We generalize a recent study of random space-filling bearings to a more realistic situation, where the spacing offset varies randomly during the space-filling procedure, and show that it reproduces well the size distributions observed in recent studies of real fault gouges. In particular, we show that the fractal dimensions of random polydisperse bearings sweep predominantly the low range of values in the spectrum of fractal dimensions observed along real faults, which strengthen the evidence that polydisperse bearings may explain the occurrence of seismic gaps in nature. In addition, the influence of different distributions on the offset is studied and we find that a uniform distribution is the best choice for reproducing the size distribution of fault gouges.

The reliable and objective assessment of chronic disease state has been and still is a very significant challenge in clinical medicine. An essential feature of human behavior related to the health status, the functional capacity, and the quality of life is the physical activity during daily life. A common way to assess physical activity is to measure the quantity of body movement. Since human activity is controlled by various factors both extrinsic and intrinsic to the body, quantitative parameters only provide a partial assessment and do not allow for a clear distinction between normal and abnormal activity. In this paper, we propose a methodology for the analysis of human activity pattern based on the definition of different physical activity time series with the appropriate analysis methods. The temporal pattern of postures, movements, and transitions between postures was quantified using fractal analysis and symbolic dynamics statistics. The derived nonlinear metrics were able to discriminate patterns of daily activity generated from healthy and chronic pain states.

We present some numerical results obtained from a simple individual-based model that describes clustering of organisms caused by competition. Our aim is to show that, even when a deterministic description developed for continuum models predicts no pattern formation, an individual-based model displays well-defined patterns, as a consequence of fluctuation effects caused by the discrete nature of the interacting agents.

We establish a general semiquantitative phase-space picture of the classical nonlinear response in a strongly chaotic system. As opposed to the case of stable dynamics, the response functions decay exponentially at long times. Damped oscillations in response functions are attributed to collective resonances which do not correspond to any periodic classical motions. We calculate analytically the second-order response in a simple chaotic system and demonstrate the relevance of the concept for the interpretation of spectroscopic data.

Highly heterogeneous degree distributions yield efficient spreading of simple epidemics through networks, but can be inefficient with more complex epidemiological processes. We study diseases with nonlinear force of infection whose prevalences can abruptly collapse to zero while decreasing the transmission parameters. We find that scale-free networks can be unable to support diseases that, on the contrary, are able to persist at high endemic levels in homogeneous networks with the same average degree.

We report strong evidence of remarkably close periodic repetitions of the structuring of the parameter space of a damped-driven Duffing oscillator as the amplitude of the drive increases. Families of period-adding cascades and some intricate networks of periodic oscillations embedded in chaotic phases are also found to recur closely as the driving force grows. Such surprising regularities suggest that some hitherto unknown renormalization mechanism may be operating in higher codimension, controlling the alternation of chaos and order in parameter space of certain flows.

A universal analytical expression for the supercritical bifurcation shape of transverse one-dimensional (1D) systems in the presence of additive noise is given. The stochastic Langevin equation of such systems is solved by using a Fokker-Planck equation, leading to the expression for the most probable amplitude of the critical mode. From this universal expression, the shape of the bifurcation, its location, and its evolution with the noise level are completely defined. Experimental results obtained for a 1D transverse Kerr-type slice subjected to optical feedback are in excellent agreement.

The hydrodynamic behavior observed for a sphere released under gravity in a Newtonian liquid is not consistent with that predicted by classical continuum theory when the sphere is near a solid wall. An irreversibility arises in the velocity of the sphere as it approaches and recedes from the plane that cannot be accounted for using continuum hydrodynamic equations alone. Earlier experiments on spheres falling from a plane were conducted under conditions such that this irreversibility could be attributed to the surface roughness of the spheres. In this investigation, we extend these studies to situations where the pressure field between the receding sphere and the plane drops to the vapor pressure of the fluid and cavitation occurs. Experimental data supports the theoretical prediction for a sphere’s motion based on the irreversible effect of cavitation.

A classical problem in elasticity theory involves an inhomogeneity embedded in a material of given stress and shear moduli. The inhomogeneity is a region of arbitrary shape whose stress and shear moduli differ from those of the surrounding medium. In this paper we present a semianalytic method for finding the stress tensor for an infinite plate with such an inhomogeneity. The solution involves two conformal maps, one from the inside and the second from the outside of the unit circle to the inside, and respectively outside, of the inhomogeneity. The method provides a solution by matching the conformal maps on the boundary between the inhomogeneity and the surrounding material. This matching converges well only for relatively mild distortions of the unit circle due to reasons which will be discussed in the article. We provide a comparison of the present result to known previous results.

Although several thermal lattice Boltzmann models have been proposed, this method has not yet been shown to be able to describe nonisothermal fully compressible flows in a satisfactory manner, mostly due to the presence of important deviations from the advection-diffusion macroscopic equations and also due to numerical instabilities. In this context, this paper presents a linear stability analysis for some lattice Boltzmann models that were recently derived as discrete forms of the continuous Boltzmann equation [P. C. Philippi, L. A. Hegele, Jr., L. O. E. dos Santos, and R. Surmas, Phys. Rev. E 63, 056702 (2006)], in order to investigate the sources of instability and to find, for each model, the upper and lower limits for the macroscopic variables, between which it is possible to ensure a stable behavior. The results for two-dimensional (2D) lattices with 9, 17, 25, and 37 velocities indicate that increasing the order of approximation of the lattice Boltzmann equation enhances stability. Results are also presented for an athermal 2D nine-velocity model, the accuracy of which has been improved with respect to the standard D2Q9 model, by adding third-order terms in the lattice Boltzmann equation.

