We investigate the temporal memory and persistence time correlations of microstructural order fluctuations in quasi-two-dimensional dusty plasma liquids through directly monitoring particle positions. The persistence length of the ordered and the disordered microstates both follow power-law distribution for the cold liquid. The correlation probabilities of the persistence lengths in different pairs of fluctuating cycles show that an order-disorder-order and a disorder-order-disorder sequence are more likely to have the long-short-long or short-long-short persistent lengths combination. The persistence time correlation lasts for several fluctuating cycles. The correlation memory is stored in the surrounding heterogeneous network through mutual coupling. Increasing thermal noise level deteriorates the memory and leads to the less correlated stretched exponential distribution of the persistent length.

We present the analytic calculation of the cross-spectral density tensor of a thermally radiative planar dielectric slab in extreme near-field, intermediate near-field, and far-field zones. We show that the spatial coherence of the thermal field exhibits distinct features in these zones. At a given wavelength $\lambda$, the coherence length is many orders of magnitude smaller than $\lambda$ in the extreme near-field zone, and is roughly $\lambda ∕2$ in the far-field zone. In the intermediate near-field zone, the coherence length can be much longer than $\lambda ∕2$ if the loss is small. The physical origin of the short-ranged spatial coherence in the extreme near-field zone is the spatially fluctuating surface charges at the air-dielectric interface. We also demonstrate that in the intermediate near-field zone, the long-ranged spatial coherence is induced by the waveguide modes of the dielectric slab. When the loss is small, the long-ranged coherence falls off approximately as $1∕\sqrt{x}$, in contrast to $1∕x$ for a blackbody radiator, where $x$ refers to displacement parallel to the slab surface.

We investigate the effects of diffusion on the evolution of steady-state dark and gray spatial solitons in biased photorefractive media. Numerical integration of the nonlinear propagation equation shows that the soliton beams experience a modification of their initial trajectory, as well as a variation of their minimum intensity. This process is further studied using perturbation analysis, which predicts that the center of the optical beam moves along a parabolic trajectory and, moreover, that its minimum intensity varies linearly with the propagation distance, either increasing or decreasing depending on the sign of the initial transverse velocity. Relevant examples are provided.

We calculate spectra of radiation produced by a relativistic particle in the presence of one-dimensional Langmuir turbulence which might be generated by a streaming instability in the plasma, in particular, in the shock front or at the shock-shock interactions. The shape of the radiation spectra is shown to depend sensitively on the angle between the particle velocity and electric field direction. The radiation spectrum in the case of exactly transverse particle motion is degenerate and similar to that of spatially uniform Langmuir oscillations. In the case of oblique propagation, the spectrum is more complex, it consists of a number of power-law regions and may contain a distinct high-frequency spectral peak. The emission process considered is relevant to various laboratory plasma settings and for astrophysical objects as gamma-ray bursts and collimated jets.

We present extensive Monte Carlo spin-dynamics simulations of the vector Blume-Emery-Griffiths model with three-dimensional spins on a simple cubic lattice and periodic boundary conditions. For a range of Hamiltonian parameters, this model reproduces the phase diagram topology of the one experimentally observed for bulk mixtures of ${}^3\mathrm{He}\text{−}{}^4\mathrm{He}$. Highly efficient decomposition time integration algorithms have been used to obtain the evolution of the equations of motion from which we have computed the dynamic structure factor $S(\mathbf{q},\omega )$ close to critical and tricritical points. The dispersion relation and the corresponding dynamic exponents have been obtained in the critical and multicritical transitions. We find that the dynamic critical exponents for in-plane and out-of-plane fluctuations are the same at the tricritical point but are in fact different along the critical line.

The polarized $\left(VV\right)$ and depolarized $\left(VH\right)$ dynamic light scattering functions of dilute solutions of semirigid macromolecules are calculated assuming that the scattering wave vector $\underset{̱}{q}$ is high compared to the chain Kuhn segment $l$: $ql⪢1$. The terminal relaxation rate is $\Gamma \propto q^{8∕3}$. Dynamics of both uniaxial and biaxial wormlike macromolecules (filaments) are considered. Biaxial macromolecules are characterized by two persistence lengths proportional to elastic constants for bending in two perpendicular directions (easy and hard bending). We showed that biaxiality may result in a significant broadening of the relaxation spectrum. A nonmonotonous $q$ dependence of the depolarized scattering intensity is predicted. Analyzing the short-time behavior of the dynamic structure factor for $t⪡1∕\Gamma$, we show that it is characterized by two additional characteristic times: $t_{\perp }\propto q^{-4}$ and $t_{\Vert }\propto q^{-8}$ reflecting the transverse and the longitudinal dynamics of polymer chains. The longitudinal motions (along the chain contour) increase the initial relaxation rate of the structure factor by a factor of 2. The longitudinal contribution to the dynamic structure factor is significant even for $t⪢t_{\Vert }$.

