A detailed x-ray scattering study has been performed in the temperature range of the smectic-$A$ phase for the liquid crystal compounds dodecylcyanobiphenyl (12CB) and octylcyanobiphenyl (8CB) confined in different controlled-pore glasses (CPGs) characterized by their average void radius $R$. On decreasing the temperature in bulk samples the layer thickness is increasing for 12CB and decreasing for 8CB, respectively. In nontreated CPG samples the layers dilate significantly with respect to the bulk liquid crystal. In order to explain the layer thickness behavior on varying temperature and $R$, one has to take into account molecular details of the liquid crystalline samples as well as memory effects.

We consider a linear polymer chain in a disordered environment modeled by percolation clusters on a square lattice. The disordered environment is meant to roughly represent molecular crowding as seen in cells. The model may be viewed as the simplest representation of biopolymers in a cell. We show the existence of intermediate states during stretching arising as a consequence of molecular crowding. In the constant distance ensemble the force-extension curves exhibit oscillations. We observe the emergence of two or more peaks in the probability distribution curves signaling the coexistence of different states and indicating that the transition is discontinuous unlike what is observed in the absence of molecular crowding.

We analyze a stochastic model for tumor cell growth with both multiplicative and additive colored noises as well as nonzero cross correlations in between. Whereas the death rate within the logistic model is altered by a deterministic term characterizing immunization, the birth rate is assumed to be stochastically changed due to biological motivated growth processes leading to a multiplicative internal noise. Moreover, the system is subjected to an external additive noise which mimics the influence of the environment of the tumor. The stationary probability distribution $P_s$ is derived depending on the finite correlation time, the immunization rate, and the strength of the cross correlation. $P_s$ offers a maximum which becomes more pronounced for increasing immunization rate. The mean-first-passage time is also calculated in order to find out under which conditions the tumor can suffer extinction. Its characteristics are again controlled by the degree of immunization and the strength of the cross correlation. The behavior observed can be interpreted in terms of a biological model of tumor evolution.

Spike-timing dependent plasticity (STDP) is an organizing principle of biological neural networks. While synchronous firing of neurons is considered to be an important functional block in the brain, how STDP shapes neural networks possibly toward synchrony is not entirely clear. We examine relations between STDP and synchronous firing in spontaneously firing neural populations. Using coupled heterogeneous phase oscillators placed on initial networks, we show numerically that STDP prunes some synapses and promotes formation of a feedforward network. Eventually a pacemaker, which is the neuron with the fastest inherent frequency in our numerical simulations, emerges at the root of the feedforward network. In each oscillatory cycle, a packet of neural activity is propagated from the pacemaker to downstream neurons along layers of the feedforward network. This event occurs above a clear-cut threshold value of the initial synaptic weight. Below the threshold, neurons are self-organized into separate clusters each of which is a feedforward network.

The Gauss linking number (Ca) of two flexible polymer rings which are tethered to one another is investigated. For ideal random walks, mean linking-squared varies with the square root of polymer length while for self-avoiding walks, linking-squared increases logarithmically with polymer length. The free-energy cost of linking of polymer rings is therefore strongly dependent on degree of self-avoidance, i.e., on intersegment excluded volume. Scaling arguments and numerical data are used to determine the free-energy cost of fixed linking number in both the fluctuation and large-Ca regimes; for ideal random walks, for $\left|\text{Ca}\right|>N^{1/4}$, the free energy of catenation is found to grow $\propto {\left|\text{Ca}/N^{1/4}\right|}^{4/3}$. When excluded volume interactions between segments are present, the free energy rapidly approaches a linear dependence on Gauss linking $\left(dF/d\text{Ca}\approx 3.7k_{B}T\right)$, suggestive of a novel “catenation condensation” effect. These results are used to show that condensation of long entangled polymers along their length, so as to increase excluded volume while decreasing number of statistical segments, can drive disentanglement if a mechanism is present to permit topology change. For chromosomal DNA molecules, lengthwise condensation is therefore an effective means to bias topoisomerases to eliminate catenations between replicated chromatids. The results for mean-square catenation are also used to provide a simple approximate estimate for the “knotting length,” or number of segments required to have a knot along a single circular polymer, explaining why the knotting length ranges from $\approx 300$ for an ideal random walk to ${10}^6$ for a self-avoiding walk.

