The interaction of a femtosecond relativistic intensity laser pulse with a grating of subwavelength periodicity was simulated numerically. Strong coherent emission at the wavelength of the grating period and its harmonics was seen, nearly parallel to the target surface, due to relativistic electron bunches emanating from each protuberance. Normal and oblique incidence $\left(30°\right)$ gave rise to trains of attosecond pulses and an efficiency greater than ${10}^{-4}$ was obtained for the ${24}^{\text{th}}$ harmonic $\left(\lambda \simeq 16.7\text{nm}\right)$. Similarity theory gives optimum conditions for harmonic emission.

The possibility of dissipative contributions to the mass flux is considered in detail. A general thermodynamically consistent framework is developed to obtain such terms, the compatibility of which with general principles is then checked—including Galilean invariance, the possibility of steady rigid rotation and uniform center-of-mass motion, the existence of a locally conserved angular momentum, and material objectivity. All previously discussed scenarios of dissipative mass fluxes are found to be ruled out by some combinations of these principles but not a new one that includes a smoothed velocity field $\overline{v}$. However, this field $\overline{v}$ is nonlocal and leads to unacceptable consequences in specific situations. Hence, we can state with confidence that a dissipative contribution to the mass flux is not possible.

Quantum effects in the noninertial Brownian motion of a particle in a one-dimensional ratchet potential are treated in the high temperature and weak bath-particle coupling limit by solving a quantum Smoluchowski equation for the time evolution of the Wigner function in configuration space. In particular, an analytical expression for the stationary average drift velocity for constant driving forces is presented including quantum corrections to any order in Planck’s constant. The corresponding frequency response is determined using continued fractions in both the linear approximation holding for small ac driving amplitude and in the nonlinear regime for arbitrary driving amplitude exhibiting pronounced ac induced frequency dependence of the dc component of the average drift velocity. Moreover, Shapiro steps are apparent in the dc characteristics for strong ac driving just as in the dc current-voltage characteristics of a point Josephson junction.

The amorphous aggregation of proteins is associated with many phenomena, ranging from the formation of protein wine haze to the development of cataract in the eye lens and the precipitation of recombinant proteins during their expression and purification. While much literature exists describing models for linear protein aggregation, such as amyloid fibril formation, there are few reports of models which address amorphous aggregation. Here, we propose a model to describe the amorphous aggregation of proteins which is also more widely applicable to other situations where a similar process occurs, such as in the formation of colloids and nanoclusters. As first applications of the model, we have tested it against experimental turbidimetry data of three proteins relevant to the wine industry and biochemistry, namely, thaumatin, a thaumatinlike protein, and $\alpha$-lactalbumin. The model is very robust and describes amorphous experimental data to a high degree of accuracy. Details about the aggregation process, such as shape parameters of the aggregates and rate constants, can also be extracted.

We formulate a theory for a self-propelled domain in an excitable reaction-diffusion system in two dimensions where the domain deforms from a circular shape when the propagation velocity is increased. In the singular limit where the width of the domain boundary is infinitesimally thin, we derive a set of equations of motion for the center of gravity and two fundamental deformation modes. The deformed shapes of a steadily propagating domain are obtained. The set of time-evolution equations exhibits a bifurcation from a straight motion to a circular motion by changing the system parameters.

The structure and the stability of the transferred monolayers of gold-thiol nanoparticles, formed at air-water interface at different surface pressure, on to silicon surface have been studied using two complementary techniques, x-ray reflectivity and atomic force microscopy (AFM). Networklike nanopatterns, observed through AFM, of the in-plane aggregated nanoparticles can be attributed to the late stage drying of the liquid trapped in the islands formed by nanoparticles. During drying process the trapped liquid leaves pinholes in the islands which by the process of nucleation and growth carry the mobile nanoparticles on their advancing fronts such that the nanoparticles are trapped at the boundaries of similar adjacent holes. This process continues bringing about in-plane as well as out-of-plane restructuring in the monolayer until the liquid evaporates completely rendering a patterned structure to the islands and instability in the monolayer is then stabilized.

