We experimentally investigate the multitime scale diffusion and the spatiotemporal behaviors of the degrees of enhancement for the longitudinal and the transverse diffusions in a confined mesoscopic quasi-two-dimensional dusty-plasma liquid sheared by two parallel counterpropagating laser beams. The steady external drive directly enhances the longitudinal cooperative hopping, associated with the shear bands that have high shear rate near boundaries. It drastically excites the slow hopping modes to high fluctuation level in the outer band region, accompanied by the enhanced superdiffusion. Through cascaded many-body interaction, the excitation flows from the outer region toward the center region, from the longitudinal modes to the transverse mode, and from the slow hopping modes to the fast caging modes, which are in better contact with the thermal bath. It causes the weaker enhancement of fluctuation level, and diffusion for the center region and the fast modes. The boundary confinement further breaks the system symmetry and enhances anisotropy. It has much stronger effect on the suppression of the transverse hopping modes than the longitudinal hopping mode. The degrees of enhancement of the fluctuations by the shear stress are highly anisotropic for the large amplitude slow modes, especially in the outer region but are more isotropic in the inner band.

The implementation of Monte Carlo methods acting in the quantum phase space is hindered by the fact that quantum phase-space information is available only through quasiprobability densities. In this work, we present a first-principles Monte Carlo method employing a hidden variables representation. This allows the full quantum time evolution of an arbitrary initial quantum state to be calculated by a classical Monte Carlo algorithm, even for systems subjected to time-dependent potentials. Guidelines for implementing a practical algorithm are presented.

Developing effective descriptions of the microscopic dynamics of many physical phenomena can both dramatically enhance their computational exploration and lead to a more fundamental understanding of the underlying physics. Previously, an effective description of a driven interface in the presence of mobile impurities, based on an Ising variant model and a single empirical coarse variable, was partially successful [M. Haataja et al., Phys. Rev. Lett. 92, 160603 (2004)]; yet it underlined the necessity of selecting additional coarse variables in certain parameter regimes. In this paper we use a data mining approach to help identify the coarse variables required. We discuss the implementation of this diffusion map approach, the selection of a similarity measure between system snapshots required in the approach, and the correspondence between empirically selected and automatically detected coarse variables. We conclude by illustrating the use of the diffusion map variables in assisting the atomistic simulations and we discuss the translation of information between fine and coarse descriptions using lifting and restriction operators.

We address a standard class of diffusion processes with linear drift and quadratic diffusion coefficients. These contributions to dynamic equations can be directly drawn from data time series. However, real data are constrained to finite sampling rates and therefore it is crucial to establish a suitable mathematical description of the required finite-time corrections. Based on Itô-Taylor expansions, we present the exact corrections to the finite-time drift and diffusion coefficients. These results allow to reconstruct the real hidden coefficients from the empirical estimates. We also derive higher-order finite-time expressions for the third and fourth conditional moments that furnish extra theoretical checks for this class of diffusion models. The analytical predictions are compared with the numerical outcomes of representative artificial time series.

In this paper we investigate the nature of the singularity of the Ising model of the four-dimensional cubic lattice. It is rigorously known that the specific heat has critical exponent $\alpha =0$ but a nonrigorous field-theory argument predicts an unbounded specific heat with a logarithmic singularity at $T_c$. We find that within the given accuracy the canonical ensemble data are consistent both with a logarithmic singularity and a bounded specific heat but that the microcanonical ensemble lends stronger support to a bounded specific heat. Our conclusion is that either much larger system sizes are needed for Monte Carlo studies of this model in four dimensions or the field-theory prediction of a logarithmic singularity is wrong.

The Maier-Saupe hard-sphere fluid is one of the simplest models that accounts for the isotropic-nematic transition characteristic of liquid crystal phases. At low temperatures the model is known to present a gas-liquid-like transition with a large difference between the densities of the coexistence phases, whereas at higher temperature the transition becomes a weak first-order transition resembling the typical order-disorder (nematic-isotropic) phase change of liquid crystals. Spatial dimensionality directly conditions the character of the orientational phase change (i.e., the high temperature transition), that goes from a first-order transition in the purely three-dimensional case, to a Berezinskii-Kosterlitz-Thouless-like continuous transition which occurs when the three dimensional Maier-Saupe spins are constrained to lie on a plane. In the latter instance, the ordered phase is not endowed with true long-range order. In this work we investigate how the continuous transition transforms into a true first-order phase change, by analyzing the phase behavior of a system of three dimensional Maier-Saupe hard spheres confined between two parallel plates, with separations ranging from the quasi-two-dimensional regime to the bulk three-dimensional limit. Our results indicate that spatial confinement in one direction induces the change from first order to a continuous transition with a corresponding decrease of the transition temperatures. As to the gas-liquid transition, the estimated “critical” temperatures and densities also decrease as the fluid is confined, in agreement with previous results for other simple systems.

