Face-centered cubic single crystals of $\sigma =1.55\mu \text{m}$ diameter hard-sphere silica colloidal particles were prepared by sedimentation onto (100) and (110) oriented templates. The crystals had a wide interface with the overlaying liquid that was parallel to the template. The location of the interface was determined by confocal microscopic location of the particles, followed by identification of the crystalline and liquid phases by a bond-orientation order parameter. Fluctuations in the height of the interface about its average position were recorded for several hundred configurations. The interfacial stiffness $\tilde{\gamma }$ was determined from the slope of the inverse squared Fourier components of the height profile vs the square of the wave number, according to the continuum capillary fluctuation method. The offset of the fit from the origin could quantitatively be accounted for by gravitational damping of the fluctuations. For the (100) interface, $\tilde{\gamma }=\left(1.3\pm 0.3\right)k_{B}T/{\sigma }^2$; for the (110) interface, $\tilde{\gamma }=\left(1.0\pm 0.2\right)k_{B}T/{\sigma }^2$. The interfacial stiffness of both interfaces was found to be isotropic in the plane. This is surprising for the (110), where crystallography predicts twofold symmetry. Sedimentation onto a (111) template yielded a randomly stacked hexagonal crystal with isotropic $\tilde{\gamma }=0.66k_{B}T/{\sigma }^2$. This value, however, is less reliable than the two others due to imperfections in the crystal.

The nonlinear Langevin equation theory of segmental relaxation, elasticity, and mechanical response of polymer glasses is extended to describe the coupled effects of physical aging, mechanical rejuvenation, and thermal history. The key structural variable is the amplitude of density fluctuations, and segmental dynamics proceeds via stress-modified activated barrier hopping on a dynamic free-energy profile. Mechanically generated disorder (rejuvenation) is quantified by a dissipative work argument and increases the amplitude of density fluctuations, thereby speeding up relaxation beyond that induced by the landscape tilting mechanism. The theory makes testable predictions for the time evolution and nonequilibrium steady state of the alpha relaxation time, density fluctuation amplitude, elastic modulus, and other properties. Model calculations reveal a rich dependence of these quantities on preaging time, applied stress, and temperature that reflects the highly nonlinear competition between physical aging and mechanical disordering. Thermal history is “erased” in the long-time limit, although the nonequilibrium steady state is not the literal “fully rejuvenated” freshly quenched glass. The present work provides the conceptual foundation for a quantitative treatment of the nonlinear mechanical response of polymer glasses under a variety of deformation protocols.

We examine the capability of mean square displacement (MSD) analysis to extract reliable values of the diffusion coefficient $D$ of a single particle undergoing Brownian motion in an isotropic medium in the presence of localization uncertainty. The theoretical results, supported by simulations, show that a simple unweighted least-squares fit of the MSD curve can provide the best estimate of $D$ provided an optimal number of MSD points are used for the fit. We discuss the practical implications of these results for data analysis in single-particle tracking experiments.

Confinement and wall effects are known to affect the kinematics and propulsive characteristics of swimming microorganisms. When a solid body is dragged through a viscous fluid at constant velocity, the presence of a wall increases fluid drag, and thus the net force required to maintain speed has to increase. In contrast, recent optical trapping experiments have revealed that the propulsive force generated by human spermatozoa is decreased by the presence of boundaries. Here, we use a series of simple models to analytically elucidate the propulsive effects of a solid boundary on passively actuated filaments and model flagella. For passive flexible filaments actuated periodically at one end, the presence of the wall is shown to increase the propulsive forces generated by the filaments in the case of displacement-driven actuation, while it decreases the force in the case of force-driven actuation. In the case of active filaments as models for eukaryotic flagella, we demonstrate that the manner in which a solid wall affects propulsion cannot be known a priori, but is instead a nontrivial function of the flagellum frequency, wavelength, its material characteristics, the manner in which the molecular motors self-organize to produce oscillations (prescribed activity model or self-organized axonemal beating model), and the boundary conditions applied experimentally to the tethered flagellum. In particular, we show that in some cases, the increase in fluid friction induced by the wall can lead to a change in the waveform expressed by the flagella, which results in a decrease in their propulsive force.

A spatially continuous force-based model for simulating pedestrian dynamics is introduced which includes an elliptical volume exclusion of pedestrians. We discuss the phenomena of oscillations and overlapping which occur for certain choices of the forces. The main intention of this work is the quantitative description of pedestrian movement in several geometries. Measurements of the fundamental diagram in narrow and wide corridors are performed. The results of the proposed model show good agreement with empirical data obtained in controlled experiments.

