The dynamical behavior of a higher-order cubic Ginzburg-Landau equation is found to include a wide range of scenarios due to the interplay of higher-order physically relevant terms. We find that the competition between the third-order dispersion and stimulated Raman scattering effects gives rise to rich dynamics: this extends from Poincaré-Bendixson–type scenarios, in the sense that bounded solutions may converge either to distinct equilibria via orbital connections or to space-time periodic solutions, to the emergence of almost periodic and chaotic behavior. One of our main results is that third-order dispersion has a dominant role in the development of such complex dynamics, since it can be chiefly responsible (even in the absence of other higher-order effects) for the existence of periodic, quasiperiodic, and chaotic spatiotemporal structures. Suitable low-dimensional phase-space diagnostics are devised and used to illustrate the different possibilities and identify their respective parametric intervals over multiple parameters of the model.

Isostables and isostable reduction, analogous to isochrons and phase reduction for oscillatory systems, are useful in the study of nonlinear equations which asymptotically approach a stationary solution. In this work, we present a general method for isostable reduction of partial differential equations, with the potential power to reduce the dimensionality of a nonlinear system from infinity to 1. We illustrate the utility of this reduction by applying it to two different models with biological relevance. In the first example, isostable reduction of the Fokker-Planck equation provides the necessary framework to design a simple control strategy to desynchronize a population of pathologically synchronized oscillatory neurons, as might be relevant to Parkinson's disease. Another example analyzes a nonlinear reaction-diffusion equation with relevance to action potential propagation in a cardiac system.

For a network formed by nodes and undirected links between pairs of nodes, the network optimal attack problem aims at deleting a minimum number of target nodes to break the network down into many small components. This problem is intrinsically related to the feedback vertex set problem that was successfully tackled by spin-glass theory and an associated belief propagation-guided decimation (BPD) algorithm [Zhou, Eur. Phys. J. B 86, 455 (2013)]. In the present work we apply the BPD algorithm (which has approximately linear time complexity) to the network optimal attack problem and demonstrate that it has much better performance than a recently proposed collective information algorithm [Morone and Makse, Nature 524, 65 (2015)] for different types of random networks and real-world network instances. The BPD-guided attack scheme often induces an abrupt collapse of the whole network, which may make it very difficult to defend.

In this article, we perform a computational investigation of a nanopore connected to external fluidic reservoirs of asymmetric geometries. The asymmetry between the reservoirs is achieved by changing the cross-sectional areas, and the reservoirs are designated as the micropore reservoir and macropore reservoir. When an electric field is applied, which is directed from the macropore towards the micropore reservoir, we observe local nonequilibrium chaotic current oscillations. The current oscillations originate at the micropore-nanopore interface owing to the local cascade of ions; we refer to this phenomenon as the “avalanche effects.” We mathematically quantify chaos in terms of the maximum Lyapunov exponent. The maximum Lyapunov exponent exhibits a monotonic increase with the applied voltage and the macropore reservoir diameter. The temporal power spectra maps of the chaotic currents depict a low-frequency “$1/f$”-type dynamics for the voltage chaos and “$1/f^2$”-type dynamics for the macropore reservoir chaos. The results presented here offer avenues to manipulate ionic diodes and fluidic pumps.

We propose a mechanism of adherent cell mechanosensing, based on the idea that the contractile actomyosin machinery behaves as a catch bond. For this, we construct a simplified model of the actomyosin structure that constitutes the building block of stress fibers and express the stability of cross bridges in terms of the force-dependent bonding energy of the actomyosin bond. Consistent with experimental measurements, we then consider that the energy barrier of the actomyosin bond increases for tension and show that this response is enough to explain the force-induced stabilization of a stress fiber. Further numerical simulations at the cellular level show that the catch-bond hypothesis can help in understanding and predict the sensitivity of adherent cells to substrate stiffness.

We report on the short-time dynamics in colloidal mixtures made up of monomers and dimers highly confined between two glass plates. At low concentrations, the experimental measurements of colloidal motion agree well with the solution of the Navier-Stokes equation at low Reynolds numbers; the latter takes into account the increase in the drag force on a colloidal particle due to wall-particle hydrodynamic forces. More importantly, we find that the ratio of the short-time diffusion coefficient of the monomer and that of the center of mass of the dimmer is almost independent of both the dimer molar fraction, $x_d$, and the total packing fraction, $\varphi$, up to $\varphi \approx 0.5$. At higher concentrations, this ratio displays a small but systematic increase. A similar physical scenario is observed for the ratio between the parallel and the perpendicular components of the short-time diffusion coefficients of the dimer. This dynamical behavior is corroborated by means of molecular dynamics computer simulations that include explicitly the particle-particle hydrodynamic forces induced by the solvent. Our results suggest that the effects of colloid-colloid hydrodynamic interactions on the short-time diffusion coefficients are almost identical and factorable in both species.

