The role of quadratic on-site pinning potentials on determining the size $\left(N\right)$ dependence of the disorder averaged steady state heat current $⟨J⟩$ in an isotopically disordered harmonic chain connected to stochastic heat baths is investigated. For two models of heat baths, namely white noise baths and Rubin’s model of baths, we find that the $N$ dependence of $⟨J⟩$ is the same and depends on the number of pinning centers present in the chain. In the absence of pinning, ${⟨J⟩}_{Fr}\sim 1∕N^{1∕2}$ while in the presence of one or two pins ${⟨J⟩}_{Fi}\sim 1∕N^{3∕2}$. For a finite $\left(n\right)$ number of pinning centers with $2⩽n⪡N$ we provide heuristic arguments and numerical evidence to show that ${⟨J⟩}_n\sim 1∕N^{n-1∕2}$. We discuss the relevance of our results in the context of recent experiments.

The distribution of recurrence times or return intervals between extreme events is important to characterize and understand the behavior of physical systems and phenomena in many disciplines. It is well known that many physical processes in nature and society display long-range correlations. Hence, in the last few years, considerable research effort has been directed towards studying the distribution of return intervals for long-range correlated time series. Based on numerical simulations, it was shown that the return interval distributions are of stretched exponential type. In this paper, we obtain an analytical expression for the distribution of return intervals in long-range correlated time series which holds good when the average return intervals are large. We show that the distribution is actually a product of power law and a stretched exponential form. We also discuss the regimes of validity and perform detailed studies on how the return interval distribution depends on the threshold used to define extreme events.

We study the dynamical behavior of a square lattice Ising model with exchange and dipolar interactions by means of Monte Carlo simulations. After a sudden quench to low temperatures, we find that the system may undergo a coarsening process where stripe phases with different orientations compete, or alternatively it can relax initially to a metastable nematic phase and then decay to the equilibrium stripe phase through nucleation. We measure the distribution of equilibration times for both processes and compute their relative probability of occurrence as a function of temperature and system size. This peculiar relaxation mechanism is due to the strong metastability of the nematic phase, which goes deep into the low-temperature stripe phase. We also measure quasiequilibrium autocorrelations in a wide range of temperatures. They show a distinct decay to a plateau that we identify as due to a finite fraction of frozen spins in the nematic phase. We find indications that the plateau is a finite-size effect. Relaxation times as a function of temperature in the metastable region show super-Arrhenius behavior, suggesting a possible glassy behavior of the system at low temperatures.

Often gaining insight into the functioning of biomolecular systems requires to follow their dynamics along a microscopic reaction coordinate (RC) on a macroscopic time scale, which is beyond the reach of current all atom molecular dynamics (MD) simulations. A practical approach to this inherently multiscale problem is to model the system as a fictitious overdamped Brownian particle that diffuses along the RC in the presence of an effective potential of mean force (PMF) due to the rest of the system. By employing the recently proposed FR method [I. Kosztin et al., J. Chem. Phys. 124, 064106 (2006)], which requires only a small number of fast nonequilibrium MD simulations of the system in both forward and time reversed directions along the RC, we reconstruct the PMF: (1) of deca-alanine as a function of its end-to-end distance, and (2) that guides the motion of potassium ions through the gramicidin A channel. In both cases the computed PMFs are found to be in good agreement with previous results obtained by different methods. Our approach appears to be about one order of magnitude faster than the other PMF calculation methods and, in addition, it also provides the position-dependent diffusion coefficient along the RC. Thus, the obtained PMF and diffusion coefficient can be used in an overdamped Brownian model to estimate important characteristics of the studied systems, e.g., the mean folding time of the stretched deca-alanine and the mean diffusion time of the potassium ion through gramicidin A.

Based on the classical Langevin equation, we have revisited the problem of orbital motion of a charged particle in two dimensions for a normal magnetic field crossed with or without an in-plane electric bias. We are led to two interesting fluctuation effects: First, we obtain not only a longitudinal “work-fluctuation” relation as expected for a barotropic type system, but also a transverse work-fluctuation relation perpendicular to the electric bias. This “Hall fluctuation” involves the product of the electric and the magnetic fields. Second, for the case of harmonic confinement without bias, the calculated probability density for the orbital magnetic moment gives nonzero even moments, not derivable as field derivatives of the classical free energy.

