We address the interesting temperature range of a glass forming system where the mechanical properties are intermediate between those of a liquid and a solid. We employ an efficient Monte Carlo method to calculate the elastic moduli, and show that in this range of temperatures the moduli are finite for short times and vanish for long times, where short and long depend on the temperature. By invoking some exact results from statistical mechanics we offer an alternative method to compute shear moduli using molecular dynamics simulations, and compare those to the Monte Carlo method. The final conclusion is that these systems are not “viscous fluids” in the usual sense, as their actual time-dependence concatenates solidlike materials with varying local shear moduli.

In this paper we study synchronized motions in complex networks in which there are distinct groups of nodes where the dynamical systems on each node within a group are the same but are different for nodes in different groups. Both continuous time and discrete time systems are considered. We initially focus on the case where two groups are present and the network has bipartite topology (i.e., links exist between nodes in different groups but not between nodes in the same group). We also show that group synchronous motions are compatible with more general network topologies, where there are also connections within the groups.

Rigid spherical particles in oscillating fluid flows form interesting structures as a result of fluid mediated interactions. Here we show that spheres under horizontal vibration align themselves at right angles to the oscillation and sit with a gap between them. The details of this behavior have been investigated through experiments and simulations. We have carried out experiments in which a pair of stainless steel spheres is shaken horizontally in a cell filled with glycerol-water fluid mixtures of three different viscosities, at various frequencies and amplitudes of oscillation. There is an equilibrium gap between the particles resulting from a long-range attraction and a short-range repulsion. The size of the gap was found to depend on the fluid viscosity and the vibratory parameters, and we have identified two distinct scaling regimes for the dependence of the gap on the system parameters. Using a Navier-Stokes solver the same system was simulated. The interaction force between the spheres was measured and the streaming flows induced by the motion were determined.

Heat conduction in simple networks consisting of different one dimensional nonlinear chains is studied. We find that the coupling between chains has a different function in heat conduction from that in electric network (circuit). The two coupled particles form an interface and introduce an interface thermal resistance which reduces the heat current. The reduction of heat current depends sensitively on the position and strength of the coupling. This might find application in controlling heat flow in complex networks.

We present an asymptotic and scaling analysis of the long-time self-diffusivity of a Brownian spherical particle in dilute polymer solutions with nonadsorbing chains. The polymer depletion zone near the particle surface is described by a continuous polymer density profile. Hydrodynamics formulated by the modified Stokes equation with nonuniform viscosity is solved by a regular perturbation approximation using the Green function method. The asymptotes predict how polymer depletion alters the friction a spherical particle experiences during translational and rotational motion within a quiescent fluid. The analysis agrees very well with full numerical computation, which enables us to investigate the scaling law for the polymer-mediated retardation effect using a stretched exponential form that is commonly applied by experimentalists. The scaling exponents revealed are consistent with the nominal values from collected experiment observations.

We investigate propagating fronts in disordered media that belong to the universality class of wetting contact lines and planar tensile crack fronts. We derive from first principles their nonlinear equations of motion, using the generalized Griffith criterion for crack fronts and three standard mobility laws for contact lines. Then we study their roughness using the self-consistent expansion. When neglecting the irreversibility of fracture and wetting processes, we find a possible dynamic rough phase with a roughness exponent of $\zeta =1∕2$ and a dynamic exponent of $z=2$. When including the irreversibility, we conclude that the front propagation can become history dependent, and thus we consider the value $\zeta =1∕2$ as a lower bound for the roughness exponent. Interestingly, for propagating contact line in wetting, where irreversibility is weaker than in fracture, the experimental results are close to 0.5, while for fracture the reported values of 0.55–0.65 are higher.

We study by Monte Carlo simulations a model of a knotted polymer ring adsorbing onto an impenetrable, attractive wall. The polymer is described by a self-avoiding polygon on the cubic lattice. We find that the adsorption transition temperature, the crossover exponent $\varphi$, and the metric exponent $\nu$ are the same as in the model where the topology of the ring is unrestricted. By measuring the average length of the knotted portion of the ring, we are able to show that adsorbed knots are localized. This knot localization transition is triggered by the adsorption transition but is accompanied by a less sharp variation of the exponent related to the degree of localization. Indeed, for a whole interval below the adsorption transition, one can not exclude a contiuous variation with temperature of this exponent. Deep into the adsorbed phase we are able to verify that knot localization is strong and well described in terms of the flat knot model.

