Systems whose potential energies consists of pieces that scale as $r^{-2}$ together with pieces that scale as $r^2$, show no violent relaxation to Virial equilibrium but may pulsate at considerable amplitude forever. Despite this pulsation these systems form lattices when the nonpulsational “energy” is low, and these disintegrate as that energy is increased. The “specific heats” show the expected halving as the “solid” is gradually replaced by the “fluid” of independent particles. The forms of the lattices are described here for $N⩽18$ and they become hexagonal close packed for large $N$. In the larger $N$ limit, a shell structure is formed. Their large $N$ behavior is analogous to a $\gamma =5∕3$ polytropic fluid with a quasigravity such that every element of fluid attracts every other in proportion to their separation. For such a fluid, we study the “rotating pulsating equilibria” and their relaxation back to uniform but pulsating rotation. We also compare the rotating pulsating fluid to its discrete counterpart, and study the rate at which the rotating crystal redistributes angular momentum and mixes as a function of extra heat content.

The Markov order of a time series is an important measure of the “memory” of a process, and its knowledge is fundamental for the correct simulation of the characteristics of the process. For this reason, several techniques have been proposed in the past for its estimation. However, most of this methods are rather complex, and often can be applied only in the case of Markov chains. Here we propose a simple and robust test to evaluate the Markov order of a time series. Only the first-order moment of the conditional probability density function characterizing the process is used to evaluate the memory of the process itself. This measure is called the “expected value Markov (EVM) order.” We show that there is good agreement between the EVM order and the known Markov order of some synthetic time series.

We investigate the effect of quenched spatial disordered hopping rates on the characteristics of the asymmetric simple exclusion process with open boundaries both numerically and by extensive simulations. Disorder averages of the bulk density and current are obtained in terms of various input and output rates. We study the binary and uniform distributions of disorder. It is verified that the effect of spatial inhomogeneity is generically to enlarge the size of the maximal-current phase. This is in accordance with the mean-field results obtained by Harris and Stinchcombe [Phys. Rev. E 70, 016108 (2004)]. Furthermore, we obtain the dependence of the current and the bulk density on the characteristics of the disorder distribution function. It is shown that the impact of disorder crucially depends on the particle input and out rates. In some situations, disorder can constructively enhance the current.

We introduce a model to describe the wide shear zones observed in modified Couette cell experiments with granular material. The model is a generalization of the recently proposed approach based on a variational principle. The instantaneous shear band is identified with the surface that minimizes the dissipation in a random potential that is biased by the local velocity difference and pressure. The apparent shear zone is the ensemble average of the instantaneous shear bands. The numerical simulation of this model matches excellently with experiments and has measurable predictions.

Jamming and force networks observed in electrorheological (ER) fluids bear many similarities to those observed in various granular and colloidal systems. We have measured the time evolution (transient stresses) of filamentous networks of colloidal particles in suspensions subjected to continuous tensile strain concomitant with the switching on and off of electric fields. The density of particle chains was found to increase exponentially with the applied tensile strain via a rapid formation of single chains followed by a slower coarsening (aggregation) of the chains. The two processes can be ascribed to the field-induced short-range and long-range interparticle forces, respectively, along with the tensile viscous force.

We develop a simple theory explaining the dependence of the gas-liquid critical point in the Stockmayer fluid on dipole strength. The theory is based on the Flory-Huggins lattice description for polymer systems in conjunction with a transfer matrix model for isolated chains of reversibly assembled dipolar particles. We find that the shift of the critical point as a function of dipole strength, which originally was found in computer simulation, strongly resembles the critical point shift as a function of chain length in ordinary linear polymer systems. In particular, the decrease of the critical density with increasing dipole strength is a consequence of the existence of reversible chains near criticality. In addition we report simulation results for gas-liquid critical points well above the limiting dipole strength found previously.

The advective Cahn-Hilliard equation describes the competing processes of stirring and separation in a two-phase fluid. Intuition suggests that bubbles will form on a certain scale, and previous studies of Cahn-Hilliard dynamics seem to suggest the presence of one dominant length scale. However, the Cahn-Hilliard phase-separation mechanism contains a hyperdiffusion term and we show that, by stirring the mixture at a sufficiently large amplitude, we excite the diffusion and overwhelm the segregation to create a homogeneous liquid. At intermediate amplitudes we see regions of bubbles coexisting with regions of hyperdiffusive filaments. Thus, the problem possesses two dominant length scales, associated with the bubbles and filaments. For simplicity, we use a chaotic flow that mimics turbulent stirring at large Prandtl number. We compare our results with the case of variable mobility, in which growth of bubble size is dominated by interfacial rather than bulk effects, and find qualitatively similar results.

