We propose an extended Ginzburg-Landau model for a description of the ambivalence region associated with the phenomenon of phase inversion observed in dispersed water-oil flow through a pipe. In analogy to the classical mean-field theory of phase transitions, it is shown that a good quantitative representation of the ambivalence region is obtained by using the injected phase volume fraction and a friction factor as the appropriate physical parameters.

We study heat transfer from a heated nanoparticle into surrounding fluid using molecular dynamics simulations. We show that the fluid next to the nanoparticle can be heated well above its boiling point without a phase change. Under increasing nanoparticle temperature, the heat flux saturates, which is in sharp contrast with the case of flat interfaces, where a critical heat flux is observed followed by development of a vapor layer and heat flux drop. These differences in heat transfer are explained by the curvature-induced pressure close to the nanoparticle, which inhibits boiling. When the nanoparticle temperature is much larger than the critical fluid temperature, a very large temperature gradient develops, resulting in close to ambient temperature just a radius away from the particle surface. The behavior reported allows us to interpret recent experiments where nanoparticles can be heated up to the melting point, without observing boiling of the surrounding liquid.

Spatial correlations in sheared isothermal liquids for both elastic and granular cases are theoretically investigated. Using the generalized fluctuating hydrodynamics, correlation functions for both the microscopic scale and the macroscopic scale are obtained. We find the existence of long-range correlations obeying power laws. The validity of our theoretical predictions has been verified from molecular-dynamics simulation.

A description of phase separation kinetics for solid binary $(A,B)$ mixtures in thin film geometry based on the Kawasaki spin-exchange kinetic Ising model is presented in a discrete lattice molecular field formulation. It is shown that the model describes the interplay of wetting layer formation and lateral phase separation, which leads to a characteristic domain size $l\left(t\right)$ in the directions parallel to the confining walls that grows according to the Lifshitz-Slyozov $t^{1∕3}$ law with time $t$ after the quench. Near the critical point of the model, the description is shown to be equivalent to the standard treatments based on Ginzburg-Landau models. Unlike the latter, the present treatment is reliable also at temperatures far below criticality, where the correlation length in the bulk is only of the order of a lattice spacing, and steep concentration variations may occur near the walls, invalidating the gradient square approximation. A further merit is that the relation to the interaction parameters in the bulk and at the walls is always transparent, and the correct free energy at low temperatures is consistent with the time evolution by construction.

Brownian dynamics simulation is employed to study the self-diffusion of tracer particles in a cross-linked gel network based on a coarse-grained bead-spring lattice model. Several effects are investigated including the network porosity, flexibility, degree of cross linking, and electrostatic interaction. For uncharged systems, the tracer long-time diffusivity is found to decrease with deceasing porosity and flexibility, but with increasing degree of cross linking. For charged systems, the diffusion is further hindered by the electrostatic interaction, regardless of whether the tracer particle and the network are oppositely or similarly charged. However, there exists a difference in the hindrance mechanism between the two cases. For the former, a substantial decrease in the diffusivity can occur at high network porosities due to electrostatic entrapment.

We consider a three-dimensional, generalized version of the original self-propelled-particles (SPP) model for collective motion. By extending the factors influencing the ordering, we investigate the case when the movement of the SPPs depends on both the velocity and the acceleration of the neighboring particles, instead of being determined solely by the former one. By changing the value of a weight parameter $s$ determining the relative influence of the velocity and the acceleration terms, the system undergoes a kinetic phase transition as a function of a behavioral pattern. Below a critical value of $s$ the system exhibits disordered motion, while above it the dynamics resembles that of the SPP model. We show that the critical value of the strategy variable could correspond to an evolutionary optimum in the sense that the information exchange between the units of the system is maximal in this point.

The retrieval abilities of spatially uniform attractor networks can be measured by the global overlap between patterns and neural states. However, we found that nonuniform networks, for instance, small-world networks, can retrieve fragments of patterns (blocks) without performing global retrieval. We propose a way to measure the local retrieval using a parameter that is related to the fluctuation of the block overlaps. Simulation of neural dynamics shows a competition between local and global retrieval. The phase diagram shows a transition from local retrieval to global retrieval when the storage ratio increases and the topology becomes more random. A theoretical approach confirms the simulation results and predicts that the stability of blocks can be improved by dilution.

