A numerical and analytical study of the role of exponentially truncated Lévy flights in the superdiffusive propagation of fronts in reaction-diffusion systems is presented. The study is based on a variation of the Fisher-Kolmogorov equation where the diffusion operator is replaced by a $\lambda$-truncated fractional derivative of order $\alpha$, where $1∕\lambda$ is the characteristic truncation length scale. For $\lambda =0$ there is no truncation, and fronts exhibit exponential acceleration and algebraically decaying tails. It is shown that for $\lambda \ne 0$ this phenomenology prevails in the intermediate asymptotic regime ${\left(\chi t\right)}^{1∕\alpha }⪡x⪡1∕\lambda$ where $\chi$ is the diffusion constant. Outside the intermediate asymptotic regime, i.e., for $x>1∕\lambda$, the tail of the front exhibits the tempered decay $\varphi \sim e^{-\lambda x}∕x^{(1+\alpha )}$, the acceleration is transient, and the front velocity $v_L$ approaches the terminal speed $v_{*}=(\gamma -{\lambda }^{\alpha }\chi )∕\lambda$ as $t\to \infty$, where it is assumed that $\gamma >{\lambda }^{\alpha }\chi$ with $\gamma$ denoting the growth rate of the reaction kinetics. However, the convergence of this process is algebraic, $v_L\sim v_{*}-\alpha ∕\left(\lambda t\right)$, which is very slow compared to the exponential convergence observed in the diffusive (Gaussian) case. An overtruncated regime in which the characteristic truncation length scale is shorter than the length scale of the decay of the initial condition, $1∕\nu$, is also identified. In this extreme regime, fronts exhibit exponential tails, $\varphi \sim e^{-\nu x}$, and move at the constant velocity $v=(\gamma -{\lambda }^{\alpha }\chi )∕\nu$.

Appreciation of stochastic Loewner evolution $\left({\text{SLE}}_{\kappa }\right)$, as a powerful tool to check for conformal invariant properties of geometrical features of critical systems has been rising. In this paper we use this method to check conformal invariance in sandpile models. Avalanche frontiers in Abelian sandpile model are numerically shown to be conformally invariant and can be described by SLE with diffusivity $\kappa =2$. This value is the same as value obtained for loop-erased random walks. The fractal dimension and Schramm’s formula for left passage probability also suggest the same result. We also check the same properties for Zhang’s sandpile model.

We consider the problem of finding the densest closed packing of hard disks with proposed different radii in a circular environment, such that the radius of the circumcircle is minimal. The subspace of the quasioptimum configurations of this problem exhibits the property of ultrametricity.

The behavior of a fluidized bed of fine magnetite particles as affected by a cross-flow magnetic field is investigated. A distinct feature of this naturally cohesive powder, as compared to noncohesive magnetic grains usually employed in magnetofluidized beds, is that the fluidized bed displays a range of stable fluidization even in the absence of an external magnetic field. Upon application of the magnetic field, the interval of stable fluidization is extended to higher gas velocities and bed expansion is enhanced. We have measured the tensile strength as affected by application of the external magnetic field according to two different operation modes. In the $H$ off-on operation mode, the bed is driven to bubbling in the absence of external magnetic field. Once the gas velocity is decreased below the bubbling onset and the bed has returned to stable fluidization due to natural cohesive forces, the field is applied. In the $H$ on-on mode, the field is maintained during the whole process of bubbling and return to stable fluidization. It is found that the tensile strength of the naturally stabilized bed is not essentially changed by application of the field ($H$ off-on) since the magnetic field cannot alter the bed structure once the particles are jammed in the stable fluidization state. Magnetic forces within the bulk of the jammed bed are partially canceled as a result of the anisotropic nature of the dipole-dipole interaction between the particles, which gives rise to just a small increment of the tensile strength. On the other hand, when the field is held on during bubbling and transition to stable fluidization ($H$ on-on mode), the tensile strength is appreciably increased. This suggests the formation of particle chains when the particles are not constrained due to the dipole-dipole attractive interaction which affects the mechanical strength of the stably fluidized bed. Experimental data are analyzed in the light of theoretical models on magnetic surface stresses.