The study of chemical segregation at interfaces, and in particular the ability to predict the thickness of segregated layers via analytical expressions or computational modeling, is a fundamentally challenging topic in the design of novel heterostructured materials. This issue is particularly relevant for the phase-field (PF) methodology, which has become a prominent tool for describing phase transitions. These models rely on phenomenological parameters that pertain to the interfacial energy and thickness, quantities that cannot be experimentally measured. Instead of back-calculating these parameters from experimental data, here we combine a set of analytical expressions based on the Cahn-Hilliard approach with ab initio calculations to compute the gradient energy parameter κ and the thickness λ of the segregated Li layer at the ${\mathrm{Li}}_x\text{Si}$-Cu interface. With this bottom-up approach we calculate the thickness λ of the Li diffuse interface to be on the order of a few nm, in agreement with prior experimental secondary ion mass spectrometry observations. Our analysis indicates that Li segregation is primarily driven by solution thermodynamics, while the strain contribution in this system is relatively small. This combined scheme provides an essential first step in the systematic evaluation of the thermodynamic parameters of the PF methodology, and we believe that it can serve as a framework for the development of quantitative interface models in the field of Li-ion batteries.

A core is formed at the center of a quasi-two-dimensional rotating drum filled more than half with granular material. The core rotates slightly faster than the drum (precession) and decreases in radius over time (erosion) due to the granular creeping motion that occurs below the freely flowing layer. This paper focuses on the effect of the surface roughness of particles on core dynamics, core precession, and core erosion. Two different surface roughness of glass particles having the same diameter were used in the experiments. The surface structures of the particles were quantitatively compared by measuring the coefficients of friction and using a simple image contrast method. The experiments were performed with five different filling levels in a 50-cm-diameter rotating drum. According to the results, core precession and core erosion are both dependent on the particle surface roughness. Core precession becomes weaker and erosion becomes stronger when using particles having a rough surface in the experiments. To explain the physics of core dynamics, the particles' surface roughness effect on the freely flowing layer and the creeping motion region were also investigated. The granular bed velocity field, maximum flowing layer depth $\delta$, shear rate in the flowing layer $\dot{\gamma }$, and the creeping region decay constant $y_0$ were also calculated in this paper. The effect of the particles' surface roughness on these physical variables well illustrates the physics of core dynamics and creeping granular motion.

Numerical simulations of the dissolution of an air nanobubble in water have been performed taking into account the effect of bubble dynamics (inertia of the surrounding liquid). The presence of stable bulk nanobubbles is not assumed in the present study because the bubble radius inevitably passes the nanoscale in the complete dissolution of a bubble. The bubble surface is assumed to be clean because attachment of hydrophobic materials on the bubble surface could considerably change the gas diffusion rate. The speed of the bubble collapse (the bubble wall speed) increases to about 90 m/s or less. The shape of a bubble is kept nearly spherical because the amplitude of the nonspherical component of the bubble shape is negligible compared to the instantaneous bubble radius. In other words, a bubble never disintegrates into daughter bubbles during the dissolution. At the final moment of the dissolution, the temperature inside a bubble increases to about 3000 K due to the quasiadiabatic compression. The bubble temperature is higher than 1000 K only for the final 19 ps. However, the Knudsen number is more than 0.2 for this moment, and the error associated with the continuum model should be considerable. In the final 2.3 ns, only nitrogen molecules are present inside a bubble as the solubility of nitrogen is the lowest among the gas species. The radical formation inside a bubble is negligible because the probability of nitrogen dissociation is only on the order of ${10}^{-15}$. The pressure inside a bubble, as well as the liquid pressure at the bubble wall, increases to about 5 GPa at the final moment of dissolution. The pressure is higher than 1 GPa for the final 0.7 ns inside a bubble and for the final 0.6 ns in the liquid at the bubble wall. The liquid temperature at the bubble wall increases to about 360 K from 293 K at the final stage of the complete dissolution.

A molecular dynamics simulation of the demixing process of a binary complex plasma is analyzed and the role of distinct interaction potentials is discussed by using morphological Minkowski tensor analysis of the minority phase domain growth in a demixing simulated binary complex plasma. These Minkowski tensor methods are compared with previous results that utilized a power spectrum method based on the time-dependent average structure factor. It is shown that the Minkowski tensor methods are superior to the previously used power-spectrum method in the sense of higher sensitivity to changes in domain size. By analysis of the slope of the temporal evolution of Minkowski tensor measures, qualitative differences between the case of particle interaction with a single length scale compared to particle interactions with two different length scales (dominating long-range interaction) are revealed. After proper scaling the graphs for the two length scale scenarios coincide, pointing toward universal behavior. The qualitative difference in demixing scenarios is evidenced by distinct demixing behavior: in the long-range dominated cases demixing occurs in two stages. At first, neighboring particles agglomerate, then domains start to merge in cascades. However, in the case of only one interaction length scale only agglomeration but no merging of domains can be observed. Thus, Minkowski tensor analysis is likely to become a useful tool for further investigation of this (and other) demixing processes. It is capable to reveal (nonlinear) local topological properties, probing deeper than (linear) global power-spectrum analysis, however, still providing easily interpretable results founded on a solid mathematical framework.

