We investigate the collision cascade that is generated by a single moving particle in a static and homogeneous hard-sphere gas. We argue that the number of moving particles at time $t$ grows as $t^{\xi }$ and the number collisions up to time $t$ grows as $t^{\eta }$, with $\xi =2d∕(d+2)$, $\eta =2(d+1)∕(d+2)$, and $d$ the spatial dimension. These growth laws are the same as those from a hydrodynamic theory for the shock wave emanating from an explosion. Our predictions are verified by molecular dynamics simulations in $d=1$ and 2. For a particle incident on a static gas in a half-space, the resulting backsplatter ultimately contains almost all the initial energy.

Properties of the one-dimensional totally asymmetric simple exclusion process (TASEP), and their connection with the dynamical scaling of moving interfaces described by a Kardar-Parisi-Zhang equation are investigated. With periodic boundary conditions, scaling of interface widths (the latter defined via a discrete occupation-number-to-height mapping), gives the exponents $\alpha =0.500\left(5\right)$, $z=1.52\left(3\right)$, $\beta =0.33\left(1\right)$. With open boundaries, results are as follows: (i) in the maximal-current phase, the exponents are the same as for the periodic case, and in agreement with recent Bethe ansatz results; (ii) in the low-density phase, curve collapse can be found to a rather good extent, with $\alpha =0.497\left(3\right)$, $z=1.20\left(5\right)$, $\beta =0.41\left(2\right)$, which is apparently at variance with the Bethe ansatz prediction $z=0$; (iii) on the coexistence line between low- and high-density phases, $\alpha =0.99\left(1\right)$, $z=2.10\left(5\right)$, $\beta =0.47\left(2\right)$, in relatively good agreement with the Bethe ansatz prediction $z=2$. From a mean-field continuum formulation, a characteristic relaxation time, related to kinematic-wave propagation and having an effective exponent $z^{\prime }=1$, is shown to be the limiting slow process for the low-density phase, which accounts for the above mentioned discrepancy with Bethe ansatz results. For TASEP with quenched bond disorder, interface width scaling gives $\alpha =1.05\left(5\right)$, $z=1.7\left(1\right)$, $\beta =0.62\left(7\right)$. From a direct analytic approach to steady-state properties of TASEP with quenched disorder, closed-form expressions for the piecewise shape of averaged density profiles are given, as well as rather restrictive bounds on currents. All these are substantiated in numerical simulations.

We study a statistical model describing the steady-state distribution of the fluxes in a metabolic network. The resulting model defined on continuous variables can be solved by the cavity method. In particular, analytical tractability is possible, solving the cavity equation over an ensemble of networks with the same degree distribution as a real metabolic network. The flux distribution that optimizes production of biomass has a fat tail with a power-law exponent independent of the structural properties of the underlying network. These results are in complete agreement with the flux-balance-analysis outcome and in qualitative agreement with the experimental results.

On the basis of the fully relativistic Dirac-Fock treatment of photoionization and radiative recombination processes with regard to all multipoles of the radiative field, we have assessed the influence of nondipole effects on the radiative recombination rate coefficients. A formula for the rate coefficient has been derived using the relativistic Maxwell-Boltzmann distribution of continuum electrons instead of the commonly used nonrelativistic distribution. This decreases the recombination rate coefficient considerably in hot thermal plasmas.

We report the observation of a strong coupling between an artificial “atom” and localized interface mode in the microwave regime. Transmittance is experimentally measured for the effective near-zero-index paired structures containing $\epsilon$-negative and $\mu$-negative materials made of composite right- and left-handed transmission lines. When the atom is embedded in the interface, because of the strong coupling between the atom and the interface mode, a Rabi splitting of $0.12\mathrm{GHz}$ is observed, which is in good agreement with numerical simulations. Different from the usual Rabi splitting observed in conventional cavities, the splitting modes in the effective zero-index media are invariant with the scaling change of the length.

Understanding the emergence of extreme opinions and in what kind of environment they might become less extreme is a central theme in our modern globalized society. A model combining continuous opinions and observed discrete actions (CODA) capable of addressing the important issue of measuring how extreme opinions might be has been recently proposed. In this paper I show extreme opinions to arise in a ubiquitous manner in the CODA model for a multitude of social network structures. Depending on network details reducing extremism seems to be possible. However, a large number of agents with extreme opinions is always observed. A significant decrease in the number of extremists can be observed by allowing agents to change their positions in the network.

We study the time evolution of perturbations in spatially extended chaotic systems in the presence of quenched disorder. We find that initially random perturbations tend to exponentially localize in space around static pinning centers that are selected by the particular configuration of disorder. The spatiotemporal behavior of typical perturbations $\delta u(x,t)$ is analyzed in terms of the Hopf-Cole transform $h(x,t)\equiv \ln \mid \delta u(x,t)\mid$. Our analysis shows that the associated surface $h(x,t)$ self-organizes into a faceted structure with scale-invariant correlations. Scaling analysis of critical roughening exponents reveals that there are three different universality classes for error propagation in disordered chaotic systems that correspond to different symmetries of the underlying disorder. Our conclusions are based on numerical simulations of disordered lattices of coupled chaotic elements and equations for diffusion in random potentials. We propose a phenomenological stochastic field theory that gives some insights on the path for a generalization of these results for a broad class of disordered extended systems exhibiting space-time chaos.

