We discuss the stability properties of a one-dimensional hard-point gas. We study the decay of the Loschmidt echo which describes the stability of the motion under system perturbations. We show a universal behavior in the echo decay which is intimately connected to the linear dynamical instability of the motion. In particular, in spite of such a weak instability, the asymptotic decay follows a simple exponential law.

A local time-splitting method (LTSM) is developed to design absorbing boundary conditions for numerical solutions of time-dependent nonlinear Schrödinger equations associated with open boundaries. These boundary conditions are significant for numerical simulations of propagations of nonlinear waves in physical applications, such as nonlinear fiber optics and Bose-Einstein condensations. Numerical examples are implemented to demonstrate the attractive features of using the LTSM.

The one-dimensional motion of a massless Brownian particle on a symmetric periodic substrate can be rectified by reinjecting its driving noise through a realistic recycling procedure. If the recycled noise is multiplicatively coupled to the substrate, the ensuing feedback system works like a passive Maxwell’s daemon, capable of inducing a net current that depends on both the delay and the autocorrelation times of the noise signals. Extensive numerical simulations show that the underlying rectification mechanism is a resonant nonlinear effect: The observed currents can be optimized for an appropriate choice of the recycling parameters with immediate application to the design of nanodevices for particle transport.

We present theoretical investigation on the high-frequency collective dynamics in liquids and glasses at microscopic length scales and in the terahertz frequency region based on the mode-coupling theory for ideal liquid-glass transition. We focus on recently investigated issues from inelastic-x-ray-scattering and computer-simulation studies for dynamic structure factors and longitudinal and transversal current spectra: the anomalous dispersion of the high-frequency sound velocity and the nature of the low-frequency excitation called the boson peak. It will be discussed how the sound mode interferes with other low-lying modes present in the system. Thereby, we provide a systematic explanation of the anomalous sound-velocity dispersion in systems—ranging from high temperature liquid down to deep inside the glass state—in terms of the contributions from the structural-relaxation processes and from vibrational excitations called the anomalous-oscillation peak (AOP). A possibility of observing negative dispersion—the decrease of the sound velocity upon increase of the wave number—is argued when the sound-velocity dispersion is dominated by the contribution from the vibrational dynamics. We also show that the low-frequency excitation, observable in both of the glass-state longitudinal and transversal current spectra at the same resonance frequency, is the manifestation of the AOP. As a consequence of the presence of the AOP in the transversal current spectra, it is predicted that the transversal sound velocity also exhibits the anomalous dispersion. These results of the theory are demonstrated for a model of the Lennard-Jones system.

Quasi-two-dimensional bidisperse amorphous systems of steel beads are fluidized by a uniform upflow of air, so that the beads roll on a horizontal plane. The short-time ballistic motion of the beads is stochastic, with non-Gaussian speed distributions and with different average kinetic energies for the two species. The approach to jamming is studied as a function of increasing bead area fraction and also as a function of decreasing air speed. The structure of the system is measured in terms of both the Voronoi tessellation and the pair distribution function. The dynamics of the system is measured in terms of both displacement statistics and the density of vibrational states. These quantities all exhibit tell-tale features as the dynamics become more constrained closer to jamming. In particular the pair distribution function and the Voronoi cell shape distribution function both develop split peaks. And the mean-squared displacement develops a plateau of subdiffusive motion separating ballistic and diffusive regimes. Though the system is driven and athermal, this behavior is remarkably reminiscent of that in dense colloidal suspensions and supercooled liquids. One possible difference is that kurtosis of the displacement distribution peaks at the beginning of the subdiffusive regime.

The hydrogen-bond geometries in water and polycrystalline ice $\mathrm{I}h$ are studied using synchrotron radiation-based Compton scattering data of unprecedented statistical accuracy and consistency. By combining the experimental data with model calculations utilizing density functional theory, we show that the technique provides unique and complementary information on hydrogen bonding in water. The comparison of water and ice indicates the necessity of including a local intra-intermolecular geometric correlation for water, relating the intramolecular $\mathrm{O}\text{−}\mathrm{H}$ bond length to the corresponding hydrogen-bond geometry. By using the hydrogen-bond geometries obeying this correlation, we demonstrate a further constraint on the angular distortions of the hydrogen bonds in water.