A finite difference lattice Boltzmann scheme for homogeneous mixture modeling, which recovers Maxwell-Stefan diffusion model in the continuum limit, without the restriction of the mixture-averaged diffusion approximation, was recently proposed [P. Asinari, Phys. Rev. E 77, 056706 (2008)]. The theoretical basis is the Bhatnagar-Gross-Krook-type kinetic model for gas mixtures [P. Andries, K. Aoki, and B. Perthame, J. Stat. Phys. 106, 993 (2002)]. In the present paper, the recovered macroscopic equations in the continuum limit are systematically investigated by varying the ratio between the characteristic diffusion speed and the characteristic barycentric speed. It comes out that the diffusion speed must be at least one order of magnitude (in terms of Knudsen number) smaller than the barycentric speed, in order to recover the Navier-Stokes equations for mixtures in the incompressible limit. Some further numerical tests are also reported. In particular, (1) the solvent and dilute test cases are considered, because they are limiting cases in which the Maxwell-Stefan model reduces automatically to Fickian cases. Moreover, (2) some tests based on the Stefan diffusion tube are reported for proving the complete capabilities of the proposed scheme in solving Maxwell-Stefan diffusion problems. The proposed scheme agrees well with the expected theoretical results.

A spectral element method (SEM) is introduced for accurate calculation of band structures of three-dimensional anisotropic photonic crystals. The method is based on the finite-element framework with curvilinear hexahedral elements. Gauss-Lobatto-Legendre polynomials are used to construct the basis functions. In order to suppress spurious modes, mixed-order vector basis functions are employed and the Bloch periodic boundary condition is imposed into the basis functions with tangential components at the boundary by multiplying a Bloch phase factor. The fields and coordinates in the curvilinear hexahedral elements are mapped to the reference domain by covariant mapping, which preserves the continuity of tangential components of the field. Numerical results show that the SEM has exponential convergence for both square-lattice and triangular-lattice photonic crystals. The sampling density as small as 3.4 points per wavelength can achieve accuracy as high as 99.9%. The band structures of several modified woodpile photonic crystals are calculated by using the SEM.

One of the most popular approaches to the study of the collective behavior of self-driven individuals is the well-known Vicsek model (VM) [T. Vicsek, A. Czirók, E. Ben-Jacob, I. Cohen, and O. Shochet, Phys. Rev. Lett. 75, 1226 (1995)]. In the VM one has that each individual tends to adopt the direction of motion of its neighbors with the perturbation of some noise. For low enough noise the individuals move in an ordered fashion with net transport of mass; however, when the noise is increased, one observes disordered motion in a gaslike scenario. The nature of the order-disorder transition, i.e., first-versus second-order, has originated an ongoing controversy. Here, we analyze the most used variants of the VM unambiguously establishing those that lead either to first- or second-order behavior. By requesting the invariance of the order of the transition upon rotation of the observational frame, we easily identify artifacts due to the interplay between finite-size and boundary conditions, which had erroneously led some authors to observe first-order transitionlike behavior.

In real situations, individuals often have moderate tolerance toward ambient cooperative environment in which they tend to avoid unfavorable interactions and search for favorable ones. How such social tolerance affects the evolution of cooperation and the resulting cooperative networks remains to be answered. To address this issue, here we present an effective model of co-evolutionary prisoner’s dilemma by introducing cooperative environment and social tolerance for networked players. An individual’s level of cooperative environment characterizes the cooperativity and sustainability of its interaction environment centered on itself. In our model, for paired individuals we assume that the one in better cooperative environment has a certain tolerance threshold to the opponent. If the opponent’s cooperative environment level is beyond the tolerance threshold, the one in better cooperative environment cuts unilaterally the link, and rewires to others. Otherwise, the link is not severed, and meanwhile an inhomogeneous strategy imitation process between them is considered. Moreover, a player’s cooperative environment is adjusted in response to the strategy choices in the neighborhood. Interestingly, we find that there exists a moderate tolerance threshold warranting the best promotion of cooperation. We explain the nontrivial results by investigating the time ratio of strategy (network) updating during the whole process and properties in emerging networks. Furthermore, we investigate the effect of memory-dependent discounting of individuals’ cooperative environment on the evolution of cooperation. We also demonstrate the robustness of our results by considering two other modified co-evolutionary rules. Our results highlight the importance of appropriate tolerance threshold for the evolution of cooperation during the entangled co-evolution of strategy and structure.

