A model of a thin straight strip with a uniformly curved section and with boundary requirements zeroing at the edges a linear superposition of the wave function and its normal derivative (Robin boundary condition) is analyzed theoretically within the framework of the linear Schrödinger equation and is applied to the study of the processes in the bent magnetic multilayers, superconducting films and metallic ferrite-filled waveguides. In particular, subband thresholds of the straight and curved parts of the film are calculated and analyzed as a function of the Robin parameter $1/\Lambda$, with $\Lambda$ being an extrapolation length entering Robin boundary condition. For the arbitrary Robin coefficients which are equal on the opposite interfaces of the strip and for all bend parameters the lowest-mode energy of the continuously curved duct is always smaller than its straight counterpart. Accordingly, the bound state below the fundamental propagation threshold of the straight arms always exists as a result of the bend. In terms of the superconductivity language it means an increased critical temperature of the curved film compared to its straight counterpart. Localized-level dependence on the parameters of the curve is investigated with its energy decreasing with increasing bend angle and decreasing bend radius. Conditions of the bound-state existence for the different Robin parameters on the opposite edges are analyzed too; in particular, it is shown that the bound state below the first transverse threshold of the straight arm always exists if the inner extrapolation length is not larger than the outer one. In the opposite case there is a range of the bend parameters where the curved film cannot trap the wave and form the localized mode; for example, for the fixed bend radius the bound state emerges from the continuum at some nonzero bend angle that depends on the difference of the two lengths $\Lambda$ at the opposite interfaces. Various transport properties of the film such as interference blockade of the current flow at some special energies is also discussed with the special attention being paid to the transformation from the Dirichlet to the Neumann case as the extrapolation length $\Lambda$ sweeps the positive axis.

The distributions of the partition function zeros in the complex $a=e^{2\beta J_1}$ plane of the square-lattice Ising model with nearest-neighbor $\left(J_1\right)$ and next-nearest-neighbor $\left(J_2\right)$ interactions are investigated as a function of $R=J_2/J_1$. Starting from the well-known two-circle distribution of the zeros $a=\pm 1+\sqrt{2}{e}^{i\theta }$ for $R=0$, finally the partition function zeros lie on the unit circle $a=e^{i\theta }$ for $R=\infty$. Between these two ends, the changes in the zero distributions are described. Using the partition function zeros, the critical point $a_c\left(R\right)$ and the thermal scaling exponent $y_t\left(R\right)$ are estimated for the Ising ferromagnet (equivalently, antiferromagnet) and superantiferromagnet. For the special case of $R=\frac{1}{2}$, the possible implications of the zero distributions are also discussed.

We introduce a family of bounded repulsive potentials, which we call the cut ramp potential, obtained by cutting a linear ramp potential at different heights. We find that for the uncut ramp potential the system shows a region of anomalous re-entrant melting (a negative slope of the melting line in the temperature-pressure phase diagram), with waterlike anomalies in the same pressure range. At high pressure the melting line recovers a positive slope, a feature that we associate with the formation of clusters of particles separated by a more or less density-independent distance, the cluster separation, which is approximately equal to the ramp width ${\sigma }_1$. As the ramp is cut at lower and lower heights, the region of anomalous behavior shrinks and eventually disappears while at the same time the formation of clusters becomes more favored, as it is energetically less unfavorable for particles to “climb up” the ramp. We relate the occurrence of anomalous behavior to the reduced efficacy of the soft repulsive length scale with increasing pressure. The clustering phenomenon partially restores this efficacy, giving rise to an approximately constant distance ${\sigma }_1$ between the clusters. Our results may be useful to better understand the phase behavior of macromolecules as well as that of substances with nondirectional interactions that are capable of displaying liquid polymorphism.

The steady-state properties of an interface in a stationary Couette flow are addressed within the framework of fluctuating hydrodynamics. Our study reveals that thermal fluctuations are driven out of equilibrium by an effective shear rate that differs from the applied one. In agreement with experiments, we find that the mean-square displacement of the interface is reduced by the flow. We also show that nonequilibrium fluctuations present a certain degree of universality in the sense that all features of the fluids can be factorized into a single control parameter. Finally, the results are discussed in the light of recent experimental and numerical studies.

We construct a coupled map lattice model for spontaneous pore formation in anodic oxidation in two dimensions and perform numerical simulations, after we explain steady flat solutions, their linear stability, and a single pore solution for a model of Parkhutik and Shershulsky.

We present extensive numerical studies to determine the phase diagrams of cubic and hexagonal blue phases in an electric field. We confirm the earlier prediction that hexagonal phases, both two and three dimensional, are stabilized by a field, but we significantly refine the phase boundaries, which were previously estimated by means of a semianalytical approximation. In particular, our simulations show that the blue phase I–blue phase II transition at fixed chirality is largely unaffected by electric field, as observed experimentally.

