Data on wealth distributions in trading markets show a power law behavior $x^{-(1+\alpha )}$ at the high end, where, in general, $\alpha$ is greater than 1 (Pareto’s law). Models based on kinetic theory, where a set of interacting agents trade money, yield power law tails if agents are assigned a saving propensity. In this paper we are solving the inverse problem, that is, in finding the saving propensity distribution which yields a given wealth distribution for all wealth ranges. This is done explicitly for two recently published and comprehensive wealth datasets.

In this Rapid communication, we show, with colloidal probe atomic force microscopy(AFM) measurements, that the formation and subsequent disruption of polymer bridges between two solid surfaces is characterized by slow relaxation times. This is due to the retardation of polymer dynamics near a surface. For colloidal particles that are in constant (Brownian) motion kinetic aspects are key. To understand these effects, we develop a model of polymer bridging and bridge disruption that agrees quantitatively with our experiments.

A unified derivation of the off-equilibrium fluctuation dissipation relations (FDRs) is given for Ising and continuous spins to arbitrary order, within the framework of Markovian stochastic dynamics. Knowledge of the FDRs allows one to develop zero field algorithms for the efficient numerical computation of the response functions. Two applications are presented. In the first one, the problem of probing for the existence of a growing cooperative length scale is considered in those cases, like in glassy systems, where the linear FDR is of no use. The effectiveness of an appropriate second order FDR is illustrated in the test case of the Edwards-Anderson spin glass in one and two dimensions. In the second application, the important problem of the definition of an off-equilibrium effective temperature through the nonlinear FDR is considered. It is shown that, in the case of coarsening systems, the effective temperature derived from the second order FDR is consistent with the one obtained from the linear FDR.

Calcium release from intracellular stores plays a key role in the regulation of a variety of cellular activities. In various cell types this release occurs through inositol-triphosphate $\left({\mathrm{IP}}_3\right)$ receptors which are ${\mathrm{Ca}}^{2+}$ channels whose open probability is modulated by the cytosolic ${\mathrm{Ca}}^{2+}$ concentration itself. Thus, the combination of ${\mathrm{Ca}}^{2+}$ release and ${\mathrm{Ca}}^{2+}$ diffusion evokes a variety of ${\mathrm{Ca}}^{2+}$ signals depending on the number and relative location of the channels that participate of them. In fact, a hierarchy of ${\mathrm{Ca}}^{2+}$ signals has been observed in Xenopus laevis oocytes, ranging from very localized events (puffs and blips) to waves that propagate throughout the cell. In this cell type channels are organized in clusters. The behavior of individual channels within a cluster cannot be resolved with current optical techniques. Therefore, a combination of experiments and mathematical modeling is unavoidable to understand these signals. However, the numerical simulation of a detailed mathematical model of the problem is very hard given the large range of spatial and temporal scales that must be covered. In this paper we present an alternative model in which the cluster region is modeled using a relatively fine grid but where several approximations are made to compute the cytosolic ${\mathrm{Ca}}^{2+}$ concentration $\left(\left[{\mathrm{Ca}}^{2+}\right]\right)$ distribution. The inner-cluster $\left[{\mathrm{Ca}}^{2+}\right]$ distribution is used to determine the openings and closings of the channels of the cluster. The spatiotemporal $\left[{\mathrm{Ca}}^{2+}\right]$ distribution outside the cluster is determined using a coarser grid in which each (active) cluster is represented by a point source whose current is proportional to the number of open channels determined before. A full reaction-diffusion system is solved on this coarser grid.

We report on the high-temperature resolution measurements of the optical and thermal parameters of a liquid-crystal–silica nanoparticle colloid, as well as its video inspection, simultaneously performed in an upgraded photopyroelectric calorimeter. Over the nematic-isotropic coexistence region, the determined nematic correlation length, obtained from turbidity measurements, showed the characteristic two-step nematic nucleation process previously reported only for the specific heat.

