We probe the local and global structure of spin-coated colloidal crystals via laser diffraction measurements and scanning electron and atomic force microscopies, and find that they are unique three-dimensional orientationally correlated polycrystals, exhibiting short-range positional order but long-range radial orientational correlations, reminiscent of—but distinct from—two-dimensional colloidal hexatic phases. Thickness and symmetries are controllable by solvent choice and spin speed. While the polycrystallinity of these colloidal films limits their applicability to photonics, we demonstrate their feasibility as templates to make crack-free magnetic patterns.

Spatiotemporal correlations of the two-dimensional (2D) spring-block (Burridge-Knopoff) models of earthquakes with the long-range interblock interactions are extensively studied by means of numerical computer simulations. The long-range interaction derived from an elastic theory, which takes account of the effect of the elastic body adjacent to the fault plane, falls off with distance $r$ as $1∕r^3$. Comparison is made with the properties of the corresponding short-range models studied earlier. Seismic spatiotemporal correlations of the long-range models generally tend to be weaker than those of the short-range models. The magnitude distribution exhibits a “near-critical” behavior, i.e., a power-law-like behavior close to the Gutenberg-Richter law, for a wide parameter range with its $B$-value, $B\simeq 0.55$, insensitive to the model parameters, in sharp contrast to that of the 2D short-range model and those of the 1D short-range and long-range models where such a near-critical behavior is realized only by fine tuning the model parameters. In contrast to the short-range case, the mean stress drop at a seismic event of the long-range model is nearly independent of its magnitude, consistent with the observation. Large events often accompany foreshocks together with a doughnutlike quiescence as their precursors, while they hardly accompany aftershocks with almost negligible seismic correlations observed after the main shock.

By using a phase-field model, we simulate formation and growth of stripe arrays starting with anisotropic growth of islands under the Ehrlich-Schwoebel barrier on metal bcc(110) surfaces. The anisotropy is incorporated in terms of attachment kinetics that is locally limited at the island edge aligned to the $\mathit{y}$ axis (or $⟨100⟩$) and instantaneous at the island edge aligned to the $\mathit{x}$ axis (or $⟨110⟩$). By reproducing the stripe arrays under various anisotropy magnitudes, we investigate dynamics of formation and growth of the stripe arrays. While enhancing coarsening in the $\mathit{y}$ direction, the anisotropy suppresses coarsening in the $\mathit{x}$ direction at the early stage, which contributes to formation of stripe arrays. At long times, the stripe arrays develop the quasiperiodic uniaxial structure with the selected transversal slope and the decreasing longitudinal slope as consequence of competition between coarsening and roughening. At the case of the large anisotropy magnitude, the fast roughening is caused by the strongly limited attachment kinetics, where the transversal coarsening turns fast and then the uniaxial growth is broken finally. For the weak roughening at the case of the reduced anisotropy magnitude, the slow transversal coarsening is achieved with the fast longitudinal coarsening, which contributes to the stripe arrays of the regular period and the increasing uniaxial length. Such arrays have the potential to be used as templates to grow one-dimensional nanostructures.

The phase diagram of hard-core nematogenic models in three-dimensional space can be studied by means of Onsager’s theory, and, on the other hand, the critical properties of continuous interaction potentials can be investigated using the molecular field approach pioneered by Maier and Saupe. Comparison between these treatments shows a certain formal similarity, reflecting their common variational root; on this basis, hard-core potential models can be mapped onto continuous ones, via their excluded volume. Some years ago, this line of reasoning had been applied to hard spherocylinders, hence the continuous potential $G\left(\tau \right)=a+b\sqrt{1-{\tau }^2},$ $b>0$ had been used to define a mesogenic model on a three-dimensional lattice [S. Romano, Int. J. Mod. Phys. B 9, 85 (1995)]; in the formula, $\tau$ denotes the scalar product between the two unit vectors defining particle orientations. Here we went on by addressing the same interaction potential on a two-dimensional lattice. Our analysis based on extensive Monte Carlo simulations found evidence of a topological transition, and the critical behavior in its vicinity was studied in detail. Results obtained for the present model were compared with those already obtained in the literature for interaction potentials defined by Legendre polynomials of second and fourth orders in the scalar product $\tau$.

In this study, active mixing in a microchannel with spatiotemporal variations in $\zeta$ potential distributions was investigated theoretically. In this mixing system, the primary flow is a pressure-driven flow (i.e., parabolic flow), and the electro-osmotic recirculating rolls induced by the heterogeneous $\zeta$ potential distributions act as the perturbation source. By timewise alterations of two different electro-osmotic recirculating flow fields, chaotic mixing can be induced. Blob deformation, Poincaré map, and Lyapunov exponent analyses were employed to describe the behaviors of the particle motion in this active mixing system. Finally, the optimal time-switching period was identified, which was also verified through direct numerical simulations.

