The response of amorphous solids to an applied shear deformation is an important problem, both in fundamental and in applied research. To tackle this problem, we focus on a system of hard spheres in infinite dimensions as a solvable model for colloidal systems and granular matter. The system is prepared above the dynamical glass transition density, and we discuss the phase diagram of the resulting glass under compression, decompression, and shear strain, expanding on previous results [Urbani and Zamponi, Phys. Rev. Lett. 118, 038001 (2017)]. We show that the solid region is bounded by a “shear jamming” line, at which the solid reaches close packing, and a “shear yielding” line, at which the solid undergoes a spinodal instability towards a liquid flowing phase. Furthermore, we characterize the evolution of these lines upon varying the glass preparation density. This paper aims to provide a general overview on yielding and jamming phenomena in hard-sphere systems by a systematic exploration of the phase diagram.

We theoretically study the modulation instability (MI) of the two-component helicoidal spin-orbit coupled Bose-Einstein condensates (BECs). The effects of spin-orbit coupling, the helicoidal gauge potential, and atomic interactions on MI are investigated. The results indicate that the presence of the helicoidal gauge potential breaks the symmetric properties of MI, strongly modifies the distribution of the MI region and the MI gain in parameters space, and the MI can be excited even when the miscibility condition for the atomic interactions is satisfied. Furthermore, the effect of the helicoidal gauge potential on MI is strongly coupled with the intra and intercomponent atomic interactions. Particularly, with the increase of the helical gauge potential, the MI gain increases for the repulsive atomic interaction case, however, the MI gain decreases for the attractive atomic interaction case. The direct numerical simulations are performed to support the analytical predictions, and a good agreement is found. Our results provide a potential way to manipulate the MI in BECs with helicoidal gauge potential.

Existing methods for estimating the largest Lyapunov exponent from a time series rely on the rate of separation of initially nearby trajectories reconstructed from the time series in phase space. According to Ueda, chaotic dynamical behavior is viewed as a manifestation of random transitions between unstable periodic orbits in a chaotic attractor, which are triggered by perturbations due to experimental observation or the roundoff error characteristic of the computing machine, and consequently consists of a sequence of piecewise deterministic processes instead of an entirely deterministic process. Chaotic trajectories might have no physical reality. Here, we propose a mathematical method for estimating a surrogate measure for the largest Lyapunov exponent on the basis of the random diffusion of the symbols generated from a time series in a chaotic attractor, without resorting to initially nearby trajectories. We apply the proposed method to numerical time series generated by chaotic flow models and verify its validity.

We found stable soliton solutions for two generalizations of the cubic complex Ginzburg-Landau equation, namely, one that includes the term that, in optics, represents a delayed response of the nonlinear gain and the other including the self-steepening term, also in the optical context. These solutions do not require the presence of the delayed response of the nonlinear refractive index, such that, they exist regardless of the term previously considered essential for stabilization. The existence of these solitons was predicted by a perturbation approach, and then confirmed by solving the ordinary differential equations, resulting from a similarity reduction, and also by applying a linear stability analysis. We found that these solitons exist for a large region of the parameter space and possess very asymmetric amplitude profiles as well as a complicated chirp characteristic.

Vortex-induced instability caused by a free-stream vortical excitation is explored here quantitatively with the help of controlled computational results. First, the computed results are compared with experimental results in Lim et al. [Exp. Fluids 37, 47 (2004)] for the purpose of validation of the three-dimensional (3D) computations. Thereafter, the computed results are explained using methods developed to study nonlinear and spatiotemporal aspects of receptivity and instability for incompressible flows. Here a zero-pressure-gradient (ZPG) boundary layer is perturbed by a constant strength vortex traveling at a fixed height, moving with constant speed, as in the cited experiment. The vortex is created by a translating and rotating circular cylinder in the experiment, with absolute control of the physical parameters. The sign of the translating vortex is fixed by the direction of rotation of the translating cylinder. A high accuracy computing method is employed to solve the 3D Navier-Stokes equation (NSE) for different translation speeds and signs of the free-stream vortex. A nonlinear disturbance enstrophy transport equation (DETE) for incompressible flows is used to explain the vortex-induced instability. This equation is exact and explains the instabilities, as governed by the NSE. The DETE approach has been successfully developed to explain two-dimensional (2D) vortex-induced instability in Sengupta et al. [Phys. Fluids 30, 054106 (2018)], to trace the linear and nonlinear stages of disturbance growth. Apart from quantification of vortex-induced instability, another major goal is to show how the disturbance evolves from an initial 2D to a 3D stage. While the sign of the translating vortex is important in creating the response field, we additionally highlight the distinct differences caused by increased translation speed and strength of the free-stream vortex on the overall instability. These explain creation of small-scale vortices via the instability of an equilibrium flow, even though the excitation is 2D only. For some cases, this causes 3D bypass transition. We also show a case which demonstrates strong unsteady separation with inflectional velocity profiles, yet the disturbance flow remains essentially 2D, which can be termed a bypass transition.