We analyze the decay of classically chaotic quantum systems in the presence of fast ballistic escape routes on the Ehrenfest time scale. For a continuous excitation process, the form factor of the decay cross section deviates from the universal random-matrix result on the Heisenberg time scale, i.e., for times much larger than the time for ballistic escape. We derive an exact analytical description and compare our results with numerical simulations for a dynamical model.

We show, numerically, that coupled soliton pairs in nonlinear dissipative systems modeled by the cubic-quintic complex Ginzburg-Landau equation can exist in various forms. They can be stationary, or they can pulsate periodically, quasiperiodically, or chaotically, as is the case for single solitons. In particular, we have found various types of vibrating and shaking soliton pairs. Each type is stable in the sense that a given bound state exists in the same form indefinitely. New solutions appear at special values of the equation parameters, thus bifurcating from stationary pairs. We also report the finding of mixed soliton pairs, formed by two different types of single solitons. We present regions of existence of the pair solutions and corresponding bifurcation diagrams.

While the standard scenario of third-harmonic generation (THG) by a dispersive-wave pump involves the emission of light with a frequency $3\omega$, thrice the frequency $\omega$ of the input pump field, solitons undergoing a continuous shift of their central frequency $\omega$ due to the Raman effect in a multimode optical fiber can generate the third harmonic in a different fashion. In the experiments reported here, we provide the first direct experimental evidence of THG by a continuously red-shifting soliton pump by studying the third-harmonic buildup in relation to the spectral evolution of the soliton pump field in a silica photonic-crystal fiber (PCF). We show that solitons excited in a PCF by unamplified femtosecond pulses of a Cr:forsterite laser sweep through the spectral range from $1.25\text{to}1.63\mu \mathrm{m}$, scanning through a manifold of THG phase-matching resonances with $3\omega$ dispersive waves in PCF modes. As a result, intense third-harmonic peaks build up in the range of wavelengths from $370\text{to}550\mathrm{nm}$ at the output of the fiber, making PCF a convenient fiber-format multifrequency source of short-wavelength radiation. Time-resolved fluorescence measurements with photoexcitation provided by the third-harmonic PCF output are presented, demonstrating the high potential of PCF sources for an ultrafast photoexcitation of fluorescent molecular systems in physics, chemistry, and biology.

It is possible that the step size, or power stroke, of a skeletal muscle myosin is not constant; rather, it fluctuates for each force generation. The estimated widths of the fluctuation are as large as the estimated values of the step size. Although such non-negligible fluctuation is presumed to affect the sliding motion, these effects remain unclear. We examined a system driven by a single myosin molecule sliding along an actin filament to reveal its basic effects. First, we calculated the sliding velocity of the system for each fluctuation width and found that the mean velocity increased with the fluctuation width. We also found that the estimated fluctuation widths satisfied the conditions for maximizing the sliding velocity. Next, we examined the sliding motion along a heterogeneous filament, on which binding sites for myosins were distributed randomly. We found that the loss in sliding velocity that was attributable to heterogeneity of the filament became small when fluctuation in the step size existed. This finding implied that the fluctuation stabilized velocity sliding along possible heterogeneous filaments. These benefits of fluctuation in step size might be used in biological systems, such as a muscle system, and are applicable to fabricated micromachines.

It is well known that in the single-spiral-stable parameter regimes of the two-dimensional complex Ginzburg-Landau equation, spiral-domain patterns spontaneously appear. These patterns are disordered cells of frozen spiral waves well separated by thin walls (shocks), and to a good approximation, the walls are segments of hyperbolas. In this paper, we take a closer look at the global structure of spiral-domain patterns by using rigorous mathematical analysis and considering the unusual effect of the chirality (handedness) of spiral wave. An equation that determines the slope of the shock line is derived. We generalize this analytical method to study the interaction of a pair of spirals with different rotation frequencies, and obtain the geometrical structures of the shock line and the wave front of the invasion wave in transient processing.

In this paper synchronization of multiplexed chaotic systems with smooth nonlinearities is studied. The strategy to establish if such synchronization is achievable is based on the master stability function approach and on the optimization of the coupling parameters. With this approach we are able to show that systems formed by three independent canonical chaotic circuits (i.e., a Lorenz system, a Rössler oscillator, and a Chua’s circuit) can be synchronized through a unique scalar signal.