We investigate experimentally the scaling properties of the number of nodal domains of the wave functions and the distribution of the nodal domain areas in a pseudointegrable barrier billiard. The number of nodal domains is smaller than expected for billiards whose dynamics is chaotic or regular. This reduction is explained by the appearance of superscars in the barrier billiard, i.e., regular structures, which are embedded into the underlying chaotic wave functions. Furthermore, the area distribution of nodal domains follows the predictions of a percolation model for chaotic systems.

Several experimental and numerical studies have shown that turbulent motions in circular pipe flow near transitional Reynolds numbers may not persist forever, but may decay. We study the properties of these decaying states within direct numerical simulations for Reynolds numbers up to 2200 and in pipes with lengths equal to 5, 9, and 15 times the diameter. We show that the choice of the ensemble of initial conditions affects the short time parts of lifetime distributions, but does not change the characteristic decay rate for long times. Comparing lifetimes for pipes of different length we notice a linear increase in the characteristic lifetime with length, which reproduces the experimental results when extrapolated to 30 diameters, the length of an equilibrium turbulent puff at these Reynolds numbers.

In this work, a molecular dynamics algorithm is proposed to study the transient and the stationary state of gravitational segregation in simple fluid mixtures. Both isothermal and stable nonisothermal (where thermodiffusion occurs) cases have been studied. This approach is applied extensively on a simple fluid model: Lennard-Jones mixtures composed of species differing only in their masses. First, using isothermal binary equimolar mixtures, it is shown that the molecular dynamics simulations provide stationary results consistent with the thermodynamic modeling in various thermodynamic conditions and for different gravity fields. Next, in stable nonisothermal mixtures heated from below, it is shown that the gravitational segregation and the thermodiffusion process (Soret effect) have an opposite effect on the concentration profiles along the fluid column. Then, molecular dynamics simulations are performed on ternary and ten-component mixtures. For these multicomponent nonisothermal mixtures, results obtained emphasize the fact that the way the thermodiffusion is estimated should be done with care. In addition, for all nonisothermal configurations, the simulation results confirm that the thermodiffusion may have a non-negligible influence on the concentration profile in a petroleum reservoir. Finally, by analyzing the transient behavior during the molecular dynamics simulations, it is shown that the dynamic of the gravitational segregation is unambiguously controlled by the mass diffusion.

We investigate the structure and mechanical behavior of assemblies of frictionless, nearly rigid equal-sized beads, in the quasistatic limit, by numerical simulation. Three different loading paths are explored: triaxial compression, triaxial extension, and simple shear. Generalizing a recent result, we show that the material, despite rather strong finite sample size effects, is able to sustain a finite deviator stress in the macroscopic limit, along all three paths, without dilatancy. The shape of the yield surface in principal stress space differs somewhat from the Mohr-Coulomb prediction, and is more adequately described by the Lade-Duncan or Matsuoka-Nakai criteria. We study geometric characteristics and force networks under varying stress levels within the supported range. Although the scalar state variables stay equal to the values observed in systems under isotropic pressure, the material, once subjected to a deviator stress, possesses some fabric and force distribution anisotropies. Each kind of anisotropy can be described, in good approximation, by a single parameter. Within the supported stress range, along each one of the three investigated stress paths, among those three quantities: deviator stress to mean stress ratio, fabric anisotropy parameter, force anisotropy parameter, any one determines the values of the two others. The pair correlation function also exhibits short range anisotropy, up to a distance between bead surfaces of the order of 10% of the diameter. The tensor of elastic moduli is shown to possess a nearly singular, uniaxial structure related to stress anisotropy. Possible stress-strain relations in monotonic loading paths are also discussed.

We develop a computational model to capture the complex, three-dimensional behavior of chemoresponsive polymer gels undergoing the Belousov-Zhabotinsky reaction. The model combines components of the finite difference and finite element techniques and is an extension of the two-dimensional gel lattice spring model recently developed by two of us [V. V. Yashin and A. C. Balazs, J. Chem. Phys. 126, 124707 (2007)]. Using this model, we undertake the first three-dimensional (3D) computational studies of the dynamical behavior of chemoresponsive BZ gels. For sufficiently large sample sizes and a finite range of reaction parameters, we observe regular and nonregular oscillations in both the size and shape of the sample that are coupled to the chemical oscillations. Additionally, we determine the critical values of these reaction parameters at the transition points between the different types of observed behavior. We also show that the dynamics of the chemoresponsive gels drastically depends on the boundary conditions at the surface of the sample. This 3D computational model could provide an effective tool for designing gel-based, responsive systems.

