We study the statistics of the relative separation between two fluid particles in a spatially smooth and temporally random flow. The Lagrangian strain is modeled by a telegraph noise, which is a stationary random Markov process that can only take two values with known transition probabilities. The simplicity of the model enables us to write closed equations for the interparticle distance in the presence of a finite-correlated noise. In one dimension, we are able to find analytically the long-time growth rates of the distance moments and the senior Lyapunov exponent, which consistently turns out to be negative. We also find the exact expression for the Cramér function and show that it satisfies the fluctuation relation (for the probability of positive and negative entropy production) despite the time irreversibility of the strain statistics. For the two-dimensional incompressible isotropic case, we obtain the Lyapunov exponent (positive) and the asymptotic growth rates of the moments in two opposite limits of fast and slow strain. The quasideterministic limit (of slow strain) turns out to be singular, while a perfect agreement is found with the already-known $\delta$-correlated case.

We present a model for the Lagrangian dynamics of inertial particles in a compressible flow, where fluid velocity gradients are modeled by a telegraph noise. The model allows for an analytic investigation of the role of time correlation of the flow in the aggregation-disorder transition of inertial particles. The dependence on the Stokes number St and the Kubo number Ku of the Lyapunov exponent of particle trajectories reveals the presence of a region in parameter space (St, Ku), where the leading Lyapunov exponent changes sign, thus signaling the transition. The asymptotics of short- and long-correlated flows are discussed, as well as the fluid-tracer limit.

Large-scale molecular dynamics simulations of an $M_s=4.3$ shock in dense argon ($\rho =532\mathrm{kg}∕{\mathrm{m}}^3$, $T=300\mathrm{K}$) and an $M_s=3.6$ shock in dense nitrogen ($\rho =371\mathrm{kg}∕{\mathrm{m}}^3$, $T=300\mathrm{K}$) have been performed. The two-point molecular velocity correlation function is calculated within slices in plane with the shock wave. Long-range ($\sim$ten molecular radii) positive correlations (correlation coefficient $0.05$) are observed for the shock-normal velocity component, the in-plane velocity component, and the rotation rates. No correlations are found upstream or downstream of the shock, indicating that this is a nonequilibrium effect. These correlations violate one of the assumptions underlying the Boltzmann equation.

Classical MD data on the charge-charge dynamic structure factor of two-component plasmas (TCP) modeled in Phys. Rev. A 23, 2041 (1981) are analyzed using the sum rules and other exact relations. The convergent power moments of the imaginary part of the model system dielectric function are expressed in terms of its partial static structure factors, which are computed by the method of hypernetted chains using the Deutsch effective potential. High-frequency asymptotic behavior of the dielectric function is specified to include the effects of inverse bremsstrahlung. The agreement with the MD data is improved, and important statistical characteristics of the model TCP, such as the probability to find both electron and ion at one point, are determined.

We propose a generalized-ensemble algorithm, which we refer to as the multicanonical-multioverlap algorithm. By utilizing a non-Boltzmann weight factor, this method realizes a random walk in the multidimensional, energy-overlap space and explores widely in the configurational space including specific configurations, where the overlap of a configuration with respect to a reference state is a measure for structural similarity. We apply the multicanonical-multioverlap molecular dynamics method to a penta peptide, Met-enkephalin, in vacuum as a test system. We also apply the multicanonical and multioverlap molecular dynamics methods to this system for the purpose of comparisons. We see that the multicanonical-multioverlap molecular dynamics method realizes effective sampling in the configurational space including specific configurations more than the other two methods. Furthermore, from the results of the multicanonical-multioverlap molecular dynamics simulation, we obtain a local-minimum state of the Met-enkephalin system.

We report a theoretical study of the escape rates of the Hénon-Heiles system above threshold. An analytic formula for the escape rate as a function of energy is presented. We also simulated the escaping process by following the motions of a large number of particles. Two algorithms are employed to solve the equations of motion. One is the Runge-Kutta-Fehlberg method, and another is a recently proposed fourth order symplectic method. Our simulations show the escape of Hénon-Heiles system follows exponential laws. We extracted the escape rates from the time dependence of particle numbers in the Hénon-Heiles potential. The extracted escape rates agree with the analytic result. Close to threshold we find the rate $\alpha \left(\Delta E\right)$ can be written as a series expansion, the first term of this expansion is $\frac{4}{3}\Delta E$.

The model of an electric circuit with dichotomous resistance is investigated. It is shown that the dichotomous resistance can induce a phenomenon of stochastic giant resonance for the signal-to-noise ratio (SNR) as a function of input signal frequency. This phenomenon is a direct consequence of the existence of a zero noise power spectrum, with a nonzero signal power spectrum for the same parameters. In addition, two kinds of the usual stochastic resonance phenomena have been obtained for the SNR. One is as a function of the correlation time of the asymmetric dichotomous resistance; the other is as a function of the input signal frequency.

