A calculation which describes the spin-up of toroidal plasmas by the radial propagation of turbulence fronts with broken parallel symmetry is presented. The associated flux of parallel momentum is calculated by using a two-scale direct-interaction approximation in the weak turbulence limit. We show that fluctuation momentum spreads faster than mean flow momentum. Specifically, the turbulent flux of wave momentum is stronger than the momentum pinch. The scattering of fluctuation momentum can induce edge-core coupling of toroidal flows, as observed in experiments.

Recommender systems play an essential role in the modern business world. They recommend favorable items such as books, movies, and search queries to users based on their past preferences. Applying similar ideas and techniques to Monte Carlo simulations of physical systems boosts their efficiency without sacrificing accuracy. Exploiting the quantum to classical mapping inherent in the continuous-time quantum Monte Carlo methods, we construct a classical molecular gas model to reproduce the quantum distributions. We then utilize powerful molecular simulation techniques to propose efficient quantum Monte Carlo updates. The recommender engine approach provides a general way to speed up the quantum impurity solvers.

This study analyzes the radiation produced by a point charge intersecting the interface between a vacuum and a chiral isotropic medium. We deduce analytical expressions for the Fourier components of an electromagnetic field in both vacuum and medium for arbitrary charge velocity. The main focus is on investigating the far field in a vacuum. The distinguishing feature of the interface with a chiral isotropic medium is that the field in the vacuum area contains both copolarization (coinciding with the polarization of the self-field of a charge) and cross-polarization (orthogonal to the polarization of the self-field). Using a saddle-point approach, we obtain asymptotic representations for the field components in the far-field zone for typical frequency ranges of the Condon model of the chiral medium. We note that a so-called lateral wave is generated in a vacuum for certain parameters. The main contribution to the radiation at large distances is presented by two (co- and cross-) spherical waves of transition radiation. These waves are coherent and result in a total spherical wave with elliptical polarization, with the polarization coefficient being determined by the chirality of the medium. We present typical radiation patterns and ellipses of polarization.

Nowadays online searches are undeniably the most common form of information gathering, as witnessed by billions of clicks generated each day on search engines. In this work we describe online searches as foraging processes that take place on the semi-infinite line. Using a variety of quantities like probability distributions and complementary cumulative distribution functions of step length and waiting time as well as mean square displacements and entropies, we analyze three different click-through logs that contain the detailed information of millions of queries submitted to search engines. Notable differences between the different logs reveal an increased efficiency of the search engines. In the language of foraging, the newer logs indicate that online searches overwhelmingly yield local searches (i.e., on one page of links provided by the search engines), whereas for the older logs the foraging processes are a combination of local searches and relocation phases that are power law distributed. Our investigation of click logs of search engines therefore highlights the presence of intermittent search processes (where phases of local explorations are separated by power law distributed relocation jumps) in online searches. It follows that good search engines enable the users to find the information they are looking for through a local exploration of a single page with search results, whereas for poor search engine users are often forced to do a broader exploration of different pages.

In this article, we introduce a backward method to model stochastic gene expression and protein-level dynamics. The protein amount is regarded as a diffusion process and is described by a backward stochastic differential equation (BSDE). Unlike many other SDE techniques proposed in the literature, the BSDE method is backward in time; that is, instead of initial conditions it requires the specification of end-point (“final”) conditions, in addition to the model parametrization. To validate our approach we employ Gillespie's stochastic simulation algorithm (SSA) to generate (forward) benchmark data, according to predefined gene network models. Numerical simulations show that the BSDE method is able to correctly infer the protein-level distributions that preceded a known final condition, obtained originally from the forward SSA. This makes the BSDE method a powerful systems biology tool for time-reversed simulations, allowing, for example, the assessment of the biological conditions (e.g., protein concentrations) that preceded an experimentally measured event of interest (e.g., mitosis, apoptosis, etc.).