Considerable attention has been paid, in recent years, to the use of networks in modeling complex real-world systems. Among the many dynamical processes involving networks, propagation processes—in which the final state can be obtained by studying the underlying network percolation properties—have raised formidable interest. In this paper, we present a bond percolation model of multitype networks with an arbitrary joint degree distribution that allows heterogeneity in the edge occupation probability. As previously demonstrated, the multitype approach allows many nontrivial mixing patterns such as assortativity and clustering between nodes. We derive a number of useful statistical properties of multitype networks as well as a general phase transition criterion. We also demonstrate that a number of previous models based on probability generating functions are special cases of the proposed formalism. We further show that the multitype approach, by naturally allowing heterogeneity in the bond occupation probability, overcomes some of the correlation issues encountered by previous models. We illustrate this point in the context of contact network epidemiology.

We propose a theoretical prediction of the self-diffusion tensor of inertial particles embedded in a viscous fluid. The derivation of the model is based on the kinetic theory for granular media including the effects of finite particle inertia and drag. The self-diffusion coefficients are expressed in terms of the components of the kinetic stress tensor in a general formulation. The model is valid from dilute to dense suspensions and its accuracy is verified in a pure shear flow. The theoretical prediction is compared to simulations of discrete particle trajectories assuming Stokes drag and binary collisions. We show that the prediction of the self-diffusion tensor is accurate provided that the kinetic stress components are correctly predicted.

We numerically examine the influence of the viscosity on the relaxation process of localized clouds in thermally unstable two-phase media, which are locally heated by cosmic ray and cooled by radiation. Pulselike stationary solutions of the media are numerically obtained by a shooting method. In one-dimensional direct numerical simulations, localized clouds are formed during the two-phase separation and sustained extraordinarily. Such long-lived clouds have been recently observed in interstellar media. We demonstrate that the balance of the viscosity with a pressure gradient remarkably suppresses the evaporation of the clouds and controls the relaxation process. This balance fixes the peak pressure of localized structures and then the structure is attracted and trapped to one of the pulselike stationary solutions. While the viscosity has been neglected in most of previous studies, our study suggests that the precise treatment of the viscosity is necessary to discuss the evaporation of the clouds.

Standard methods for lattice Boltzmann simulations of suspended particles, based on the momentum exchange algorithm, might lack accuracy or violate Galilean invariance in some particular situations. Aiming at simulations of dense suspensions in high-shear flows, we motivate and investigate necessary correction terms. We propose an approach which, combining accurate treatments of fluid-structure interaction and moving boundaries, is able to preserve Galilean invariance in relevant orders and to improve the physical behavior of the system. We validate the approach in a comparison with standard methods in simple test problems.

When sheared suspensions are simulated, Lees-Edwards boundary conditions allow more realistic computational setups as they remove the need of a domain bounded by shearing walls (as in Couette-type flow) which bias typical flow structures. Lees-Edwards boundary conditions therefore allow investigation of pure bulk properties in a quasi-infinite system. In addition, they improve the computational efficiency of the simulations as the whole domain can be used to calculate averages. We propose an implementation of Lees-Edwards boundary conditions for lattice Boltzmann simulations of particulate suspensions, combined with an accurate treatment of fluid-particle interactions. The algorithm is validated using a simple single-particle benchmark and further applied to a fully resolved suspension flow. Shear-thickening behavior, which is prolonged to higher shear rates as compared to Couette flow results, could be observed.

Our recently developed Fourier Monte Carlo algorithm permits a nonperturbative calculation of momentum-shell renormalization-group flows by simulation which despite its apparent simplicity is illustrative both numerically as well as conceptually interesting. We study the example of a ${\varphi }^4$ model with long-range lattice interaction. For this model we show that the topology of the renormalization flow is globally accessible in a particularly convenient way. The nontrivial fixed point of Wilson-Fisher type is observed its accompanying critical exponents are numerically determined from fitting its surrounding flow pattern to a linearized renormalization-group transformation. The results are compared to those obtained from perturbation theory, $ϵ$-expansion and earlier Monte Carlo simulations. Application of our method is also expected to be rewarding in other models with long-range interactions.