We demonstrate that scale-free patterns are observed in a spatially extended stochastic system whose deterministic part undergoes a saddle-node bifurcation. Remarkably, the scale-free patterns appear only at a particular time in relaxation processes from a spatially homogeneous initial condition. We characterize the scale-free nature in terms of the spatial configuration of the exiting time from a marginal saddle where the pair annihilation of a saddle and a node occurs at the bifurcation point. Critical exponents associated with the scale-free patterns are determined by numerical experiments.

The characteristics of filaments formed by femtosecond-laser pulses freely propagating in air are different from those of filaments generated with a focal lens. A scheme combining $(2\mathrm{D}+1)$ modeling of the nonlinear Schrödinger equation and ray-tracing method is proposed to provide a fast estimate of the long-range filamentation process in a single-filament regime. A filament with a length of more than $100\mathrm{m}$ is formed by a $10\text{−}\mathrm{mJ}$, negative chirped $350\text{−}\mathrm{fs}$ laser pulse freely propagating in air. A ray-tracing calculation based on the refractive index field obtained from the nonlinear Schrödinger simulation shows that, in the $100\text{−}\mathrm{m}$ propagation range, the main mechanism of filamentation is the spatiotemporal moving focus induced by the initial distribution of the laser intensity. The analysis of ray trajectories suggests that the energy exchange between background and filament core due to refocusing of light rays can be induced by Kerr self-focusing without the help of the ionization effect. The plasma defocusing can be observed only at a very short distance on the propagation track, and it prevents the collapse of the laser field.

We examine the global organization of heterogeneous equilibrium networks consisting of a number of well-distinguished interconnected parts—“communities” or modules. We develop an analytical approach allowing us to obtain the statistics of connected components and the intervertex distance distribution in these modular networks, and to describe their global organization and structure. In particular, we study the evolution of the intervertex distance distribution with an increasing number of interlinks connecting two infinitely large uncorrelated networks. We demonstrate that even a relatively small number of shortcuts unite the networks into one. In more precise terms, if the number of interlinks is any finite fraction of the total number of connections, then the intervertex distance distribution approaches a $\delta$-function peaked form, and so the network is united.

Nonequilibrium magnetization states predict non-Newtonian ferrofluid properties. It is desirable to understand the corresponding flow fields and characteristics. In this study, we derive a magnetoviscosity expression coming from the effective-field method and describing the shear-thinning non-Newtonian behavior of dilute ferrofluids with finite magnetic anisotropy. A mathematical model is developed of non-Newtonian plane flow with respect to shear and pressure driving mechanisms in the presence of an applied stationary uniform magnetic field oriented in the direction perpendicular to vorticity. The results reveal that the non-Newtonian effect tends to increase the velocity and angular velocity but to reduce the magnetization strength. Moreover, an enhanced flow rate and reduced flow drag may be obtained. The maximum non-Newtonian effect is found at a ratio of the Néel relaxation time to the Brownian relaxation time of the order of 0.1.

Studying spin-glass physics through analyzing their ground-state properties has a long history. Although there exist polynomial-time algorithms for the two-dimensional planar case, where the problem of finding ground states is transformed to a minimum-weight perfect matching problem, the reachable system sizes have been limited both by the needed CPU time and by memory requirements. In this work, we present an algorithm for the calculation of exact ground states for two-dimensional Ising spin glasses with free boundary conditions in at least one direction. The algorithmic foundations of the method date back to the work of Kasteleyn from the 1960s for computing the complete partition function of the Ising model. Using Kasteleyn cities, we calculate exact ground states for huge two-dimensional planar Ising spin-glass lattices (up to ${3000}^2$ spins) within reasonable time. According to our knowledge, these are the largest sizes currently available. Kasteleyn cities were recently also used by Thomas and Middleton in the context of extended ground states on the torus. Moreover, they show that the method can also be used for computing ground states of planar graphs. Furthermore, we point out that the correctness of heuristically computed ground states can easily be verified. Finally, we evaluate the solution quality of heuristic variants of the L. Bieche et al. approach.