This paper is devoted to studying wave-particle interaction at “double resonance” condition, i.e., when two waves interact resonantly with the same group of charged particles. A theoretical Hamiltonian model and a symplectic numerical code are built to describe the three-dimensional interactions of wave spectra with resonant electrons in a magnetized plasma. Related simulations on the evolution of two waves of close parallel phase velocities interacting resonantly with particles’ fluxes have been performed, which reveal some common features which do not depend on the kind of waves, instabilities, and particles’ distributions: after the stage of linear instability, when the waves’ amplitudes saturate due to particle trapping, a nonlinear process takes place which is characterized by a quasiperiodical exchange of energy between the waves, depending in particular on the value of the mismatch between the waves’ resonant velocities. In order to explain such observations, a simple Hamiltonian model describing the interaction of two different waves of close resonant velocities with a periodical train of bunches of trapped particles moving synchronously has been built. It allows one to describe the nonlinear characteristics of this process as well as to estimate analytically its time scale and shows a good agreement with the numerical simulation results.

The influence of the space charge of ions emitted from the surface of a conical spike on its shape has been studied. The problem of the calculation of the spatial distributions of the electric field, ion velocity field, and the space charge density near the cone tip has been reduced to the analysis of a system of ordinary differential equations. As a result of numerical solution of these equations, the criterion for the balance of the capillary and electrostatic forces on the conic surface of a liquid-metal anode has been determined. It has allowed us to relate the electrical current flowing through the system, the applied potential difference, and the cone angle. We have compared the results of our calculations with available experimental data concerning emission from the surface of pure liquid gallium, indium, tin, and some liquid alloys, such as $\text{Au}+\text{Si}$, $\text{Co}+\text{Ge}$, and $\text{Au}+\text{Ge}$. On the basis of the proposed model, explanations have been given for a number of specific features of the emissive behavior of different systems.

A lattice Boltzmann scheme is developed for homogeneous mixture modeling, based on the multiple-relaxation-time (MRT) formulation, which fully recovers the Maxwell-Stefan diffusion model in the continuum limit with (a) external force and (b) tunable Schmidt number. The theoretical basis of the proposed MRT formulation is a recently proposed Bhatnagar-Gross-Krook-type kinetic model for gas mixtures [Andries et al., J. Stat. Phys. 106, 993 (2002)] and it substantially extends the applicability of a scheme already proposed by the same author, which used only one relaxation parameter. The recovered equations at the macroscopic level are derived by an innovative expansion technique, based on the Grad moment system. Some numerical simulations are reported for the solvent test case with external force, aiming to find the numerical ranges for the transport coefficients that ensure acceptable accuracies. The numerical results reduce the theoretical expectations, which are based on a strong separation among the characteristic scales.

The ground states of Lennard-Jones (LJ) clusters are estimated by finding the Gaussian wave packets that minimize the energy functional. A “phase diagram” for ${\text{LJ}}_n$ as a function of size $\left(n=31,\dots ,45\right)$ and de Boer quantum delocalization length $\left(\Lambda \in \left[0;0.3\right]\right)$ is constructed, showing the stability ranges for the two competing structural motifs, the Mackay and anti-Mackay icosahedra. An increase of $\Lambda$ has an effect similar to heating and as such may induce structural transformations.

Recent single-molecule experiments found that the thioredoxin-catalyzed reduction of individual disulfide bonds placed under a stretching mechanical force has distinct characteristics: the reduction rate of human thioredoxin monotonically decreases with the force, while the rate of E. coli thioredoxin first decreases and then increases as the force goes beyond a certain threshold. In this work, we present a force-dependent two-pathway four-state model to uniformly quantify these intriguing observations. Although our model is indistinguishable from the previous two-pathway three-state model in predicting the mean reduction rate, the distributions of dwell times of the two models are significantly distinctive. The very recent experiment favors our model.

Real-time fluorescence measurements have been developed for measuring the fractal dimension $d_f$ and critical exponents $\gamma$ and $\beta$ simultaneously during the sol-gel transition of acrylamide bisacrylamide cross-linking copolymerization. We observed that $d_f$ passes through a minimum value of $\sim 2.5$ at a critical time $t_c$ and crossover to 3 above it. The exponents $\gamma$ and $\beta$, measured at $t_c$, were found to be around 1.8 and 0.45, respectively. All parameters $d_f$, $\beta$, and $\gamma$ measured at the critical point $t_c$ agree with three-dimensional percolation results.

We study the critical properties of the majority voter model on $d$-dimensional hypercubic lattices. In two dimensions, the majority voter model belongs to the same universality class as that of the Ising model. However, the critical behaviors of the majority voter model on four dimensions do not exhibit mean-field behavior. Using the Monte Carlo simulation on $d$-dimensional hypercubic lattices, we obtain the critical exponents up to $d=7$, and find that the upper critical dimension is 6 for the majority voter model. We also confirm our results using mean-field calculation.

