We derive an exact spectral representation for the Green’s function of Maxwell equations in a two-dimensional homogeneous and rotating environment. The formulation is developed in the medium (noninertial) rest frame, and it represents the response to a point source, where both the source and observation points rotate together with the medium. The closed form expression for the Green’s function is derived for (nonrelativistic) slowly rotating media at finite distances. An approximate expression for the efficient evaluation of the Green’s function, that avoids laborious summation of rotating-medium spherical harmonics, is provided and tested against the exact expression. Furthermore, it is shown that our spectral theory can provide a broad view of the optical response of rotating systems, from which the classical Sagnac effect is obtained as a special case.

A powerful computational method for dealing with correlation functions in magnetic systems, based on damage-spreading simulations, is reviewed and tested, by investigating the $q$-state Potts ferromagnet, on a square lattice, at criticality. Exact relations involving special kinds of damage and the spin-spin correlation function, as well as the magnetization, are used. The efficiency of the method arises with a significant reduction of the finite-size effects, with respect to conventional Monte Carlo simulations. Correlation functions, which represent usually a hard task within this latter procedure, appear to be much more easily estimated through the present damage-spreading simulations. The effectiveness of the technique is illustrated by an accurate estimate of the exponent $\eta$, of the spin-spin correlation function, for $q=2$, 3, and 4, with rather small lattice sizes. In the cases $q⩾5$, an analysis of the magnetization is consistent with the well-known first-order phase transition.

We study a model for neural activity on the small-world topology of Watts and Strogatz and on the scale-free topology of Barabási and Albert. We find that the topology of the network connections may spontaneously induce periodic neural activity, contrasting with nonperiodic neural activities exhibited by regular topologies. Periodic activity exists only for relatively small networks and occurs with higher probability when the rewiring probability is larger. The average length of the periods increases with the square root of the network size.

X-ray photon correlation spectroscopy was employed in a surface standing wave geometry in order to resolve the thermally driven in-plane dynamics at both the surface/vacuum (top) and polymer/polymer (bottom) interfaces of a thin polystyrene (PS) film on top of Poly(4-bromo styrene) $\left(\mathrm{PBrS}\right)$ and supported on a Si substrate. The top vacuum interface shows two relaxation modes: one fast and one slow, while the buried polymer-polymer interface shows a single slow mode. The slow mode of the top interface is similar in magnitude and wave vector dependence to the single mode of the buried interface. The dynamics are consistent with a low-viscosity mixed layer between the PS and $\mathrm{PBrS}$ and coupling of the capillary wave fluctuations between this layer and the PS.

The theory for surface dynamics of the thermally excited fluctuations on a homogenous single-layer film of arbitrary depth is generalized to describe surface and interfacial dynamics of polymeric liquid bilayer films in terms of susceptibilities, power spectra, and characteristic relaxation time constants. The effects on surface dynamics originating from viscosity inhomogeneities close to the surface and interfacial regions are investigated by the bilayer theory and compared with the surface dynamics of homogeneous single-layer films under nonslip and slip boundary conditions. Our bilayer theory can also be extended to study interfacial dynamics of more generalized multilayer systems. The effects of viscoelasticity and van der Waals interactions on surface and interfacial dynamics are also briefly discussed.

The pretransitional equilibrium properties of isotropic liquids in the proximity of the isotropic-nematic phase transition are well known and successfully modeled. Much less is known about the dynamic behavior, and in particular about the pretransitional viscosity. In this work we combine two techniques [dynamic light scattering (DLS) and electric birefringence spectroscopy (EBS)] offering complementary insights into both static and dynamic pretransitional behavior of the homologous $n\mathrm{CB}$ family ($n\text{−}\mathrm{alkyl}$ cyanobiphenyl). EBS explores the single molecule flipping dynamics retarded by a paranematic potential barrier and enables extracting the associated transport coefficient, which is found to be of Arrhenius type in the whole temperature range explored. DLS reflects the collective dynamics of correlated domains and depends on the viscous damping of the orientational order. Such a viscosity displays Arrhenius behavior only sufficiently far from the transition temperature, with deviations growing as a power law of the appropriate reduced temperature with exponents around 0.1.

The ordinary refractive indices of some smectic-$A$ liquid crystals have been measured by means of interference spectra of free standing films as a function of wavelength and temperature. Numerical data are presented for further use. In the $\mathrm{Sm}\text{−}C$ phase one of the principal indices can be measured. If the three principal indices in the $\mathrm{Sm}\text{−}C$ phase would be known the tilt angle could be measured by means of the interference technique with high precision. Predictions of the refractive index of liquid crystals based on quantum chemical calculations of polarizabilities are presented. Using an expression derived by de Jeu and Bordewijk [J. Chem. Phys. 68, 109 (1978)] values for the principal refractive indices have been calculated that can be compared with our experimental results.