We experimentally study the level of organization of dendritic sidebranching in directional solidification. For this, we extract successive interface positions at a fixed distance from the dendrite tips and we perform various correlation analyses. The sidebranching signals appear composed of randomly distributed bursts in which sidebranching coherence is surprisingly large and robust. This is attested by the large autocorrelation found in single bursts and the large cross-correlation found in any couple of bursts, even belonging to different sides of a dendrite or to different dendrites. However, the phase coherence of sidebranching breaks down at the transition between bursts. This restricts the coherence of extended sidebranching signals to a mean burst length and prevents the occurrence of large scale cross-correlation between them. This balanced view on sidebranching coherence stresses the capability of self-organization of dendrites in material science and sheds light on the nature of sidebranching on curved growing forms.

An achiral fixed bent-core nematic liquid crystal in an antiparallel aligned planar device is observed to form three distinct domains. Regions are observed which are achiral planar, as well as domains displaying both positive and negative chirality that are stable over a significant temperature interval. In such a device the presence of spontaneous positive and negatively twisted domains is highly unusual. By studying the electro-optics of the device relevant director structures are inferred, and it is additionally found that a sufficiently large applied electric field will drive the chiral domains into the achiral state.

Conical inclusions in a lipid bilayer generate an overall spontaneous curvature of the membrane that depends on concentration and geometry of the inclusions. Examples are integral and attached membrane proteins, viruses, and lipid domains. We propose an analytical model to study budding and vesiculation of the lipid bilayer membrane, which is based on the membrane bending energy and the translational entropy of the inclusions. If the inclusions are placed on a membrane with similar curvature radius, their repulsive membrane-mediated interaction is screened. Therefore, for high inclusion density the inclusions aggregate, induce bud formation, and finally vesiculation. Already with the bending energy alone our model allows the prediction of bud radii. However, in case the inclusions induce a single large vesicle to split into two smaller vesicles, bending energy alone predicts that the smaller vesicles have different sizes whereas the translational entropy favors the formation of equal-sized vesicles. Our results agree well with those of recent computer simulations.

We report the formation of a ringlike structure in the flow of particular non-Newtonian liquids coating a rotating vertical disk. Experiments were performed with a known volume of the liquid and at varying rotation rates such that the inertial effects were negligible. The liquid injected on the rotating disk initially coats the surface uniformly, which then redistributes itself such that at steady state a significant amount collected into a circular ring, off center with the axis of rotation. Beyond a critical rotation speed and for a given liquid volume, the ring formation did not occur. The ring formation was not observed in the case of Newtonian liquids. Rheological measurements along with the shear rate calculations suggest that the shear thinning nature of the liquids could be responsible for the observed ring formation.

Based on the Reynolds averaged Navier-Stokes (RANS) equations and the time-averaged continuity equation, a theory of turbulent shear flow over an undulating sand bed is developed addressing the instability criterion of plane sand beds in free-surface flows leading to the formation of sand waves. In the analysis, the integration of RANS equations leads to generalized Saint Venant equations, in which the time-averaged streamwise velocity is characterized by a power law obtained from turbulence closure, treating the curvilinear streamlines by the Boussinesq approximation. As a consequence, the modified pressure distribution has a departure from the traditionally linear hydrostatic pressure distribution. The instability analysis of a plane sand bed yields the curves of the Froude number versus nondimensional wave number, determining an instability zone for which at lower Froude numbers (less than 0.8), the plane bed becomes unstable with the formation of dunes; whereas at higher Froude numbers, the plane bed becomes unstable with the formation of standing waves and antidunes. For higher Froude numbers, the experimental data for antidunes lie within the unstable zone; while for lower Froude numbers, the same is found for dunes with some experimental scatter.

The dynamics of an initially localized Anderson mode is studied in the framework of the nonlinear Schrödinger equation in the presence of disorder. It is shown that the dynamics can be described in the framework of the Liouville operator. An analytical expression for a wave function of the initial time dynamics is found by a perturbation approach. As follows from a perturbative solution the initially localized wave function remains localized. At asymptotically large times the dynamics can be described qualitatively in the framework of a phenomenological probabilistic approach by means of a probability distribution function. It is shown that the probability distribution function may be governed by the fractional Fokker-Planck equation and corresponds to subdiffusion.