An x-ray specular reflectivity (XR) and off-specular diffuse scattering (XDS) study of the coupled thermal capillary fluctuations and the intrinsic profiles of two interacting fluid-fluid interfaces is presented. The measurements are carried out on complete wetting films of perfluoromethylcyclohexane (PFMC) on the surface of bulk liquid eicosane (C20), as a function of film thickness $30<D<160\mathrm{\AA }$. In order to facilitate the analysis and interpretation of the data with minimal complexity, approximate methods for calculating scattering intensities are developed to take into account the subtleties of thermal diffuse scattering from layered liquid surfaces. With these methods, the calculations of XR/XDS intensities are reduced to a single numerical integration of simple functions in real space. In addition, an analytic expression is derived for small-angle XR that contains Debye-Waller-like factors with effective capillary roughness and takes into account the partial correlations of the two interfaces. The expression for the XR is quantitatively accurate so long as the reflection angle is small enough that the scattering from interfaces is distinguishable from bulk scattering. The results of the XR and XDS data analysis indicate that the capillary fluctuations at the two interfaces of the wetting films are partially correlated and their coupling is consistent with the van der Waals interactions. The relatively large intrinsic width $(4\sim 6\mathrm{\AA })$ of the liquid-liquid interface observed for thicker films $(D\gtrsim 50\mathrm{\AA })$ is comparable to the value expected for the bulk liquid-liquid interface $(D\to \infty )$, determined by either the radius of gyration $\left(5.3\mathrm{\AA }\right)$ or the bulk correlation length $\left(4.8\mathrm{\AA }\right)$ of the alkane C20. The intrinsic liquid-vapor interfacial width is sharper $(\sim 2\mathrm{\AA })$ and remains essentially constant over the entire probed range of $D$.

We study adsorption of liquid at a one-dimensional substrate composed of a single chemical inhomogeneity of width $2L$ placed on an otherwise homogeneous, planar, solid surface. The excess point free energy $\eta (L,T)$ associated with the adsorbed layer’s inhomogeneity induced by the substrate’s chemical structure is calculated within exact continuum transfer-matrix approach. It is shown that the way $\eta (L,T)$ varies with $L$ depends sensitively on the temperature regime. It exhibits logarithmic divergence as a function of $L$ in the limit $L\to \infty$ for temperatures such that the chemical inhomogeneity is completely wetted by the liquid. In the opposite case $\eta (L,T)$ converges for large $L$ to $2{\eta }_0$, where ${\eta }_0$ is the corresponding point tension, and the dominant $L$-dependent correction to $2{\eta }_0$ decays exponentially. The interaction between the liquid layer inhomogeneities at $-L$ and $L$ for the two temperature regimes is discussed and compared to earlier mean-field theory predictions.

We present a general theory of liquid crystals under inhomogeneous electric field in a Ginzburg-Landau scheme. The molecular orientation can be deformed by electric field when the dielectric tensor is orientation dependent. We then investigate the influence of a charged particle on the orientation order in a nematic state. The director is aligned either along or perpendicular to the local electric field around the charge, depending on the sign of the dielectric anisotropy. The deformation becomes stronger with increasing the ratio $Ze∕R$, where $Ze$ is the charge and $R$ is the radius of the particle. Numerical analysis shows the presence of defects around the particle for large $Ze∕R$. They are nanometer-scale defects for microscopic ions. If the dielectric anisotropy is positive, a Saturn ring defect appears. If it is negative, a pair of point defects appear apart from the particle surface, each being connected to the surface by a disclination line segment.

We model the spontaneous assembly of a capsid (a virus’ closed outer shell) from many copies of identical units, using entirely irreversible steps and only information local to the growing edge. Our model is formulated in terms of (i) an elastic Hamiltonian with stretching and bending stiffness and a spontaneous curvature, and (ii) a set of rate constants for the addition of new units or bonds. An ensemble of highly irregular capsids is generated, unlike the well-known icosahedrally symmetric viruses, but (we argue) plausible as a way to model the irregular capsids of retroviruses such as HIV. We found that (i) the probability of successful capsid completion decays exponentially with capsid size; (ii) capsid size depends strongly on spontaneous curvature and weakly on the ratio of the bending and stretching elastic stiffnesses of the shell; (iii) the degree of localization of Gaussian curvature (a measure of facetedness) depends heavily on the ratio of elastic stiffnesses.

Lanthanide ions such as ${\mathrm{La}}^{3+}$ and ${\mathrm{Gd}}^{3+}$ are well known to have large effects on the structure of phospholipid membranes. Unilamellar vesicles of dipalmitoylphosphatidylcholine (DPPC) were prepared by sonication method and confirmed by transmission electron microscopy. The effects of concentration of gadolinium ions ${\mathrm{Gd}}^{3+}$ on DPPC unilamellar vesicles in aqueous media were studied by different techniques. As physical techniques, photon correlation spectroscopy, electrophoretic mobility, and differential scanning calorimetry were used. The theoretical predictions of the colloidal stability of liposomes were followed using the Derjaguin-Landau-Verwey-Overbeek theory. Changes in the size of liposomes and high polydispersities values were observed as ${\mathrm{Gd}}^{3+}$ concentration increases, suggesting that this cation induces the aggregation of vesicles. Electrophoretic mobility measurements on unilamellar vesicles as a function of ${\mathrm{Gd}}^{3+}$ ion concentration show that the vesicles adsorb ${\mathrm{Gd}}^{3+}$ ions. Above ${\mathrm{Gd}}^{3+}$ concentrations of $0.1\mathrm{mol}{\mathrm{dm}}^{-3}$, the $\zeta$ potential and light scattering measurements indicate the beginning of aggregation process. For comparison with similar phospholipids, the zeta potential of phosphatidylcholine interacting with ${\mathrm{Gd}}^{3+}$ was measured, showing an analogous behavior. Differential scanning calorimetry has been used to determine the effect of ${\mathrm{Gd}}^{3+}$ on the transition temperature $\left(T_c\right)$ and on the enthalpy $\left(\mathrm{\Delta }{H}_c\right)$ associated with the process.

