We carried out a molecular-dynamics (MD) study of the self-diffusion tensor of a Lennard-Jones-type fluid, confined in a slit pore with attractive walls. We developed Bayesian equations, which modify the virtual layer sampling method proposed by Liu, Harder, and Berne (LHB) [P. Liu, E. Harder, and B. J. Berne, J. Phys. Chem. B 108, 6595 (2004)]. Additionally, we obtained an analytical solution for the corresponding nonhomogeneous Langevin equation. The expressions found for the mean-squared displacement in the layers contain naturally a modification due to the mean force in the transverse component in terms of the anisotropic diffusion constants and mean exit time. Instead of running a time consuming dual MD-Langevin simulation dynamics, as proposed by LHB, our expression was used to fit the MD data in the entire survival time interval not only for the parallel but also for the perpendicular direction. The only fitting parameter was the diffusion constant in each layer.

We enumerate and classify nearly all of the possible mechanically stable (MS) packings of bidipserse mixtures of frictionless disks in small sheared systems. We find that MS packings form continuous geometrical families, where each family is defined by its particular network of particle contacts. We also monitor the dynamics of MS packings along geometrical families by applying quasistatic simple shear strain at zero pressure. For small numbers of particles $\left(N<16\right)$, we find that the dynamics is deterministic and highly contracting. That is, if the system is initialized in a MS packing at a given shear strain, it will quickly lock into a periodic orbit at subsequent shear strain, and therefore sample only a very small fraction of the possible MS packings in steady state. In studies with $N>16$, we observe an increase in the period and random splittings of the trajectories caused by bifurcations in configuration space. We argue that the ratio of the splitting and contraction rates in large systems will determine the distribution of MS-packing geometrical families visited in steady state. This work is part of our long-term research program to develop a master-equation formalism to describe macroscopic slowly driven granular systems in terms of collections of small subsystems.

The spatial distribution of structural relaxation in a supercooled liquid is studied using molecular dynamics simulations of a two-dimensional binary mixture. It is shown that the spatial heterogeneity of the relaxation along with the time scale of the relaxation is determined, not by the frequency with which particles move a distance $\pi /2k_{\text{Bragg}}$, but by the frequency with which particles can achieve persistent displacements. We show that these persistent displacements are achieved through the coupled action of local reorganizations and unrecoverable thermal strains.

Cooperative jump motions are studied for mutually interacting particles in a one-dimensional periodic potential. The diffusion constant for the cooperative motion in systems including a small number of particles is numerically calculated and it is compared with theoretical estimates. We find that the size distribution of the cooperative jump motions obeys an exponential law in a large system.

Coupling (or connection) in complex systems is of crucial importance in determining the system’s dynamics and realizing certain system’s functions. In this work, we propose a coupling form, partial time-delay coupling in coupled oscillator systems, in which some oscillators are time-delay coupled and the others remain instantaneously coupled, and study its impact on dynamics. We find that the partial time-delay coupling greatly enlarges the domain of oscillation death island in parameter space. In particular, the smaller the ratio $p$ of time-delay coupled oscillators, the larger death island is. For a sufficiently large system, a universal amplification scaling, $R=p^{-1}\left(0<p\le 1\right)$, is uncovered. These findings are proved to be very general and suggest that a tiny amount of time-delay couplings in coupled systems may tremendously change the dynamics of whole systems.

Three-dimensional x-ray tomography is performed to investigate the internal structure and its evolution of a crumpled aluminum foil ball. The upper and lower bounds of the internal geometric fractal dimension are determined, which increase with the compression. Contrary to the simulation results, we find that the mass distribution changes from being inhomogeneous to uniform. Corroborated with the evidence from previous experiments, these findings support the physical picture that the elastic property precedes the plastic one at dominating the deformation and mechanical response for all crumpled structures. We show that the interior of a crumpled ball at the plastic regime can be mapped to the compact packing of a granular system.

We propose a method for the reconstruction of time-delayed feedback systems from time series. The method is based on the analysis of the system response to a weak external disturbance having the form of rectangular pulses. To apply the method one must have access to the state variable of the system in order to perturb it and the time series of the driving signal and the system response having at least about one hundred points on the time interval equal to the delay time. The method is intended to recover delays in low-order time-delay systems performing periodic oscillations, but can also be applied to systems in chaotic regimes in the presence of high level of noise. We verify the method by applying it to both numerical and experimental data.

