We present laboratory experiments of a vertically vibrated granular medium consisting of 1-mm-diameter glass beads with embedded 8-mm-diameter intruder glass beads. The experiments were performed in the laboratory as well as in a parabolic flight under reduced-gravity conditions (on Martian and Lunar gravity levels). We measured the mean rise velocity of the large glass beads and present its dependence on the fill height of the sample containers, the excitation acceleration, and the ambient gravity level. We find that the rise velocity scales in the same manner for all three gravity regimes and roughly linearly with gravity.

The effect of Coulomb friction is studied in the framework of collisional ratchets. It turns out that the average drift of these devices can be expressed as the combination of a term related to the lack of equipartition between the probe and the surrounding bath, and a term featuring the average frictional force. We illustrate this general result in the asymmetric Rayleigh piston, showing how Coulomb friction can induce a ratchet effect in a Brownian particle in contact with an equilibrium bath. An explicit analytical expression for the average velocity of the piston is obtained in the rare collision limit. Numerical simulations support the analytical findings.

The dynamical regimes of models belonging to the Kardar-Parisi-Zhang (KPZ) universality class are investigated in $d=2+1$ by extensive simulations considering flat and curved geometries. Geometry-dependent universal distributions, different from their Tracy-Widom counterpart in one dimension, were found. Distributions exhibit finite-time corrections hallmarked by a shift in the mean decaying as $t^{-\beta }$, where $\beta$ is the growth exponent. Our results support a generalization of the ansatz $h=v_{\infty }t+{\left(\Gamma t\right)}^{\beta }\chi +\eta +\zeta t^{-\beta }$ to higher dimensions, where $v_{\infty }$, $\Gamma$, $\zeta$, and $\eta$ are nonuniversal quantities whereas $\beta$ and $\chi$ are universal and the last one depends on the surface geometry. Generalized Gumbel distributions provide very good fits of the distributions in at least four orders of magnitude around the peak, which can be used for comparisons with experiments. Our numerical results call for analytical approaches and experimental realizations of the KPZ class in two-dimensional systems.

The Hilbert-Huang transform is applied to analyze single-particle Lagrangian velocity data from numerical simulations of hydrodynamic turbulence. The velocity trajectory is described in terms of a set of intrinsic mode functions $C_i\left(t\right)$ and of their instantaneous frequency ${\omega }_i\left(t\right)$. On the basis of this decomposition we define the $\omega$-conditioned statistical moments of the $C_i$ modes, named $q$-order Hilbert spectra (HS). We show that such quantities have enhanced scaling properties as compared to traditional Fourier transform- or correlation-based (structure functions) statistical indicators, thus providing better insights into the turbulent energy transfer process. We present clear empirical evidence that the energylike quantity, i.e., the second-order HS, displays a linear scaling in time in the inertial range, as expected from a dimensional analysis. We also measure high-order moment scaling exponents in a direct way, without resorting to the extended self-similarity procedure. This leads to an estimate of the Lagrangian structure function exponents which are consistent with the multifractal prediction in the Lagrangian frame as proposed by Biferale et al. [Phys. Rev. Lett. 93, 064502 (2004)].

An airplane-boarding model, introduced earlier by Frette and Hemmer [Phys. Rev. E 85, 011130 (2012)], is studied with the aim of determining precisely its asymptotic power-law scaling behavior for a large number of passengers $N$. Based on Monte Carlo simulation data for very large system sizes up to $N=2^{16}=65536$, we have analyzed numerically the scaling behavior of the mean boarding time $\langle t_b\rangle$ and other related quantities. In analogy with critical phenomena, we have used appropriate scaling Ansätze, which include the leading term as some power of $N$ (e.g., $\propto$$N^{\alpha }$ for $\langle t_b\rangle$), as well as power-law corrections to scaling. Our results clearly show that $\alpha =1/2$ holds with a very high numerical accuracy ($\alpha =0.5001\pm 0.0001$). This value deviates essentially from $\alpha \simeq 0.69$, obtained earlier by Frette and Hemmer from data within the range $2\le N\le 16$. Our results confirm the convergence of the effective exponent ${\alpha }_{\mathrm{eff}}\left(N\right)$ to $1/2$ at large $N$ as observed by Bernstein. Our analysis explains this effect. Namely, the effective exponent ${\alpha }_{\mathrm{eff}}\left(N\right)$ varies from values about $0.7$ for small system sizes to the true asymptotic value $1/2$ at $N\to \infty$ almost linearly in $N^{-1/3}$ for large $N$. This means that the variation is caused by corrections to scaling, the leading correction-to-scaling exponent being $\theta \approx 1/3$. We have estimated also other exponents: $\nu =1/2$ for the mean number of passengers taking seats simultaneously in one time step, $\beta =1$ for the second moment of $t_b$, and $\gamma \approx 1/3$ for its variance.

