The effective medium theory is a useful approach for investigating the electromagnetic wave propagation in periodic multilayer slabs. It allows accurate computation of transmission and reflection spectra as well as of phase and group velocities. In this paper we derive an exact analytical expression for the energy velocity of a one-dimensional finite photonic crystal based on the effective medium approach. It accounts for the multiple reflections within the structure which results in the characteristic oscillations of the transmission spectrum. Our analytical expression holds for an arbitrary refractive index contrast and goes beyond the limits of the standard homogenization method. In order to validate our approach, results obtained by using the all-frequency effective energy velocity have been compared to those obtained using the transfer matrix method.

The results of an experimental investigation of granular segregation in a thin rotating drum are presented. A mechanism based on the presence of an uphill wave of particles has been found to govern the observed pattern of petals. Specifically we develop a simple model that captures the essential physics of the segregation and yields an algebraic expression that predicts the number of petals in the pattern.

Thermomechanical oscillations observed previously in hybrid oriented nematic liquid crystals (NLCs) are explained theoretically. The effect is conditioned by the hydrodynamic flow tendency to reduce the curvature of the “flexible ribbon” of hybrid NLCs. There is qualitative agreement between the theoretical calculations and the experimental results.

We study the time evolution of fidelity in a dynamical many-body system, namely, a kicked Ising model, modified to allow for a time-reversal invariance breaking. We find good agreement with the random matrix predictions in the realm of strong perturbations. In particular for the time-reversal symmetry breaking case the predicted revival at the Heisenberg time is clearly seen.

Low-dimensional ordered arrays of optical elements can possess bound modes having an extremely high quality factor. Typically, these arrays consist of metal elements which have significantly high light absorption thus restricting performance. In this paper we address the following question: can bound modes be formed in dielectric systems where the absorption of light is negligible? Our investigation of circular arrays of spherical particles shows that (1) high quality modes in an array of ten or more particles can be attained at least for a refractive index $n_r>2$, so optical materials like ${\mathrm{TiO}}_2$ or $\mathrm{GaAs}$ can be used; (2) the most bound modes have nearly transverse polarization perpendicular to the circular plane; (3) in a particularly interesting case of ${\mathrm{TiO}}_2$ particles (rutile phase, $n_r=2.7$), the quality factor of the most bound mode increases almost by an order of magnitude with the addition of ten extra particles, while for particles made of $\mathrm{GaAs}$ the quality factor increases by almost two orders of magnitude with the addition of ten extra particles. We hope that this preliminary study will stimulate experimental investigations of bound modes in low-dimensional arrays of dielectric particles.

A technique is introduced which allows us to extract information on the solitonic content from a nonlinear wave. Its applicability is not as narrowly restricted as that of inverse scattering theory; therefore, it works in situations that could not be studied before. As an example we identify and demonstrate a higher order dispersion-managed soliton.

Orientational dynamics in a liquid crystalline system near the isotropic-nematic (IN) phase transition is studied using molecular dynamics simulations of the well-known Lebwohl-Lasher model. As the IN transition temperature is approached from the isotropic side, we find that the decay of the orientational time correlation functions (OTCF) slows down noticeably, giving rise to a power law decay at intermediate time scales. The angular velocity time correlation function also exhibits a rather pronounced power law decay near the IN boundary. In the mean squared angular displacement at comparable time scales, we observe the emergence of a subdiffusive regime which is followed by a superdiffusive regime before the onset of the long-time diffusive behavior. We observe signature of dynamical heterogeneity through pronounced non-Gaussian behavior in orientational motion particularly at lower temperatures. This behavior closely resembles what is usually observed in supercooled liquids. We obtain the free energy as a function of orientational order parameter by the use of the transition matrix Monte Carlo method. The free energy surface is flat for the system considered here and the barrier between isotropic and nematic phases is vanishingly small for this weakly first-order phase transition, hence allowing large scale, collective, and correlated orientational density fluctuations. This might be responsible for the observed power law decay of the OTCFs.