Turbulent motion increases very significantly the collision rate between particles in dilute suspensions. In the case of heavy inertial particles, the collision rate enhancement results both from the intermittent concentration in the flow, and also from the large relative velocity between colliding particles. The latter effect is a consequence of the ejection of particles out of curved streamlines, denoted here as the “sling effect.” Here, we quantitatively study the collision rate between heavy particles in the presence of gravity, with the simplified synthetic model of turbulent flow known as kinematic simulation. Monitoring the velocity of colliding particles and comparing it with the local velocity gradient of the flow of particles allowed us to identify the collision induced by the sling effect and to evaluate their contribution to the total collision rate. Our numerical results are then systematically compared with the estimates based on the properties of particle trajectories in the flow recently proposed by Falkovich and Pumir [G. Falkovich and A. Pumir, J. Atmos. Sci. 64, 4497 (2007)]. At moderate values of the Stokes numbers $\left(\text{St}\lesssim 1\right)$, we demonstrate that the resulting parametrization describes quantitatively correctly the collision rate, and that the sling effect can be responsible for up to $\sim 50\%$ of the total collision rate.

This paper studies the occurrence of record events in score populations which grow stochastically in time. In Rényi’s basic record model, a population of independent and identically distributed (i.i.d.) random scores grows deterministically—a single new score being added at each time step. Rényi’s record theorem asserts that the resulting record events are independent, and that their occurrence probabilities decrease harmonically in time. Moreover, Rényi’s result is universal—being independent of the distribution of the i.i.d. random scores. This paper considers an arbitrary stochastic growth of the score population—allowing the number of the i.i.d. random scores added at each time step to follow arbitrary stochastic dynamics. Exploring the stochastic growth model we: (i) establish a general analog of Rényi’s record theorem; (ii) show that universality with respect to the distribution of the i.i.d. random scores is maintained; (iii) compute the distribution of the waiting times for record events; (iv) analyze the dependencies/independencies of the record events; and (v) analyze the aging/stationarity of the record events.

The temporal autocorrelation (AC) function associated with monitoring order parameters characterizing conformational fluctuations of an enzyme is analyzed using a collection of surrogate models. The surrogates considered are phenomenological stochastic differential equation (SDE) models. It is demonstrated how an ensemble of such surrogate models, each surrogate being calibrated from a single trajectory, indirectly contains information about unresolved conformational degrees of freedom. This ensemble can be used to construct complex temporal ACs associated with a “non-Markovian” process. The ensemble of surrogates approach allows researchers to consider models more flexible than a mixture of exponentials to describe relaxation times and at the same time gain physical information about the system. The relevance of this type of analysis to matching single-molecule experiments to computer simulations and how more complex stochastic processes can emerge from a mixture of simpler processes is also discussed. The ideas are illustrated on a toy SDE model and on molecular-dynamics simulations of the enzyme dihydrofolate reductase.

Thermally induced variation in wetting ability in a confined nanoenvironment, indicated by the change in infiltration pressure as water molecules enter a model single-walled carbon nanotube submerged in aqueous environment, is investigated using molecular dynamics simulations. The temperature-dependent infiltration behavior is impacted in part by the thermally excited radial oscillation of the carbon nanotube, and in part by the variations of fundamental physical properties at the molecular level, including the hydrogen bonding interaction. The thermal effect is also closely coupled with the nanotube size effect and loading rate effect. Manipulation of the thermally responsive infiltration properties could facilitate the development of a next-generation thermal energy converter based on nanoporous materials.

Suspensions containing noncolloidal aluminum particles in a Newtonian carrier liquid and the effects of shear history on the rheological properties of suspensions are investigated showing a critical concentration ${\varphi }_c$, which is close to the “freezing” packing fraction of spherical particle suspensions. An apparent liquid-to-solid transition was clearly found for suspensions below ${\varphi }_c$ via transient step shear after long shear history as well as via the large amplitude oscillatory shear flow with controlled shear stress. The microstructures or the local flow characteristics of suspensions with $\varphi <{\varphi }_c$ and with $\varphi >{\varphi }_c$ are still different according to the Fourier Transform Rheological analysis. Although suspensions with $\varphi <{\varphi }_c$ show solidlike behaviors after long shear history, the flow behaviors keep unchanged as shear stress increases, and typically show solidlike, liquid-solid coexistence, liquidlike, and jamming behaviors, successively. However, liquidlike regime of concentrated suspensions with $\varphi >{\varphi }_c$ disappears after preshear.