Disordered systems present multifractal properties at criticality. In particular, as discovered by Ludwig [A.W.W. Ludwig, Nucl. Phys. B 330, 639 (1990)] in the case of a diluted two-dimensional Potts model, the moments $\overline{{\rho }^q\left(r\right)}$ of the local order parameter $\rho \left(r\right)$ scale with a set $x\left(q\right)$ of nontrivial exponents $x\left(q\right)\ne qx\left(1\right)$. We reexamine these ideas to incorporate more recent findings: (i) whenever a multifractal measure $w\left(r\right)$ normalized over space ${\sum }_{r}w\left(r\right)=1$ occurs in a random system, it is crucial to distinguish between the typical values and the disorder-averaged values of the generalized moments $Y_q={\sum }_r{w}^q\left(r\right)$, since they may scale with different generalized dimensions $D\left(q\right)$ and $\tilde{D}\left(q\right)$, and (ii), as discovered by Wiseman and Domany [S. Wiseman and E. Domany, Phys. Rev. E 52, 3469 (1995)], the presence of an infinite correlation length induces a lack of self-averaging at critical points for thermodynamic observables, in particular for the order parameter. After this general discussion, valid for any random critical point, we apply these ideas to random polymer models that can be studied numerically for large sizes and good statistics over the samples. We study the bidimensional wetting or the Poland-Scheraga DNA model with loop exponents $c=1.5$ (marginal disorder) and $c=1.75$ (relevant disorder). Finally, we argue that the presence of finite Griffiths-ordered clusters at criticality determines the asymptotic value $x(q\to \infty )=d$ and the minimal value ${\alpha }_{min}=D(q\to \infty )=d-x\left(1\right)$ of the typical multifractal spectrum $f\left(\alpha \right)$.

A single particle within a periodically driven Sinai-billiard-like system is tracked experimentally and is simulated via hard-sphere molecular dynamics. Both experiments and simulations confirm the fluctuation theorem (FT); thus, in this setup, one driven particle is sufficient for the FT to hold. Furthermore, in the simulations the chaoticity of the system can be adjusted using the restitution coefficient of collisions. It is also shown that the FT breaks down when unstable periodic orbits appear for small restitution coefficients.

The fractional Laplacian operator $-{\left(-\Delta \right)}^{\alpha ∕2}$ appears in a wide class of physical systems, including Lévy flights and stochastic interfaces. In this paper, we provide a discretized version of this operator which is well suited to deal with boundary conditions on a finite interval. The implementation of boundary conditions is justified by appealing to two physical models, namely, hopping particles and elastic springs. The eigenvalues and eigenfunctions in a bounded domain are then obtained numerically for different boundary conditions. Some analytical results concerning the structure of the eigenvalue spectrum are also obtained.

We study a system composed of two parallel totally asymmetric simple exclusion processes with open boundaries, where the particles move in the two lanes in opposite directions and are allowed to jump to the other lane with rates inversely proportional to the length of the system. Stationary density profiles are determined and the phase diagram of the model is constructed in the hydrodynamic limit, by solving the differential equations describing the steady state of the system, analytically for vanishing total current and numerically for nonzero total current. The system possesses phases with a localized shock in the density profile in one of the lanes, similarly to exclusion processes endowed with nonconserving kinetics in the bulk. Besides, the system undergoes a discontinuous phase transition, where coherently moving delocalized shocks emerge in both lanes and the fluctuation of the global density is described by an unbiased random walk. This phenomenon is analogous to the phase coexistence observed at the coexistence line of the totally asymmetric simple exclusion process, however, as a consequence of the interaction between lanes, the density profiles are deformed and in the case of asymmetric lane change, the motion of the shocks is confined to a limited domain.

We study the interface between a solid trapped within a bath of liquid by a suitably shaped nonuniform external potential. Such a potential may be constructed using lasers, external electric or magnetic fields, or a surface template. We study a two-dimensional case where a thin strip of solid, created in this way, is surrounded on either side by a bath of liquid with which it can easily exchange particles. Since height fluctuations of the interface cost energy, this interface is constrained to remain flat at all length scales. However, when such a solid is stressed by altering the depth of the potential beyond a certain limit, it responds by relieving stress by novel interfacial fluctuations, which involve addition or deletion of entire lattice layers of the crystal. This “layering” transition is a generic feature of the system regardless of the details of the interaction potential. We show how such interfacial fluctuations influence mass, momentum, and energy transport across the interface. Tiny momentum impulses produce weak shock waves, which travel through the interface and cause the spallation of crystal layers into the liquid. Kinetic and energetic constraints prevent spallation of partial layers from the crystal, a fact which may be of some practical use. We also study heat transport through the liquid-solid interface and obtain the resistances in liquid, solid, and interfacial regions (Kapitza resistance) as the solid undergoes such layering transitions. Heat conduction, which shows strong signatures of the structural transformations, can be understood using a free volume calculation.

We propose a simple model for DNA denaturation bases on the pendulum model of Englander et al. [Proc. Natl. Acad. Sci. U.S.A. 77, 7222 (1980)] and the microscopic model of Peyrard and Bishop [Phys. Rev. Lett. 62, 2755 (1989)], so-called “combined model.” The main parameters of our model are the coupling constant $k$ along each strand, the mean stretching $y^{*}$ of the hydrogen bonds, the ratio of the damping constant and driven force $\gamma ∕F$. We show that both the length $L$ of unpaired bases and the velocity $v$ of kinks depend on not only the coupling constant $k$ but also the temperature $T$. Our results are in good agreement with previous works.