Stochastic resonance (SR) is theoretically investigated for a double quantum dot system represented by two discrete levels in respective wells. The system is driven by a periodic signal and a white noise source with variable amplitude, and thus displays an improved output signal-to-noise ratio, a characteristic signature of SR.

We measure the dependence of the interparticle force $F$ on the distance $R$ between two colloidal particles with hyperbolic hedgehog defects in a nematic liquid crystal using optical tweezers. The particle-defect pair can be regarded as an elastic “dipole” in the electrostatic analogy. In a parallel configuration, where the dipole vectors are parallel with each other, $F$ is attractive and proportional to $R^{-4}$. However, $F$ becomes repulsive at small $R$ due to the existence of a defect between the particles. In an antiparallel configuration, where the particles directly face each other, $F$ is repulsive over the whole range of $R$ and proportional to $R^{-3.6}$. In another antiparallel configuration, where two hyperbolic hedgehog defects directly face each other, $F$ is proportional to $R^{-3.6}$ and $F$ at small $R$ turns out to be attractive upon tilting the dipoles. Furthermore, we yield the force between particles connected by a stringlike defect called a bubblegum defect.

Grand canonical and canonical ensembles become equivalent in the thermodynamic limit, but when the system size is finite the results obtained in the two ensembles deviate from each other. In many important cases, the canonical ensemble provides an appropriate physical description but it is often much easier to perform the calculations in the corresponding grand canonical ensemble. We present a method to compute averages in the canonical ensemble based on calculations of the expectation values in the grand canonical ensemble. The number of particles, which is fixed in the canonical ensemble, is not necessarily the same as the average number of particles in the grand canonical ensemble.

In this paper, site percolation on random ${\Phi }^3$ planar graphs is studied by Monte Carlo numerical techniques. The method consists in randomly removing a fraction $q=1-p$ of vertices from graphs generated by Monte Carlo simulations, where $p$ is the occupation probability. The resulting graphs are made of clusters of occupied sites. By measuring several properties of their distribution, it is shown that percolation occurs for an occupation probability above a percolation threshold $p_c=0.7360\left(5\right)$. Moreover, critical exponents are compatible with those analytically known for bond percolation.

We present a numerical method for the Monte Carlo simulation of uncoupled continuous-time random walks with a Lévy $\alpha$-stable distribution of jumps in space and a Mittag-Leffler distribution of waiting times, and apply it to the stochastic solution of the Cauchy problem for a partial differential equation with fractional derivatives both in space and in time. The one-parameter Mittag-Leffler function is the natural survival probability leading to time-fractional diffusion equations. Transformation methods for Mittag-Leffler random variables were found later than the well-known transformation method by Chambers, Mallows, and Stuck for Lévy $\alpha$-stable random variables and so far have not received as much attention; nor have they been used together with the latter in spite of their mathematical relationship due to the geometric stability of the Mittag-Leffler distribution. Combining the two methods, we obtain an accurate approximation of space- and time-fractional diffusion processes almost as easy and fast to compute as for standard diffusion processes.

In the force-ramp mode of the atomic force microscope, the force with which a macromolecule is stretched is increased linearly in time by properly controlling the motion of the cantilever through a feedback loop. Using a master equation approach for the coupled cantilever-macromolecule system, we mimic such a feedback loop, to study nonequilibrium effects in the measurements of force-extension curves and fluctuations. In particular, it is shown that the fluctuations are the same for force-ramp experiments and for the more commonly used constant velocity experiments. Thus the exact same statistics suffice for the explanation of either experiment. Specific results are presented for the stretching of Dextran.

In this work the dynamics of a chain consisting of a set of beads attached to the ends of segments of fixed lengths is investigated. The chain fluctuates at constant temperature in a viscous medium. For simplicity, all interactions among the beads have been switched off and the number of spatial dimensions has been limited to two. In the limit in which the chain becomes a continuous system, its behavior may be described by a path integral, in which the rigid constraints coming from the infinitesimally small segments are imposed by means of a functional $\delta$ function. In this way a model of the dynamics of the chain is obtained, which closely resembles a two-dimensional nonlinear $\sigma$ model. The partition function of this generalized nonlinear $\sigma$ model is computed explicitly for a ring-shaped chain in the semiclassical approximation. The behavior of the chain at both long and short scales of time and distances is investigated. The connection between the generalized nonlinear $\sigma$ model presented here and the Rouse model is discussed.

The problem of temporal localization and directional mapping of the dynamic interdependencies between parts of a complex system is addressed. We present a technique that weights the sampled values so as to minimize the mutual prediction error between pairs of measured signals. The reliability of the detected intermittent causal interactions is maximized by (a) smoothing the weight landscape through regularization, and (b) using a nonlinear (polynomial) variant of the conventional embedding vector. The effectiveness of the proposed technique is demonstrated by studying three numerical examples of dynamically coupled chaotic maps and by comparing it with two other measures of causal dependency.

Fast adiabatic plasma heating of a thin solid target irradiated by a high intensity laser has been observed by an optical fast interferometry diagnostic. It is driven by the hot electron current induced by the laser plasma interaction at the front side of the target. Radial and longitudinal temperature profiles are calculated to reproduce the observed rear-side plasma expansion. The main parameters of the suprathermal electrons (number, temperature, and divergence) have been deduced from these observations.