Vascularization of embryonic organs or tumors starts from a primitive lattice of capillaries. Upon perfusion, this lattice is remodeled into branched arteries and veins. Adaptation to mechanical forces is implied to play a major role in arterial patterning. However, numerical simulations of vessel adaptation to haemodynamics has so far failed to predict any realistic vascular pattern. We present in this article a theoretical modeling of vascular development in the yolk sac based on three features of vascular morphogenesis: the disconnection of side branches from main branches, the reconnection of dangling sprouts (“dead ends”), and the plastic extension of interstitial tissue, which we have observed in vascular morphogenesis. We show that the effect of Poiseuille flow in the vessels can be modeled by aggregation of random walkers. Solid tissue expansion can be modeled by a Poiseuille (parabolic) deformation, hence by deformation under hits of random walkers. Incorporation of these features, which are of a mechanical nature, leads to realistic modeling of vessels, with important biological consequences. The model also predicts the outcome of simple mechanical actions, such as clamping of vessels or deformation of tissue by the presence of obstacles. This study offers an explanation for flow-driven control of vascular branching morphogenesis.

We propose a measure to quantify the efficiency of classical and quantum mechanical transport processes on graphs. The measure only depends on the density of states (DOS), which contains all the necessary information about the graph. For some given (continuous) DOS, the measure shows a power law behavior, where the exponent for the quantum transport is twice the exponent of its classical counterpart. For small-world networks, however, the measure shows rather a stretched exponential law but still the quantum transport outperforms the classical one. Some finite tree graphs have a few highly degenerate eigenvalues, such that, on the other hand, on them the classical transport may be more efficient than the quantum one.

We reconsider the no-tie-breaking two-state Galam contrarian model of opinion dynamics for update groups of size 3. While the initial model assumes a constant density of contrarians $a$ for both opinions, the density now depends for each opinion on its global support. Proportionate contrarians are thus found to indeed preserve the main results of the former case. However, restricting the contrarian behavior to only the current collective majority makes the dynamics more complex with additional features. For a density $a<a_c=1∕9$ of one-sided contrarians, a chaotic basin is found in the 50-50 region separated from two majority-minority point attractors, one on each side. For $1∕9<a\lesssim 0.301$ only the chaotic basin survives. In the range $a>0.301$ the chaotic basin disappears and the majority starts to alternate between the two opinions with a staggered flow toward two point attractors. We then study the effect of both decoupling the local update time sequence from the contrarian behavior activation and a smoothing of the majority rule. A status quo–driven bias for contrarian activation is also considered. Introduction of unsettled agents driven in the debate on a contrarian basis is shown only to shrink the chaotic basin. The model may shed light on recent apparent contradictory elections with on the one hand very close results as in the United States in 2000 and in Germany in 2002 and 2005, and on the other hand, a huge majority as in France in 2002.

The issue of the Gibbs paradox is that when considering mixing of two gases within classical thermodynamics, the entropy of mixing appears to be a discontinuous function of the difference between the gases: it is finite for whatever small difference, but vanishes for identical gases. The resolution offered in the literature, with help of quantum mixing entropy, was later shown to be unsatisfactory precisely where it sought to resolve the paradox. Macroscopic thermodynamics, classical or quantum, is unsuitable for explaining the paradox, since it does not deal explicitly with the difference between the gases. The proper approach employs quantum thermodynamics, which deals with finite quantum systems coupled to a large bath and a macroscopic work source. Within quantum thermodynamics, entropy generally loses its dominant place and the target of the paradox is naturally shifted to a decrease of the maximally available work before and after mixing (mixing ergotropy). In contrast to entropy this is an unambiguous quantity. For almost identical gases the mixing ergotropy continuously goes to zero, thus resolving the paradox. In this approach the concept of “difference between the gases” gets a clear operational meaning related to the possibilities of controlling the involved quantum states. Difficulties which prevent resolutions of the paradox in its entropic formulation do not arise here. The mixing ergotropy has several counterintuitive features. It can increase when less precise operations are allowed. In the quantum situation (in contrast to the classical one) the mixing ergotropy can also increase when decreasing the degree of mixing between the gases or when decreasing their distinguishability. These points go against a direct association of physical irreversibility with lack of information.