A mechanism is proposed by which the patch of baroreceptors along the inner curvature of the arch of the aorta can sense hemodynamic events occurring downstream from the aortic arch, in the periphery of the arterial tree. Based on a solution of equations governing the elastic movements of the aortic wall, it is shown that the pressure distribution along the patch of baroreceptors has the same functional form as the distribution of strain along the patch. The significance of these findings are discussed, particularly as they relate to the possibility of a neuromechanical basis of essential hypertension.

We present a continuous time generalization of a random walk with complete memory of its history [Phys. Rev. E 70, 045101(R) (2004)] and derive exact expressions for the first four moments of the distribution of displacement when the number of steps is Poisson distributed. We analyze the asymptotic behavior of the normalized third and fourth cumulants and identify new transitions in a parameter regime where the random walk exhibits superdiffusion. These transitions, which are also present in the discrete time case, arise from the memory of the process and are not reproduced by Fokker-Planck approximations to the evolution equation of this random walk.

We consider propagation models that describe the spreading of an attribute, called “damage,” through the nodes of a random network. In some systems, the average fraction of nodes that remain undamaged vanishes in the large system limit, a phenomenon we refer to as exhaustive percolation. We derive scaling law exponents and exact results for the distribution of the number of undamaged nodes, valid for a broad class of random networks at the exhaustive percolation transition and in the exhaustive percolation regime. This class includes processes that determine the set of frozen nodes in random Boolean networks with in-degree distributions that decay sufficiently rapidly with the number of inputs. Connections between our calculational methods and previous studies of percolation beginning from a single initial node are also pointed out. Central to our approach is the observation that key aspects of damage spreading on a random network are fully characterized by a single function, specifying the probability that a given node will be damaged as a function of the fraction of damaged nodes. In addition to our analytical investigations of random networks, we present a numerical example of exhaustive percolation on a directed lattice.

The knowledge of real-life traffic patterns is crucial for a good understanding and analysis of transportation systems. These data are quite rare. In this paper we propose an algorithm for extracting both the real physical topology and the network of traffic flows from timetables of public mass transportation systems. We apply this algorithm to timetables of three large transportation networks. This enables us to make a systematic comparison between three different approaches to construct a graph representation of a transportation network; the resulting graphs are fundamentally different. We also find that the real-life traffic pattern is very heterogenous, in both space and traffic flow intensities, which makes it very difficult to approximate the node load with a number of topological estimators.

Columnar jointing is a fracture pattern common in igneous rocks in which cracks self-organize into a roughly hexagonal arrangement, leaving behind an ordered colonnade. We report observations of columnar jointing in a laboratory analog system, desiccated corn starch slurries. Using measurements of moisture density, evaporation rates, and fracture advance rates as evidence, we suggest that an advective-diffusive system is responsible for the rough scaling behavior of columnar joints. This theory explains the order of magnitude difference in scales between jointing in lavas and in starches. We investigated the scaling of average columnar cross-sectional areas due to the evaporation rate, the analog of the cooling rate of igneous columnar joints. We measured column areas in experiments where the evaporation rate depended on lamp height and time, in experiments where the evaporation rate was fixed using feedback methods, and in experiments where gelatin was added to vary the rheology of the starch. Our results suggest that the column area at a particular depth is related to both the current conditions, and hysteretically to the geometry of the pattern at previous depths. We argue that there exists a range of stable column scales allowed for any particular evaporation rate.

We present an analysis of the statistical properties and growth of the free on-line encyclopedia Wikipedia. By describing topics by vertices and hyperlinks between them as edges, we can represent this encyclopedia as a directed graph. The topological properties of this graph are in close analogy with those of the World Wide Web, despite the very different growth mechanism. In particular, we measure a scale-invariant distribution of the in and out degree and we are able to reproduce these features by means of a simple statistical model. As a major consequence, Wikipedia growth can be described by local rules such as the preferential attachment mechanism, though users, who are responsible of its evolution, can act globally on the network.

The study of the information flow through communication networks, such as the Internet, is of great importance. In the Internet, information flows in discrete units (“packets”), and the capacity of storage and processing of information of computers is finite. Thus if there are many packets walking on the network at the same time, they will interfere with each other. To understand this, we propose an idealized model, in which many particles move randomly on the network, and the nodes support limited numbers of particles. The maximum number of packets supported by a node can be any positive integer, and can be different for each node. We analyze the statistical properties of this model, obtaining analytical expressions for the mean occupation of each node, for different network topologies. The analytical results are shown to be in agreement with numerical simulations.