In the absence of nonlinearity all normal modes (NMs) of a chain with disorder are spatially localized (Anderson localization). We study the action of nonlinearity, whose strength is ramped linearly in time. It leads to a spreading of a wave packet due to interaction with and population of distant NMs. Eventually nonlinearity-induced frequency shifts take over and the wave packet becomes self-trapped. On finite chains a critical ramping speed is obtained, which separates delocalized final states from localized ones. The critical value depends on the strength of disorder and is largest when the localization length matches the system size.

Viscous fingering (VF) is a hydrodynamical instability that occurs in porous media when a less viscous fluid displaces a more viscous one. We investigate here numerically how such an instability can be triggered by a simple $A+B\to C$ reaction when a solution of one reactant is displacing linearly a miscible solution of another reactant of same viscosity producing a more viscous product $C$ at the interface. The properties of the fingering pattern observed in the zone where the less viscous reactant pushes more viscous products are studied as a function of the relevant parameters of the problem. These are the Damköhler number, the viscosity contrast between reactants and product, the ratio of initial concentrations of $A$ and $B$, and the diffusion coefficients of each species. Our study shows that the fingering pattern can in some cases be different whether $A$ displaces $B$ or vice versa, enlightening recent experimental observations of such asymmetries in micellar systems. In particular, we show that in this asymmetric case, VF is more intense when the invading chemical solution is either the less concentrated one for equal diffusivities or when it contains the slower diffusing reactant for fixed equimolar initial concentrations.

We study local power fluctuations in numerical simulations of stationary, homogeneous, isotropic turbulence in two and three dimensions with Gaussian forcing. Due to the near-Gaussianity of the one-point velocity distribution, the probability distribution function (pdf) of the local power is well modeled by the pdf of the product of two joint normally distributed variables. In appropriate units, this distribution is parametrized only by the mean dissipation rate, $ϵ$. The large deviation function for this distribution is calculated exactly and shown to satisfy a fluctuation relation (FR) with a coefficient which depends on $ϵ$. This FR is entirely statistical in origin. The deviations from the model pdf are most pronounced for positive fluctuations of the power and can be traced to a slightly faster than Gaussian decay of the tails of the one-point velocity pdf. The resulting deviations from the FR are consistent with several recent experimental studies.

An experimental and theoretical study on the kinetics of the aggregation process of magnetic particles dispersed in mineral oils is presented. A static magnetic field and an oscillating magnetic perturbation are applied on the dispersion. In the low-particle concentrations, the effects on the aggregation of the frequency, the concentration of particles and the viscosity of the liquid are analyzed. It was found that the behavior of the cluster length as a function of the main control parameters can be accurately characterized by scaling relations. The physical characteristics of the aggregates are discussed in relation to measurements of viscosity as a function of time.

We study numerically the phase diagram and the response under a driving force of the phase field crystal model for pinned lattice systems introduced recently for both one- and two-dimensional systems. The model describes the lattice system as a continuous density field in the presence of a periodic pinning potential, allowing for both elastic and plastic deformations of the lattice. We first present results for phase diagrams of the model in the absence of a driving force. The nonlinear response to a driving force on an initially pinned commensurate phase is then studied via overdamped dynamic equations of motion for different values of mismatch and pinning strengths. For large pinning strength the driven depinning transitions are continuous, and the sliding velocity varies with the force from the threshold with power-law exponents in agreement with analytical predictions. Transverse depinning transitions in the moving state are also found in two dimensions. Surprisingly, for sufficiently weak pinning potential we find a discontinuous depinning transition with hysteresis even in one dimension under overdamped dynamics. We also characterize structural changes of the system in some detail close to the depinning transition.

The free energy of classical density functional theory of an inhomogeneous fluid at coexistence with its solid is used to describe solidification in two-dimensional hexagonal crystals. A coarse-graining formalism from the microscopic density functional level to the macroscopic single order parameter level is provided. An analytic expression for the surface energy and the angular dependence of its anisotropy is derived and its coefficients related to the two-point direct correlation function of the liquid phase at coexistence.