Dendritic spines, the sites where excitatory synapses are made in most neurons, can dynamically regulate diffusing molecules by changing their shape. We present here a combination of theory, simulations, and experiments to quantify the diffusion time course in dendritic spines. We derive analytical formulas and compared them to Brownian simulations for the mean sojourn time a diffusing molecule stays inside a dendritic spine when either the molecule can reenter the spine head or not, once it is located in the spine neck. We show that the spine length is the fundamental regulatory geometrical parameter for the diffusion decay rate in the neck only. By changing the spine length, dendritic spines can be dynamically coupled or uncoupled to their parent dendrites, which regulates diffusion, and this property makes them unique structures, different from static dendrites.

We investigate a set of directed sandpile models on the Apollonian network, which are inspired by the work of Dhar and Ramaswamy [Phys. Rev. Lett. 63, 1659 (1989)] on Euclidian lattices. They are characterized by a single parameter $q$, which restricts the number of neighbors receiving grains from a toppling node. Due to the geometry of the network, two- and three-point correlation functions are amenable to exact treatment, leading to analytical results for avalanche distributions in the limit of an infinite system for $q=1,2$. The exact recurrence expressions for the correlation functions are numerically iterated to obtain results for finite-size systems when larger values of $q$ are considered. Finally, a detailed description of the local flux properties is provided by a multifractal scaling analysis.

Using an open-flow reactor periodically perturbed with light, we observe subharmonic frequency locking of the oscillatory Belousov-Zhabotinsky chemical reaction at one-sixth the forcing frequency (6:1) over a region of the parameter space of forcing intensity and forcing frequency where the Farey sequence dictates we should observe one-third the forcing frequency (3:1). In this parameter region, the spatial pattern also changes from slowly moving traveling waves to standing waves with a smaller wavelength. Numerical simulations of the FitzHugh-Nagumo equations show qualitative agreement with the experimental observations and indicate that the oscillations in the experiment are a result of period doubling.

The rotation of a single spheroid in a planar Couette flow as a model for simple shear flow is numerically simulated with the distributed Lagrangian multiplier based fictitious domain method. The study is focused on the effects of inertia on the orbital behavior of prolate and oblate spheroids. The numerical orbits are found to be well described by a simple empirical model, which states that the rate of the spheroid rotation about the vorticity axis is a sinusoidal function of the corresponding projection angle in the flow-gradient plane, and that the exponential growth rate of the orbit function is a constant. The following transitions in the steady state with increasing Reynolds number are identified: Jeffery orbit, tumbling, quasi-Jeffery orbit, log rolling, and inclined rolling for a prolate spheroid; and Jeffery orbit, log rolling, inclined rolling, and motionless state for an oblate spheroid. In addition, it is shown that the orbit behavior is sensitive to the initial orientation in the case of strong inertia and there exist different steady states for certain shear Reynolds number regimes.

Water flow between porous grains varies widely depending on the water distribution in contacts between grains. The hydraulic behavior of contacts varies from highly conductive when water fills the contacts to a bottleneck to flow as water pressure drops and contact asperities rapidly drain. Such changes greatly impact the hydraulic conductivity of porous grain packs such as aggregated soil. The dominant driving force of water flow across contacts is capillarity, often quantified relative to gravity and viscous forces using the capillary and Bond numbers. For fast water infiltration, viscous forces dominate. For simplicity we modeled the water distribution between spherical porous grains whose surfaces are covered by spherical bumps of much smaller radii. We provide experimental evidence obtained by neutron radiography and synchrotron-based x-ray tomographic microscopy documenting transitions in the flow behavior across contacts.

We investigate the interaction of a periodic solution and a one-soliton solution for the spin-polarized current in a uniaxial ferromagnetic nanowire. The amplitude and wave number of the periodic solution for the spin current give different contributions to the width, velocity, and amplitude of the soliton. Moreover, we found that the soliton can be trapped only in space with proper conditions. Finally, we analyze the modulation instability and discuss dark solitary wave propagation for a spin current on the background of a periodic solution. In some special cases, the solution can be expressed as the linear combination of the periodic and soliton solutions.

The discrete variable representation (DVR) is a well known and widely used computational technique in many areas of physics. Recently, the Lagrange-Lobatto basis has attracted increasing attention, especially for radial Hamiltonians with a singular potential at the origin and finite element DVR constructions. However, unlike standard DVR functions, the Lagrange-Lobatto basis functions are not orthogonal. The overlap matrix is usually approximated as the identity using the same quadrature approximation as for the potential. Based on the special properties of overlap matrix of Lagrange-Lobatto polynomials, an explanation of the success of the identity approximation, including error bounds, is presented. Results for hydrogen and the more nontrivial potentials of self-consistent all-electron density functional atomic calculations are also given.