Quantized systems whose underlying classical dynamics possess an elaborate mixture of regular and chaotic motion can exhibit rather subtle long-time quantum transport phenomena. In a short wavelength regime where semiclassical theories are most relevant, such transport phenomena, being quintessentially interference based, are difficult to understand with the system’s specific long-time classical dynamics. Fortunately, semiclassical methods applied to wave packet propagation can provide a natural approach to understanding the connections, even though they are known to break down progressively as time increases. This is due to the fact that some long-time transport properties can be deduced from intermediate-time behavior. Thus, these methods need only retain validity and be carried out on much shorter time scales than the transport phenomena themselves in order to be valuable. The initial value representation of the semiclassical propagator of Herman and Kluk [Chem. Phys. 91, 27 (1984)] is heavily used in a number of molecular and atomic physics contexts, and is of interest here. It is known to be increasingly challenging to implement as the underlying classical chaos strengthens, and we ask whether it is possible to implement it well enough to extract the kind of intermediate-time information that reflects wave packet localization at long times. Using a system of two coupled quartic oscillators, we focus on the localizing effects of transport barriers formed by stable and unstable manifolds in the chaotic sea and show that these effects can be captured with the Herman-Kluk propagator.

Single vehicle data obtained from magnetic loops on an expressway allowed us to measure velocity correlations and velocity differences between non–neighbor vehicles on the same lane, showing some strong correlations even for platoons of 7 or 8 vehicles. The corresponding time headway distribution for non–neighbor vehicles is also presented. We were also able to get some informations about interlane structures, through crossed time headway distributions. It should be noticed that these last results on crossed time headways are meaningful only because the subset of data we used corresponds to a unique stationary traffic state and still contains a large amount of data, with a large fraction of short time headways. The link with passing maneuvers is discussed.

We introduce a simple model of a growing system with $m$ competing communities. The model corresponds to the phenomenon of defeats suffered by social groups living in isolation. A nonequilibrium phase transition is observed when at critical time $t_c$ the first isolated cluster occurs. In the one-dimensional system the volume of the new phase, i.e., the number of the isolated individuals, increases with time as $Z\sim t^3$. For a large number of possible communities, the critical density of filled space is equal to ${\rho }_c={\left(m/N\right)}^{1/3}$, where $N$ is the system size. A similar transition is observed for Erdős-Rényi random graphs and Barabási-Albert scale-free networks. Analytical results are in agreement with numerical simulations.

We analyze a system-level model for lytic repression of $\lambda$ phage in E. coli using reliability theory, showing that the repressor circuit comprises four redundant components whose failure mode is prophage induction. Our model reflects the specific biochemical mechanisms involved in regulation, including long-range cooperative binding, and its detailed predictions for prophage induction in E. coli under ultraviolet radiation are in good agreement with experimental data.

We introduce a framework wherein various measurements of a pulse-coupled network’s stationary dynamics can be expanded in terms of the network’s connectivity. Such measurements include the occurrence rate of pulses (e.g., firing rates within a neuronal network) as well as higher-order correlations in activity between various nodes in the network. The various terms in this expansion can be interpreted as diagrams corresponding to subnetworks of the original network, which span both space (in terms of the network’s graph) as well as time (in the sense of causality).

By using the techniques developed for generating high-speed droplets, we have systematically investigated binary droplet collision when the Weber number (We) was increased from the range usually tested in previous studies on the order of 10 to a much larger value of about 5100 for water (a droplet at 23 m/s with a diameter of 0.7 mm). Various liquids were also used to explore the effects of viscosity and surface tension. Specifically, beyond the well-known regimes at moderate We’s, which exhibited coalescence, separation, and separation followed by satellite droplets, we found different behaviors showing a fingering lamella, separation after fingering, breakup of outer fingers, and prompt splattering into multiple secondary droplets as We was increased. The critical Weber numbers that mark the boundaries between these impact regimes are identified. The specific impact behaviors, such as fingering and prompt splattering or splashing, share essential similarity with those also observed in droplet-surface impacts, whereas substantial variations in the transition boundaries may result from the disparity of the boundary conditions at impacts. To compare the outcomes of both types of collisions, a simple model based on energy conservation was carried out to predict the maximum diameter of an expanding liquid disk for a binary droplet collision. The results oppose the dominance of viscous drag, as proposed by previous studies, as the main deceleration force to effect a Rayleigh-Taylor instability and ensuing periphery fingers, which may further lead to the formations of satellite droplets.

Nanoscale fluid flow systems involve both microscopic and macroscopic parameters, which compete with each another and lead to different flow regimes. In this work, we investigate the interactions of four fundamental parameters, including the fluid-fluid, fluid-wall binding energies, temperature of the system, and driving force, and their effects on the flow motion in nanoscale Poiseuille flows. By illustrating the fluid flux as a function of a dimensionless number, which represents the effective surface effect on the fluid, we show that the fluid motion in nanochannels falls into different regimes, each of which is associated with a distinct mechanism. The mechanisms in different situations reveal the effects of the parameters on the fluid dynamics.