A profile-evolving simulation of the Controlled Shear Decorrelation Experiment (CSDX) linear device is performed with our newly developed code. The simulation result shows an excellent agreement with the experimental observations of profiles and fluctuations of plasma density and electric potential in the $B=1000$ G standard discharges, suggesting the mechanism of their evolutions. According to our simulation, an avalanche of plasma density, featuring a rapid destruction of particle profile, is triggered every time the dominant instability transits from near adiabatic collisional drift wave to non-adiabatic Kelvin-Helmholtz instability. The avalanches always start at the point where the local vorticity is the maximum among the whole device. A critical vorticity is found for any avalanche to happen. The avalanches always lead to intermittent particle and heat convective structures outside the main plasma column, and these structures are ejected out as avaloids when zonal flow intensity at birth time is weak.

A new analysis of elastic properties of dense hard-sphere (HS) fluids is presented, based on the expressions derived by Miller [J. Chem. Phys. 50, 2733 (1969)]. Important consequences for HS fluids in terms of sound waves propagation, Poisson's ratio, Stokes-Einstein relation, and generalized Cauchy identity are explored. Conventional expressions for high-frequency elastic moduli for simple systems with continuous and differentiable interatomic interaction potentials are known to diverge when approaching the HS repulsive limit. The origin of this divergence is identified here. It is demonstrated that these conventional expressions are only applicable for sufficiently soft interactions and should not be applied to HS systems. The reported results can be of interest in the context of statistical physics, physics of fluids, soft condensed matter, and granular materials.

Understanding heat transport in one-dimensional systems remains a major challenge in theoretical physics, both from the quantum as well as from the classical point of view. In fact, steady states of one-dimensional systems are commonly characterized by macroscopic inhomogeneities, and by long-range correlations, as well as large fluctuations that are typically absent in standard three-dimensional thermodynamic systems. These effects violate locality—material properties in the bulk may be strongly affected by the boundaries, leading to anomalous energy transport—and they make more problematic the interpretation of mechanical microscopic quantities in terms of thermodynamic observables. Here, we revisit the problem of heat conduction in chains of classical nonlinear oscillators, following a Lagrangian and a Eulerian approach. The Eulerian definition of the flux is composed of a convective and a conductive component. The former component tends to prevail at large temperatures where the system behavior is increasingly gaslike. Finally, we find that the convective component tends to be negative in the presence of a negative pressure.

Integrable many-body systems are characterized by a complete set of preserved actions. Close to an integrable limit, a nonintegrable perturbation creates a coupling network in action space which can be short or long ranged. We analyze the dynamics of observables which become the conserved actions in the integrable limit. We compute distributions of their finite time averages and obtain the ergodization time scale $T_E$ on which these distributions converge to $\delta$ distributions. We relate $T_E$ to the statistics of fluctuation times of the observables, which acquire fat-tailed distributions with standard deviations ${\sigma }_{\tau }^{+}$ dominating the means ${\mu }_{\tau }^{+}$ and establish that $T_E\sim {\left({\sigma }_{\tau }^{+}\right)}^2/{\mu }_{\tau }^{+}$. The Lyapunov time $T_{\mathrm{\Lambda }}$ (the inverse of the largest Lyapunov exponent) is then compared to the above time scales. We use a simple Klein-Gordon chain to emulate long- and short-range coupling networks by tuning its energy density. For long-range coupling networks $T_{\mathrm{\Lambda }}\approx {\sigma }_{\tau }^{+}$, which indicates that the Lyapunov time sets the ergodization time, with chaos quickly diffusing through the coupling network. For short-range coupling networks we observe a dynamical glass, where $T_E$ grows dramatically by many orders of magnitude and greatly exceeds the Lyapunov time, which satisfies $T_{\mathrm{\Lambda }}\lesssim {\mu }_{\tau }^{+}$. This effect arises from the formation of highly fragmented inhomogeneous distributions of chaotic groups of actions, separated by growing volumes of nonchaotic regions. These structures persist up to the ergodization time $T_E$.

Autonomy is an important concept when investigating the mechanism whereby biological systems exhibit flexibility against unpredictable environmental changes. Herein we propose a parameter-tuning algorithm, based on a selection principle, that allows the emergence of synchronization between populations of oscillators through autonomous changes of the intrinsic parameters. With the algorithm, the populations exhibit self-recovery of the synchronized state after the existing synchronized state is broken suddenly; that is, the system chooses appropriate values of the intrinsic parameters to recover the synchronized state. We also propose a continuous model in which the selection is described by the replicator model and the parameter values are determined by the density profile of the oscillators in parameter space.