A microcanonical finite-size ansatz in terms of quantities measurable in a finite lattice allows extending phenomenological renormalization (the so-called quotients method) to the microcanonical ensemble. The ansatz is tested numerically in two models where the canonical specific heat diverges at criticality, thus implying Fisher renormalization of the critical exponents: the three-dimensional ferromagnetic Ising model and the two-dimensional four-state Potts model (where large logarithmic corrections are known to occur in the canonical ensemble). A recently proposed microcanonical cluster method allows simulating systems as large as $L=1024$ (Potts) or $L=128$ (Ising). The quotients method provides accurate determinations of the anomalous dimension, $\eta$, and of the (Fisher-renormalized) thermal $\nu$ exponent. While in the Ising model the numerical agreement with our theoretical expectations is very good, in the Potts case, we need to carefully incorporate logarithmic corrections to the microcanonical ansatz in order to rationalize our data.

We consider the one-dimensional transport of ions into a perm-selective solid. Direct attempts to evaluate the current-voltage characteristics for currents exceeding the diffusion limit are frustrated by the appearance of nonconverging integrals. We describe how to overcome this obstacle using a regularization scheme.

High shear rate experiments have been performed with capillary microviscometers onto ${\text{SiO}}_2$ nanoparticles dispersed in alcohol (so-called nanofluids). The aim of these experiments was to investigate the processes of aggregation and dislocation of the nanoparticles in a shear flow under perikinetic and orthokinetic conditions. Shear rates as high as $2\times {10}^5{\text{s}}^{-1}$ were obtained in pressure-driven microchannels laminar flows. All the nanofluids under test have displayed a Newtonian behavior but with a strong enhanced viscosity, that is, the consequence of an effective volume concentration higher than the real one. It was possible to determine the average size of the aggregates and to find a correlation between their structure and the range of the hydrodynamic Peclet number at which experiments were performed. These results display a strong evidence of the role of aggregates and support the recent conclusions about the controversy of the thermal properties of nanofluids.

A theory of a reconstructive structural transformation in icosahedral capsid shells is developed for a whole family of virulent human viruses. It is shown that the reversible rearrangement of proteins during the virus maturation transformation is driven by the variation in the wave number $l$ associated with the protein density distribution function. The collective displacement field of protein centers from their positions in the initial (procapsid) and the final (capsid) two-dimensional icosahderal structures is derived. The amplitude of the displacement field is shown to be small and it minimizes the calculated free energy of the transformation. The theory allows us to propose a continuous thermodynamical mechanism of the reconstructive procapsid-to-capsid transformation. In the frame of the density-wave approach, we also propose to take an equivalent plane-wave vector as a common structural feature for different icosahedral capsid shells formed by the same proteins. Using these characteristics, we explain the relation between the radii of the procapsid and capsid shells and generalize it to the case of the viral capsid polymorphism.

A blind identification method of transfer functions in feedback systems is introduced for examination of dynamical activities of cortices by magnetoencephalography study. Somatosensory activities are examined in 5 Hz periodical median nerve stimulus. In the present paper, we will try two careful preprocessing procedures for the identification method to obtain impulse responses between primary somatosensory cortices. Time series data of the somatosensory evoked field are obtained by using a blind source separation of the T/k type (fractional) decorrelation method. Time series data of current dipoles of primary somatosensory cortices are transformed from the time series data of the somatosensory evoked field by the inverse problem. Fluctuations of current dipoles of them are obtained after elimination of deterministic periodical evoked waveforms. An identification method based on feedback system theory is used for estimation of transfer functions in a feedback model from obtained fluctuations of currents dipoles of primary somatosensory cortices. Dynamical activities between them are presented by Bode diagrams of transfer functions and their impulse responses: the time delay of about 30 ms via corpus callosum is found in the impulse response of identified transfer function.

We investigated the properties of Boolean networks that follow a given reliable trajectory in state space. A reliable trajectory is defined as a sequence of states, which is independent of the order in which the nodes are updated. We explored numerically the topology, the update functions, and the state space structure of these networks, which we constructed using a minimum number of links and the simplest update functions. We found that the clustering coefficient is larger than in random networks and that the probability distribution of three-node motifs is similar to that found in gene regulation networks. Among the update functions, only a subset of all possible functions occurs, and they can be classified according to their probability. More homogeneous functions occur more often, leading to a dominance of canalyzing functions. Finally, we studied the entire state space of the networks. We observed that with increasing systems size, fixed points become more dominant, moving the networks close to the frozen phase.