The paper by Belyaev et al. [Phys. Rev. E 72, 026406 (2005)] reported the first experimental observation of alpha particles produced in the thermonuclear reaction ${}^{11}\text{B}\left(p,\alpha \right){}^8\text{B}\text{e}$ induced by laser irradiation on a ${}^{11}\text{B}$ polyethylene $\left({\text{CH}}_2\right)$ composite target. The laser used in the experiment is characterized by a picosecond pulse duration and a peak of intensity of $2\times {10}^{18}\text{W}/{\text{cm}}^2$. We suggest that both the background-reduction method adopted in their detection system and the choice of the detection energy region of the reaction products are possibly inadequate. Consequently the total yield reported underestimates the true yield. Based on their observation, we give an estimation of the total yield to be higher than their conclusion, i.e., of the order of ${10}^5\alpha$ per shot.

Diffusivity, ionic conductivity, and viscosity of network-forming ionic melts are examined using molecular dynamics simulations of $\mathrm{Be}{\mathrm{F}}_2$ and $\mathrm{Si}{\mathrm{O}}_2$ melts. These tetrahedral, network-forming ionic melts are shown to possess a conductivity anomaly, in addition to waterlike viscosity and diffusivity anomalies, corresponding to a striking breakdown of the Nernst-Einstein relation. The contrasting scaling behavior of the different mobility measures with different structural contributions to the excess entropy is demonstrated.

A density functional route to the pair structure of quenched-annealed fluid mixtures is presented. The bulk two-body partial pair correlation functions of the mixture are identified with the one-body density distributions in an external potential that models a fixed test particle. Quenched-annealed (replica) density functional theory is used to calculate the inhomogeneous one-body density distributions. A closed theory is obtained by using an exact sum rule that equates two different expressions for the cross pair correlation function between unlike species. Results for binary quenched-annealed hard sphere mixtures are found to agree well with computer simulation data, improving over results from the replica Ornstein-Zernike equations using the direct correlation functions, obtained as second functional derivatives of the quenched-annealed excess free energy functional, as input. The proposed framework allows for the independent determination of the blocked part of the fluid-fluid partial pair correlation function.

We report the results of an experimental study of a colloid fluid confined to a quasi-one-dimensional (q1D) ribbon channel as a function of channel width and colloid density. Our findings confirm the principal predictions of previous theoretical studies of such systems. These are (1) that the density distribution of the liquid transverse to the ribbon channel exhibits stratification; (2) that even at the highest density the order along the strata, as measured by the longitudinal pair correlation function, is characteristic of a liquid; and (3) the q1D pair correlation functions in different strata exhibit anisotropic behavior resembling that found in a Monte Carlo simulation for the in-plane pair correlation function of a hard sphere fluid in a planar slit.

Rather than forming a simple and uniform nematic liquid crystal, concentrated solutions of semiflexible polymers, such as F-actin, have been observed to display a spatially periodic switching of the nematic director. When observed with polarization microscopy, these patterns appear as alternating light and dark bands, often referred to as zebra stripe patterns. Zebra stripe patterns, although not fully characterized, are due to periodic orientation distortions in the nematic order. We characterize such patterns by using a combination of two techniques. Using polarization microscopy, we quantify the periodic orientation distortions and show that the magnitude of the order parameter also varies periodically in the striped domains. When using fluorescently labeled filaments as markers, filaments spanning the striped domains are seen to undergo large angle bends. With fluorescence, clear density differences between adjacent stripes are also observed with domains of lesser density corresponding to strongly bent filaments. By directly comparing patterned areas with both polarization and fluorescence techniques, we show that periodic variation in the orientation, order parameter, filament bending, and density are correlated. We propose that these effects originate from the coupling of orientation and density that occurs for highly concentrated solutions of long semiflexible polymers subject to shear flows, as previously proposed [P. de Gennes, Mol. Cryst. Liq. Cryst. (Phila. Pa.) 34, 177 (1977)]. After cessation of shearing, strong interfilament interactions and high compressibility can lead to periodic buckling from the relaxation of filaments stretched during flows. The characterization of zebra stripe patterns presented here provides evidence that buckling in confined F-actin nematics produces strong periodic bending that is responsible for the observed features.