We present the results of an experimental and numerical study of the distribution of the reflection coefficient $P\left(R\right)$ and the distributions of the imaginary $P\left(v\right)$ and the real $P\left(u\right)$ parts of the Wigner reaction $K$ matrix for irregular fully connected hexagon networks (graphs) in the presence of strong absorption. In the experiment we used microwave networks, which were built of coaxial cables and attenuators connected by joints. In the numerical calculations experimental networks were described by quantum fully connected hexagon graphs. The presence of absorption introduced by attenuators was modeled by optical potentials. The distribution of the reflection coefficient $P\left(R\right)$ and the distributions of the reaction $K$ matrix were obtained from measurements and numerical calculations of the scattering matrix $S$ of the networks and graphs, respectively. We show that the experimental and numerical results are in good agreement with the exact analytic ones obtained within the framework of random matrix theory.

We apply periodic orbit theory to a two-dimensional nonintegrable billiard system whose boundary is varied smoothly from a circular to an equilateral triangular shape. Although the classical dynamics becomes chaotic with increasing triangular deformation, it exhibits an astonishingly pronounced shell effect on its way through the shape transition. A semiclassical analysis reveals that this shell effect emerges from a codimension-2 bifurcation of the triangular periodic orbit. Gutzwiller’s semiclassical trace formula, using a global uniform approximation for the bifurcation of the triangular orbit and including the contributions of the other isolated orbits, describes very well the coarse-grained quantum-mechanical level density of this system. We also discuss the role of discrete symmetry for the large shell effect obtained here.

We study the stability of the steady state of coupled chaotic maps with randomly distributed time delays evolving on a random network. An analysis method is developed based on the peculiar mathematical structure of the Jacobian of the steady state due to time-delayed coupling, which enables us to relate the stability of the steady state to the locations of the roots of a set of lower-order bound equations. For $\delta$-distributed time delays (or fixed time delay), we find that the stability of the steady state is determined by the maximum modulus of the roots of a set of algebraic equations, where the only nontrivial coefficient in each equation is one of the eigenvalues of the normalized adjacency matrix of the underlying network. For general distributed time delays, we find a necessary condition for the stable steady state based on the maximum modulus of the roots of a bound equation. When the number of links is large, the nontrivial coefficients of the bound equation are just the probabilities of different time delays. Our study thus establishes the relationship between the stability of the steady state and the probability distribution of time delays, and provides a better way to investigate the influence of the distributed time delays in coupling on the global behavior of the systems.

We report experimental measurements of the acoustic emission associated with the bursting of a gas bubble at the free surface of a non-Newtonian fluid. On account of the viscoelastic properties of the fluid, the bubble is generally elongated. The associated frequency and duration of the acoustic signal are discussed with regard to the shape of the bubble and successfully accounted for by a simple linear model. The acoustic energy exhibits a high sensitivity to the dynamics of the thin film bursting, which demonstrates that, in practice, it is barely possible to deduce from the acoustic measurements the total amount of energy released by the event. Our experimental findings provide clues for the understanding of the signals from either volcanoes or foams, where one observes respectively, the bursting of giant bubbles at the free surface of lava and bubble bursting avalanches.

We present a stochastic Green function algorithm designed for bosons on lattices. This quantum Monte Carlo algorithm is independent of the dimension of the system, works in continuous imaginary time, and is exact (no error beyond statistical errors). Hamiltonians with several species of bosons (and one-dimensional Bose-Fermi Hamiltonians) can be easily simulated. Some important features of the algorithm are that it works in the canonical ensemble and gives access to $n$-body Green functions.

Entangled polymer melts exhibit a variety of flow instabilities that limit production rates in industrial applications. We present both experimental and computational findings, using flow of monodisperse linear polystyrenes in a contraction-expansion geometry, which illustrate the formation and development of one such flow instability. This viscoelastic disturbance is observed at the slit outlet and subsequently produces large-scale fluid motions upstream. A numerical linear stability study using the molecular structure based Rolie-Poly model confirms the instability and identifies important parameters within the model, which gives physical insight into the underlying mechanism. Chain stretch was found to play a critical role in the instability mechanism, which partially explains the effectiveness of introducing a low-molecular weight tail into a polymer blend to increase its processability.

We propose the self-organized relaxation process which drives a collisionless self-gravitating system to the equilibrium state satisfying local virial (LV) relation. During the violent relaxation process, particles can move widely within the time interval as short as a few free-fall times, because of the effective potential oscillations. Since such particle movement causes further potential oscillations, it is expected that the system approaches the critical state where such particle activities, which we call gravitational fugacity, is independent of the local position as much as possible. Here we demonstrate that gravitational fugacity can be described as the functional of the LV ratio, which means that the LV ratio is a key ingredient estimating the particle activities against gravitational potential. We also demonstrate that the LV relation is attained if the LV ratio exceeds the critical value $b=1$ everywhere in the bound region during the violent relaxation process. The local region which does not meet this criterion can be trapped into the presaturated state. However, small phase-space perturbation can bring the inactive part into the LV critical state.