By modifying the Fermi updating rule, we present the diversity of individual rationality to the evolutionary prisoner’s dilemma game, and our results shows that this diversity heavily influences the evolution of cooperation. Cluster-forming mechanism of cooperators can either be highly enhanced or severely deteriorated by different distributions of rationality. Slight change in the rationality distribution may transfer the whole system from the global absorbing state of cooperators to that of defectors. Based on mean-field argument, quantitative analysis of the stability of cooperative clusters reveals the critical role played by agents with moderate degree values in the evolution of the whole system. The inspiration from our work may provide us a deeper comprehension toward some social phenomena.

The probability distribution of sums of iterates of the logistic map at the edge of chaos has been recently shown [U. Tirnakli et al., Phys. Rev. E 75, 040106(R) (2007)] to be numerically consistent with a $q$-Gaussian, the distribution which—under appropriate constraints—maximizes the nonadditive entropy $S_q$, which is the basis of nonextensive statistical mechanics. This analysis was based on a study of the tails of the distribution. We now check the entire distribution, in particular, its central part. This is important in view of a recent $q$ generalization of the central limit theorem, which states that for certain classes of strongly correlated random variables the rescaled sum approaches a $q$-Gaussian limit distribution. We numerically investigate for the logistic map with a parameter in a small vicinity of the critical point under which conditions there is convergence to a $q$-Gaussian both in the central region and in the tail region and find a scaling law involving the Feigenbaum constant $\delta$. Our results are consistent with a large number of already available analytical and numerical evidences that the edge of chaos is well described in terms of the entropy $S_q$ and its associated concepts.

We investigate the singularity structure analysis of a $\left(2+1\right)$-dimensional coupled nonlinear extension of the reaction-diffusion (NLERD) equation by means of the Painlevé (P) test. Following the Weiss et al.’s formalism [J. Math. Phys. 24, 522 (1983)], we prove the arbitrariness of the expansion coefficients of the observables. Thus, without the use of the Kruskal’s simplification, we obtain a Bäcklund transformation of the coupled NLERD equation via a consistent truncation procedure stemming from the Weiss et al.’s methodology [J. Weiss, M. Tabor, and G. Carnevale, J. Math. Phys. 25, 13 (1984)]. In the wake of such results, we unveil a typical spectrum of localized and periodic coherent patterns. We also investigate the scattering properties of such structures and we unearth two peculiar soliton phenomena, namely, the fusion and the fission.

Rotating spiral waves are a form of self-organization observed in spatially extended systems of physical, chemical, and biological natures. A small perturbation causes gradual change in spatial location of spiral’s rotation center and frequency, i.e., drift. The response functions (RFs) of a spiral wave are the eigenfunctions of the adjoint linearized operator corresponding to the critical eigenvalues $\lambda =0,\pm i\omega$. The RFs describe the spiral’s sensitivity to small perturbations in the way that a spiral is insensitive to small perturbations where its RFs are close to zero. The velocity of a spiral’s drift is proportional to the convolution of RFs with the perturbation. Here we develop a regular and generic method of computing the RFs of stationary rotating spirals in reaction-diffusion equations. We demonstrate the method on the FitzHugh-Nagumo system and also show convergence of the method with respect to the computational parameters, i.e., discretization steps and size of the medium. The obtained RFs are localized at the spiral’s core.

We check claims for a generalized central limit theorem holding at the Feigenbaum (infinite bifurcation) point of the logistic map made recently by Tirnakli et al., Phys. Rev. 75, 040106(R) (2007); this issue, Phys. Rev.79, 056209 (2009). We show that there is no obvious way that these claims can be made consistent with high statistics simulations. Instead, we find other scaling laws for related quantities.