Local conditional Lyapunov exponents are introduced and plotted in dynamical phase space to visualize the local susceptibility of the Lorenz system driven by chaos and noise signals when the system produces consistent response outputs. The dependence of the distribution of the local conditional Lyapunov exponent on changes in the drive signal is investigated. We consider the existence of multiple basins of consistent response for the same drive signal and the dependence of the basins on the drive signal.

The temporal linear instability of a coaxial jet with two immiscible Newtonian liquids in both the axial and radial electric fields is studied. The outer liquid is supposed to be a leaky dielectric and the inner liquid a perfect dielectric. The eigenvalue problem for both axisymmetric instability and helical instability is formulated and solved using the spectral method. Different from axisymmetric instability, for helical instability there is only one unstable mode, i.e., the helical mode, located in the long wave region. The axial electric field is found to have a strong stabilization effect on both the axisymmetric and helical modes, and the radial electric field has a great destabilization effect on them. The competition between the axisymmetric and helical instability under the action of the axial and radial electric fields is calculated. The boundary curve separating the stabilization and destabilization regions of the parasinuous mode, the neutral stability curve of the helical mode, and the boundary curve between the dominant regions of the axisymmetric and helical instability are plotted on the $Q_0\text{−}{E}_u$ plane and $\Pi \text{−}{E}_u$ plane, respectively ($Q_0$ is the dimensionless surface charge density; $E_u$ is the electrical Euler number representing the characteristic tangential electrostatic force; and $\Pi =Q_0^2{E}_u$ is the dimensionless parameter representing the characteristic normal electrostatic force). In general, when surface charge density is small, the helical mode is stable, and the parasinuous mode is dominant; however, when surface charge density is sufficiently large, the helical mode is destabilized and becomes dominant in jet instability. Liquid viscosity influences the predominance of the helical mode significantly. Although liquid viscosity decreases the growth rates of both the axisymmetric and helical modes, it suppresses the axisymmetric instability much more than the helical instability, and therefore favors the realization of the helical instability in experiments.

Wavelet analysis is applied to examine two-dimensional (2D) structures of pure electron plasma density distribution observed in a free-decaying turbulent stage starting from an unstable distribution. In contrast to the traditional Fourier analysis, the simultaneous resolution of the structures in terms of the physical coordinates and length scales (or wave numbers) allows us to discriminate instrumental dot noises without generating spurious high wave-number components that tend to distort the energy and enstrophy spectra. With this analysis at each time segment, the following features are clearly observed: Intermittency in the structures of electron density distribution, that is equivalent to the 2D vorticity distribution, is clearly demonstrated in terms of the scale-resolved kurtosis. The upward cascade of the enstrophy in the wave-number space is associated with the development of vortex filamentation in the physical space. Controlled discrimination of the coherent component in terms of the wavelet coefficients of the observed density distribution indicates significant contribution of persisting coherent vortices in steepening the energy spectra of the 2D turbulence far above the theoretically predicted power law of $k^{-3}$.

A lattice Boltzmann method is developed for incompressible axisymmetric flows. Both force and source or sink terms are incorporated into the lattice Boltzmann equation in a natural way, which is consistent in dimension with the lattice Boltzmann equation. The correct macroscopic equations for incompressible axisymmetric flows are recovered through the Chapman-Enskog expansion. It turns out that the added terms are nothing but the additional in the governing equations for the axisymmetric flows compared with the Navier-Stokes equations, resulting in a simple and efficient model. This provides an additional unique advantage that the proposed scheme is naturally suitable for general axisymmetric flows involving more physical phenomena. Two numerical simulations have been presented to verify the method.

The Blume-Emery-Griffiths spin glass is studied by renormalization-group theory in $d=3$. The boundary between the ferromagnetic and paramagnetic phases has first-order and two types of second-order segments. This topology includes an inverted tricritical point, first-order transitions replacing second-order transitions as temperature is lowered. The phase diagrams show disconnected spin-glass regions, spin-glass and paramagnetic reentrances, and complete reentrance, where the spin-glass phase replaces the ferromagnet as temperature is lowered for all chemical potentials.

The nearest-neighbor-interaction spin-1 Ising model is investigated within the damage-spreading approach. Exact relations involving quantities computable through damage-spreading simulations and thermodynamic properties are derived for such a model, defined in terms of a very general Hamiltonian that covers several spin-1 models of interest in the literature. Such relations presuppose translational invariance and hold for any ergodic dynamical procedure, leading to an efficient tool for obtaining thermodynamic properties. The implementation of the method is illustrated through damage-spreading simulations for the ferromagnetic spin-1 Ising model on a square lattice. The two-spin correlation function and the magnetization are obtained, with precise estimates of their associated critical exponents and of the critical temperature of the model, in spite of the small lattice sizes considered. These results are in good agreement with the universality hypothesis, with critical exponents in the same universality class of the spin-$1∕2$ Ising model. The advantage of the present method is shown through a significant reduction of finite-size effects by comparing its results with those obtained from standard Monte Carlo simulations.