In a recent paper, Zikic et al. [Phys. Rev. E 74, 011919 (2006)] present first-principles calculations of the DNA nucleotides’ electrical conductance. They report qualitative and quantitative differences with previous work, in particular with that of Zwolak and Di Ventra [Nano Lett. 5, 421 (2005)] and Lagerqvist et al. [Nano Lett. 6, 779 (2006)]. In this comment we address the alleged discrepancies, showing that they come from a misrepresentation of our research. Further, we discuss in more detail the issue of geometric fluctuations previously investigated by us, and raised again in the work of Zikic et al. In addition, we point out erroneous comments made by Zikic et al. regarding the use of density functional theory calculations in transport.

Lagerqvist et al.’s Comment regarding the calculation of the transverse conductance of a single-strand DNA heteropolymer translocated through a nanogap between two metal electrodes fully confirms the main conclusions of our study [Phys. Rev. E 74, 011919 (2006)]. In the absence of resonant tunneling, the sensitivity to geometrical factors and the uncertainty in the density functional theory model, which is used in our study and is the basis for the parametrization of the model used by Lagerqvist et al., raises doubt about the utility of static-bias measurements for DNA sequencing. A possible scheme discussed by Lagerqvist et al., the stabilization of geometry by an applied strong transverse voltage $\left(1\mathrm{V}\right)$, is outside the applicability range of the near-equilibrium theory they (and we) used. More advanced theories and precise gap measurements are needed to resolve these issues.

Motivated by recent observations that long-range connections (LRCs) play a role in various brain phenomena, we have observed two distinct dynamical transitions in the activity of excitable media where waves propagate both between neighboring regions and through LRCs. When the LRC density $p$ is low, single or multiple spiral waves are seen to emerge and cover the entire system. This state is self-sustaining and robust against perturbations. At $p=p_c^l$, the spirals are suppressed, and there is a transition to a spatially homogeneous, temporally periodic state. Finally, above $p=p_c^u$, activity ceases after a brief transient.

We investigate amplitude death in a regular array of nonlinear oscillators. We find that the system undergoes three transitions during the road to complete amplitude death. The first two are related to partial amplitude death: one induces partial amplitude death and the other enhances it. The last transition establishes complete amplitude death. We also find that the first two belong to a second-order transition and are universal while the last one is strongly dependent on the system parameters.

We study the Bragg resonance of surface water waves by a two-dimensional array of vertical cylinders covering a large area of the sea. Starting from the resonance criterion known in the physics of solid state and crystallography, we employ asymptotic techniques to derive two-dimensional coupled-mode equations for the envelopes of scattered waves resonated by a plane incident wave. Explicit analytical solutions are obtained for a long strip of cylinder array which may be used for supporting a future offshore airport. Examples of both two-wave and three-wave resonances are discussed in detail. Roles of the band gaps are examined.

We study the stability of a compressible magnetic plane Couette flow and show that compressibility profoundly alters the stability properties if the magnetic field has a component perpendicular to the direction of flow. The necessary condition of an instability can be satisfied in a wide variety of flows in laboratory and astrophysical conditions. The instability can operate even in a very strong magnetic field which entirely suppresses other magnetohydrodynamics (MHD) instabilities. The growth time of this instability can be rather short and reach $\sim 10$ shear time scales.

The existence of highly localized multisite oscillatory structures (discrete multibreathers) in a nonlinear Klein-Gordon chain which is characterized by an inverse dispersion law is proven and their linear stability is investigated. The results are applied in the description of vertical (transverse, off-plane) dust grain motion in dusty plasma crystals, by taking into account the lattice discreteness and the sheath electric and/or magnetic field nonlinearity. Explicit values from experimental plasma discharge experiments are considered. The possibility for the occurrence of multibreathers associated with vertical charged dust grain motion in strongly coupled dusty plasmas (dust crystals) is thus established. From a fundamental point of view, this study aims at providing a rigorous investigation of the existence of intrinsic localized modes in Debye crystals and/or dusty plasma crystals and, in fact, suggesting those lattices as model systems for the study of fundamental crystal properties.

The recently introduced consistent lattice Boltzmann model with energy conservation [S. Ansumali and I. V. Karlin, Phys. Rev. Lett. 95, 260605 (2005)] is extended to the simulation of thermal flows on standard lattices. The two-dimensional thermal model on the standard square lattice with nine velocities is developed and validated in the thermal Couette and Rayleigh-Bénard natural convection problems.