We consider complex clustered networks with a gradient structure, where the sizes of the clusters are distributed unevenly. Such networks describe actual networks in biophysical systems and in technological applications more closely than the previous models. Theoretical analysis predicts that the network synchronizability can be optimized by the strength of the gradient field, but only when the gradient field points from large to small clusters. A remarkable finding is that, if the gradient field is sufficiently strong, synchronizability of the network is mainly determined by the properties of the subnetworks in the two largest clusters. These results are verified by numerical eigenvalue analysis and by direct simulation of synchronization dynamics on coupled-oscillator networks.

We consider sound wave propagation in a range-periodic acoustic waveguide in the deep ocean. It is demonstrated that vertical oscillations of a sound-speed perturbation, induced by ocean internal waves, influence near-axial rays in a resonant way, producing ray chaos and forming a wide chaotic sea in the underlying phase space. We study interplay between chaotic ray dynamics and wave motion with signal frequencies of 50–100 Hz. The Floquet modes of the waveguide are calculated and visualized by means of the Husimi plots. Despite of irregular phase space distribution of periodic orbits, the Husimi plots display the presence of ordered peaks within the chaotic sea. These peaks, not being supported by certain periodic orbits, draw the specific “chainlike” pattern, reminiscent of KAM resonance. The link between the peaks and KAM resonance is confirmed by ray calculations with lower amplitude of the sound-speed perturbation, when the periodic orbits are well-ordered. We associate occurrence of the peaks with the recovery of ordered periodic orbits, corresponding to KAM resonance, due to suppressing of wave-field sensitivity to small-scale features of the sound-speed profile that take place with increasing wavelength.

We consider discrete dynamical networks, and analytically demonstrate the relation between transverse stability in the Milnor sense and contraction stability, the stability for synchronous manifolds obtained via the partial contraction principle. By contraction for a system, we mean that initial conditions or temporary disturbances are forgotten exponentially fast, so that all trajectories of this system converge to a unique trajectory. In addition, synchronization of star-shaped complex networks is investigated via the partial contraction principle. This example further verifies the interrelation between contraction and transverse stability.

The scaling properties of the rough liquid-air interface formed in the spontaneous imbibition of a viscous liquid by a model porous medium are found to be very sensitive to the magnitude of the pressure difference applied at the liquid inlet. Interface fluctuations change from obeying intrinsic anomalous scaling at large negative pressure differences, to being super-rough with the same dynamic exponent $z\simeq 3$ at less negative pressure differences, to finally obeying ordinary Family-Vicsek scaling with $z\simeq 2$ at large positive pressure differences. This rich scenario reflects the relative importance on different length scales of capillary and permeability disorder, and the role of surface tension and viscous pressure in damping interface fluctuations.

We investigate the locality or nonlocality of the energy transfer and the spectral interactions involved in the cascade for decaying magnetohydrodynamic (MHD) flows in the presence of a uniform magnetic field $\mathbf{B}$ at various intensities. The results are based on a detailed analysis of three-dimensional numerical flows at moderate Reynolds numbers. The energy transfer functions, as well as the global and partial fluxes, are examined by means of different geometrical wave number shells. On the one hand, the transfer functions of the two conserved Elsässer energies $E^{+}$ and $E^{-}$ are found local in both the directions parallel ($k_{\Vert }$ direction) and perpendicular ($k_{\perp }$ direction) to the magnetic guide field, whatever the $\mathbf{B}$ strength. On the other hand, from the flux analysis, the interactions between the two counterpropagating Elsässer waves become nonlocal. Indeed, as the $\mathbf{B}$ intensity is increased, local interactions are strongly decreased and the interactions with small $k_{\Vert }$ modes dominate the cascade. Most of the energy flux in the $k_{\perp }$ direction is due to modes in the plane at $k_{\Vert }=0$, while the weaker cascade in the $k_{\Vert }$ direction is due to the modes with $k_{\Vert }=1$. The stronger magnetized flows tend thus to get closer to the weak turbulence limit, where three-wave resonant interactions are dominant. Hence, the transition from the strong to the weak turbulence regime occurs by reducing the number of effective modes in the energy cascade.