A narrow-escape problem is considered to calculate the mean first passage time (MFPT) needed for a Brownian particle to leave a unit sphere through one of its $N$ small boundary windows (traps). A procedure is established to calculate optimal arrangements of $N\gg 1$ equal small boundary traps that minimize the asymptotic MFPT. Based on observed characteristics of such arrangements, a remarkable property is discovered, that is, the sum of squared pairwise distances between optimally arranged $N$ traps on a unit sphere is integer, equal to $N^2$. It is observed for $2\le N\le 1004$ with high precision. It is conjectured that this is the case for such optimal arrangements for all $N$. A dilute trap limit of homogenization theory when $N\to \infty$ can be used to replace the strongly heterogeneous Dirichlet-Neumann MFPT problem with a spherically symmetric Robin problem for which an exact solution is readily found. Parameters of the Robin homogenization problem are computed that capture the first four terms of the asymptotic MFPT. Close agreement of asymptotic and homogenization MFPT values is demonstrated. The homogenization approach provides a radically faster way to estimate the MFPT since it is given by a simple formula and does not involve expensive global optimization to determine locations of $N\gg 1$ boundary traps.

We utilize the tools of persistent homology to analyze features of force networks in dense granular matter, modeled as a collection of circular, inelastic frictional particles. The proposed approach describes these networks in a precise and tractable manner, allowing us to identify features that are difficult or impossible to characterize by other means. In contrast to other techniques that consider each force threshold level separately, persistent homology allows us to consider all threshold levels at once to describe the force network in a complete and insightful manner. We consider continuously compressed system of particles characterized by varied polydispersity and friction in two spatial dimensions. We find significant differences between the force networks in these systems, suggesting that their mechanical response may differ considerably as well.

For low-water-content aqueous solutions, the primary α process due to the cooperative motion of solute and water molecules and the secondary Johari-Goldstein (JG) process of solute are observed. For high-water-content aqueous solutions, the α process due to the cooperative motion of solute and water molecules and the secondary β process due to the motion of excess water are observed. However, the JG process of solute has not been observed. To clarify this difference, we measured the dielectric spectra of supercooled triethyleneglycol-water mixtures in a wide temperature range. We discuss the effect of excess water on the molecular dynamics relating to the JG process of solute in high-water-content aqueous solutions.

Rapidly cooling a liquid may result in a glass transition, creating an amorphous solid whose shear and bulk moduli are finite. Even when done with constant density, these resulting moduli depend strongly on the rate of cooling. Understanding this phenomenon calls for analyzing separately the “Born term” that exists also in perfectly ordered materials and the contributions of the “excess modes” that result from glassy disorder. We show that the Born term is very insensitive to the cooling rate, and all the variation in the shear modulus is due to the excess modes. We argue that this approach provides a quantitative understanding of the cooling rate dependence of a basic linear response coefficient, i.e., the shear modulus.

Smectic-$A$${}^{*}$ monolayers self-assembled from aqueous solutions of chiral $\mathit{fd}$ viruses and a polymer depletant can assume a variety of shapes such as flat disks and twisted ribbons. A first order phase transition from a flat disk to a ribbon occurs upon lowering the concentration of polymer depletant or the temperature. A theoretical model based on the de Gennes model for the smectic-$A$ phase, the Helfrich model of membrane elasticity, and a simple edge energy has been previously used to calculate the disk-ribbon phase diagram. In this paper we apply this model to the nucleation process of ribbons. First, we study the “rippled disks” that have been observed as precursors of ribbons. Using a model shape proposed by Meyer which includes rippling in both the in-plane and out-of-plane directions, we study the energetics of the disks as functions of the edge energy modulus (a measure of the polymer concentration) and the mean curvature modulus $k$. We find that as the edge energy modulus is reduced the radial size of the ripples grows rapidly in agreement with experimental observations. For small enough $k$ we find that the out-of-plane size of the ripples grows but its value saturates at a fraction of the twist penetration depth, too small to be experimentally observable. For large $k$ the membrane remains flat though rippled in the radial direction. Such membranes do not have negative Gaussian curvature and thus will not likely spawn twisted ribbons. We also study the creation of twisted ribbons produced by stretching the edge of a flat membrane in a localized region. In experiments using a pair of optical traps it has been observed that once the membrane has been sufficiently stretched a ribbon forms on the stretched edge. We study this process theoretically using a free energy consisting of the Helfrich and edge energies alone. We add a small ribbonlike perturbation to the protrusion produced by stretching and determine whether it is energetically favorable as a function of the size of the protrusion. In qualitative agreement with experiment we find a nonzero value for the critical size of the protrusion needed to make a ribbon energetically favorable, though the value we find is an order of magnitude lower than the experimental value possibly due to our neglect of the director field. As in the case of the rippled disks we find that the mean curvature energy acts as a barrier between the disk and twisted ribbon structures.

