We describe a numerical scheme for exactly simulating the heat current behavior in a quantum harmonic chain with self-consistent reservoirs. Numerically exact results are compared to classical simulations and to the quantum behavior under the linear-response approximation. In the classical limit or for small temperature biases our results coincide with previous calculations. At large bias and for low temperatures the quantum dynamics of the system fundamentally differs from the close-to-equilibrium behavior, revealing in particular the effect of thermal rectification for asymmetric chains. Since this effect is absent in the classical analog of our model, we conclude that in the quantum model studied here thermal rectification is a purely quantum phenomenon, rooted in the quantum statistics.

Granular material freely discharging from a hopper under gravity is one of the oldest and most widely studied problems in granular flow. Despite the apparent simplicity of the system, expressions relating the discharge rate of the hopper to the properties of the individual grains are difficult to determine and typically empirical in nature. A mathematical model for discharge from a hopper is derived based on the dynamics of individual particles just within the outlet. In contrast to previous models, this analysis derives a flow rate from granular dynamics, rather than dimensional arguments. The model, therefore, uses no assumptions about the form of the stress distribution within the hopper, or the addition of empirical factors or fitting parameters. Our model gives a flow rate identical in form to a well-known empirical expression, showing that an experimentally determined constant used in this expression is purely geometry-dependent. Our analysis is also extended to derive an expression for the flow rate incorporating gas drag, which becomes dominant at small grain sizes, significantly reducing the outflow rate. The resulting expression shows excellent agreement with a range of computational simulations using a coupled discrete element and Navier-Stokes method. These simulations also show that the gas flow is much more complex than previously assumed in this region, and simplified assumptions used in prior hopper flow models do not hold.

Three-dimensional phase-field simulations are employed to investigate rod-type eutectic growth morphologies in confined geometry. Distinct steady-state solutions are found to depend on this confinement effect with the rod array basis vectors and their included angle ($\alpha$) changing to accommodate the geometrical constraint. Specific morphologies are observed, including rods of circular cross sections, rods of distorted (elliptical) cross sections, rods of peanut-shaped cross-sections, and lamellar structures. The results show that, for a fixed value of $\alpha >{10}^{\circ }$, the usual (triangular) arrays of circular rods are stable in a broad range of spacings, with a transition to the peanut-shaped cross sectioned rods occurring at large spacings (above 1.5 times the minimum undercooling spacing ${\lambda }_{\mathrm{m}}$), and the advent of rod eliminations at low spacings. Furthermore, a transition from rod to lamellar structures is observed for $\alpha <{10}^{\circ }$ for the phase fraction of 10.5% used in the present paper.

We propose a field-theoretical approach to a polymer system immersed in an ideal mixture of clustering centers. The system contains several species of these clustering centers with different functionality, each of which connects a fixed number segments of the chain to each other. The field theory is solved using the saddle point approximation and evaluated for dense polymer melts using the random phase approximation. We find a short-ranged effective intersegment interaction with strength dependent on the average segment density and discuss the structure factor within this approximation. We also determine the fractions of linkers of the different functionalities.

The possibility of inducing a magnetic field via surface plasma-wave excitation is investigated with a simple nonrelativistic hydrodynamic model. A static magnetic field is predicted at the plasma surface, scaling with the square of the surface-wave field amplitude, and the influence of the electron plasma density is studied. In the case of resonant surface-wave excitation by laser this result can be applied to low intensities such that the electron quiver velocity in the field of the surface wave is less than its thermal velocity.

We study some properties of eigenvalue spectra of financial correlation matrices. In particular, we investigate the nature of the large eigenvalue bulks which are observed empirically, and which have often been regarded as a consequence of the supposedly large amount of noise contained in financial data. We challenge this common knowledge by acting on the empirical correlation matrices of two data sets with a filtering procedure which highlights some of the cluster structure they contain, and we analyze the consequences of such filtering on eigenvalue spectra. We show that empirically observed eigenvalue bulks emerge as superpositions of smaller structures, which in turn emerge as a consequence of cross correlations between stocks. We interpret and corroborate these findings in terms of factor models, and we compare empirical spectra to those predicted by random matrix theory for such models.