In the field of inertial confinement fusion (ICF), work has been consistently progressing in the past decade toward a more fundamental understanding of the plasma conditions in ICF implosion cores. The research presented here represents a substantial evolution in the ability to diagnose plasma temperatures and densities, along with characteristics of mixing between fuel and shell materials. Mixing is a vital property to study and quantify, since it can significantly affect implosion quality. We employ a number of new spectroscopic techniques that allow us to probe these important quantities. The first technique developed is an emissivity analysis, which uses the emissivity ratio of the optically thin $\mathrm{Ly}\beta$ and $\mathrm{He}\beta$ lines to spectroscopically extract temperature profiles, followed by the solution of emissivity equations to infer density profiles. The second technique, an intensity analysis, models the radiation transport through the implosion core. The nature of the intensity analysis allows us to use an optically thick line, the $\mathrm{Ly}\alpha$, to extract information on mixing near the core edge. With this work, it is now possible to extract directly from experimental data not only detailed temperature and density maps of the core, but also spatial mixing profiles.

A coupled double-distribution-function lattice Boltzmann method is developed for the compressible Navier-Stokes equations. Different from existing thermal lattice Boltzmann methods, this method can recover the compressible Navier-Stokes equations with a flexible specific-heat ratio and Prandtl number. In the method, a density distribution function based on a multispeed lattice is used to recover the compressible continuity and momentum equations, while the compressible energy equation is recovered by an energy distribution function. The energy distribution function is then coupled to the density distribution function via the thermal equation of state. In order to obtain an adjustable specific-heat ratio, a constant related to the specific-heat ratio is introduced into the equilibrium energy distribution function. Two different coupled double-distribution-function lattice Boltzmann models are also proposed in the paper. Numerical simulations are performed for the Riemann problem, the double-Mach-reflection problem, and the Couette flow with a range of specific-heat ratios and Prandtl numbers. The numerical results are found to be in excellent agreement with analytical and/or other solutions.

We implement an adaptive mesh algorithm for calculating the space and time dependence of the atomic density field in microscopic material processes. Our numerical approach uses the systematic renormalization-group formulation of a phase-field crystal model of a pure material to provide the underlying equations for the complex amplitude of the atomic density field—a quantity that is spatially uniform except near topological defects, grain boundaries, and other lattice imperfections. Our algorithm employs a hybrid formulation of the amplitude equations, combining Cartesian and polar decompositions of the complex amplitude. We show that this approach leads to an acceleration by three orders of magnitude in model calculations of polycrystalline grain growth in two dimensions.

We address the problem of estimating multiple parameters of a chaotic dynamical model from the observation of a scalar time series. We assume that the series is produced by a chaotic system with the same functional form as the model, so that synchronization between the two systems can be achieved by an adequate coupling. In this scenario, we propose an efficient Monte Carlo optimization algorithm that iteratively updates the model parameters in order to minimize the synchronization error. As an example, we apply it to jointly estimate the three static parameters of a chaotic Lorenz system.

We consider a random walk in confined geometry, starting from a site and eventually reaching a target site. We calculate analytically the distribution of the occupation time on a third site, before reaching the target site. The obtained distribution is exact and completely explicit in the case or parallelepipedic confining domains. We discuss implications of these results in two different fields: The mean first passage time for the random trap model is computed in dimensions greater than 1 and is shown to display a nontrivial dependence with the source and target positions. The probability of reaction with a given imperfect center before being trapped by another one is also explicitly calculated, revealing a complex dependence both in geometrical and chemical parameters.

Thermodynamic behavior of a binary monolayer of Ising dipolar particles is studied using numerical simulation. The thermal equilibrium states of the system under the canonical ensemble are observed. The boundary of gas-liquid phase is determined from the power law growth of critical clusters. But that temperature is slightly lower than that of solidification. So it means that this system does not have a liquid phase. This system is also studied theoretically using virial expansion. The coefficients obtained from standard virial expansion, however, do not show any phase transition. An improvement of the virial expansion is also given by taking tetragonal local structures of alternate types of particles into consideration. Such structures are observed within critical clusters of our simulation. The thermodynamic state equation obtained from the improved virial expansion agrees well with the simulation result, and this expansion also shows that the critical point is almost at the same temperature with solidification. These results suggest that not simply the strength of attractive force by the dipole interaction but a typical configuration caused by the binary condition of this system plays a dominant role in phase transitions.

Recent advances in nonequilibrium statistical mechanics shed new light on the ratchet effect. The ratchet motion can thus be understood in terms of symmetry (breaking) considerations. We introduce an additional symmetry operation besides time reversal, that switches between two modes of operation. That mode reversal combined with time reversal decomposes the nonequilibrium action so as to clarify under what circumstances the ratchet current is a second order effect around equilibrium, what is the direction of the ratchet current, and what are possibly the symmetries in its fluctuations.