We propose a phase-space Wigner harmonics entropy measure for many-body quantum dynamical complexity. This measure, which reduces to the well-known measure of complexity in classical systems and which is valid for both pure and mixed states in single-particle and many-body systems, takes into account the combined role of chaos and entanglement in the realm of quantum mechanics. The effectiveness of the measure is illustrated in the example of the Ising chain in a homogeneous tilted magnetic field. We provide numerical evidence that the multipartite entanglement generation leads to a linear increase in entropy until saturation in both integrable and chaotic regimes, so that in both cases the number of harmonics of the Wigner function grows exponentially with time. The entropy growth rate can be used to detect quantum phase transitions. The proposed entropy measure can also distinguish between integrable and chaotic many-body dynamics by means of the size of long-term fluctuations which become smaller when quantum chaos sets in.

The dynamics of escape from an attractive state due to random perturbations is of central interest to many areas in science. Previous studies of escape in chaotic systems have rather focused on the case of unbounded noise, usually assumed to have Gaussian distribution. In this paper, we address the problem of escape induced by bounded noise. We show that the dynamics of escape from an attractor’s basin is equivalent to that of a closed system with an appropriately chosen “hole.” Using this equivalence, we show that there is a minimum noise amplitude above which escape takes place, and we derive analytical expressions for the scaling of the escape rate with noise amplitude near the escape transition. We verify our analytical predictions through numerical simulations of two well-known two-dimensional maps with noise.

Recently, a new algorithm for the computation of covariant Lyapunov vectors and of corresponding local Lyapunov exponents has become available. Here we study the properties of these still unfamiliar quantities for a simple model representing a harmonic oscillator coupled to a thermal gradient with a two-stage thermostat, which leaves the system ergodic and fully time reversible. We explicitly demonstrate how time-reversal invariance affects the perturbation vectors in tangent space and the associated local Lyapunov exponents. We also find that the local covariant exponents vary discontinuously along directions transverse to the phase flow.

Statistical properties of nonsymmetric real random matrices of size $M$, obtained as truncations of random orthogonal $N\times N$ matrices, are investigated. We derive an exact formula for the density of eigenvalues which consists of two components: finite fraction of eigenvalues are real, while the remaining part of the spectrum is located inside the unit disk symmetrically with respect to the real axis. In the case of strong nonorthogonality, $M/N=\text{const}$, the behavior typical to real Ginibre ensemble is found. In the case $M=N-L$ with fixed $L$, a universal distribution of resonance widths is recovered.

We show, using molecular-dynamics simulations, that a two-dimensional Lennard-Jones solid exhibits droplet fluctuations characterized by nonaffine deviations from local crystallinity. The fraction of particles in these droplets increases as the mean density of the solid decreases and approaches $\approx 20\mathrm{\%}$ of the total number in the vicinity of the fluid-solid phase boundary. We monitor the geometry, local equation of state, density correlations, and Van Hove functions of these droplets. We provide evidence that these nonaffine heterogeneities should be interpreted as being droplet fluctuations from nearby metastable minima. The local excess pressure of the droplets plotted against the local number density shows a van der Waal loop with distinct branches corresponding to fluidlike compact and stringlike glassy droplets. The distinction between fluidlike and glassy droplets disappears above a well-defined temperature.

Directed transport in ratchets is determined by symmetry breaking in a system out of equilibrium. A hallmark of rocking ratchets is current reversals: an increase in the rocking force changes the direction of the current. In this work for a biharmonically driven spatially symmetric rocking ratchet we show that a class of current reversal is precisely determined by symmetry breaking, thus creating a link between dynamical and symmetry-breaking mechanisms.

We investigate experimentally a Casimir-like effect in a three-dimensional pile of rice, which has a power-law avalanche size distribution. We observe the change in distance between two Plexiglas sheets placed on the pile parallel to each other and parallel to the mean avalanche flow direction, while rice grains are continuously and uniformly falling on top of the pile. The resulting avalanches are fluctuations, confinement of which is found to drive the two plates together. During 25-h experimental runs, for initial intersheet distances ranging from 20.0 to 90.0 mm we observe changes in the range from 6.0 mm to less than 1.0 mm. A similar distance dependence is obtained from a simple analytical model.

A model of homonuclear dimer adsorption in terms of two possible molecule orientations with respect to the surface on a square lattice has been constructed and studied. The dimers can occupy one or two sites on the lattice. The thermodynamics of this system has been studied by transfer-matrix and Monte Carlo methods. The phase diagram has been constructed. It was shown that in the vicinity of the tricritical point the coverage as a function of chemical potential possesses a minimum. This phenomenon seems to be the common one for molecules with several ways of adsorption.

In this paper we investigate the coarsening dynamics of liquid crystal textures in a two-dimensional nematic under applied electric fields, using numerical simulations performed using a publicly available liquid crystal algorithm developed by the authors. We consider both positive and negative dielectric anisotropies and two different possibilities for the orientation of the electric field (parallel and perpendicular to the two-dimensional lattice). We determine the effect of an applied electric field pulse on the evolution of the characteristic length scale and other properties of the liquid crystal texture network. In particular, we show that different types of defects are produced after the electric field is switched on, depending on the orientation of the electric field and the sign of the dielectric anisotropy.