Based on the nonequilibrium Green’s function technique, a unified theory is developed that covers quantum transport and quantum diffusion in bulk semiconductors on the same footing. This approach, which is applicable to transport via extended and localized states, extends previous semiphenomenological studies and puts them on a firm microscopic basis. The approach is sufficiently general and applies not only to well-studied quantum-transport problems, but also to models, in which the Hamiltonian does not commute with the dipole operator. It is shown that even for the unified treatment of quantum transport and quantum diffusion in homogeneous systems, all quasimomenta of the carrier distribution function are present and fulfill their specific function. Particular emphasis is put on the double-time nature of quantum kinetics. To demonstrate the existence of robust macroscopic transport effects that have a true double-time character, a phononless steady-state current is identified that appears only beyond the generalized Kadanoff-Baym ansatz.

The phase diagram and critical behavior of a simple toy model for DNA zipping/unzipping are examined in the framework of the Bethe approximation. The effects of solvent quality are included and found to lead to a variety of different thermodynamic behaviors.

We study the effective interaction between two ellipsoidal particles at the interface of two fluid phases which are mediated by thermal fluctuations of the interface. In this system the restriction of the long-ranged interface fluctuations by particles gives rise to fluctuation-induced forces which are equivalent to interactions of Casimir type and which are anisotropic in the interface plane. Since the position and the orientation of the colloids with respect to the interface normal may also fluctuate, this system is an example of the Casimir effect with fluctuating boundary conditions. In the approach taken here, the Casimir interaction is rewritten as the interaction between fluctuating multipole moments of an auxiliary charge-density-like field defined on the area enclosed by the contact lines. These fluctuations are coupled to fluctuations of multipole moments of the contact line position (due to the possible position and orientational fluctuations of the colloids). We obtain explicit expressions for the behavior of the Casimir interaction at large distances for arbitrary ellipsoid aspect ratios. If colloid fluctuations are suppressed, the Casimir interaction at large distances is isotropic, attractive, and long ranged (double logarithmic in the distance). If, however, colloid fluctuations are included, the Casimir interaction at large distances changes to a power law in the inverse distance and becomes anisotropic. The leading power is 4 if only vertical fluctuations of the colloid center are allowed, and it becomes 8 if also orientational fluctuations are included.

The effects of substrate rotation on the surface morphology in oblique-incidence metal(100) epitaxial growth are studied via kinetic Monte Carlo simulations of a simplified model, and compared with previous results obtained without rotation. In general, we find that substrate rotation leads to two main effects. At high deposition angles with respect to the substrate normal, rotation leads to a significant change in the surface morphology. In particular, it leads to isotropic mounds and pyramids with (111) facets rather than the anisotropic ripples and rods observed in the absence of rotation. Due to the existence of rapid transport on these facets, the lateral feature size increases approximately linearly with film thickness. Due to the fact that substrate rotation tends to reduce the effects of shadowing, the surface roughness is also decreased compared to the roughness in the absence of rotation. While this leads to a moderate reduction in the roughness for the case of ballistic deposition, the effect is significantly larger in the case of deposition with attraction. In the case of ballistic deposition, we also find that the surface roughness increases with rotation rate $\Omega$ for $\Omega <1$ rev/monolayer (ML) before saturating at larger rotation rates ($\Omega >1$ rev/ML). In contrast, for the case of attraction the surface roughness exhibits a negligible dependence on rotation rate for finite rotation rate.

We consider the effect of a localized surface viscosity on the relaxation of an imposed deformation in nematic liquid crystal cells. The simple case in which the samples are in the shape of a slab and the differential equations can be linearized is considered. The apparent inconsistence between the initial values of the time derivatives at the border evaluated by means of the bulk equation and of the boundary condition is related to the assumption that the distorting field is removed in a discontinuous manner. In this framework we shall see that the dynamical problem relevant to the relaxation of the deformation is a well posed problem. In particular, the time derivatives of the nematic director evaluated on the surface by means of the bulk differential equation and by means of the dynamical boundary condition are identical for times larger than the switching time of the deforming field. The analysis of the relaxation of the imposed deformation based on the diffusion equation, with the boundary condition containing the surface viscosity, is then valid only for times larger than the switching time of the deforming field. From this observation we conclude that the concept of localized surface viscosity is useful in the description of slow dynamics of nematic liquid crystals.