Brownian dynamics simulations are used to study highly entangled solutions of semiflexible polymers. Bending fluctuations of semiflexible rods are significantly affected by entanglement only above a concentration $c^{**}$, where $c^{**}\sim {10}^3{L}^{-3}$ for chains of length $L$ similar to their persistence length. For $c>c^{**}$, the tube radius $R_e$ approaches a dependence $R_e\propto c^{-3∕5}$ and the linear viscoelastic response develops an elastic plateau that is absent for $c<c^{**}$. Experiments on isotropic solutions of F-actin are shown to span concentrations near $c^{**}$ for which the predicted asymptotic scaling of the plateau modulus, $G\propto c^{7∕5}$, is not yet valid.

The Ehrenfest urn process, also known as the dogs and fleas model, is realistically simulated by molecular dynamics of the Lennard-Jones fluid. The key variable is $\Delta z$—i.e., the absolute value of the difference between the number of particles in one half of the simulation box and in the other half. This is a pure-jump stochastic process induced, under coarse graining, by the deterministic time evolution of the atomic coordinates. We discuss the Markov hypothesis by analyzing the statistical properties of the jumps and the waiting times between the jumps. In the limit of a vanishing integration time step, the distribution of waiting times becomes closer to an exponential and, therefore, the continuous-time jump stochastic process is Markovian. The random variable $\Delta z$ behaves as a Markov chain and, in the gas phase, the observed transition probabilities follow the predictions of the Ehrenfest theory.

The nature of the individual transitions on the potential energy landscape (PEL) associated with particle motion are directly examined for model fragile glass-forming polymer melts, and the results are compared to those of an antiplasticized polymer system. In previous work, we established that the addition of antiplasticizer reduces the fragility of glass formation so that the antiplasticized material is a stronger glass former. In the present work, we find that the antiplasticizing molecules reduce the energy barriers for relaxation compared to the pure polymer, implying that the antiplasticized system has smaller barriers to overcome in order to explore its configuration space. We examine the cooperativity of segmental motion in these bulk fluids and find that more extensive stringlike collective motion enables the system to overcome larger potential energy barriers, in qualitative agreement with both the Stillinger-Weber and Adam-Gibbs views of glass formation. Notably, the stringlike collective motion identified by our PEL analysis corresponds to incremental displacements that occur within larger-scale stringlike particle displacement processes associated with PEL metabasin transitions that mediate structural relaxation. These “substrings” nonetheless seem to exhibit changes in relative size with antiplasticization similar to those observed in “superstrings” that arise at elevated temperatures. We also study the effects of confinement on the energy barriers in each system. Film confinement makes the energy barriers substantially smaller in the pure polymer, while it has little effect on the energy barriers in the antiplasticized system. This observation is qualitatively consistent with our previous studies of stringlike motion in these fluids at higher temperatures and with recent experimental measurements by Torkelson and co-workers.

The effect of an externally applied flow on symmetry degenerated waves propagating into opposite directions and standing waves that exchange stability with the traveling waves via mixed states is analyzed. Wave structures that consist of spiral vortices in the counter rotating Taylor-Couette system are investigated by full numerical simulations and explained quantitatively by amplitude equations containing quintic coupling terms. The latter are appropriate to describe the influence of inversion-symmetry-breaking perturbations on many oscillatory instabilities with O(2) symmetry.

We discuss two methods of an exact stochastic representation of the non-Markovian quantum dynamics of open systems. The first method employs a pair of stochastic product vectors in the total system’s state space, while the second method uses a pair of state vectors in the open system’s state space and a random operator acting on the state space of the environment. Both techniques lead to an exact solution of the von Neumann equation for the density matrix of the total system. Employing a spin star model describing a central spin coupled to the bath of surrounding spins, we perform Monte Carlo simulations for both variants of the stochastic dynamics. In addition, we derive an analytical expression for the expectation values of the stochastic dynamics to obtain the exact solution for the density matrix of the central spin.

We report on an experimental study of the shear-banding phenomenon in the concentrated wormlike micellar system CTAB at $20\mathrm{wt.}\%$ in ${\mathrm{D}}_2\mathrm{O}$. Time-resolved velocity profiles are recorded using ultrasonic velocimetry simultaneously to global rheological data. Our results confirm the studies performed previously by Fischer and Callaghan [Phys. Rev. E 64, 011501 (2001)]. Time averaged velocity profiles display an unsheared “nematic gel.” In the range of applied shear rate, the flow field exhibits very fast temporal fluctuations. Suspicions for the presence of three-dimensional flow are evidenced and possible causes for a three-dimensional instability are discussed together with the coupling of wall slip to bulk dynamic.