We analyze the dynamics of the parallel mutation-selection quasispecies model with a changing environment. For an environment with the sharp-peak fitness function in which the most fit sequence changes by $k$ spin flips every period $T$, we find analytical expressions for the minimum and maximum mutation rates for which a quasispecies can survive, valid in the limit of large sequence size. We find an asymptotic solution in which the quasispecies population changes periodically according to the periodic environmental change. In this state we compute the mutation rate that gives the optimal mean fitness over a period. We find that the optimal mutation rate per genome, $k/T$, is independent of genome size, a relationship which is observed across broad groups of real organisms.

Electrical characterization of a nonthermal radio-frequency atmospheric-pressure microplasma in a parallel plate configuration has shown that reducing electrode gap into the submillimeter range increases current and power density at a reduced voltage as compared to similar plasmas at larger electrode gaps which have no gap dependence. Calculation of sheath thickness and electric fields in the sheath and in the bulk demonstrate a dependence on the electrode gap as it is reduced into the submillimeter regime, indicating a distinct regime of operation.

We study the impact of strain localization on the stability of frictional slipping in dense amorphous materials. We model the material using shear transformation zone (STZ) theory, a continuum approximation for plastic deformation in amorphous solids. In the STZ model, the internal state is quantified by an effective disorder temperature, and the effective temperature dynamics capture the spontaneous localization of strain. We study the effect of strain localization on stick-slip instabilities by coupling the STZ model to a noninertial spring slider system. We perform a linear stability analysis to generate a phase diagram that connects the small scale physics of strain localization to the macroscopic stability of sliding. Our calculations determine the values of spring stiffness and driving velocity where steady sliding becomes unstable and we confirm our results through numerical integration. We investigate both homogeneous deformation, where no shear band forms, and localized deformation, where a narrow shear band spontaneously forms and accommodates all of the deformation. Our results show that at a given velocity, strain localization leads to unstable frictional sliding at a much larger spring stiffness compared to homogeneous deformation, and that localized deformation cannot be approximated by a homogeneous model with a narrower material. We also find that strain localization provides a physical mechanism for irregular stick-slip cycles in certain parameter ranges. Our results quantitatively connect the internal physics of deformation in amorphous materials to the larger scale frictional dynamics of stick-slip.

We report experimental observation of an instability in a Couette-Taylor flow of a polymer fluid in a thin gap between two coaxially rotating cylinders in a regime where their angular velocity decreases with the radius while the specific angular momentum increases with the radius. In the considered regime, neither the inertial Rayleigh instability nor the purely elastic instability is possible. We propose that the observed “elastorotational” instability is an analog of the magnetorotational instability which plays a fundamental role in astrophysical Keplerian accretion disks.

The hydrodynamic effect on a thin particle layer, which moves relative to fluid by an external force, is investigated theoretically and numerically. Because of the presence of layer ends, the arrangement of particles in the layer is anisotropic and the drag force acting on them varies according to the position. The resulting relative motion of particles brings about the spreading of the layer. We have studied such a diffusive behavior of particle layers, which have various internal arrangements. We have assumed a non-Brownian system in which the particles move relatively owing to only the variance of hydrodynamic force. The hydrodynamic force on each particle was calculated by Stokesian dynamics approach. The results show that the relative motion of particles is greatly influenced by the internal arrangement of the particle layer. In consequence, the overall diffusive motion of particle layer varies with the arrangement even if the particle concentration is similar. It is in contrast to the gradient diffusion of Brownian particles.

Two-point correlation functions of sufficiently diffuse wave fields generated by uncorrelated random sources are known to approximate deterministic Green’s functions between the two points. This property is utilized increasingly for passive imaging and remote sensing of the environment. Here we show that the relation between the Green’s functions and the noise cross-correlation function holds under much less restrictive conditions than previously thought. It can even hold when ambient noise sources have correlation ranges large compared to the wavelength. Admissible correlation ranges are limited from above by the size of the Fresnel zone at wave propagation between the points where noise cross correlation is evaluated.

We explore the penetration dynamics of an intruder in a granular medium composed of expanded polystyrene spherical particles. Three features distinguish our experiment from others studied so far in granular physics: (a) the impact is horizontal, decoupling the effects of gravity and the drag force; (b) the density of the intruder ${\rho }_i$ is up to 350 times larger than the density of the granular medium ${\rho }_m$; and (c) the way the intruder moves through the material, sliding at the bottom of the column with small friction. Under these conditions we find that the final penetration $D$ scales with $\left({\rho }_i/{\rho }_m\right)$ and the drag force $F_d$ and $D$ saturate with the height of the granular bed.