The nature of the velocity distribution of a driven granular gas, though well studied, is unknown as to whether it is universal or not, and, if universal, what it is. We determine the tails of the steady state velocity distribution of a driven inelastic Maxwell gas, which is a simple model of a granular gas where the rate of collision between particles is independent of the separation as well as the relative velocity. We show that the steady state velocity distribution is nonuniversal and depends strongly on the nature of driving. The asymptotic behavior of the velocity distribution is shown to be identical to that of a noninteracting model where the collisions between particles are ignored. For diffusive driving, where collisions with the wall are modeled by an additive noise, the tails of the velocity distribution is universal only if the noise distribution decays faster than exponential.

We perform a direct numerical simulation of the forced, incompressible two-dimensional Navier-Stokes equation coupled with the FENE-P equations for the polymer-conformation tensor. The forcing is such that, without polymers and at low Reynolds numbers $\text{Re}$, the film attains a steady state that is a square lattice of vortices and antivortices. We find that, as we increase the Weissenberg number $\text{Wi}$, a sequence of nonequilibrium phase transitions transforms this lattice, first to spatially distorted, but temporally steady, crystals and then to a sequence of crystals that oscillate in time, periodically, at low $\text{Wi}$, and quasiperiodically, for slightly larger $\text{Wi}$. Finally, the system becomes disordered and displays spatiotemporal chaos and elastic turbulence. We then obtain the nonequilibrium phase diagram for this system, in the $\text{Wi}-\mathrm{\Omega }$ plane, where $\mathrm{\Omega }\propto \text{Re}$, and show that (a) the boundary between the crystalline and turbulent phases has a complicated, fractal-type character and (b) the Okubo-Weiss parameter $\mathrm{\Lambda }$ provides us with a natural measure for characterizing the phases and transitions in this diagram.

We propose a model of superdiffusive Lévy walk as an emergent nonlinear phenomenon in systems of interacting individuals. The aim is to provide a qualitative explanation of recent experiments [G. Ariel et al., Nat. Commun. 6, 8396 (2015)] revealing an intriguing behavior: swarming bacteria fundamentally change their collective motion from simple diffusion into a superdiffusive Lévy walk dynamics. We introduce microscopic mean-field kinetic equations in which we combine two key ingredients: (1) alignment interactions between individuals and (2) non-Markovian effects. Our interacting run-and-tumble model leads to the superdiffusive growth of the mean-squared displacement and the power-law distribution of run length with infinite variance. The main result is that the superdiffusive behavior emerges as a cooperative effect without using the standard assumption of the power-law distribution of run distances from the inception. At the same time, we find that the collision and repulsion interactions lead to the density-dependent exponential tempering of power-law distributions. This qualitatively explains the experimentally observed transition from superdiffusion to the diffusion of mussels as their density increases [M. de Jager et al., Proc. R. Soc. B 281, 20132605 (2014)].

We model a set of point-to-point transports on a network as a system of polydisperse interacting self-avoiding walks (SAWs) over a finite square lattice. The ends of each SAW may be located both at random, uniformly distributed, positions or with one end fixed at a lattice corner. The total energy of the system is computed as the sum over all SAWs, which may represent either the time needed to complete the transport over the network, or the resources needed to build the networking infrastructure. We focus especially on the second aspect by assigning a concave cost function to each site to encourage path overlap. A simulated annealing optimization, based on a modified Berg-Foerster-Aragao de Carvalho-Caracciolo-Froehlich (BFACF) algorithm developed for polymers, is used to probe the complex conformational substate structure at zero temperature. We characterize the average cost gains (and path-length variations) for increasing polymer density with respect to a Dijkstra routing and find a nonmonotonic behavior as recently found for random networks. We observe the emergence of ergodicity breaking and of nontrivial overlap distributions among replicas when switching from a convex to a concave cost function (e.g., $x^{\gamma }$, where $x$ represents the node overlap). Finally, we show that the space of ground states for $\gamma <1$ is compatible with an ultrametric structure, as seen in many complex systems such as some spin glasses.