Powerful coherent terahertz (THz) pulses with a broad spectrum $(0.1–3\mathrm{THz})$ can be produced from a laser-driven wakefield through linear mode conversion in inhomogeneous magnetized plasmas with the maximum plasma density of ${10}^{17}{\mathrm{cm}}^{-3}$. This occurs when a laser pulse, with an optimized duration about $300\mathrm{fs}$, is incident either normally or obliquely to the density gradient of inhomogeneous magnetized plasmas. The external dc magnetic field has a magnitude of a few tesla. By changing the strength and direction of the magnetic field, one can enhance or suppress the THz emission. The maximum energy conversion efficiency in the magnetized plasmas can be double that in the unmagnetized plasmas. Such wakefield emission can be a powerful THz source at the MW level and capable of affording field strength of a few MV/cm, suitable for THz nonlinear physics. Because these THz emissions are always with a positive chirp, with a proper dispersion compression, single-cycle THz pulses can be generated with higher peak powers and field strengths.

We analyze the physical-chemical surface properties of single-slit, single-groove subwavelength-structured silver films with high-resolution transmission electron microscopy and calculate exact solutions to Maxwell’s equations corresponding to recent far-field interferometry experiments using these structures. Contrary to a recent suggestion the surface analysis shows that the silver films are free of detectable contaminants. The finite-difference time-domain calculations, in excellent agreement with experiment, show a rapid fringe amplitude decrease in the near zone (slit-groove distance out to 3–4 wavelengths). Extrapolation to slit-groove distances beyond the near zone shows that the surface wave evolves to the expected bound surface plasmon polariton (SPP). Fourier analysis of these results indicates the presence of a distribution of transient, evanescent modes around the SPP that dephase and dissipate as the surface wave evolves from the near to the far zone.

The vast majority of sampling systems operate in a standard way: at each tick of a fixed-frequency master clock a digitizer reads out a voltage that corresponds to the value of some physical quantity and translates it into a bit pattern that is either transmitted, stored, or processed right away. Thus signal sampling at evenly spaced time intervals is the rule: however, this is not always the case, and uneven sampling is sometimes unavoidable. While periodic or quasiperiodic uneven sampling of a deterministic signal can reasonably be expected to produce artifacts, it is much less obvious that the same happens with noise: here I show that this is indeed the case only for long-memory noise processes, i.e., power-law noises $1∕f^{\alpha }$ with $\alpha >2$. The resulting artifacts are usually a nuisance although they can be eliminated with a proper processing of the signal samples, but they could also be turned to advantage and used to encode information.

We study critical point finite-size effects in the case of the susceptibility of a film in which interactions are characterized by a van der Waals-type power law tail. The geometry is appropriate to a slablike system with two bounding surfaces. Boundary conditions are consistent with surfaces that both prefer the same phase in the low temperature, or broken symmetry, state. We take into account both interactions within the system and interactions between the constituents of the system and the material surrounding it. Specific predictions are made with respect to the behavior of ${}^3\mathrm{He}$ and ${}^4\mathrm{He}$ films in the vicinity of their respective liquid-vapor critical points.

A model based on a single Brownian particle moving in a periodic effective field is used to understand the non-Gaussian dynamics in glassy systems of cage escape and subsequent recaging, often thought to be caused by a heterogeneous glass structure. The results are compared to molecular-dynamics simulations of systems with varying complexity: quasi-two-dimensional colloidlike particles, atactic polystyrene, and a dendritic glass. The model nicely describes generic features of all three topologically different systems, in particular around the maximum of the non-Gaussian parameter. This maximum is a measure for the average distance between cages.

Dynamic heterogeneities in a supercooled system of diatomic molecules with an associated dipole moment have been investigated. To this end, three-time correlation functions have been evaluated. Correlations between molecular displacements performed during consecutive time intervals are apparent at low temperatures in the $\beta$-relaxation regime, whereas they tend to disappear during the $\alpha$-relaxation regime. These correlations maximize when the deviation from Gaussian dynamics takes a maximum, and they reveal the existence of different dynamic domains. Directionality of translational motions has also been studied. At low temperatures, and in the $\beta$-relaxation zone, the molecular vector displacement in a given time interval has an important component in the opposite direction of the vector displacement corresponding to the initial time interval. The amplitudes associated with this quasi-oscillatory behavior become larger as the system is cooled. Dynamic heterogeneities in reorientation have been observed in the $\beta$-relaxation regime, and it has been obtained that molecules that perform faster translational motions experience faster reorientational motions too. This effect increases as temperature decreases.