We present a study of the effects of nanoconfinement on a system of hard Gaussian overlap particles interacting with planar substrates through the hard-needle-wall potential, extending earlier work by two of us [D. J. Cleaver and P. I. C. Teixeira, Chem. Phys. Lett. 338, 1 (2001)]. Here, we consider the case of hybrid films, where one of the substrates induces strongly homeotropic anchoring, while the other favors either weakly homeotropic or planar anchoring. These systems are investigated using both Monte Carlo simulation and density-functional theory, the latter implemented at the level of Onsager’s second-virial approximation with Parsons-Lee rescaling. The orientational structure is found to change either continuously or discontinuously depending on substrate separation, in agreement with earlier predictions by others. The theory is seen to perform well in spite of its simplicity, predicting the positional and orientational structure seen in simulations even for small particle elongations.

We discuss the stability of icosadeltahedral shells subjected to a uniform external load in the form of an isotropic pressure. We demonstrate that there exists a universal critical buckling pressure scaling form that defines a locus of buckling instabilities. The parameter that uniquely determines this scaling form is shown to be the Föppl–von Karman number of nonpressurized shells. Numerical results are interpreted in terms of scaling forms for buckling instabilities of spheres and cylinders under isotropic mechanical pressure, and are applied to the case of viruses under osmotic pressure.

One-dimensional (1D) nanoelements, such as nanotubes and nanowires, making up percolation networks are typically modeled as fixed length sticks in order to calculate their electrical properties. In reality, however, the lengths of these 1D nanoelements comprising such networks are not constant, rather they exhibit a length distribution. Using Monte Carlo simulations, we have studied the effect of this nanotube and/or nanowire length distribution on the resistivity in 1D nanoelement percolation networks. We find that, for junction resistance-dominated random networks, the resistivity correlates with root-mean-square element length, whereas for element resistance-dominated random networks, the resistivity scales with average element length. If the elements are preferentially aligned, we find that these two trends shift toward higher power means. We explain the physical origins of these simulation results using geometrical arguments. These results emphasize the importance of the element length distribution in determining the resistivity in these networks.

We report the results of a series of simulations of a susceptible-infected-recovered epidemic model in heterogeneous spatial metapopulation networks with quantitative knowledge of human traveling statistics that human travel behavior obeys scaling laws in the sense of geographical distance and period of waiting time. By tuning the edge length distribution of the spatial metapopulation network, we can conveniently control the distribution of human travel distance. The simulation results show that the occurrence probability of global outbreaks is significantly dependent on the characteristic travel distance, the characteristic waiting time, and the memory effects of human travel. We also present some preliminary results on the effects of travel restrictions in epidemic control.

Within the chemical picture, it is shown that self-consistent Coulomb nonideality corrections that satisfy Maxwell’s thermodynamic identities can be constructed from formulas for lowering of ionization potentials, obtained from plasma electrostatic microfields or derived in ad hoc or empirical fashion, provided that a necessary integrability criterion is satisfied. The solution of such an inverse problem is formulated and introduced in terms of a simple integral that gives the correction to Helmholtz free energy function. The required integrability criterion is derived and applied to investigate the thermodynamic consistency of some models in the literature. Maintaining the same functional dependence on species densities as in the original models, a routine to fix thermodynamic inconsistencies found in some of these models is introduced. The advantages and usefulness of such a reverse scheme are discussed.

Quantitative comparison between the measured deformation of a neutrally buoyant drop, obtained with an appropriately conceived three-dimensional, multicomponent lattice Boltzmann equation simulation methods for continuum multicomponent hydrodynamics [Phys. Rev. E 76, 026708 (2007); 76, 026709 (2007)], are shown to be in agreement with the theoretical predictions of Taylor and Acrivos [J. Fluid. Mech. 18(3), 466 (1964)].

In the framework of the stochastic dynamics of open Markov systems, we derive an extension of the Clausius inequality for transitions between states of the system. We give a formula for the power produced when the system is in its stationary state and relate it to the dissipation of energy needed to maintain the system out of equilibrium. We deduce that, near equilibrium, maximal power production requires an energy dissipation of the same order of magnitude as the power production.

The percolation transitions on hyperbolic lattices are investigated numerically using finite-size scaling methods. The existence of two distinct percolation thresholds is verified. At the lower threshold, an unbounded cluster appears and reaches from the middle to the boundary. This transition is of the same type and has the same finite-size scaling properties as the corresponding transition for the Cayley tree. At the upper threshold, on the other hand, a single unbounded cluster forms which overwhelms all the others and occupies a finite fraction of the volume as well as of the boundary connections. The finite-size scaling properties for this upper threshold are different from those of the Cayley tree and two of the critical exponents are obtained. The results suggest that the percolation transition for the hyperbolic lattices forms a universality class of its own.