The relative importance of the contributions of droplet excitations and domain walls on the ordering of short-range Edwards-Anderson spin glasses in three and four dimensions is studied. We compare the spin overlap distribution functions of periodic and free boundary conditions using population annealing Monte Carlo. For system sizes up to about 1000 spins, spin glasses show nontrivial spin overlap distributions. Periodic boundary conditions may trap diffusive domain walls which can contribute to small spin overlaps, and the other contribution is the existence of low-energy droplet excitations within the system. We use free boundary conditions to minimize domain-wall effects, and show that low-energy droplet excitations are the major contribution to small overlaps in numerical simulations. Free boundary conditions has stronger finite-size effects, and is likely to have the same thermodynamic limit with periodic boundary conditions.

In this paper we present an analytic method for calculating the transition probability between two random Gaussian matrices with given eigenvalue spectra in the context of Dyson Brownian motion. We show that in the Coulomb gas language, in large $N$ limit, memory of the initial state is preserved in the form of a universal linear potential acting on the eigenvalues. We compute the likelihood of any given transition as a function of time, showing that as memory of the initial state is lost, transition probabilities converge to those of the static ensemble.

We discuss synchronization patterns in networks of FitzHugh-Nagumo and leaky integrate-and-fire oscillators coupled in a two-dimensional toroidal geometry. A common feature between the two models is the presence of fast and slow dynamics, a typical characteristic of neurons. Earlier studies have demonstrated that both models when coupled nonlocally in one-dimensional ring networks produce chimera states for a large range of parameter values. In this study, we give evidence of a plethora of two-dimensional chimera patterns of various shapes, including spots, rings, stripes, and grids, observed in both models, as well as additional patterns found mainly in the FitzHugh-Nagumo system. Both systems exhibit multistability: For the same parameter values, different initial conditions give rise to different dynamical states. Transitions occur between various patterns when the parameters (coupling range, coupling strength, refractory period, and coupling phase) are varied. Many patterns observed in the two models follow similar rules. For example, the diameter of the rings grows linearly with the coupling radius.

The behavior of a model granular material, made of slightly polydisperse beads with Hertz-Mindlin elastic-frictional contacts, in oedometric compression (i.e., compression along one axis, with no lateral strain) is studied by grain-level numerical simulations. We systematically investigate the influence of the (idealized) packing process on the microstructure and stresses in the initial, weakly confined equilibrium state, and prepare both isotropic and anisotropic configurations differing in solid fraction $\mathrm{\Phi }$ and coordination number $z$. $\mathrm{\Phi }$ (ranging from maximally dense to moderately loose), $z$ (which might vary independently of $\mathrm{\Phi }$ in dense systems), fabric and force anisotropy parameters, and the ratio $K_0$ of lateral stresses ${\sigma }_2={\sigma }_3$ to stress ${\sigma }_1$ in the compression direction are monitored in oedometric compression in which ${\sigma }_1$ varies by more than three orders of magnitude. $K_0$ reflects the anisotropy of the assembling process and may remain nearly constant in further loading if the material is already oedometrically compressed (as a granular gas) in the preparation stage. Otherwise, it tends to decrease steadily over the investigated stress range. It is related to force and fabric anisotropy parameters by a simple formula. Elastic moduli, separately computed with an appropriate matrix method, may express the response to very small stress increments about the transversely isotropic well-equilibrated states along the loading path, although oedometric compression proves an essentially anelastic process, mainly due to friction mobilization, with large irreversible effects apparent upon unloading. While the evolution of axial strain ${\epsilon }_1$ and solid fraction $\mathrm{\Phi }$ (or of the void ratio $e=-1+1/\mathrm{\Phi }$) with axial stress ${\sigma }_1$ is very nearly reversible, especially in dense samples, $z$ is observed to decrease (as previously observed in isotropic compression) after a compression cycle if its initial value was high. $K_0$ relates to the evolution of internal variables and may exceed 1 in unloading. The considerably greater irreversibility of oedometric compression reported in sands, compared to our model systems, should signal contact plasticity or damage.