Liquid crystals interacting with light represent a unique class of soft-matter systems that exhibit various generic nonlinear behaviors, including chaotic rotational dynamics. Despite several experimental observations, complex nematic liquid crystal director rotations in presence of spin and orbital angular momentum transfer processes were left unexplained. We present a self-consistent three-dimensional model able to describe the previous experimental observations, accounting for the dependence on the incident beam intensity, polarization, finite size and shape. More generally, our model is able to describe quantitatively the dynamics of, and beyond, the optical Fréedericksz transition under realistic experimental conditions almost three decades after its experimental discovery.

We study anomalous elasticity in the tubule phases of nematic and smectic elastomer membranes, which are flat in one direction and crumpled in another. These phases share the same macroscopic symmetry properties including spontaneously broken in-plane isotropy and hence belong to the same universality class. Below an upper critical value $D_c=3$ of the membranes’ intrinsic dimension $D$, thermal fluctuations renormalize the elasticity with respect to elastic displacements along the tubule axis so that elastic moduli for compression along the tubule axis and for bending the tubule axis become length-scale dependent. This anomalous elasticity belongs to the same universality class as that of $d$-dimensional conventional smectic liquid crystals with $D$ taking on the role of $d$. For physical tubule phases, $D=2$, this anomaly is of power-law type and thus might by easier to detect experimentally than the logarithmic anomaly in conventional smectics.

We extend our recent work on phase-field model for vesicles [D. Jamet and C. Misbah, Phys. Rev. E 76, 051907 (2007)]—where only the membrane local incompressibility was treated—to the situation where the bending forces and spontaneous curvature are included. We show how the general phase-field equations can be derived within a thermodynamic consistent picture. We analyze a general form of the bending energy, where the Helfrich bending force is treated as a special case. The dynamical evolution equation derived here for the velocity field allows one to write down a constitutive law of the composite fluid: The ambient fluid plus the membrane. This constitutive law has a viscoelastic form, the viscous part arises from the fluid, while the elastic one represents the action of the membrane. It is shown that the elastic stress tensor is not symmetric, owing to bending torque, inherent to a diffuse membrane model.

The influence of the patchiness and correlations in the distribution of hydrophobic and polar residues at the interface between two rigid biomolecules on their recognition ability is investigated in idealized coarse-grained lattice models. A general two-stage approach is utilized where an ensemble of probe molecules is designed first and the recognition ability of the probe ensemble is related to the free energy of association with both the target molecule and a different rival molecule in a second step. The influence of correlation effects are investigated using numerical Monte Carlo techniques and mean field methods. Correlations lead to different optimum characteristic lengths of the hydrophobic and polar patches for the mutual design of the two biomolecules on the one hand and their recognition ability in the presence of other molecules on the other hand.

The time-resolved spectra of single-bubble sonoluminescence (SBSL) in sulfuric acid have been observed with a streak camera after a spectrograph. The spectral center evolves from infrared to ultraviolet gradually within a SBSL duration, which corresponds to an increase of temperature. The peak temperature within one sonoluminescence (SL) duration is 5–9 times higher than the average temperature based on the average spectrum in our experiment. Furthermore, the ratio of the peak temperature to average temperature increases with the increase of driving pressure. The SBSL flash dies out after a dramatic heating-up, and there is no cooling procedure observed at the time resolution of $1∕10$ SL duration, which is incompatible with the radius-related adiabatic heating model as the mechanism of SBSL.

Intervehicle communication enables vehicles to exchange messages within a limited broadcast range and thus self-organize into dynamical and geographically embedded wireless ad hoc networks. We study the longitudinal hopping mode in which messages are transported using equipped vehicles driving in the same direction as a relay. Given a finite communication range, we investigate the conditions where messages can percolate through the network, i.e., a linked chain of relay vehicles exists between the sender and receiver. We simulate message propagation in different traffic scenarios and for different fractions of equipped vehicles. Simulations are done with both, modeled and empirical traffic data. These results are used to test the limits of applicability of an analytical model assuming a Poissonian distance distribution between the relays. We found a good agreement for homogeneous traffic scenarios and sufficiently low percentages of equipped vehicles. For higher percentages, the observed connectivity was higher than that of the model while in stop-and-go traffic situations it was lower. We explain these results in terms of correlations of the distances between the relay vehicles. Finally, we introduce variable transmission ranges and found that this additional stochastic component generally increased connectivity compared to a deterministic transmission with the same mean.

Detrended fluctuation analysis (DFA) is a useful tool to measure the long-range power-law correlations in $1∕f$ noise. In this paper, we investigate the power-law dynamics behavior of the density fluctuation time series generated by the famous Kerner-Klenov-Wolf cellular automata model in road traffic. Then the complexities of spatiotemporal, average speed, and the average density have been analyzed in detail. By introducing the DFA method, our main observation is that the free flow and wide moving jam phases correspond to the long-range anticorrelations. On the contrary, at the synchronized flow phase, the long-range correlated property is observed.