We show that managing time-dependent polarization of the relativistically intense laser pulse incident on a plasma surface allows us to gate a single (sub)attosecond x-ray burst even when a multicycle driver is used. The single x-ray burst is emitted when the tangential component of the vector potential at the plasma surface vanishes. This relativistic plasma control is based on the theory of relativistic spikes [T. Baeva, S. Gordienko, and A. Pukhov, Phys. Rev. E 74, 046404 (2006)]. The relativistic plasma control is demonstrated here numerically by particle-in-cell simulations.

A complex network processing information or physical flows is usually characterized by a number of macroscopic quantities such as the diameter and the betweenness centrality. An issue of significant theoretical and practical interest is how such quantities respond to sudden changes caused by attacks or disturbances in recoverable networks, i.e., functions of the affected nodes are only temporarily disabled or partially limited. By introducing a model to address this issue, we find that, for a finite-capacity network, perturbations can cause the network to oscillate persistently in the sense that the characterizing quantities vary periodically or randomly with time. We provide a theoretical estimate of the critical capacity-parameter value for the onset of the network oscillation. The finding is expected to have broad implications as it suggests that complex networks may be structurally highly dynamic.

Motion of a fluid interface in the Richtmyer-Meshkov instability in cylindrical geometry is examined analytically and numerically. Nonlinear stability analysis is performed in order to clarify the dependence of growth rates of a bubble and spike on the Atwood number and mode number $n$ involved in the initial perturbations. We discuss differences of weakly and fully nonlinear evolution in cylindrical geometry from that in planar geometry. It is shown that the analytical growth rates coincide well with the numerical ones up to the neighborhood of the break down of numerical computations. Long-time behavior of the fluid interface as a vortex sheet is numerically investigated by using the vortex method and the roll up of the vortex sheet is discussed for different Atwood numbers. The temporal evolution of the curvature of a bubble and spike for several mode numbers is investigated and presented that the curvature of spikes is always larger than that of bubbles. The circulation and the strength of the vortex sheet at the fully nonlinear stage are discussed, and it is shown that their behavior is different for the cases that the inner fluid is heavier than the outer one and vice versa.

A cubic Rayleigh-Bénard cell is operated at a Rayleigh number of $1.5\times {10}^9$ and a Prandtl number of 6.1. The cell is equipped with thermistors placed along the vertical line through the center of the cell. The spatial correlation of temperature is deduced from simultaneous temperature recordings from these thermistors. The correlation function is well fitted by the sum of two exponentials. There is no cascade in the temperature field as only two characteristic length scales appear. The direct measurement of spatial correlations allows us to test the validity of Taylor’s hypothesis in this flow.

The influence of the kinetics of excited atoms on the characteristics of an inductively coupled plasma in argon during the early afterglow is studied. A self-consistent model including the nonlocal approach for the kinetic treatment of the electrons is applied. Parameters of both the steady state of the rf discharge and the decay phase are presented. Results for the steady-state densities of excited atoms as well as temporal evolutions of the wall potential and mean energy of electrons are discussed in comparison with experimental data available from the literature. The ionization kinetics of the electrons, the electron power balance, and the main kinetic pathways for excited argon atoms are analyzed in the pressure range between 0.5 and $133\mathrm{Pa}$. In particular, a significant influence of the excited atoms on the plasma behavior in steady state and during the afterglow is found.

Thin films deposited on substrates are usually submitted to large residual compression stresses, causing delamination and buckling of the film into various patterns. The present study is focused on the different equilibria arising on strip-shaped delaminated areas. The three most common types of buckling patterns observed on such strips are known as the straight-sided wrinkles, bubble pattern, and telephone cord blisters. The stability of those equilibria as a function of the two stress components of the loading is investigated. The Föppl–Von Karman model for elastic plates is used for theoretical aspects. The post-critical equilibrium paths of the buckling patterns are investigated numerically by means of the finite-element method. The substrate is assumed to be rigid and the contact to be frictionless. The equilibrium solutions can be classified into families of homologous equilibria allowing the identification of dimensionless parameters for the study of stability. A mapping of the different stable post-critical equilibria is given. It is shown that the straight-sided wrinkles and the bubbles are associated with anisotropy of stresses and/or of elastic properties, whereas the telephone cords are stable at high isotropic stresses. The morphological transitions are experimentally evidenced by in situ atomic force microscopy observations of a nickel $50\text{−}\mathrm{nm}$-thick film under stress.