It has been shown experimentally that contact interactions may influence the migration of cancer cells. Previous works have modelized this thanks to stochastic, discrete models (cellular automata) at the cell level. However, for the study of the growth of real-size tumors with several million cells, it is best to use a macroscopic model having the form of a partial differential equation (PDE) for the density of cells. The difficulty is to predict the effect, at the macroscopic scale, of contact interactions that take place at the microscopic scale. To address this, we use a multiscale approach: starting from a very simple, yet experimentally validated, microscopic model of migration with contact interactions, we derive a macroscopic model. We show that a diffusion equation arises, as is often postulated in the field of glioma modeling, but it is nonlinear because of the interactions. We give the explicit dependence of diffusivity on the cell density and on a parameter governing cell-cell interactions. We discuss in detail the conditions of validity of the approximations used in the derivation, and we compare analytic results from our PDE to numerical simulations and to some in vitro experiments. We notice that the family of microscopic models we started from includes as special cases some kinetically constrained models that were introduced for the study of the physics of glasses, supercooled liquids, and jamming systems.

Velocity inversion in a nanoscale cylindrical Couette flow is investigated with the Navier-Stokes (NS) equation and molecular-dynamics (MD) simulation. With general slip boundary conditions in the NS equation, the flow can be classified into five distinct profiles. The condition of velocity inversion is explored in the whole space of four dimensionless variables of $\beta$, slip velocity ratio $u^{\prime }$, radius ratio $a^{\prime }$, and angular velocity ratio ${\omega }^{\prime }$. MD computer simulations are performed to estimate the constitutive coefficient of the slip velocities at the walls. The flow is generated by a rotating inner wall and a stationary outer wall in conformity with the theoretical result. By varying an attraction parameter in the Lennard-Jones potential, the slip velocities can be easily controlled. The theoretical predictions are compared with the simulation results. We find that in the intermediate range of the attraction parameter the two results are quite comparable to some extent, but at both extreme values of the attraction parameter, they are quite different.

A two-phase model, where the plasma expansion is an isothermal one when laser irradiates and a following adiabatic one after laser ends, has been proposed to predict the maximum energy of the proton beams induced in the ultraintense laser-foil interactions. The hot-electron recirculation in the ultraintense laser-solid interactions has been accounted in and described by the time-dependent hot-electron density continuously in this model. The dilution effect of electron density as electrons recirculate and spread laterally has been considered. With our model, the scaling laws of maximum ion energy have been achieved and the dependence of the scaling coefficients on laser intensity, pulse duration, and target thickness have been obtained. Some interesting results have been predicted: the adiabatic expansion is an important process of the ion acceleration and cannot be neglected; the whole acceleration time is about 10–20 times of laser-pulse duration; the larger the laser intensity, the more sensitive the maximum ion energy to the change of focus radius, and so on.

We consider the problem of optical tomographic imaging in the mesoscopic regime where the photon mean-free path is on the order of the system size. It is shown that a tomographic imaging technique can be devised which is based on the assumption of single scattering and utilizes a generalization of the Radon transform which we refer to as the broken-ray transform. The technique can be used to recover the extinction coefficient of an inhomogeneous medium from angularly resolved measurements and is illustrated with numerical simulations. The forward data for these simulations were obtained by numerically solving the radiative transport equation without any approximations. Tomographic imaging in slabs of different widths was considered and it was shown that the technique can tolerate a maximum width that corresponds to approximately six scattering events. It is also shown that the use of broken rays does not result in additional ill posedness of the inverse problem in comparison to the classical problem of inverting the Radon transform. Applications to biomedical imaging are described.

In random matrix theory, the Tracy-Widom (TW) distribution describes the behavior of the largest eigenvalue. We consider here two models in which TW undergoes transformations. In the first one disorder is introduced in the Gaussian ensembles by superimposing an external source of randomness. A competition between TW and a normal (Gaussian) distribution results, depending on the spreading of the disorder. The second model consists of removing at random a fraction of (correlated) eigenvalues of a random matrix. The usual formalism of Fredholm determinants extends naturally. A continuous transition from TW to the Weilbull distribution, characteristic of extreme values of an uncorrelated sequence, is obtained.