A formalism to determine coexistence points by means of Monte Carlo simulations is presented. The general idea of the method is to perform a simulation simultaneously in several unconnected boxes which can exchange particles. At equilibrium, most of the boxes will be occupied by a homogeneous phase. The compositions of these boxes yield coexisting points on the binodal. However, since the overall composition is fixed, at least one of the boxes will contain an interface. We show that this does not affect the results, provided that the interface has no net curvature. We coin the name “Helmholtz-ensemble method,” because the method is related to the well-known Gibbs-ensemble method, but the volume of the boxes is constant. Since the box volumes are constant, we expect that this method will be particularly useful for lattice models. The accuracy of the Helmholtz-ensemble method is benchmarked against known coexistence curves of the three-dimensional Ising model with excellent results.

We study the average excitation density in a simple model of excitable dynamics on graphs and find that this density strongly depends on certain topological features of the graph, namely connectivity and degree correlations, but to a lesser extent on the degree distribution. Remarkably, the average excitation density is changed via the distribution pattern of excitations: An increase in connectivity induces a transition from globally to locally organized excitations and, as a result, leads to an increase in the excitation density. A similar transition can be induced by increasing the rate of spontaneous excitations while keeping the graph architecture constant.

We study the relaxation towards thermodynamical equilibrium of a one-dimensional gravitational system. This model shows a series of critical energies $E_{cn}$ where different equilibria appear and we focus on the homogeneous $(n=0)$, one-peak $(n=\pm 1)$, and two-peak $(n=2)$ states. Using numerical simulations we investigate the relaxation to the stable equilibrium $n=\pm 1$ of this $N$-body system starting from initial conditions defined by equilibria $n=0$ and $n=2$. We find that in a fashion similar to other long-range systems the relaxation involves a fast violent relaxation phase followed by a slow collisional phase as the system goes through a series of quasistationary states. Moreover, in cases where this slow second stage leads to a dynamically unstable configuration (two peaks with a high mass ratio) it is followed by a different sequence, “violent relaxation–slow collisional relaxation.” We obtain an analytical estimate of the relaxation time $t_{2\to \pm 1}$ through the mean escape time of a particle from its potential well in a bistable system. We find that the diffusion and dissipation coefficients satisfy Einstein’s relation and that the relaxation time scales as $N{e}^{1∕T}$ at low temperature, in agreement with numerical simulations.

A class of discrete nonlinear Schrödinger equations with arbitrarily high-order nonlinearities is introduced. These equations are derived from the same Hamiltonian using different Poisson brackets and include as particular cases the saturable discrete nonlinear Schrödinger equation and the Ablowitz-Ladik equation. As a common property, these equations possess three kinds of exact analytical stationary solutions for which the Peierls-Nabarro barrier is zero. Several properties of these solutions, including stability, discrete breathers, and moving solutions, are investigated.

We report experimental studies of the effect of interstitial gas on mass-density segregation in a vertically vibrated mixture of equal-sized bronze and glass spheres. Sufficiently strong vibration in the presence of interstitial gas induces vertical segregation into sharply separated bronze and glass layers. We find that the segregated steady state (i.e., bronze or glass layer on top) is a sensitive function of gas pressure and viscosity, as well as vibration frequency and amplitude. In particular, we identify distinct regimes of behavior that characterize the change from bronze-on-top to glass-on-top steady state.

The effective pair potential between mesoscopic charged particles in a neutralizing background medium takes a Yukawa form $\exp (-\lambda r)∕r$ with screening length ${\lambda }^{-1}$. We consider a dilute suspension of such Yukawa particles dispersed in a solvent with correlation length $\xi <{\lambda }^{-1}$ and show that the Yukawa interaction is screened if the pair potentials between solvent particles exhibit Yukawa decay with the same screening length ${\lambda }^{-1}$. However, if the solvent pair potentials are shorter ranged than the solute Yukawa potentials, then the effective potential between pairs of solute particles is unscreened, i.e., the effective potential between the solute particles is equal to the bare potential at large particle separations.

We suggest an explanation for the anomalous behavior of the polymer surface-diffusion coefficient $D$ reported by Zhao and Granick [J. Am. Chem. Soc. 126, 6242 (2004)]: $D$ first increased with increasing polymer surface concentration $\Gamma$, then suddenly dropped at a threshold value ${\Gamma }^{*}$. Our molecular dynamics simulations show the same behavior. We find that polymers form single-layered pancake structures for $\Gamma <{\Gamma }^{*}$, while double layers form for $\Gamma >{\Gamma }^{*}$. The double-layer structures allow the polymers to better adapt to the substrate corrugation. This increases barriers for lateral diffusion and is thus consistent with small values of $D$ at larger $\Gamma$.