Detecting communities in large networks has drawn much attention over the years. While modularity remains one of the more popular methods of community detection, the so-called resolution limit remains a significant drawback. To overcome this issue, it was recently suggested that instead of comparing the network to a random null model, as is done in modularity, it should be compared to a constant factor. However, it is unclear what is meant exactly by “resolution-limit-free,” that is, not suffering from the resolution limit. Furthermore, the question remains what other methods could be classified as resolution-limit-free. In this paper we suggest a rigorous definition and derive some basic properties of resolution-limit-free methods. More importantly, we are able to prove exactly which class of community detection methods are resolution-limit-free. Furthermore, we analyze which methods are not resolution-limit-free, suggesting there is only a limited scope for resolution-limit-free community detection methods. Finally, we provide such a natural formulation, and show it performs superbly.

We discuss avalanche and finite-size fluctuations in a mesoscopic model to describe the shear plasticity of amorphous materials. Plastic deformation is assumed to occur through series of local reorganizations. Yield stress criteria are random while each plastic slip event induces a quadrupolar long-range elastic stress redistribution. The model is discretized on a regular square lattice. Shear plasticity can be studied in this context as a depinning dynamic phase transition. We show evidence for a scale-free distribution of avalanches $P(s)\propto S^{-\kappa }$ with a nontrivial exponent $\kappa \approx 1.25$ significantly different from the mean field result $\kappa =1.5$. Finite-size effects allow for a characterization of the scaling invariance of the yield stress fluctuations observed in small samples. We finally identify a population of precursors of plastic activity and characterize its spatial distribution.

Many real networks display modular organization, which can influence dynamical clustering on the networks. Therefore, there have been proposals put forth recently to detect network communities by using dynamical clustering. In this paper, we study how the feedback from dynamical clusters can shape the network connection weights with a weight-adaptation scheme motivated from Hebbian learning in neural systems. We show that such a scheme generically leads to the formation of community structure in globally coupled chaotic oscillators. The number of communities in the adaptive network depends on coupling strength $c$ and adaptation strength $r$. In a modular network, the adaptation scheme will enhance the intramodule connection weights and weaken the intermodule connection strengths, generating effectively separated dynamical clusters that coincide with the communities of the network. In this sense, the modularity of the network is amplified by the adaptation. Thus, for a network with a strong community structure, the adaptation scheme can evidently reflect its community structure by the resulting amplified weighted network. For a network with a weak community structure, the statistical properties of synchronization clusters from different realizations can be used to amplify the modularity of the communities so that they can be detected reliably by the other traditional algorithms.

We study a chain of $N+1$ phase oscillators with asymmetric but uniform coupling. This type of chain possesses $2^N$ ways to synchronize in so-called traveling wave states, i.e., states where the phases of the single oscillators are in relative equilibrium. We show that the number of unstable dimensions of a traveling wave equals the number of oscillators with relative phase close to $\pi$. This implies that only the relative equilibrium corresponding to approximate in-phase synchronization is locally stable. Despite the presence of a Lyapunov-type functional, periodic or chaotic phase slipping occurs. For chains of lengths $3$ and $4$ we locate the region in parameter space where rotations (corresponding to phase slipping) are present.

The paper proposes an approach to constructing feasible examples of dynamical systems with hyperbolic chaotic attractors based on the successive transfer of excitation between two pairs of self-oscillators that are alternately active. An angular variable that measures the relations of the current amplitudes for the two oscillators of each pair undergoes a transformation in accordance with the expanding circle map during each cycle of the process. We start with equations describing the dynamics in terms of complex or real amplitudes and then examine two models based on van der Pol oscillators. One model corresponds to the situation of equality of natural frequencies of the partial oscillators, and another to a nonresonant ratio of the oscillation frequencies relating to each of the two pairs. Dynamics of all models are illustrated with diagrams indicating the transformation of the angular variables, portraits of attractors, Lyapunov exponents, etc. The uniformly hyperbolic nature of the attractor in the stroboscopic Poincaré map is confirmed for a real-amplitude version of the equations by computations of statistical distribution of angles between stable and unstable manifolds at a representative set of points on the attractor. In other versions of the equations the attractors relate presumably to the partially hyperbolic class.

We consider optimization of phase response curves for stochastic synchronization of noninteracting limit-cycle oscillators by common Poisson impulsive signals. The optimal functional shape for sufficiently weak signals is sinusoidal, but can differ for stronger signals. By solving the Euler-Lagrange equation associated with the minimization of the Lyapunov exponent characterizing synchronization efficiency, the optimal phase response curve is obtained. We show that the optimal shape mutates from a sinusoid to a sawtooth as the constraint on its squared amplitude is varied.