A set of precise measurements of UV-Vis absorption spectrum for the classical bent-shaped molecule, P-12-OPIMB, revealed that molecular exciton interactions exist even in the mesophases of this system, as manifested as an obvious and abrupt change in the positional and spectral shape at phase-transition points. Based on Kasha’s molecular exciton model, we successfully conducted a quantitative analysis of the spectral shift and could determine the local structure of the B4 phase. To the best of our knowledge, such a spectroscopic analysis for the liquid crystals has not been connected with the local structure.

The existence of uniaxial liquid crystals comprising polar molecules, with all the dipoles aligned in a parallel pattern, is classically ruled out. Generally, there are two different avenues to a mean-field theory for liquid crystals: one is based on short-range, repulsive, steric forces, and the other is based on long-range, globally attractive, dispersion forces. Purely polar steric interactions have been shown to have the potential of inducing unexpected orientationally ordered states. In real molecules, anisotropies both in shape and in polarizability coexist; it has been shown that dispersion forces interaction can be combined with hard-core repulsion in a formal theory, based on a steric tensor. Starting from this, we build an interaction Hamiltonian featuring the average electric dipolar energy exchanged between molecules with the same excluded region. Under the assumption that the molecular shape is spheroidal, we propose a mean-field model for polar nematic liquid crystals which can exhibit both uniaxial and biaxial polar phases. By means of a numerical bifurcation analysis, we discuss the stability of the equilibrium against the choice of two model parameters, one describing the degree of molecular shape biaxiality and the other describing the relative orientation of the electric dipole within each molecule. We find only uniaxial stable phases, which are effectively characterized by a single scalar order parameter.

We find a transformation in the probability density of intensity for light transmitted through stacks of glass slides of increasing thickness from one-dimensional (1D) to quasi-1D statistics. We argue that this represent a crossover to universal first order intensity statistics beyond 1D associated with the appearance of phase singularities at intensity nulls in the speckle pattern.

We study the dynamical properties of the propagation of innovation on a two-dimensional lattice, random network, scale-free network, and Cayley tree. In order to investigate the diversity of technological level, we study the scaling property of width, $W\left(N,t\right)$, which represents the root mean square of the technological level of agents. Here, $N$ is the total number of agents. From the numerical simulations, we find that the steady-state value of $W\left(N,t\right)$, $W_{sat}\left(N\right)$, scales as $W_{sat}\left(N\right)\sim N^{-1/2}$ when the system is in a flat ordered phase for $d\ge 2$. In the flat ordered phase, most of the agents have the same technological level. On the other hand, when the system is in a smooth disordered phase, the value of $W_{sat}\left(N\right)$ does not depend on $N$. These behaviors are completely different from those observed on a one-dimensional (1D) lattice. By considering the effect of the underlying topology on the propagation dynamics for $d\ge 2$, we also provide a mean-field analysis for $W_{sat}\left(N\right)$, which agrees very well with the observed behaviors of $W_{sat}\left(N\right)$. This directly shows that the morphological properties in order-disorder transition on a 1D lattice is completely different from that on higher dimensions. It also provides an evidence that the upper critical dimension for the roughening transition of the propagation of innovation is $d_u=2$.

Rotating spiral waves appear ubiquitously in a wide range of nonlinear systems, and they play important roles in many biological phenomena. Recently, unusual spiral waves, which support period-2 dynamics, have been found in several different systems including cardiac tissues as well as nonlinear chemical reaction-diffusion systems. They are potentially significant as an intermediate dynamic state linking regularly rotating period-1 spiral waves to complex dynamic states such as cardiac fibrillations; for example, it is intrinsic of period-2 spiral waves to have “line defects” and their instability can lead to a spatiotemporal chaos. Previous mathematical models regarding period-2 spiral waves are mostly based on a coupled system of period-2 oscillators, but these are inappropriate for the description of a large class of systems that are composed of (nonoscillatory) excitable elements—a good example being the heart. In this paper we hypothesize that excitable media, which support a nonmonotonic conduction velocity dispersion relation, can sustain period-2 oscillatory spiral waves. We explicitly demonstrate that the new mechanism can create period-2 spirals by computer simulations on a simple mathematical model describing spiral wave front dynamics.

Finding unstable periodic orbits (UPOs) is always a challenging demand in biophysics and computational biology, which needs efficient algorithms. To meet this need, an approach to locating unstable periodic orbits in chaotic dynamical system is presented. The uniqueness of the approach lies in the introduction of adaptive rules for both feedback gain and time delay in the system without requiring any information of the targeted UPO periods a priori. This approach is theoretically validated under some mild conditions and successfully tested with some practical strategies in several typical chaotic systems with or without significant time delays.