We perform statistical analysis on discrete nonlinear waves generated through modulational instability in the context of the Salerno model that interpolates between the intregable Ablowitz-Ladik (AL) equation and the nonintegrable discrete nonlinear Schrödinger equation. We focus on extreme events in the form of discrete rogue or freak waves that may arise as a result of rapid coalescence of discrete breathers or other nonlinear interaction processes. We find power law dependence in the wave amplitude distribution accompanied by an enhanced probability for freak events close to the integrable limit of the equation. A characteristic peak in the extreme event probability appears that is attributed to the onset of interaction of the discrete solitons of the AL equation and the accompanied transition from the local to the global stochasticity monitored through the positive Lyapunov exponent of a nonlinear map.

In evolutionary dynamics the understanding of cooperative phenomena in natural and social systems has been the subject of intense research during decades. We focus attention here on the so-called “lattice reciprocity” mechanisms that enhance evolutionary survival of the cooperative phenotype in the prisoner’s dilemma game when the population of Darwinian replicators interact through a fixed network of social contacts. Exact results on a “dipole model” are presented, along with a mean-field analysis as well as results from extensive numerical Monte Carlo simulations. The theoretical framework used is that of standard statistical mechanics of macroscopic systems, but with no energy considerations. We illustrate the power of this perspective on social modeling, by consistently interpreting the onset of lattice reciprocity as a thermodynamical phase transition that, moreover, cannot be captured by a purely mean-field approach.

A comprehensive linear stability analysis of convection in the thermogravitational column is first performed for multicomponent fluids. Two types of perturbations are investigated: Longitudinal waves propagating in vertical direction of the column and transversal waves propagating perpendicular to the vertical axis and temperature gradient. The stability problems are reduced to those without cross-diffusion effect by a special transformation. The calculations are performed for binary and ternary mixtures by the Galerkin method. It is found that in binary fluids, the onset of longitudinal instability can be monotonic or oscillatory depending on the separation ratio, which characterizes the Soret effect. The difference between stability characteristics of binary and ternary fluids is associated with different diffusion times of components in a ternary system. It is shown that the mechanism of transversal instability is related to the unstable density stratification in the column (in total or due to individual components). The unstable stratification can only be realized in fluids with negative Soret effect. The analogue of exchange of stabilities principle for a plane column with a multicomponent fluid is proved. The obtained results indicate that the thermogravitational column can be used for measuring diffusion and thermal diffusion coefficients in ternary and higher mixtures with one or several components having negative Soret effect.

In this paper, we present a framework based on the generalized lattice Boltzmann equation (GLBE) using multiple relaxation times with forcing term for eddy capturing simulation of wall-bounded turbulent flows. Due to its flexibility in using disparate relaxation times, the GLBE is well suited to maintaining numerical stability on coarser grids and in obtaining improved solution fidelity of near-wall turbulent fluctuations. The subgrid scale (SGS) turbulence effects are represented by the standard Smagorinsky eddy viscosity model, which is modified by using the van Driest wall-damping function to account for reduction of turbulent length scales near walls. In order to be able to simulate a wider class of problems, we introduce forcing terms, which can represent the effects of general nonuniform forms of forces, in the natural moment space of the GLBE. Expressions for the strain rate tensor used in the SGS model are derived in terms of the nonequilibrium moments of the GLBE to include such forcing terms, which comprise a generalization of those presented in a recent work [Yu et al., Comput. Fluids 35, 957 (2006)]. Variable resolutions are introduced into this extended GLBE framework through a conservative multiblock approach. The approach, whose optimized implementation is also discussed, is assessed for two canonical flow problems bounded by walls, viz., fully developed turbulent channel flow at a shear or friction Reynolds number (Re) of 183.6 based on the channel half-width and three-dimensional (3D) shear-driven flows in a cubical cavity at a Re of 12 000 based on the side length of the cavity. Comparisons of detailed computed near-wall turbulent flow structure, given in terms of various turbulence statistics, with available data, including those from direct numerical simulations (DNS) and experiments showed good agreement. The GLBE approach also exhibited markedly better stability characteristics and avoided spurious near-wall turbulent fluctuations on coarser grids when compared with the single-relaxation-time (SRT)-based approach. Moreover, its implementation showed excellent parallel scalability on a large parallel cluster with over a thousand processors.