We have investigated the director reorientation behavior of unconstrained nematic gels (nematic elastomer swollen by low molecular mass liquid crystals) under electric fields by means of polarized Fourier transform infrared (FTIR) spectroscopy. The polarized FTIR reveals that the director rotates about the $\left(y\right)$ axis normal to the original director ($x$ axis) and field directions ($z$ axis), and the nematic order remains unchanged in the plane where the director stays confined during rotation. The rotation angle of director $\left(\theta \right)$ is estimated as a function of imposed voltage amplitude on the basis of the absorbances of the cyano group which is aligned along the long axis of the mesogen for light linearly polarized in the $x$ and $y$ directions. The director-rotation drives a two-dimensional macroscopic deformation which is characterized by a contraction along the $x$ axis, an extension in the $z$ direction, and nonappreciable length change along the $y$ axis. The strain in the $x$ direction is linearly proportional to ${\text{sin}}^2\theta$ in agreement with the expectation of soft or semisoft elasticity theory for thin nematic elastomer films where the shear contribution becomes negligibly small.

This paper describes a quantitative analysis of the trapping probability for the DNA trap, which is a method of trapping and concentrating DNA in a tapered microchannel by electric and hydrodrag force fields. In order to calculate the trapping probability, a series of connections of triangle-shaped taper stages was used. The fluorescent intensity of trapped DNA molecules at each stage was measured. The trapping probability per stage was calculated from the distribution of the fluorescent increase rate along with the stage number. The trapping probabilities were measured as a function of DNA size, electric field, and average hydraulic velocity. The electric field that gives a trap probability of 0.5 was found to be proportional to the average hydraulic velocity for all DNA sizes. For all measured conditions and accuracy, the trapping probability was found to be determined only by the ratio of the electric field to the average hydraulic velocity. These results reveal that the DNA trap is not simply caused by balance between the dielectrophoresis and hydrodrag forces.

A network of chaotic units is investigated where the units are coupled by signals with a transmission delay. Any arbitrary finite network is considered where the chaotic trajectories of the uncoupled units are a solution of the dynamic equations of the network. It is shown that chaotic trajectories cannot be synchronized if the transmission delay is larger than the time scales of the individual units. For several models the master stability function is calculated which determines the maximal delay time for which synchronization is possible.

We examine the problem of reconstructing input-output systems from time series data. Although the method of delays has already been used in the case where both input and output are measured, in some cases, the inputs cannot be measured, and hence, the method of delays cannot be used. On the basis of ideas derived from existing embedding theorems, we propose to build models by using delays of multivariate observations of output data. Assuming that the inputs are few, we use several observations for obtaining information about the inputs, and the remaining observations for obtaining information about the state of the system. Numerical examples on a discrete map and a continuous-time system show that input-output systems can indeed be identified by using multivariate observations of output data only. We also discuss the application of this method to the analysis of coupled systems or complex networks, by partitioning such large systems and analyzing each subsystem separately. The models used in this paper are nonpredictive models; thus, they cannot be used to predict the future behavior of the system. However, since they model the dynamics of the system, they have other possible applications such as change detection and noise reduction.

Linear stability of a binary mixture buoyant return flow in a differentially heated inclined infinite layer is investigated by asymptotic long-wave analysis and pseudospectral Chebyshev numerical solutions. The Soret coefficient is negative so that thermodiffusion separates the species with the heavier component migrating to the hot wall, thus, promoting unstable stratification except in the classical Rayleigh-Benard arrangement. It is shown that longitudinal instabilities with small wave numbers are triggered at any finite temperature difference at all angles of inclination except very close to the horizontal heated from the above or below arrangements. Numerical results are given for a specific water-ethanol mixture and are in excellent agreement with the asymptotic results. As is well known the heated from below horizontal layer is overstable while that heated from above is doubly-diffusive unstable. Transition from the longitudinal stationary instabilities in inclined layers to these instabilities in horizontal layers is also given for this mixture.