We present a study of focal conic domains in smectic-$A$ liquid-crystal films on solid substrates. The antagonistic anchoring conditions of the film surfaces, random planar at the substrate interface and homeotropic at the air interface, enforce the formation of focal conic domains the lateral size of which is dependent on the film thickness. The strength of the planar anchoring on the solid substrate is systematically varied by coating the substrate with special alkoxysilane compounds. For each anchoring strength value, the relation between the size of the focal conic domains and the film thickness is determined. Increasing the planar anchoring strength influences the size-thickness relation and leads to the formation of larger focal conic domains.

We have carried out a numerical study of a system of hydrodynamic equations including director reorientation, fluid flow, temperature, and density redistribution across a compressible hybrid-oriented liquid crystal (HOLC) cell under the influence of a temperature gradient $\nabla T$ directed normal to the restricting surfaces, when the sample is heated both from below and above. Calculations show that under the influence of $\nabla T$ the compressible HOLC sample settles down to a stationary flow regime, both with the horizontal $u$ and vertical $w$ components of velocity $\mathbf{v}$, and $u$ is directed in the opposite direction, approximately one order of magnitude less, than the one in the case of an incompressible HOLC cell. The role of hydrodynamic flow in the relaxation processes of the stress tensor components, for a number of dynamic regimes in the compressible HOLC cell containing $4\text{−}n\text{−}\mathit{\text{pentyl}}\text{−}{4}^{\prime }\text{−}\mathit{\text{cyanobiphenyl}}$, has been investigated.

We search for conditions under which a characteristic time scale for ordering dynamics toward either of two absorbing states in a finite complex network of interactions does not exist. With this aim, we study random networks and networks with mesoscale community structure built up from randomly connected cliques. We find that large heterogeneity at the mesoscale level of the network appears to be a sufficient mechanism for the absence of a characteristic time for the dynamics. Such heterogeneity results in dynamical metastable states that survive at any time scale.

We use shear transformation zone (STZ) theory to develop a deformation map for amorphous solids as a function of the imposed shear rate and initial material preparation. The STZ formulation incorporates recent simulation results [T. K. Haxton and A. J. Liu, Phys. Rev. Lett. 99, 195701 (2007)] showing that the steady state effective temperature is rate dependent. The resulting model predicts a wide range of deformation behavior as a function of the initial conditions, including homogeneous deformation, broad shear bands, extremely thin shear bands, and the onset of material failure. In particular, the STZ model predicts homogeneous deformation for shorter quench times and lower strain rates, and inhomogeneous deformation for longer quench times and higher strain rates. The location of the transition between homogeneous and inhomogeneous flow on the deformation map is determined in part by the steady state effective temperature, which is likely material dependent. This model also suggests that material failure occurs due to a runaway feedback between shear heating and the local disorder, and provides an explanation for the thickness of shear bands near the onset of material failure. We find that this model, which resolves dynamics within a sheared material interface, predicts that the stress weakens with strain much more rapidly than a similar model which uses a single state variable to specify internal dynamics on the interface.

The influences of delayed feedback on the oscillating behaviors are numerically investigated by using the photosensitive Oregonator model with a Hopf point. We find that the time delay in the robust entrainment phenomena determines the time scale of the system, that is, $T_m=(\tau +\delta )∕N$ $(N=1,2,\cdots )$, where $T_m$ is the mean period of the oscillation and $\delta$ is a small constant compared with the delay time $\tau$. Further, our numerical simulation shows that, when the system has a characteristic period $T_0$ under the feedback with time delay, there exists an asymptotical line $\delta ={\delta }_0{T}_0$ (${\delta }_0$ independent of any parameters) in the entrainment region with increasing strength of the feedback control $c$; when the system has no characteristic period, the above linear relation is also kept, and $\delta$ decreases with increasing $c$.

We study relevant features of the spectrum of the quantum open baker map. The opening consists of a cut along the momentum $p$ direction of the 2-torus phase space, modeling an open chaotic cavity. We study briefly the classical forward trapped set and analyze the corresponding quantum nonunitary evolution operator. The distribution of eigenvalues depends strongly on the location of the escape region with respect to the central discontinuity of this map. This introduces new ingredients to the association among the classical escape and quantum decay rates. Finally, we could verify that the validity of the fractal Weyl law holds in all cases.