We investigate numerically the relaxational dynamics of the orientational order of a cholesteric blue phase (BP) in a planar cell enforcing normal alignment in response to the application and cessation of an external electric field. We focus on the cases where blue phase I (BP I) is stable in the bulk. We show how the reorganization processes of the network of disclinations depend on the field strength and the history of the application of the field. We also demonstrate that the relaxation processes following the cessation of the field are particularly complex and depend sensitively on the profile of the orientational order before the cessation of the field.

Thermal effects affecting spatiotemporal behavior of cardiac tissue are discussed by relating temperature variations to proarrhythmic dynamics in the heart. By introducing a thermoelectric coupling in a minimal model of cardiac tissue, we are able to reproduce experimentally measured dynamics obtained simultaneously from epicardial and endocardial canine right ventricles at different temperatures. A quantitative description of emergent proarrhythmic properties of restitution, conduction velocity, and alternans regimes as a function of temperature is presented. Complex discordant alternans patterns that enhance tissue dispersion consisting of one wave front and three wave backs are described in both simulations and experiments. Possible implications for model generalization are finally discussed.

In this paper we propose a new model for volatility fluctuations in financial time series. This model relies on a nonstationary Gaussian process that exhibits aging behavior. It turns out that its properties, over any finite time interval, are very close to continuous cascade models. These latter models are indeed well known to reproduce faithfully the main stylized facts of financial time series. However, it involves a large-scale parameter (the so-called “integral scale” where the cascade is initiated) that is hard to interpret in finance. Moreover, the empirical value of the integral scale is in general deeply correlated to the overall length of the sample. This feature is precisely predicted by our model, which, as illustrated by various examples from daily stock index data, quantitatively reproduces the empirical observations.

Networks are commonly used to define underlying interaction structures where infections, information, or other quantities may spread. Although the standard approach has been to aggregate all links into a static structure, some studies have shown that the time order in which the links are established may alter the dynamics of spreading. In this paper, we study the impact of the time ordering in the limits of flow on various empirical temporal networks. By using a random walk dynamics, we estimate the flow on links and convert the original undirected network (temporal and static) into a directed flow network. We then introduce the concept of flow motifs and quantify the divergence in the representativity of motifs when using the temporal and static frameworks. We find that the regularity of contacts and persistence of vertices (common in email communication and face-to-face interactions) result on little differences in the limits of flow for both frameworks. On the other hand, in the case of communication within a dating site and of a sexual network, the flow between vertices changes significantly in the temporal framework such that the static approximation poorly represents the structure of contacts. We have also observed that cliques with 3 and 4 vertices containing only low-flow links are more represented than the same cliques with all high-flow links. The representativity of these low-flow cliques is higher in the temporal framework. Our results suggest that the flow between vertices connected in cliques depend on the topological context in which they are placed and in the time sequence in which the links are established. The structure of the clique alone does not completely characterize the potential of flow between the vertices.

We study the formation of localized structures, often called localized spots, in reaction-diffusion systems subject to time delayed feedback control. We focus on the regime close to a second-order critical point marking the onset of a hysteresis loop. We show that the space-time dynamics of the FitzHugh-Nagumo model in the vicinity of that critical point could be described by the delayed Swift-Hohenberg equation. We show that the delayed feedback induces a spontaneous motion of localized spots. We characterize this motion by computing analytically the velocity and the threshold above which localized structures start to move in an arbitrary direction. Numerical solutions of the governing equation are in close agreement with those obtained from the delayed Swift-Hohenberg equation.