Turbulent flow in a straight square duct driven by a pressure gradient exhibits remarkable flow structures such as the presence of mean streamwise vorticity or secondary flows. These secondary circulations take the form of two counter-rotating vortices near each corner of the duct. Even though their magnitudes are small compared with primary streamwise motions, they have a significant influence on flow and scalar transport and are challenging to accurately predict using computational approaches. In this paper, we employ a recently developed formulation of the generalized lattice Boltzmann equation (GLBE) with forcing term to perform large eddy simulation of fully developed turbulent flow in a square duct at a shear Reynolds number based on duct width equal to 300. Subgrid scale effects are represented by the Smagorinsky eddy viscosity model, which is modified by the van Driest damping function in the near-wall regions, in this GLBE approach, which is based on multiple relaxation times. It was found that the GLBE is able to correctly reproduce the existence of mean secondary motions and the computed detailed structure of first- and second-order statistics of main and secondary motions are in good agreement with prior direct numerical simulations based on the solution of the Navier-Stokes equations and experimental data.

We introduce a family of molecular rotors that may convert light or chemical energy into directed translational motion along surfaces. The dependencies of diffusion coefficient and drift velocity of the rotating molecule on the magnitude of external torque, symmetry of surface potential, and temperature have been investigated. Our simulations show that the rotation-translation coupling could be very effective, and the molecule may move by approximately one surface lattice spacing per complete rotation. We have found that the unidirectionality of the rotary motion is not required to produce efficient directed sliding; this effect can be achieved by applying a time-periodic, or even randomly, oscillating torque which induces alternating molecular reorientations but does not generate complete rotations.

We investigate the long time behavior of the one-dimensional ballistic aggregation model that represents a sticky gas of $N$ particles with random initial positions and velocities, moving deterministically, and forming aggregates when they collide. We obtain a closed formula for the stationary measure of the system which allows us to analyze some remarkable features of the final “fan” state. In particular, we identify universal properties which are independent of the initial position and velocity distributions of the particles. We study cluster distributions and derive exact results for extreme value statistics (because of correlations these distributions do not belong to the Gumbel-Fréchet-Weibull universality classes). We also derive the energy distribution in the final state. This model generates dynamically many different scales and can be viewed as one of the simplest exactly solvable model of $N$-body dissipative dynamics.

The ferromagnetic phase of an Ising model in $d=3$, with any amount of quenched antiferromagnetic bond randomness, is shown to undergo a transition to a spin-glass phase under sufficient quenched bond dilution. This result, demonstrated here with the numerically exact global renormalization-group solution of a $d=3$ hierarchical lattice, is expected to hold true generally, for the cubic lattice and for quenched site dilution. Conversely, in the ferromagnetic–spin-glass–antiferromagnetic phase diagram, the spin-glass phase expands under quenched dilution at the expense of the ferromagnetic and antiferromagnetic phases. In the ferromagnetic–spin-glass phase transition induced by quenched dilution, reentrance as a function of temperature is seen, as previously found in the ferromagnetic–spin-glass transition induced by increasing the antiferromagnetic bond concentration.

A collection of spherical particles subjected to horizontal oscillatory fluid flow is known to form chains perpendicular to the direction of the oscillation. We have developed computer simulations to model such a system and have validated them against experiments carried out in a small fluid-filled cell. In both experiment and simulation we find that the particles go through the same stages of evolution from a dispersed initial configuration to an ordered chain structure. We then use our computer simulations to investigate in detail the interactions responsible for chain formation and the interaction between fully formed chains.