We study the heat conduction of two nonlinear lattices joined by a weak harmonic link. When the system reaches a steady state, the heat conduction of the system is decided by the tunneling heat flow through the weak link. We present an analytical analysis by the combination of the self-consistent phonon theory and the heat tunneling transport formalism, and then the tunneling heat flow can be obtained. Moreover, the nonequilibrium molecular dynamics simulations are performed and the simulations results are consistent with the analytical predictions.

We present hard-sphere crystallization kinetics for three samples with small differences in polydispersity. We show that an increase in polydispersity of 1% is sufficient to cause dramatic changes in the crystallization kinetics: Crystallization is delayed by almost one decade in time and quantitative and qualitative changes in the crystallization scenario are observed. Surprisingly the nucleation rate density is enhanced by almost a factor of 10. We interpret these results in terms of polydispersity limited growth, where local fractionation processes lead to a delayed but faster nucleation.

We study the stationary properties as well as the nonstationary dynamics of the one-dimensional partially asymmetric exclusion process with position-dependent random hop rates. Relating the hop rates to an energy landscape the stationary current $J$ is determined by the largest barrier in a finite system of $L$ sites and the corresponding waiting time $\tau \sim J^{-1}$ is related to the waiting time of a single random walker, ${\tau }_{rw}$, as $\tau \sim {\tau }_{rw}^{1∕2}$. The current is found to vanish as $J\sim L^{-z∕2}$, where $z$ is the dynamical exponent of the biased single-particle Sinai walk. Typical stationary states are phase separated: At the largest barrier almost all particles queue at one side and almost all holes are at the other side. The high-density (low-density) region is divided into $\sim L^{1∕2}$ connected parts of particles (holes) which are separated by islands of holes (particles) located at the subleading barriers (valleys). We also study nonstationary processes of the system, like coarsening and invasion. Finally we discuss some related models, where particles of larger size or multiple occupation of lattice sites is considered.

The classical monomer-dimer model in two-dimensional lattices has been shown to belong to the “$\#P$-complete” class, which indicates the problem is computationally “intractable.” We use exact computational method to investigate the number of ways to arrange dimers on $m\times n$ two-dimensional rectangular lattice strips with fixed dimer density $\rho$. For any dimer density $0<\rho <1$, we find a logarithmic correction term in the finite-size correction of the free energy per lattice site. The coefficient of the logarithmic correction term is exactly $-1∕2$. This logarithmic correction term is explained by the newly developed asymptotic theory of Pemantle and Wilson. The sequence of the free energy of lattice strips with cylinder boundary condition converges so fast that very accurate free energy $f_2\left(\rho \right)$ for large lattices can be obtained. For example, for a half-filled lattice, $f_2(1∕2)=0.633195588930$, while $f_2(1∕4)=0.4413453753046$ and $f_2(3∕4)=0.64039026$. For $\rho <0.65$, $f_2\left(\rho \right)$ is accurate at least to ten decimal digits. The function $f_2\left(\rho \right)$ reaches the maximum value $f_2\left({\rho }^{*}\right)=0.662798972834$ at ${\rho }^{*}=0.6381231$, with 11 correct digits. This is also the monomer-dimer constant for two-dimensional rectangular lattices. The asymptotic expressions of free energy near close packing are investigated for finite and infinite lattice widths. For lattices with finite width, dependence on the parity of the lattice width is found. For infinite lattices, the data support the functional form obtained previously through series expansions.