The dynamics of two mutually coupled chaotic diode lasers are investigated experimentally and numerically. By adding self-feedback to each laser, stable isochronal synchronization is established. This stability, which can be achieved for symmetric operation, is essential for constructing an optical public-channel cryptographic system. The experimental results on diode lasers are well described by rate equations of coupled single mode lasers.

On the basis of the classical tree statistics, being combined with the lattice theory of a polymer solution, we prove that within the mean-field approximation thermoreversible gelation of polyfunctional molecules is a third order phase transition analogous to the Bose-Einstein condensation of ideal Bose gases. The derivative of the osmotic compressibility with respect to the concentration of primary functional molecules is shown to reveal a discontinuity at the sol/gel transition point, whose width is directly related to the amplitude of the divergent term in the weight-average molecular weight of clusters. An inclusion of cycle formation, as well as concentration fluctuations, may, however, change the nature of the phase transition.

We demonstrate, within the framework of the FitzHugh-Nagumo model, that a firing neuron can respond to a noisy driving in a nonreliable manner: the same Gaussian white noise acting on identical neurons evokes different patterns of spikes. The effect is characterized via calculations of the Lyapunov exponent and the event synchronization correlations. We construct a theory that explains the antireliability as a combined effect of a high sensitivity to noise of some stages of the dynamics and nonisochronicity of oscillations. Geometrically, the antireliability is described by a random noninvertible one-dimensional map.

Motivated by a synchronization problem in distributed computing we studied a simple growth model on regular and small-world networks, embedded in one and two dimensions. We find that the synchronization landscape (corresponding to the progress of the individual processors) exhibits Kardar-Parisi-Zhang-like kinetic roughening on regular networks with short-range communication links. Although the processors, on average, progress at a nonzero rate, their spread (the width of the synchronization landscape) diverges with the number of nodes (desynchronized state) hindering efficient data management. When random communication links are added on top of the one and two-dimensional regular networks (resulting in a small-world network), large fluctuations in the synchronization landscape are suppressed and the width approaches a finite value in the large system-size limit (synchronized state). In the resulting synchronization scheme, the processors make close-to-uniform progress with a nonzero rate without global intervention. We obtain our results by “simulating the simulations,” based on the exact algorithmic rules, supported by coarse-grained arguments.

We study the bond-percolation model in two and three dimensions by Monte Carlo simulation, and investigate the finite-size scaling behavior of several quantities that account for fluctuations of the total numbers of clusters and occupied bonds, $N_c$ and $N_b$, respectively. These quantities include $C_{2c}=(⟨N_c^2⟩-{⟨N_c⟩}^2)∕L^d$ and $C_{cb}=(⟨N_c{N}_b⟩-⟨N_c⟩⟨N_b⟩)∕L^d$, where $L$ is the linear system size and $d$ is the spatial dimensionality. In statistical models with thermal fluctuations, $C_{2c}$ and $C_{cb}$ are specific heatlike quantities. Despite the absence of thermal fluctuations in percolation, we find that the leading finite-size scaling of $C_{2c}$ and $C_{cb}$ is described by the thermal critical exponent $y_t\text{−}d$. We also measure quantity ${\kappa }_b=2⟨N_b{S}_2⟩∕⟨S_2⟩-⟨N_b{\tilde{S}}_4⟩∕⟨{\tilde{S}}_4⟩-⟨N_b⟩$ and an analogous quantity ${\kappa }_c$ for $N_c$, where $S_2$ and ${\tilde{S}}_4$ are quantities associated with the second and the fourth moments of cluster sizes, respectively. At criticality, we show that ${\kappa }_b$ and ${\kappa }_c$ diverge as $L^{y_t}$ for $L\to \infty$. The analysis of the data of ${\kappa }_b$ and ${\kappa }_c$ yields $y_t=1.145\left(2\right)$ for the three-dimensional percolation, in good agreement with existing results.