We develop a density functional theory for infinitely long flexible and semiflexible polymers, as an appropriate simplification of the corresponding treatment of finite chains. We demonstrate that very long chains sometimes are required to reproduce even qualitatively correct limiting behaviors.

We find that multifractal scaling is a robust property of a large class of continuous stochastic processes, constructed as exponentials of long-memory processes. The long memory is characterized by a power law kernel with tail exponent $\phi +1∕2$, where $\phi >0$. This generalizes previous studies performed only with $\phi =0$ (with a truncation at an integral scale) by showing that multifractality holds over a remarkably large range of dimensionless scales for $\phi >0$. The intermittency multifractal coefficient can be tuned continuously as a function of the deviation $\phi$ from $1∕2$ and of another parameter ${\sigma }^2$ embodying information on the short-range amplitude of the memory kernel, the ultraviolet cutoff (“viscous”) scale, and the variance of the white-noise innovations. In these processes, both a viscous scale and an integral scale naturally appear, bracketing the “inertial” scaling regime. We exhibit a surprisingly good collapse of the multifractal spectra $\zeta \left(q\right)$ on a universal scaling function, which enables us to derive high-order multifractal exponents from the small-order values and also obtain a given multifractal spectrum $\zeta \left(q\right)$ by different combinations of $\phi$ and ${\sigma }^2$.

We consider the dynamics of a gas of free bosons within a semiclassical Fokker-Planck equation for which we give a physical justification. In this context, we find a striking similarity between the Bose-Einstein condensation in the canonical ensemble, and the gravitational collapse of a gas of classical self-gravitating Brownian particles. The paper is mainly devoted to the complete study of the Bose-Einstein “collapse” within this model. We find that at the Bose-Einstein condensation temperature $T_c$, the chemical potential $\mu \left(t\right)$ vanishes exponentially with a universal rate that we compute exactly. Below $T_c$, we show analytically that $\sqrt{\mu \left(t\right)}$ vanishes linearly in a finite time $t_{coll}$. After $t_{coll}$, the mass of the condensate grows linearly with time and saturates exponentially to its equilibrium value for large time. We also give analytical results for the density scaling functions, for the corrections to scaling, and for the exponential relaxation time. Finally, we find that the equilibration time (above $T_c$) and the collapse time $t_{coll}$ (below $T_c$) both behave like $-T_c^{-3}\ln \mid T-T_c\mid$, near $T_c$.

A longstanding problem in the study of sediment transport in gravel-bed rivers is related to the physical mechanisms governing bed resistance and particle motion. To study this problem, we investigated the motion of coarse spherical glass beads entrained by a steady shallow turbulent water flow down a steep two-dimensional channel with a mobile bed. This experimental facility is the simplest representation of sediment transport on the laboratory scale, with the tremendous advantages that boundary conditions are perfectly controlled and a wealth of information can be obtained using imaging techniques. Flows were filmed from the side by a high-speed camera. Using image processing software made it possible to determine the flow characteristics such as particle trajectories, their state of motion (rest, rolling, or saltating motion), and flow depth. In accordance with earlier investigations, we observed that over short time periods, sediment transport appeared as a very intermittent process. To interpret these results, we revisited Einstein’s theory on sediment and derived the statistical properties (probability distribution and autocorrelation function) of the key variables such as the solid discharge and the number of moving particles. Analyzing the autocorrelation functions and the probability distributions of our measurements revealed the existence of long-range correlations. For instance, whereas theory predicts a Binomial distribution for the number of moving particles, experiments demonstrated that a negative binomial distribution best fit our data, which emphasized the crucial role played by wide fluctuations. These frequent wide fluctuations stemmed particle entrainment and motion being collective phenomena rather than individual processes, contrary to what is assumed in most theoretical models.

We introduced two point island models with island disaggregation. In the first one, particles can detach from islands with an odd number of particles and from those with two particles. In the second model, particles can detach from all islands with more than two particles. The scaling exponents are analytically obtained and verified with Monte Carlo simulations. Specially, the power-law scalings of the island and monomer densities are analyzed. Comparison with other models indicates that the models introduced here present different scaling behaviors.

We investigated three models of Brownian motors which convert rotational diffusion into directed translational motion by switching on and off a potential. In the first model a spatially asymmetric potential generates directed translational motion by rectifying rotational diffusion. It behaves much like a conventional flashing ratchet. The second model utilizes both rotational diffusion and drift to generate translational motion without spatial asymmetry in the potential. This second model can be driven by a combination of a Brownian motor mechanism (diffusion driven) or by powerstroke (drift driven) depending on the chosen parameters. In the third model, elements of both the Brownian motor and powerstroke mechanisms are combined by switching between three distinct states. Relevance of the model to biological motor proteins is discussed.