We report experiments on the overall phase diagram of granular flows on an incline with emphasis on high inclination angles where the mean layer velocity approaches the terminal velocity of a single particle free falling in air. The granular flow was characterized by measurements of the surface velocity, the average layer height, and the mean density of the layer as functions of the hopper opening, the plane inclination angle, and the downstream distance $x$ of the flow. At high inclination angles the flow does not reach an $x$-invariant steady state over the length of the inclined plane. For low volume flow rates, a transition was detected between dense and very dilute (gas) flow regimes. We show using a vacuum flow channel that air did not qualitatively change the phase diagram and did not quantitatively modify mean flow velocities of the granular layer except for small changes in the very dilute gaslike phase.

Coexistence of individuals with different species or phenotypes is often found in nature in spite of competition between them. Stable coexistence of multiple types of individuals have implications for maintenance of ecological biodiversity and emergence of altruism in society, to name a few. Various mechanisms of coexistence including spatial structure of populations, heterogeneous individuals, and heterogeneous environments, have been proposed. In reality, individuals disperse and interact on complex networks. We examine how heterogeneous degree distributions of networks influence coexistence, focusing on models of cyclically competing species. We show analytically and numerically that heterogeneity in degree distributions promotes stable coexistence.

The phenomenon of wave splitting is investigated in a two-dimensional excitable light-sensitive Belousov-Zhabotinsky reaction medium after extremely changing the intensity of illuminated light for a short time. It is found that successive wave splitting and nonannihilation collision between two waves of different amplitudes occur spontaneously under narrow experimental conditions. Experimental observations are approximately reproduced in the specific parameter range by a numerical simulation with a Bär-Eiswirth model.

Leading order Lyapunov exponents and their corresponding eigenvectors have been computed numerically for small aspect ratio, three-dimensional Rayleigh-Benard convection cells with no-slip boundary conditions. The parameters are the same as those used by Ahlers and Behringer [Phys. Rev. Lett. 40, 712 (1978)] and Gollub and Benson [J. Fluid Mech. 100, 449 (1980)] in their work on a periodic time dependence in Rayleigh-Benard convection cells. Our work confirms that the dynamics in these cells truly are chaotic as defined by a positive Lyapunov exponent. The time evolution of the leading order Lyapunov eigenvector in the chaotic regime will also be discussed. In addition we study the contributions to the leading order Lyapunov exponent for both time periodic and aperiodic states and find that while repeated dynamical events such as dislocation creation/annihilation and roll compression do contribute to the short time Lyapunov exponent dynamics, they do not contribute to the long time Lyapunov exponent. We find instead that nonrepeated events provide the most significant contribution to the long time leading order Lyapunov exponent.

Kelvin’s theorem on conservation of circulations is an essential ingredient of Taylor’s theory of turbulent energy dissipation by the process of vortex-line stretching. In previous work, we have proposed a nonlinear mechanism for the breakdown of Kelvin’s theorem in ideal turbulence at infinite Reynolds number. We develop here a detailed physical theory of this cascade of circulations. Our analysis is based upon an effective equation for large-scale coarse-grained velocity, which contains a turbulent-induced vortex force that can violate Kelvin’s theorem. We show that singularities of sufficient strength, which are observed to exist in turbulent flow, can lead to nonvanishing dissipation of circulation for an arbitrarily small coarse-graining length in the effective equations. This result is an analog for circulation of Onsager’s theorem on energy dissipation for singular Euler solutions. The physical mechanism of the breakdown of Kelvin’s theorem is diffusion of lines of large-scale vorticity out of the advected loop. This phenomenon can be viewed as a classical analog of the Josephson-Anderson phase-slip phenomenon in superfluids due to quantized vortex lines. We show that the circulation cascade is local in scale and use this locality to develop concrete expressions for the turbulent vortex force by a multiscale gradient expansion. We discuss implications for Taylor’s theory of turbulent dissipation and we point out some related cascade phenomena, in particular for magnetic flux in magnetohydrodynamic turbulence.