We study the dynamical response of a two-dimensional Ising model subject to a square-wave oscillating external field. In contrast to earlier studies, the system evolves under a so-called soft Glauber dynamic [Rikvold and Kolesik, J. Phys. A 35, L117 (2002)], for which both nucleation and interface propagation are slower and the interfaces smoother than for the standard Glauber dynamic. We choose the temperature and magnitude of the external field such that the metastable decay of the system following field reversal occurs through nucleation and growth of many droplets of the stable phase, i.e., the multidroplet regime. Using kinetic Monte Carlo simulations, we find that the system undergoes a nonequilibrium phase transition, in which the symmetry-broken dynamic phase corresponds to an asymmetric stationary limit cycle for the time-dependent magnetization. The critical point is located where the half period of the external field is approximately equal to the metastable lifetime of the system. We employ finite-size scaling analysis to investigate the characteristics of this dynamical phase transition. The critical exponents and the fixed-point value of the fourth-order cumulant are found to be consistent with the universality class of the two-dimensional equilibrium Ising model. This universality class has previously been established for the same nonequilibrium model evolving under the standard Glauber dynamic, as well as in a different nonequilibrium model of CO oxidation. The results reported in the present paper support the hypothesis that this far-from-equilibrium phase transition is universal with respect to the choice of the stochastic dynamics.

We explore the distribution of paths followed in fluctuation-induced switching between coexisting stable states. We introduce a quantitative characteristic of the path distribution in phase space that does not require a priori knowledge of system dynamics. The theory of the distribution is developed and its direct measurement is performed in a micromechanical oscillator driven into parametric resonance. The experimental and theoretical results on the shape and position of the distribution are in excellent agreement, with no adjustable parameters. In addition, the experiment provides the first demonstration of the lack of time-reversal symmetry in switching of systems far from thermal equilibrium. The results open the possibility of efficient control of the switching probability based on the measured narrow path distribution.

Dielectric response functions of polar particles (macromolecules) diluted in a nonpolar solvent subjected to a strong external dc electric field are evaluated using the anisotropic noninertial rotational diffusion model. Simple analytic formulas for the longitudinal and transverse components of the dielectric susceptibility and relaxation times are given using the effective relaxation time method. These formulas are tested against numerical solutions of the underlying infinite hierarchy of differential-recurrence equations for statistical moments (ensemble averages of the Wigner $D$ functions) which are obtained by averaging the governing Langevin equation for noninertial rotational Brownian motion over its realizations. The calculations, involving matrix continued fractions, ultimately yield the exact solution of the infinite hierarchy of differential-recurrence relations for the dielectric response functions. In the isotropic rotational diffusion limit, the solution reduces to the known results.

In the present paper we developed a model for calculating the energy of single-wall carbon nanotubes of arbitrary chirality. This model, which we call as the liquid surface model, predicts the energy of a nanotube with relative error less than 1% once its chirality and the total number of atoms are known. The parameters of the liquid surface model and its potential applications are discussed. The model has been suggested for open end and capped nanotubes. The influence of the catalytic nanoparticle, atop which nanotubes grow, on the nanotube stability is also discussed. The suggested model gives an important insight in the energetics and stability of nanotubes of different chirality and might be important for the understanding of nanotube growth process. For the computations we use empirical Brenner and Tersoff potentials and discuss their applicability to the study of carbon nanotubes. From the calculated energies we determine the elastic properties of the single-wall carbon nanotubes (Young modulus, curvature constant) and perform a comparison with available experimental measurements and earlier theoretical predictions.

We present a numerical analysis of the mean-field theory for the structure of semiflexible polymer solutions near spherical surfaces, and use the framework to study the depletion characteristics of semiflexible polymers near colloids and nanoparticles. Our results suggest that the depletion characteristics depend sensitively on the polymer concentrations, the persistence lengths, and the radius of the particles. Broadly, two categories of features are identified based on the relative ratios of the persistence lengths to the correlation length of the polymer solution. For the limit where the correlation length is larger than the persistence length, the correlation length proves to be the critical length scale governing both the depletion thickness and the curvature effects. In contrast, for the opposite limit, the depletion thickness and the curvature effects are dependent on a length scale determined by an interplay between the persistence length and the correlation length. This leads to nontrivial (numerical) scaling laws governing the concentration and radii dependence of the depletion thicknesses. Our study also highlights the manner by which the preceding features rationalize the parametric dependencies of insertion free energies of small probes in semiflexible polymer solutions.