We study temporally localized structures in doubly resonant degenerate optical parametric oscillators in the absence of temporal walk-off. We focus on states formed through the locking of domain walls between the zero and a nonzero continuous-wave solution. We show that these states undergo collapsed snaking and we characterize their dynamics in the parameter space.

The existence of topological order is frequently associated with strongly coupled quantum matter. Here, we demonstrate the existence of topological phases in classical systems of densely packed, hard, anisotropic polyhedrally shaped colloidal particles. We show that previously reported transitions in dense packings lead to the existence of topologically ordered thermodynamic phases, which we show are stable away from the dense packing limit. Our work expands the library of known topological phases, whose experimental realization could provide new means for constructing plasmonic materials that are robust in the presence of fluctuations.

Recent research on interfacial instabilities of smectic films has shown unexpected morphologies that are not fully explained by classical local equilibrium thermodynamics. Annealing focal conic domains can lead to conical pyramids, changing the sign of the Gaussian curvature and exposing smectic layers at the interface. In order to explore the role of the Gaussian curvature on the stability and evolution of the film-vapor interface, we introduce a phase-field model of a smectic-isotropic system as a first step in the study. Through asymptotic analysis of the model, we generalize the classical condition of local equilibrium, the Gibbs-Thomson equation, to include contributions from surface bending and torsion and a dependence on the layer orientation at the interface. A full numerical solution of the phase-field model is then used to study the evolution of focal conic structures in smectic domains in contact with the isotropic phase via local evaporation and condensation of smectic layers. As in experiments, numerical solutions show that pyramidal structures emerge near the center of the focal conic owing to evaporation of adjacent smectic planes and to their orientation relative to the interface. Near the center of the focal conic domain, a correct description of the motion of the interface requires the additional curvature terms obtained in the asymptotic analysis, thus clarifying the limitations in modeling motion of hyperbolic surfaces solely driven by mean curvature.

We investigate Fickian diffusion in two-dimensional (2D) Yukawa liquids using molecular dynamics simulations. We compute the self–van Hove correlation function $G_s(r,t)$ and the self-intermediate scattering function $F_s(k,t)$, and we compare these functions with those obtained from mean-squared displacement (MSD) using the Gaussian approximation. According to this approximation, a linear MSD with time implies a Gaussian behavior for $G_s(r,t)$ and $F_s(k,t)$ at all times. Surprisingly, we find that these functions deviate from Gaussian at intermediate timescales, indicating the failure of the Gaussian approximation. Furthermore, we quantify these deviations by the non-Gaussian parameter, and we find that the deviations increase when the temperature of the liquid decreases. The origin of the non-Gaussian behavior may be the heterogeneous dynamics of dust particles observed in 2D Yukawa liquids.

We derive nonparaxial input conditions for simulations of tightly focused electromagnetic fields by means of unidirectional nonparaxial vectorial propagation equations. The derivation is based on the geometrical optics transfer of the incident electric field from significantly curved reflecting surfaces such as parabolic and conical mirrors to the input plane, with consideration of the finite thickness of the focusing element and large convergence angles, making the propagation vectorial and nonparaxial. We have benchmarked numerical solutions of propagation equations initiated with the nonparaxial input conditions against the solutions of Maxwell equations obtained by vectorial diffraction integrals. Both transverse and longitudinal components of the electric field obtained by these methods are in excellent agreement.

We add extreme driving to the Kob-Andersen kinetically constrained lattice-gas model in order to mimic the effect of gravity on dense granular systems. For low particle densities, the current that develops in the system agrees at arbitrary field intensity with a mean-field theory. At intermediate densities, spatial correlations give rise to nonmonotonic dependence of the current on field intensity. At higher densities, the current ultimately vanishes at a finite, field-dependent density. We supplement the study of this bulk behavior with an investigation of the current through a narrow hole. There, lateral flow decreases the local density in front of the hole. Remarkably, the current through the hole quantitatively agrees with a theoretical prediction based on the bulk current at the measured local density.

Topological solitons can propagate without radiation in discrete media. These solutions are known as embedded solitons (ES). They come as isolated solutions and exist despite their resonance with the linear spectrum of the respective lattices. In this paper the properties of embedded solitons in the discrete double sine-Gordon equation with next-neighbor and second-neighbor interactions are investigated. Depending on the sign of these interactions they can be either destructive or favorable for the ES creation. The ES existence area depends on the width of the linear spectrum: narrowing of the spectrum widens the ES existence range and vice versa. The application to the Josephson junction arrays is discussed.