In this Brief Report, we consider parametrically driven bright solitons in the vicinity of the anticontinuum limit. We illustrate the mechanism through which these solitons become unstable due to the collision of the phase mode with the continuous spectrum, or eigenvalues bifurcating thereof. We show how this mechanism typically leads to complete destruction of the bright solitary wave.

We compare the results of three-dimensional molecular-dynamics (MD) simulations of a Lennard-Jones (LJ) liquid with a hydrostatic (HS) solution of a high temperature liquid channel which is surrounded by a fluid at lower temperature. The maximum temperature gradient, $dT∕dx$, between the two temperature regions ranged from $\infty$ (step function) to $dT∕dx=0.1$ (in the usual LJ units). Because the systems were in stationary-nonequilibrium states with no fluid flow, both MD simulation and the HS solution gave flat profiles for the normal pressure in all temperature-gradient cases. However, the other quantities showed differences between the two methods. The MD-derived density was found to oscillate over the length of ca. 8 LJ particle diameters from the boundary plane in the system with the infinite temperature gradient, while the HS-derived density showed simply a stepwise profile. The MD simulation also showed another anomaly near the boundary in potential energy. We have found systems in which the HS treatment works well and those where the HS approach breaks down, and therefore established the minimum length scale for the HS treatment to be valid. We also compare the kinetic temperature and the configurational temperature in these systems, and show that these can differ in the transition zone between the two temperatures.

We discuss the far-from-equilibrium interfacial phenomena occurring in the multilayer homoepitaxial growth and erosion on (110) crystal surfaces. Experimentally, these rectangular symmetry surfaces exhibit a multitude of interesting nonequilibrium interfacial structures, such as the rippled one-dimensional periodic states that are not present in the homoepitaxial growth and erosion on the high symmetry (100) and (111) crystal surfaces. Within a unified phenomenological model, we reveal and elucidate this multitude of states on (110) surfaces as well as the transitions between them. By analytic arguments and numerical simulations, we address experimentally observed transitions between two types of rippled states on (110) surfaces. We discuss several intermediary interface states intervening, via consecutive transitions, between the two rippled states. One of them is the rhomboidal pyramid state, theoretically predicted by Golubovic et al. [Phys. Rev. Lett. 89, 266104 (2002)] and subsequently seen, by de Mongeot and co-workers, in the epitaxial erosion of Cu(110) and Rh(110) surfaces [A. Molle et al., Phys. Rev. Lett. 93, 256103 (2004), and A. Molle et al., Phys. Rev. B 73, 155418 (2006)]. In addition, we find a number of interesting intermediary states having structural properties somewhere between those of rippled and pyramidal states. Prominent among them are the rectangular rippled states of long rooflike objects (huts) recently seen on Ag(110) surface. We also predict the existence of a striking interfacial structure that carries nonzero, persistent surface currents. Periodic surface currents vortex lattice formed in this so-called buckled rippled interface state is a far-from-equilibrium relative of the self-organized convective flow patterns in hydrodynamic systems. We discuss the coarsening growth of the multitude of the interfacial states on (110) crystal surfaces.

The two-dimensional cage model for polymer motion is discussed with an emphasis on the effect of sideways motions, which cross the barriers imposed by the lattice. Using the density matrix method as a solver of the master equation, the renewal time and the diffusion coefficient are calculated as a function of the strength of the barrier crossings. A strong crossover influence of the barrier crossings is found and it is analyzed in terms of effective exponents for a given chain length. The crossover scaling functions and the crossover scaling exponents are calculated.

We report on the formation of dark discrete solitons in a nonlinear periodic system consisting of evanescently coupled channel waveguides in defocusing lithium niobate. Localized nonlinear dark modes displaying a phase jump in the center that is located either on-channel (mode $A$) or in-between channels (mode $B$) are formed, which is to our knowledge the first experimental observation of mode $B$. By numerical simulations we find that the saturable nature of the nonlinearity is responsible for the improved stability of mode $B$. The ability of the induced refractive index structures to guide light of a low-power probe beam is demonstrated.