The structure of energy landscapes for a minimalist coarse-grained off-lattice protein model is presented to investigate the folding behaviors of heteropolymers. The obtained energy landscapes serve as a useful tool for visualization of the funnel-like structure of a considered system in the configuration space. Despite the simplicity of the model, the knowledge of the free-energy landscape enables us to show different folding characteristics known from real proteins and synthetic peptides, such as two-state folding and metastability.

It was recently demonstrated that one can reconstruct the impulse response between passive sensors by cross-correlating diffuse waves or ambient noise. Using seismic waves recorded on the moon, we show here that not only direct waves can be retrieved, but also late arrivals that have been scattered before reaching the seismometers. As these late arrivals propagate for a longer time, they are more sensitive to weak perturbations of the medium such as velocity changes. This high sensitivity of scattered waves is used to monitor periodic velocity changes in the lunar soil by measuring small delays of the passively retrieved coda waves. The velocity changes result from temperature variations due to periodic heating of the lunar surface by the sun.

Particle random motion can exhibit both anomalous diffusion and non-Gaussian statistics in some physical systems. Anomalous diffusion is quantified by a deviation from $\alpha =1$ in a power law for a particle’s mean-square displacement, $\mathrm{MSD}\propto {\left(\Delta t\right)}^{\alpha }$. A deviation from Gaussian statistics for a probability distribution function (PDF) is quantified by fitting to a $\kappa$ function or Tsallis distribution, with a fit parameter $q$. We report an experiment and simulations to test a theory that connects anomalous diffusion and non-Gaussian statistics. In the experiment, a single-layer dusty plasma, which behaved as a two-dimensional (2D) driven-dissipative system, had a non-Gaussian PDF. By adjusting an externally applied laser heating, $q$ was varied over a wide range. A correlation between the deviations from Gaussian statistics and normal diffusion for a 2D liquid was found in the experiment. This correlation indicates a connection between anomalous diffusion and non-Gaussian statistics. However, such a connection is lacking in equilibrium 2D Yukawa liquids, as demonstrated in numerical simulations.

We introduce a $2N$-parametric family of maximally superintegrable systems in $N$ dimensions, obtained as a reduction of an anisotropic harmonic oscillator in a $2N$-dimensional configuration space. These systems possess closed bounded orbits and integrals of motion which are polynomial in the momenta. They generalize known examples of superintegrable models in the Euclidean plane.

We establish an account of electromagnetic scattering by coated spheres with radial dielectric and magnetic anisotropy. Within full-wave scattering theory, we show that the total scattering cross section $Q_s$ is strongly dependent on both the dielectric anisotropy and magnetic anisotropy. As a consequence, by a suitable adjustment of the radius ratio, one may make the anisotropic coated particle nearly transparent or invisible. In the quasistatic case, we take one step forward to derive the effective permittivity and permeability for the coated particle, and the near-zero scattering radius ratio can be well described within effective medium theory. To one’s interest, the introduction of radial anisotropy is helpful to achieve better transparency quality such as a much smaller $Q_s$ and wider range of near-zero scattering ratio. Moreover, when the coated particle is anisotropic, the position of the near-zero scattering radius ratio can be tunable, resulting in a tunable electromagnetic cloaking.