Two-dimensional particle-in-cell (PIC) simulations have been performed to demonstrate how chirping the pump laser beam can make the seed backward Raman amplification more efficient. The PIC code ocean is detailed and validated with theoretical analysis of the three-wave coupling. Particular attention is devoted to the impact of numerical noise on Raman scattering. Once the numerical parameters are set, one- and two-dimensional simulations exhibit the ability to suppress the pedestal pulse preceding the amplified seed laser beam and lower the spontaneous Raman scattering by appropriately choosing the pump chirp value.

The expansion of a semi-infinite plasma slab into vacuum is analyzed with a hydrodynamic model implying a steplike electron energy distribution function. Analytic expressions for the maximum ion energy and the related ion distribution function are derived and compared with one-dimensional numerical simulations. The choice of the specific non-Maxwellian initial electron energy distribution automatically ensures the conservation of the total energy of the system. The estimated ion energies may differ by an order of magnitude from the values obtained with an adiabatic expansion model supposing a Maxwellian electron distribution. Furthermore, good agreement with data from experiments using laser pulses of ultrashort durations ${\tau }_{\mathrm{L}}\lesssim 80\mathrm{fs}$ is found, while this is not the case when a hot Maxwellian electron distribution is assumed.

The law for the refraction of a wave when the two fluids and the interface are moving with relativistic velocities is given in an exact form, at the same time correcting a first order error in a previous paper [Cavalleri and Tonni, Phys. Rev. E 57, 3478 (1998)]. The treatment is then extended to a generally moving fluid with variable refractive index, ready to be applied to the refraction of acoustic, electromagnetic, or magnetohydrodynamic waves in the atmosphere of rapidly rotating stars. In the particular case of a gas cloud receding because of the universe expansion, our result can be applied to predict observable micro- and mesolensings. The first order approximation of our exact result for the deviation due to refraction of the light coming from a further quasar has a relativistic dependence equal to the one obtained by Einsteins’ linearized theory of gravitation.

We outline a possibility of hyperbolic chaotic dynamics associated with the expanding circle map for spatial phases of parametrically excited standing wave patterns. The model system is governed by a one-dimensional wave equation with nonlinear dissipation. The phenomenon arises due to the pump modulation providing the alternating excitation of modes with the ratio of characteristic scales $1:3$.

Experimental realizations of a one-dimensional (1D) interface always exhibit a finite microscopic width $\xi >0$; its influence is erased by thermal fluctuations at sufficiently high temperatures, but turns out to be a crucial ingredient for the description of the interface fluctuations below a characteristic temperature $T_c\left(\xi \right)$. Exploiting the exact mapping between the static 1D interface and a 1+1 directed polymer (DP) growing in a continuous space, we study analytically both the free-energy and geometrical fluctuations of a DP, at finite temperature $T$, with a short-range elasticity and submitted to a quenched random-bond Gaussian disorder of finite correlation length $\xi$. We derive the exact time-evolution equations of the disorder free energy $\overline{F}(t,y)$, which encodes the microscopic disorder integrated by the DP up to a growing time $t$ and an endpoint position $y$, its derivative $\eta (t,y)$, and their respective two-point correlators $\overline{C}(t,y)$ and $\overline{R}(t,y)$. We compute the exact solution of its linearized evolution ${\overline{R}}^{\mathrm{lin}}(t,y)$ and we combine its qualitative behavior and the asymptotic properties known for an uncorrelated disorder ($\xi =0$) to justify the construction of a “toy model” leading to a simple description of the DP properties. This model is characterized by Gaussian Brownian-type free-energy fluctuations, correlated at small $\left|y\right|\lesssim \xi$, and of amplitude ${\tilde{D}}_{\infty }(T,\xi )$. We present an extended scaling analysis of the roughness, supported by saddle-point arguments on its path-integral representation, which predicts ${\tilde{D}}_{\infty }\sim 1/T$ at high temperatures and ${\tilde{D}}_{\infty }\sim 1/T_c\left(\xi \right)$ at low temperatures. We identify the connection between the temperature-induced crossover of ${\tilde{D}}_{\infty }(T,\xi )$ and the full replica symmetry breaking in previous Gaussian variational method (GVM) computations. In order to refine our toy model with respect to finite-time geometrical fluctuations, we propose an effective time-dependent amplitude ${\tilde{D}}_t$. Finally, we discuss the consequences of the low-temperature regime for two experimental realizations of Kardar-Parisi-Zhang interfaces, namely, the static and quasistatic behavior of magnetic domain walls and the high-velocity steady-state dynamics of interfaces in liquid crystals.