The elastic moduli of a transversely isotropic model granular material, made of slightly polydisperse elastic-frictional spherical beads, in equilibrium along a one-dimensional (oedometric) compression path, as described in the companion paper [M. H. Khalili et al., Phys. Rev. E 95, 032907 (2017)], are investigated by numerical simulations. The relations of the five independent moduli to stresses, density, coordination number, fabric and force anisotropies are studied for different internal material states along the oedometric loading path. It is observed that elastic moduli, as in isotropic packs, are primarily determined by the coordination number, with anomalously small shear moduli in poorly coordinated systems, whatever their density. Such states also exhibit faster increasing moduli in compression, and larger off-diagonal moduli and Poisson ratios. Anisotropy affects the longitudinal moduli $C_{11}$ in the axial direction and $C_{22}$ in the transverse directions, and the shear modulus in the transverse plane $C_{44}$, more than the shear modulus in a plane containing the axial direction $C_{55}$. The results are compared to available experiments on anisotropic bead packs, revealing, despite likely differences in internal states, a very similar range of stiffness level (linked to coordination), and semiquantitative agreement as regards the influence of anisotropy. Effective medium theory (the Voigt approach) provides quite inaccurate predictions of the moduli. It also significantly underestimates ratios $C_{11}/C_{22}$ (varying between 1 and 2.2) and $C_{55}/C_{44}$ (varying from 1 to 1.6), which characterize elastic anisotropy, except in relatively weakly anisotropic states. The bulk modulus for isotropic compression and the compliance corresponding to stress increments proportional to the previous stress values are the only elastic coefficients to be correctly estimated by available predictive relations. We discuss the influences of fabric and force anisotropies onto elastic anisotropy, showing in particular that the former dominates in sample series that are directly assembled in anisotropic configurations and keep a roughly constant lateral to axial stress ratio under compression.

We characterize shear transformations (STs) at the atomic scale in a model of amorphous silicon using a mapping on Eshelby inclusions. We investigate the effect of pressure, glass relaxation, as well as damage on the ST characteristics. We show that the characteristic ST effective volume, ${\gamma }_0{V}_0$, product of the ST plastic shear strain ${\gamma }_0$ and volume $V_0$, does not depend significantly on an applied pressure but increases with accumulated plastic deformation from about $10{\AA }^3$ in the pseudoelastic regime to about $60{\AA }^3$ once plastic flow sets in. Furthermore, by using nudged elastic band calculations, we measure the energy barrier against ST activation. Analyzing different paths leading to either an isolated ST or an avalanche, we show that the barrier is systematically controlled by the first ST with an activation volume equal to the effective volume of the ST at the activated state, which represents only a fraction of the complete ST volume. The activation volume is also found smaller for avalanches, presumably because of accumulated local damage. This work provides essential information to build reliable mesoscale models of plasticity.

Nuclear-magnetic-resonance (NMR) relaxation experimentation is an effective technique for nondestructively probing the dynamics of proton-bearing fluids in porous media. The frequency-dependent relaxation rate $T_1^{-1}$ can yield a wealth of information on the fluid dynamics within the pore provided data can be fit to a suitable spin diffusion model. A spin diffusion model yields the dipolar correlation function $G\left(t\right)$ describing the relative translational motion of pairs of ${}^1\mathrm{H}$ spins which then can be Fourier transformed to yield $T_1^{-1}$. $G\left(t\right)$ for spins confined to a quasi-two-dimensional (Q2D) pore of thickness $h$ is determined using theoretical and Monte Carlo techniques. $G\left(t\right)$ shows a transition from three- to two-dimensional motion with the transition time proportional to $h^2$. $T_1^{-1}$ is found to be independent of frequency over the range 0.01–100 MHz provided $h\gtrsim 5$ nm and increases with decreasing frequency and decreasing $h$ for pores of thickness $h<3$ nm. $T_1^{-1}$ increases linearly with the bulk water diffusion correlation time ${\tau }_b$ allowing a simple and direct estimate of the bulk water diffusion coefficient from the high-frequency limit of $T_1^{-1}$ dispersion measurements in systems where the influence of paramagnetic impurities is negligible. Monte Carlo simulations of hydrated Q2D pores are executed for a range of surface-to-bulk desorption rates for a thin pore. $G\left(t\right)$ is found to decorrelate when spins move from the surface to the bulk, display three-dimensional properties at intermediate times, and finally show a bulk-mediated surface diffusion (Lévy) mechanism at longer times. The results may be used to interpret NMR relaxation rates in hydrated porous systems in which the paramagnetic impurity density is negligible.