A valid fluid equation of state (EOS) must satisfy the thermodynamic conditions of consistency (derivation from a free energy) and stability (positive sound speed squared). Numerical simulations of compressible fluid flow for realistic materials require a tabular EOS, but typical software interfaces to such tables based on polynomial or rational interpolants may enforce the stability conditions, but do not enforce the consistency condition and its derivatives. The consistency condition is important for the computation of various dimensionless parameters of an EOS that may involve derivatives of up to second order which are important for the development of more sensitive artificial viscosities and Riemann solvers that accurately model shock structure in regions near phase transitions. We describe a table interface based on the tuned regression method, which is derived from a constrained local least-squares regression technique. It is applied to several SESAME EOS showing how the consistency and stability conditions can be satisfied to round-off while computing first and second derivatives with demonstrated second-order convergence. An improvement of 14 orders of magnitude over conventional derivatives is demonstrated, although the method is apparently two orders of magnitude slower, due to the fact that every evaluation requires solving an 11-dimensional nonlinear system. Application is made to the computation of the fundamental derivative.

In the present Rapid Communication we present an analytical and numerical solution of the self-consistent mode-coupling equations for the problem of heat conductivity in one-dimensional systems. Such a solution leads us to propose a different scenario to accommodate the known results obtained so far for this problem. More precisely, we conjecture that the universality class is determined by the leading order of the nonlinear interaction potential. Moreover, our analysis allows us to determine the memory kernel, whose expression puts on a more firm basis the previously conjectured connection between anomalous heat conductivity and anomalous diffusion.

We investigate shear-induced crystallization in a very dense flow of monodisperse inelastic hard spheres. We consider a steady plane Couette flow under constant pressure and neglect gravity. We assume that the granular density is greater than the melting point of the equilibrium phase diagram of elastic hard spheres. We employ a Navier-Stokes hydrodynamics with constitutive relations all of which (except the shear viscosity) diverge at the crystal-packing density, while the shear viscosity diverges at a smaller density. The phase diagram of the steady flow is described by three parameters: an effective Mach number, a scaled energy loss parameter, and an integer number $m$: the number of half-oscillations in a mechanical analogy that appears in this problem. In a steady shear flow the viscous heating is balanced by energy dissipation via inelastic collisions. This balance can have different forms, producing either a uniform shear flow or a variety of more complicated, nonlinear density, velocity, and temperature profiles. In particular, the model predicts a variety of multilayer two-phase steady shear flows with sharp interphase boundaries. Such a flow may include a few zero-shear (solidlike) layers, each of which moving as a whole, separated by fluidlike regions. As we are dealing with a hard sphere model, the granulate is fluidized within the “solid” layers: the granular temperature is nonzero there, and there is energy flow through the boundaries of the solid layers. A linear stability analysis of the uniform steady shear flow is performed, and a plausible bifurcation diagram of the system, for a fixed $m$, is suggested. The problem of selection of $m$ remains open.

In this paper we discuss continuum models of phase separation in polymer solutions, with emphasis on the thermodynamic foundation of these models. We demand that these models obey a free energy dissipation relation, which in the present context plays the role of the second law of thermodynamics, since the system is isothermal. First, we derive a modified two-fluid model for viscoelastic phase separation from nonequilibrium thermodynamics. Then we study the special case when only diffusion is present, and hydrodynamic effects are neglected. Numerical results demonstrate that our models show better stability properties and at the same time reproduce the expected physical phenomena such as volume shrinking and phase inversion. Our findings suggest that these important phenomena are caused by a diffusional asymmetry of the constituent molecules.