We consider enzymes involved in a three-state Michaelis-Menten kinetics and submitted to well-chosen temperature modulations of small amplitude. From the first-order amplitudes of concentration oscillations, we design a response function that is maximum for targeted values of the chemical relaxation times. This resonant function can be used to screen a large set of enzymes and identify the one governed by the desired kinetics. The method gives access to all the dynamical parameters of the targeted enzyme without resorting to a fit. We show how to estimate the precision of this parameter determination and give some hints for experimental validation.

The African shield-backed bug Calidea panaethiopica is a very colorful insect which produces a range of iridescent yellow, green, and blue reflections. The cuticle of the dorsal side of the insect, on the shield, the prothorax and part of the head, is pricked of uniformly distributed hemispherical hollow cavities a few tens micrometers deep. Under normal illumination and viewing the insect’s muffin-tin shaped surface gives rise to two distinct colors: a yellow spot arising from the bottom of the well and a blue annular cloud that appears to float around the yellow spot. This effect is explained by multiple reflections on a hemispherical Bragg mirror with a mesoscopic curvature. A multiscale computing methodology was found to be needed to evaluate the reflection spectrum for such a curved multilayer. This multiscale approach is very general and should be useful for dealing with visual effects in many natural and artificial systems.

The formation and development of spiral defects is one of the major causes of order-disorder transitions in spatiotemporal patterns. In this paper, line defect formation and development in a three-dimensional reaction-diffusion system with gradients of control parameters in the third dimension is investigated. The system can be considered as diffusively coupled two-dimensional spatiotemporal patterns with dissimilarities. We observed that under certain conditions, as the gradients are varied, ordered and disordered spatiotemporal patterns appear alternately and line defects of various configurations form. This scenario is found to be in qualitative agreement with the experimental findings in the Belousov-Zhabotinsky reaction. We thus demonstrate that the line defect which was usually expected in two-dimensional complex oscillatory media can also be generated from the reconciliation between the coupled simple spiral waves with dissimilarity.

The response of a nonlinear optical oscillator subject to a delayed broadband bandpass filtering feedback is studied experimentally, numerically, and analytically. The oscillator loop is characterized by a high cutoff frequency with a response time $\tau \sim 10\mathrm{ps}$ and by a low cutoff frequency with a response time $\theta \sim 1\mu \mathrm{s}$. Moreover, the optoelectronic feedback also consists of a significant delay ${\tau }_D$ of the order of $100\mathrm{ns}$. Depending on two key physical parameters, the loop gain $\beta$ and the nonlinearity operating point $\Phi$, a large variety of multiple time scale regimes are reported, including slow or fast periodic oscillations with different waveforms, regular or chaotic breathers, slow time envelope dynamics, complex and irregular self-pulsing, and fully developed chaos. Many of these regimes are exhibiting new features that are absent in the classical first-order scalar nonlinear delay differential equations (DDEs), which differ in the modeling by the low cutoff only. Nearly all kinds of solutions are recovered numerically by a new class of integro-DDE (iDDE) that take into account both the high and low cutoff frequencies of the feedback loop. For moderate feedback gain, asymptotic solutions are determined analytically by taking advantage of the relative values of the time constants $\tau$, $\theta$, and ${\tau }_D$. We confirm the experimental observation of two distinct routes to oscillatory instabilities depending on the value of $\Phi$. One route is reminiscent of the square wave oscillations of the classical first-order DDE, but the other route is quite different and allows richer wave forms. For higher feedback gain, these two distinct regimes merge leading to complex nonperiodic regimes that still need to be explored analytically and numerically. Finally, we investigate the theoretical limits of our iDDE model by experimentally exploring phenomena at extreme physical parameter setting, namely, high-frequency locking at strong feedback gain or pulse packages for very large delays. The large variety of oscillatory regimes of our broadband bandpass delay electro-optic oscillator is attractive for applications requiring rich optical pulse sources with different frequencies and/or wave forms (chaos-based communications, random number generation, chaos computing, and generation of stable multiple GHz frequency oscillations).