We have investigated low Reynolds number flow past single dissipative-particle-dynamics particles (point centers of repulsion), their clusters, and their filaments using dissipative-particle-dynamics (DPD) simulations. The objective of our study was to verify whether DPD particles immersed in a sea of DPD particles behave like Langevin particles suspended in a continuous Newtonian fluid solvent, the basis of Brownian dynamics. Our principal test is to compare two effective DPD radii calculated by independent means. From the calculated coefficients of self-diffusion and viscosity the Stokes-Einstein equation yields an intrinsic radius, and from simulations of flow past a single fixed DPD particle a second radius is calculated from Stokes law. In the limit of small Reynolds number the two radii were found to approach each other. Hydrodynamic interactions were studied with Stokes flow past two DPD particles, and single DPD particles in bounded uniform flow and in-plane Poiseuille flow. Additional simulations examined closely spaced multiparticle clusters (straight-chains and hexagonal-packed aggregates). For all cases of rigid bodies the simulation results are in good agreement with predictions derived analytically from the continuum Stokes system. Elastic filaments, DPD-particle chains with bending resistance, were also simulated to examine hydrodynamically induced distortions, and the results show that the model captures the correct hydrodynamic interactions among filament beads.

We investigate the dynamics of a two-dimensional axial next-nearest-neighbor Ising model following a quench to zero temperature. The Hamiltonian is given by $H=-J_0{\sum }_{i,j=1}^L{S}_{i,j}{S}_{i+1,j}-J_1{\sum }_{i,j=1}(S_{i,j}{S}_{i,j+1}-\kappa S_{i,j}{S}_{i,j+2})$. For $\kappa <1$, the system does not reach the equilibrium ground state but slowly evolves to a metastable state. For $\kappa >1$, the system shows a behavior similar to that of the two-dimensional ferromagnetic Ising model in the sense that it freezes to a striped state with a finite probability. The persistence probability shows algebraic decay here with an exponent $\theta =0.235\pm 0.001$ while the dynamical exponent of growth $z=2.08\pm 0.01$. For $\kappa =1$, the system belongs to a completely different dynamical class; it always evolves to the true ground state with the persistence and dynamical exponent having unique values. Much of the dynamical phenomena can be understood by studying the dynamics and distribution of the number of domain walls. We also compare the dynamical behavior to that of a Ising model in which both the nearest and next-nearest-neighbor interactions are ferromagnetic.

The study of granular flows in physics has always been important because of their recurring presence in nature and industry. However, the nonlinear and multiphase behavior exhibited by these particulate systems makes them hard to model and predict. Several experiments were conducted in the past to gain insight into granular flows. The current experimental work furthers this insight and specifically attempts to understand the effect of rough surfaces on granular flows, namely, their local flow behavior. Understanding this interaction can have implications on industrial-scale granular problems. In this work, a granular shear cell, a two-dimensional annular shear cell, was developed to conduct shear experiments where roughness is imposed on the driving surface and experimentally quantified. A digital particle tracking velocimetry data retrieval scheme was developed to extract solid fraction, velocity, and granular temperature data from the experiments as a function of the roughness factor and wheel rotation rate. In general, the steady-state results show the two distinct regions as expected—a high-velocity and dilute-gas-like kinetic region near the moving wall and a high-solid-fraction liquid-like frictional flow regime away from the moving wall. Parametric studies conducted show that the normalized slip near the moving wall decreases with increasing wall roughness and decreasing wall rotation rate. Slip is an important parameter which can be easily interpreted as momentum transfer or traction performance in granular systems related to wheel-terrain interaction, agricultural processing, and most notably granular lubrication.

The anisotropic optical properties of thermotropic columnar liquid crystals absorbing in the visible range are investigated for different discotic compounds unidirectionally oriented in open supported thin films. Two methods to monitor the alignment of columnar mesophases in thin films are reported, making possible to achieve either homeotropic anchoring (columns normal to the substrate) by a specific thermal annealing, or unidirectional planar orientation (columns parallel to the substrate) by using a rubbed Teflon coating. The columnar liquid crystal anchoring is found to depend on the nature of the compound, either parallel or perpendicular to the Teflon orientation. Based on this control of the mesophase alignment, the dichroic ratio and the orientational order parameter of oriented samples are measured, and a high order parameter of 0.9 is found in the case of parallel alignment. From the polarized absorption data of the columnar liquid crystal films, the light wavelength dependence of the birefringence and of the real and imaginary parts (refractive index and extinction coefficient, respectively) of the anisotropic optical indices are determined over the whole visible range.