Nuclear-magnetic-resonance (NMR) spin-lattice ($T_1^{-1}$) and spin-spin ($T_2^{-1}$) relaxation rate measurements can act as effective nondestructive probes of the nanoscale dynamics of ${}^1\mathrm{H}$ spins in porous media. In particular, fast-field-cycling $T_1^{-1}$ dispersion measurements contain information on the dynamics of diffusing spins over time scales spanning many orders of magnitude. Previously published experimental $T_1^{-1}$ dispersions from a plaster paste, synthetic saponite, mortar, and oil-bearing shale are reanalyzed using a model and associated theory which describe the relaxation rate contributions due to the interaction between spin ensembles in quasi-two-dimensional pores. Application of the model yields physically meaningful diffusion correlation times for all systems. In particular, the surface diffusion correlation time and the surface desorption time take similar values for each system, suggesting that surface mobility and desorption are linked processes. The bulk fluid diffusion correlation time is found to be two to five times the value for the pure liquid at room temperature for each system. Reanalysis of the oil-bearing shale yields diffusion time constants for both the oil and water constituents. The shale is found to be oil wetting and the water $T_1^{-1}$ dispersion is found to be associated with aqueous ${\mathrm{Mn}}^{2+}$ paramagnetic impurities in the bulk water. These results escalate the NMR $T_1^{-1}$ dispersion measurement technique as the primary probe of molecular-scale dynamics in porous media yielding diffusion parameters and a wealth of information on pore morphology.

Two modes of the asymmetric sound transmission are observed experimentally in a one-dimensional system composed of coupled two layers of liquids. Their cavitation thresholds are different from each other. When the sound wave propagates from the high-threshold liquid to the low-threshold liquid, the two liquids can avoid the cavitation for a medium driving pressure. When it propagates from the low-threshold liquid to the high-threshold liquid, however, the low-threshold liquid can be cavitated by the same driving pressure, though the high-threshold liquid remains uncavitated. Therefore, there is a sound transmission asymmetry, or sound rectification in this double-layer liquid. Furthermore, when the system is driven by a high pressure, cavitation can take place in both high- and low-threshold liquids in the sound transmission from the high-threshold liquid to the low-threshold liquid, but only the low-threshold liquid can be cavitated in the opposite transmission. This mechanism gives an asymmetry with reversed rectifying direction. The efficiency of rectification is related to the driving sound pressure and the cavitation thresholds of the two liquids based on experimental results. Finally, the experimental observations are reproduced by the numerical simulation based on the modified two-phase fluid mechanics.

Fast collisionless shocks in cosmic plasmas convert their kinetic energy flow into the hot downstream thermal plasma with a substantial fraction of energy going into a broad spectrum of superthermal charged particles and magnetic fluctuations. The superthermal particles can penetrate into the shock upstream region producing an extended shock precursor. The cold upstream plasma flow is decelerated by the force provided by the superthermal particle pressure gradient. In high Mach number collisionless shocks, efficient particle acceleration is likely coupled with turbulent magnetic field amplification (MFA) generated by the anisotropic distribution of accelerated particles. This anisotropy is determined by fast particle transport, making the problem strongly nonlinear and multiscale. Here, we present a nonlinear Monte Carlo model of collisionless shock structure with superdiffusive propagation of high-energy Fermi accelerated particles coupled to particle acceleration and MFA, which affords a consistent description of strong shocks. A distinctive feature of the Monte Carlo technique is that it includes the full angular anisotropy of the particle distribution at all precursor positions. The model reveals that the superdiffusive transport of energetic particles (i.e., Lévy-walk propagation) generates a strong quadruple anisotropy in the precursor particle distribution. The resultant pressure anisotropy of the high-energy particles produces a nonresonant mirror-type instability that amplifies compressible wave modes with wavelengths longer than the gyroradii of the highest-energy protons produced by the shock.