This paper derives theoretical results for the periodic splay-twist Fréedericksz transition in nematic liquid crystals confined between two infinite concentric cylinders. The calculation of Lonberg and Meyer [Phys. Rev. Lett. 55, 718 (1985)], for nematics sandwiched between two infinite planes, is extended to annular domains. The phase transition is triggered by an applied voltage between the outer and the inner delimiting walls. The critical threshold behavior is analyzed via the linearized Euler-Lagrange equations related to the Frank’s free energy. It is found that, the threshold depends on both the ratio between the twist and the splay elastic constants, and the sample radii ratio. Results for planar samples are recovered in the thin cell limit. With respect to the planar geometry, our analysis predicts that for annular geometries the periodic Fréedericksz transition is also allowed for elastic anisotropies $K_2/K_1>0.303$.

The internal structures, stability, and elastic properties of free-standing filament bundles of bent-core smectic liquid crystals are studied using polarizing microscopy, scanning electron microscopy, and a customized cantilever containing, temperature controlled heat stage for force measurements. We find that in bundles, the individual filaments fuse together to form semiseparable filaments with radii approximately two and three times larger than the individual fibers. We also find that the effective surface tension of wide bundles is about 10% smaller than a single filament. Finally, we describe the metastable coexistences of single fibers within the bundles that lead to bending of the bundles. All of these observations were explained with simple macroscopic models.

Some important biomolecules (for instance, bacterial FtsZ and eukaryotic DNA) are known to posses spontaneous (intrinsic) curvature. Using a simple extension of the wormlike chain model, we study the response of a weakly bending filament in two dimensions to a pulling force applied at its ends (a configuration common in classical in-vitro experiments and relevant to several in-vivo cell cases). The spontaneous curvature of such a chain or filament can in general be arc-length dependent and we study a case of sinusoidal variation, from which an arbitrary case can be reconstructed via Fourier transformation. We obtain analytic results for the force-extension relationship and the width of transverse fluctuations. We show that spontaneous-curvature undulations can affect the force-extension behavior even in relatively flexible filaments with a persistence length smaller than the contour length.

The properties of actin network growth against a flat obstacle are studied using several different sets of molecular-level assumptions regarding filament growth and nucleation. These assumptions are incorporated into a multifilament methodology which treats both the distribution of filament orientations and bending of filaments. Three single-filament force-generation mechanisms in the literature are compared within this framework. Each mechanism is treated using two different filament nucleation modes, namely, spontaneous nucleation and branching off pre-existing filaments. We find that the shape of the force-velocity relation depends mainly on the ratio of the thermodynamic and mechanical stall forces of the filaments. If the thermodynamic stall force greatly exceeds the mechanical stall force, the velocity drops abruptly to zero when the mechanical stall force is reached; otherwise, it goes more gradually to zero. In addition, branching nucleation gives a steeper increase in the filament number with opposing force than spontaneous nucleation does. Finally, the zero-force velocity of the obstacle as a function of the detachment and capping rates differs significantly between the different single-filament growth mechanisms. Experiments are proposed to use these differences to discriminate between the network growth models.

The dynamical evolution of a recently introduced one-dimensional model [S. Biswas and P. Sen, Phys. Rev. E 80, 027101 (2009)] (henceforth, referred to as model I), has been made stochastic by introducing a parameter $\beta$ such that $\beta =0$ corresponds to the Ising model and $\beta \to \infty$ to the original model I. The equilibrium behavior for any value of $\beta$ is identical: a homogeneous state. We argue, from the behavior of the dynamical exponent $z$, that for any $\beta \ne 0$, the system belongs to the dynamical class of model I indicating a dynamic phase transition at $\beta =0$. On the other hand, the persistence probabilities in a system of $L$ spins saturate at a value $P_{sat}\left(\beta ,L\right)={\left(\beta /L\right)}^{\alpha }f\left(\beta \right)$, where $\alpha$ remains constant for all $\beta \ne 0$ supporting the existence of the dynamic phase transition at $\beta =0$. The scaling function $f\left(\beta \right)$ shows a crossover behavior with $f\left(\beta \right)=\text{constant}$ for $\beta ⪡1$ and $f\left(\beta \right)\propto {\beta }^{-\alpha }$ for $\beta ⪢1$.

Stochastic differential equations with multiplicative noise need a mathematical prescription due to different interpretations of the stochastic integral. This fact implies specific algorithms to perform numerical integrations or simulations of the stochastic trajectories. Moreover, if the multiplicative noise function is not continuous then the standard algorithms cannot be used. We present an explicit algorithm to avoid this problem and we apply it to a well controlled example. Finally, we discuss on the existence of higher-order algorithms for this specific situation.

This article focuses on the identification of the number of paths with different lengths between pairs of nodes in complex networks and how these paths can be used for characterization of topological properties of theoretical and real-world complex networks. This analysis revealed that the number of paths can provide a better discrimination of network models than traditional network measurements. In addition, the analysis of real-world networks suggests that the long-range connectivity tends to be limited in these networks and may be strongly related to network growth and organization.