The motion of small cargo particles on microtubules by means of motor proteins in disordered microtubule networks is investigated theoretically using both analytical tools and computer simulations. Different network topologies in two and three dimensions are considered, one of which has been recently studied experimentally by Salman et al. [Biophys. J. 89, 2134 (2005)]. A generalization of the random velocity model is used to derive the mean-square displacement of the cargo particle. We find that all cases belong to the class of anomalous superdiffusion, which is sensitive mainly to the dimensionality of the network and only marginally to its topology. Yet in three dimensions the motion is very close to simple diffusion, with sublogarithmic corrections that depend on the network topology. When details of the thermal diffusion in the bulk solution are included, no significant change to the asymptotic time behavior is found. However, a small asymmetry in the mean microtubule polarity affects the corresponding long-time behavior. We also study a three-dimensional model of the microtubule network in living animal cells. Three first-passage-time problems of intracellular transport are simulated and analyzed for different motor processivities: (i) cargo that originates near the nucleus and has to reach the membrane, (ii) cargo that originates from the membrane and has to reach the nucleus, and (iii) cargo that leaves the nucleus and has to reach a specific target in the cytoplasm. We conclude that while a higher motor processivity increases the transport efficiency in cases (i) and (ii), in case (iii) it has the opposite effect. We conjecture that the balance between the different network tasks, as manifested in cases (i) and (ii) versus case (iii), may be the reason for the evolutionary choice of a finite motor processivity.

We study the dynamics of a reaction-diffusion system comprising two mutually coupled excitable fibers. We consider a case in which the dynamical properties of the two fibers are nonidentical due to the parameter mismatch between them. By using the spatially one-dimensional FitzHugh-Nagumo equations as a model of a single excitable fiber, synchronized pulses are found to be stable in some parameter regime. Furthermore, there exists a critical coupling strength beyond which the synchronized pulses are stable for any amount of parameter mismatch. We show the bifurcation structures of the synchronized and solitary pulses and identify a codimension-2 cusp singularity as the source of the destabilization of synchronized pulses. When stable solitary pulses in both fibers disappear via a saddle-node bifurcation on increasing the coupling strength, a reentrant wave is formed. The parameter region, where a stable reentrant wave is observed in direct numerical simulation, is consistent with that obtained by bifurcation analysis.

We consider the motion of a contact line between a fluid, gas, and solid, as it occurs when a drop advances over a solid surface. This motion is controlled by a microscopic length scale near the contact line, such as a slip length or the precursor thickness. The capillary profile inside the drop is linked to the contact line through an intermediate region which is characterized by an interface slope which varies logarithmically. The intermediate solution contains a single adjustable constant, which can be computed either by matching to the capillary region or to the contact line. We describe a simple method to perform the matching and to compute the required constant. This extends and/or simplifies results known previously. We apply our results to the case of a spreading drop in the presence of an interface potential and derive the equation of motion by combining the inner and outer expansions.

We study the energy decay properties of a pulse propagating in a strongly nonlinear granular chain with damping proportional to the relative velocity of the grains. We observe a wave disturbance that at low viscosities consists of two parts exhibiting two entirely different time scales of dissipation. One part is an attenuating solitary wave, dominated by discreteness and nonlinearity effects as in a dissipationless chain, and has the shorter lifetime. The other is a purely dissipative shocklike structure with a much longer lifetime and exists only in the presence of dissipation. The range of viscosities and initial configurations that lead to this complex wave disturbance are explored.

The biaxial nematic phase was recently observed in different thermotropic liquid crystals, namely bent-core compounds, side-chain polymers, bent-core dimers, and organosiloxane tetrapodes. In this work, a series of experiments with a nematic organosiloxane tetrapode where nuclear magnetic resonance (NMR) spectra are collected while the sample is continuously rotating around an axis perpendicular to the magnetic field, are discussed in conjunction with the analysis of a deuterium NMR experiment on the same system reported earlier. The sample used is a mixture of a deuterated probe with the tetrapode. The mixture exhibits a nematic range between $-40°\mathrm{C}$ and $37°\mathrm{C}$. The results of the two independent, but complementary deuterium NMR experiments confirm the existence of a biaxial nematic phase for temperatures below $0°\mathrm{C}$ with high values of the asymmetry parameter at low temperatures. The presence of slow movements of the tetrapode mesogenic units in the low-temperature regime could also be detected through the analysis of the NMR spectra. Simulations indicate that these movements are mainly slow molecular reorientations of the mesogenic units associated with the presence of collective modes in the nematic phases of this compound. In the case of tetrapodes, recent investigations attribute the origin of biaxiality to the hindering of reorientations of the laterally attached mesogenic units which constitute the tetrapode. This study relates the molecular movements with the nematic biaxial ordering of the system.