Large deviations play a significant role in many branches of nonequilibrium statistical physics. They are difficult to handle because their effects, though small, are not amenable to perturbation theory. Even the Gaussian model, which is the usual initial step for most perturbation theories, fails to be a starting point while discussing intermittency in fluid turbulence, where large deviations dominate. Our contention is: in the large deviation theory, the central role is played by the distribution associated with the tossing of a coin and the simple coin toss is the “Gaussian model” of problems where rare events play significant role. We illustrate this by applying it to calculate the multifractal exponents of the order structure factors in fully developed turbulence.

An analytical expression is proposed to describe the front shape of a non-quasi-neutral plasma expansion with anisotropic electron pressures. It is of significance in the study of ultrashort plasma expansions generated from laser-foil interactions and anisotropic astroplasma expansions in space science. It is found that the plasma front shape depends on the relationship between the ratio of the longitudinal and the transverse temperature of hot electrons ${\kappa }^2$ and the electron-ion mass ratio $\mu$. For ${\kappa }^2∊\left(\mu ,1\right]$, the ion front is a part of an ellipse and the major axis is in the lower-temperature axis. For ${\kappa }^2\le \mu$, the ion front is composed by a part of a hyperbolic and a small pointed projection at the center. In the strongly anisotropic region, there is an ultrashort anomalous plasma emission of tens of femtoseconds at the angle of near $90°$. The ion-velocity distribution and angular-energy distribution at the ion front have also been given. Particularly, anomalous positron emissions exist in the electron-positron plasma anisotropic expansion.

We illustrate a network approach to the phase-space study by using two geometrical frustration models: antiferromagnet on triangular lattice and square ice. Their highly degenerated ground states are mapped as discrete networks such that the quantitative network analysis can be applied to phase-space studies. The resulting phase spaces share some comon features and establish a class of complex networks with unique Gaussian spectral densities. Although phase-space networks are heterogeneously connected, the systems are still ergodic due to the random Poisson processes. This network approach can be generalized to phase spaces of some other complex systems.

We solve a nonequilibrium statistical-mechanics problem exactly, namely, the single-file dynamics of $N$ hard-core interacting particles (the particles cannot pass each other) of size $\Delta$ diffusing in a one-dimensional system of finite length $L$ with reflecting boundaries at the ends. We obtain an exact expression for the conditional probability density function ${\rho }_{\mathcal{T}}\left(y_{\mathcal{T}},t\mid y_{\mathcal{T},0}\right)$ that a tagged particle $\mathcal{T}$ $\left(\mathcal{T}=1,\dots ,N\right)$ is at position $y_{\mathcal{T}}$ at time $t$ given that it at time $t=0$ was at position $y_{\mathcal{T},0}$. Using a Bethe ansatz we obtain the $N$-particle probability density function and, by integrating out the coordinates (and averaging over initial positions) of all particles but particle $\mathcal{T}$, we arrive at an exact expression for ${\rho }_{\mathcal{T}}\left(y_{\mathcal{T}},t\mid y_{\mathcal{T},0}\right)$ in terms of Jacobi polynomials or hypergeometric functions. Going beyond previous studies, we consider the asymptotic limit of large $N$, maintaining $L$ finite, using a nonstandard asymptotic technique. We derive an exact expression for ${\rho }_{\mathcal{T}}\left(y_{\mathcal{T}},t\mid y_{\mathcal{T},0}\right)$ for a tagged particle located roughly in the middle of the system, from which we find that there are three time regimes of interest for finite-sized systems: (A) for times much smaller than the collision time $t⪡{\tau }_{\text{coll}}=1/\left({\varrho }^{2}D\right)$, where $\varrho =N/L$ is the particle concentration and $D$ is the diffusion constant for each particle, the tagged particle undergoes a normal diffusion; (B) for times much larger than the collision time $t⪢{\tau }_{\text{coll}}$ but times smaller than the equilibrium time $t⪡{\tau }_{\text{eq}}=L^2/D$, we find a single-file regime where ${\rho }_{\mathcal{T}}\left(y_{\mathcal{T}},t\mid y_{\mathcal{T},0}\right)$ is a Gaussian with a mean-square displacement scaling as $t^{1/2}$; and (C) for times longer than the equilibrium time $t⪢{\tau }_{\text{eq}}$, ${\rho }_{\mathcal{T}}\left(y_{\mathcal{T}},t\mid y_{\mathcal{T},0}\right)$ approaches a polynomial-type equilibrium probability density function. Notably, only regimes (A) and (B) are found in the previously considered infinite systems.