We carry out systematic and high-resolution studies of dynamo action in a shell model for magnetohydrodynamic (MHD) turbulence over wide ranges of the magnetic Prandtl number ${\text{Pr}}_{\text{M}}$ and the magnetic Reynolds number ${\text{Re}}_{\text{M}}$. Our study suggests that it is natural to think of dynamo onset as a nonequilibrium first-order phase transition between two different turbulent, but statistically steady, states. The ratio of the magnetic and kinetic energies is a convenient order parameter for this transition. By using this order parameter, we obtain the stability diagram (or nonequilibrium phase diagram) for dynamo formation in our MHD shell model in the $\left({\text{Pr}}_{\text{M}}^{-1},{\text{Re}}_{\text{M}}\right)$ plane. The dynamo boundary, which separates dynamo and no-dynamo regions, appears to have a fractal character. We obtain a hysteretic behavior of the order parameter across this boundary and suggestions of nucleation-type phenomena.

A lattice Boltzmann (LB) method based on the linearized Boltzmann Bhatnagar-Gross-Krook equation for numerical simulation of oscillatory (unsteady) Stokes flow is proposed. Unlike the conventional (nonlinear) LB method that utilizes the time domain exclusively, the proposed method is formulated in the frequency domain to allow for direct access to the complex-valued stress, force, and velocity field—these parameters are of direct interest in characterizing microelectromechanical systems (MEMS) and nanoelectromechanical systems (NEMS). The proposed method circumvents the requirement for time-dependent boundary velocities, as is needed in the conventional LB method, and convergence of the two methods is compared. Validity of the proposed method is assessed using three classical (unsteady) flows: (1) one-dimensional oscillatory Couette flow between two plates; (2) two-dimensional flow generated by an oscillating circular cylinder; (3) three-dimensional flow generated by an oscillating sphere. The observed excellent numerical performance in all three cases demonstrates that this linear lattice Boltzmann method can be used to study the dynamics of micro- and nanoscale devices of any dimensionality. This is particularly relevant to MEMS and NEMS, where the resonance properties of individual nanomechanical components immersed in fluid can underpin overall device performance.

Percolation is one of the most studied processes in statistical physics. A recent paper by Achlioptas et al. [Science 323, 1453 (2009)] showed that the percolation transition, which is usually continuous, becomes discontinuous (“explosive”) if links are added to the system according to special cooperative rules (Achlioptas processes). In this paper, we present a detailed numerical analysis of Achlioptas processes with product rule on various systems, including lattices, random networks á la Erdös-Rényi, and scale-free networks. In all cases, we recover the explosive transition by Achlioptas et al. However, the explosive percolation transition is kind of hybrid as, despite the discontinuity of the order parameter at the threshold, one observes traces of analytical behavior such as power-law distributions of cluster sizes. In particular, for scale-free networks with degree exponent $\lambda <3$, all relevant percolation variables display power-law scaling, just as in continuous second-order phase transitions.

The effect of noise on a system of globally coupled chaotic maps is considered. Demographic stochasticity is studied since it provides both noise and a natural definition for extinction. A two-step model is presented, where the intrapatch chaotic dynamics is followed by a migration step with global dispersal. The addition of noise to the already chaotic system is shown to dramatically change its behavior. The level of migration in which the system attains maximal sustainability is identified. This determines the optimal way to manipulate a fragmented habitat in order to conserve endangered species. The quasideterministic dynamics that appears in the large $N$ limit of the stochastic system is analyzed. In the clustering phase, the infinite degeneracy of deterministic solutions emerges from the single steady state of the stochastic system via a mechanism that involves an almost defective Markov matrix.

The cooperative behaviors of players on weighted networks are investigated by incorporation of trust mechanisms into a well-accepted game model, i.e., the networked prisoner’s dilemma game, afterwards some weight-updating schemes are designed according to the credit records. Despite the differences in network topologies and strategy updating protocols, a simple yet significant principle surfaces that, to promote the emergence of cooperation over abundant weighted networks, only the latest credit record of partners is required to be taken into consideration, whereas incorporating more previous records may even deteriorate the cooperation performance. To support such an appealing principle, we have investigated more deeply into the role of credit records so as to give a detailed explanation underlying it. The virtue of this work lies in providing insights into the effective usage of the currently available credit records.

In this paper, we formulate Bulgac-Kusnezov constant temperature dynamics in phase space by means of non-Hamiltonian brackets. Two generalized versions of the dynamics are similarly defined, one where the Bulgac-Kusnezov demons are globally controlled by means of a single additional Nosé variable, and another where each demon is coupled to an independent Nosé-Hoover thermostat. Numerically stable and efficient measure-preserving time-reversible algorithms are derived in a systematic way for each case. The chaotic properties of the different phase space flows are numerically illustrated through the paradigmatic example of the one-dimensional harmonic oscillator. It is found that, while the simple Bulgac-Kusnezov thermostat is apparently not ergodic, both of the Nosé-Hoover controlled dynamics sample the canonical distribution correctly.

The initial stages of transcription by RNA polymerase are frequently marked by pausing and stalling events. These events have been linked to an inactive backtracked state in which the polymerase diffuses along the template DNA. We investigate theoretically the influence of RNA secondary structure in confining this diffusion. The effective confinement length peaks at transcript lengths commensurate with early stalling. This finite-size effect accounts for slow progress at the beginning of transcription, which we illustrate via stochastic hopping models for backtracking polymerases.