, a fact that reflects the generic impossibility of imposing a global twisting of layered materials. We explore the consequences of this frustration for hexagonally ordered assemblies of chiral filaments that are finite in lateral dimension. Specifically, we employ a continuum-elastic description of cylindrical bundles of filaments, allowing us to consider the most general resistance to and preference for chiral ordering of the assembly. We explore two distinct mechanisms by which chirality at the molecular scale of the filament frustrates the assembly into aggregates. In the first, chiral interactions between filaments impart an overall twisting of filaments around the central axis of the bundle. In the second, we consider filaments that are inherently helical in structure, imparting a writhing geometry to the central axis. For both mechanisms, we find that a thermodynamically stable state of dispersed bundles of finite width appears close to but below the point of bulk filament condensation. The range of thermodynamic stability of dispersed bundles is sensitive only to the elastic cost and preference for chiral filament packing. The self-limited assembly of chiral filaments has particular implications for a large class of biological molecules—DNA, filamentous proteins, viruses, and bacterial flagella—which are universally chiral and are observed to form compact bundles under a broad range of conditions.

Many physical and physiological signals exhibit complex scale-invariant features characterized by $1/f$ scaling and long-range power-law correlations, indicating a possibly common control mechanism. Specifically, it has been suggested that dynamical processes, influenced by inputs and feedback on multiple time scales, may be sufficient to give rise to $1/f$ scaling and scale invariance. Two examples of physiologic signals that are the output of hierarchical multiscale physiologic systems under neural control are the human heartbeat and human gait. Here we show that while both cardiac interbeat interval and gait interstride interval time series under healthy conditions have comparable $1/f$ scaling, they still may belong to different complexity classes. Our analysis of the multifractal scaling exponents of the fluctuations in these two signals demonstrates that in contrast to the multifractal behavior found in healthy heartbeat dynamics, gait time series exhibit less complex, close to monofractal behavior. Further, we find strong anticorrelations in the sign and close to random behavior for the magnitude of gait fluctuations at short and intermediate time scales, in contrast to weak anticorrelations in the sign and strong positive correlation for the magnitude of heartbeat interval fluctuations—suggesting that the neural mechanisms of cardiac and gait control exhibit different linear and nonlinear features. These findings are of interest because they underscore the limitations of traditional two-point correlation methods in fully characterizing physiological and physical dynamics. In addition, these results suggest that different mechanisms of control may be responsible for varying levels of complexity observed in physiological systems under neural regulation and in physical systems that possess similar $1/f$ scaling.

In one-component Abelian sandpile models, the toppling probabilities are independent quantities. This is not the case in multicomponent models. The condition of associativity of the underlying Abelian algebras imposes nonlinear relations among the toppling probabilities. These relations are derived for the case of two-component quadratic Abelian algebras. We show that Abelian sandpile models with two conservation laws have only trivial avalanches.

Large-scale dynamo action due to turbulence in the presence of a linear shear flow is studied. Our treatment is quasilinear and kinematic but is nonperturbative in the shear strength. We derive the integrodifferential equation for the evolution of the mean magnetic field by systematic use of the shearing coordinate transformation and the Galilean invariance of the linear shear flow. For nonhelical turbulence the time evolution of the cross-shear components of the mean field does not depend on any other components excepting themselves. This is valid for any Galilean-invariant velocity field, independent of its dynamics. Hence the shear-current assisted dynamo is essentially absent, although large-scale nonhelical dynamo action is not ruled out.

We study the effect of latency on binary-choice opinion formation models. Latency is introduced into the models as an additional dynamic rule: after a voter changes its opinion, it enters a waiting period of stochastic length where no further changes take place. We first focus on the voter model and show that as a result of introducing latency, the average magnetization is not conserved, and the system is driven toward zero magnetization, independently of initial conditions. The model is studied analytically in the mean-field case and by simulations in one dimension. We also address the behavior of the majority-rule model with added latency, and show that the competition between imitation and latency leads to a rich phenomenology.

We study the effects of bounded confidence thresholds and of interaction and external noise on Axelrod’s model of social influence. Our study is based on a combination of numerical simulations and an integration of the mean-field master equation describing the system in the thermodynamic limit. We find that interaction thresholds affect the system only quantitatively, but that they do not alter the basic phase structure. The known crossover between an ordered and a disordered state in finite systems subject to external noise persists in models with general confidence threshold. Interaction noise here facilitates the dynamics and reduces relaxation times. We also study Axelrod systems with metric features and point out similarities and differences compared to models with nominal features.