In this work we investigate the inverse of the celebrated Bohigas-Giannoni-Schmit conjecture. Using two inversion methods we compute a one-dimensional potential whose lowest $N$ eigenvalues obey random matrix statistics. Our numerical results indicate that in the asymptotic limit $N\to \infty$ the solution is nowhere differentiable and most probably nowhere continuous. Thus such a counterexample does not exist.

The collective dynamics of oscillator networks with phase-repulsive coupling is studied, considering various network sizes and topologies. The notion of link frustration is introduced to characterize and quantify the network dynamical states. In opposition to widely studied phase-attractive case, the properties of final dynamical states in our model critically depend on the network topology. In particular, each network’s total frustration value is intimately related to its topology. Moreover, phase-repulsive networks in general display multiple final frustration states, whose statistical and stability properties are uniquely identifying them.

The question of whether liquid atomization depends on instability dynamics (through refinements of Rayleigh-Plateau, Rayleigh-Taylor, or Kelvin-Helmholtz mechanisms) or on turbulent cascades, as suggested by Richardson and Kolmogorov, is still open. In this paper, experimental results reveal that both mechanisms are needed to explain the probability density functions (PDFs) of the droplets in a spray obtained from an industrial fan spray nozzle. Instability of Rayleigh-Taylor type controls the size of the largest droplets while the smallest droplets follow a PDF given by a turbulent cascading mechanism characterized by a log-Lévy stable law that has a stability parameter equal to 1.70. This value is very close to the inverse value of the Flory exponent and can be related to a recent model developed by N. Rimbert for intermittency modeling stemming from self-avoiding random vortex stretching.

We introduce a general implementation of the recently proposed homogenization theory [Tsukerman, J. Opt. Soc. Am. B 28, 577 (2011)] allowing one to retrieve all 36 linear constitutive parameters of any 3D metamaterial with parallelepipedal unit cells. The effective parameters are defined directly as linear relations between pairs of coarse-grained fields, in contrast with methods where these parameters are obtained from reflection and transmission data or other indirect considerations. The method is applied to plasmonic metamaterials with spherical gold particles and split-ring resonators (SRR), respectively. In both cases, the expected physical behavior is reproduced almost perfectly, with no unphysical artifacts.

I use quaternion free probability calculus—an extension of free probability to non-Hermitian matrices (which is introduced in a succinct but self-contained way)—to derive in the large-size limit the mean densities of the eigenvalues and singular values of sums of independent unitary random matrices, weighted by complex numbers. In the case of circular unitary ensemble summands, I write them in terms of two “master equations,” which I then solve and numerically test in four specific cases. I conjecture a finite-size extension of these results, exploiting the complementary error function. I prove a central limit theorem, and its first subleading correction, for independent identically distributed zero-drift unitary random matrices.

The position of propagating population fronts fluctuates because of the discreteness of the individuals and stochastic character of processes of birth, death, and migration. Here we consider a Markov model of a population front propagating into a metastable state, and focus on the weak noise limit. For typical, small fluctuations the front motion is diffusive, and we calculate the front diffusion coefficient. We also determine the probability distribution of rare, large fluctuations of the front position and, for a given average front velocity, find the most likely population density profile of the front. Implications of the theory for population extinction risk are briefly considered.

Using contact dynamics simulations, we compare the effect of rolling resistance at the contacts in granular systems composed of disks with the effect of angularity in granular systems composed of regular polygonal particles. In simple shear conditions, we consider four aspects of the mechanical behavior of these systems in the steady state: shear strength, solid fraction, force and fabric anisotropies, and probability distribution of contact forces. Our main finding is that, based on the energy dissipation associated with relative rotation between two particles in contact, the effect of rolling resistance can explicitly be identified with that of the number of sides in a regular polygonal particle. This finding supports the use of rolling resistance as a shape parameter accounting for particle angularity and shows unambiguously that one of the main influencing factors behind the mechanical behavior of granular systems composed of noncircular particles is the partial hindrance of rotations as a result of angular particle shape.

The transient microstructural response of dilute, depletion-induced colloidal gels to shear deformation is probed using a custom-built cone-and-plate shear cell mounted on a fast scanning confocal microscope. We directly unveil an important mode of nonlinear gel yielding, which marks the transition from an immobilized gel network to disconnected flowing clusters at large values of the accumulated strain ($\gamma \sim$ 0.7). The transition is mediated by a cascade of local rupture events that initiate at the sample's outer edges and propagate inward, resulting in transient dynamic and microstructural heterogeneities in the gel network. Based on the findings, we propose solvent-induced drag as the primary cause of nonlinear rupture, and discuss the coupling between the microstructural evolution and transient rheology in this system.