We investigate the onset of intermittency for vibrating elastic plate turbulence in the framework of the weak wave turbulence theory using a numerical approach. The spectrum of the displacement field and the structure functions of the fluctuations are computed for different forcing amplitudes. At low forcing, the spectrum predicted by the theory is observed, while the fluctuations are consistent with Gaussian statistics. When the forcing is increased, the spectrum varies at large scales, corresponding to the oscillations of nonlinear structures made of ridges delimited by $d$ cones. In this regime, the fluctuations exhibit small-scale intermittency that can be fitted via a multifractal model. The analysis of the nonlinear frequency shows that the intermittency is linked to the breakdown of the weak turbulence at large scales only.

Recently, anomalous subdiffusion, aging, and scatter of the diffusion coefficient have been reported in many single-particle-tracking experiments, though the origins of these behaviors are still elusive. Here, as a model to describe such phenomena, we investigate a Langevin equation with diffusivity fluctuating between a fast and a slow state. Namely, the diffusivity follows a dichotomous stochastic process. We assume that the sojourn time distributions of these two states are given by power laws. It is shown that, for a nonequilibrium ensemble, the ensemble-averaged mean-square displacement (MSD) shows transient subdiffusion. In contrast, the time-averaged MSD shows normal diffusion, but an effective diffusion coefficient transiently shows aging behavior. The propagator is non-Gaussian for short time and converges to a Gaussian distribution in a long-time limit; this convergence to Gaussian is extremely slow for some parameter values. For equilibrium ensembles, both ensemble-averaged and time-averaged MSDs show only normal diffusion and thus we cannot detect any traces of the fluctuating diffusivity with these MSDs. Therefore, as an alternative approach to characterizing the fluctuating diffusivity, the relative standard deviation (RSD) of the time-averaged MSD is utilized and it is shown that the RSD exhibits slow relaxation as a signature of the long-time correlation in the fluctuating diffusivity. Furthermore, it is shown that the RSD is related to a non-Gaussian parameter of the propagator. To obtain these theoretical results, we develop a two-state renewal theory as an analytical tool.

We study traffic in a roundabout model, where the dynamics along the interior lane of the roundabout are described by the totally asymmetric simple exclusion process (TASEP). Vehicles can enter the interior lane or exit from it via $S$ intersecting streets with given rates, and locally modified dynamics at the junctions take into account that collisions of entering vehicles with vehicles approaching the entrance point from the interior lane should be avoided. A route matrix specifies the probabilities for vehicles to arrive from and to exit to certain intersecting streets. By subdividing the interior lane into segments between consecutive intersecting streets with effective entrance and exit rates, a classification of the stationary roundabout traffic in terms of TASEP multiphases is given, where each segment can be in either the low-density, high-density, or maximum current TASEP phase. A general methodology is developed, which allows one to calculate the multiphases and optimal throughput conditions based on a mean-field treatment. Explicit analytical results from this treatment are derived for equivalent interesting streets. The results are shown to be in good agreement with kinetic Monte Carlo simulations.

The phase-field crystal (PFC) technique is a widely used approach for modeling crystal growth phenomena with atomistic resolution on mesoscopic time scales. We use a two-dimensional PFC model for a binary system based on the work of Elder et al. [Phys. Rev. B 75, 064107 (2007)] to study the effect of the curved, diffuse solid-liquid interface on the interfacial energy as well as the nucleation barrier. The calculation of the interfacial energy and the nucleation barrier certainly depends on the proper definition of the solid-liquid dividing surface and the corresponding nucleus size. We define the position of the sharp interface at which the interfacial energy is to be evaluated by using the concept of equimolar dividing surface ($r^e$) and the minimization of the interfacial energy ($r^s$). The comparison of the results based on both radii shows that the difference $r^e-r^s$ is always positive and has a limit for large cluster sizes which is comparable to the Tolman length. Furthermore, we found the real nucleation barrier for small cluster sizes, which is defined as a function of the radius $r^s$, and compared it with the classical nucleation theory. The simulation results also show that the extracted interfacial energy as function of both radii is independent of system size, and this dependence can be reasonably described by the nonclassical Tolman formula with a positive Tolman length.

Hyperuniformity characterizes a state of matter that is poised at a critical point at which density or volume-fraction fluctuations are anomalously suppressed at infinite wavelengths. Recently, much attention has been given to the link between strict jamming (mechanical rigidity) and (effective or exact) hyperuniformity in frictionless hard-particle packings. However, in doing so, one must necessarily study very large packings in order to access the long-ranged behavior and to ensure that the packings are truly jammed. We modify the rigorous linear programming method of Donev et al. [J. Comput. Phys. 197, 139 (2004)] in order to test for jamming in putatively collectively and strictly jammed packings of hard disks in two dimensions. We show that this rigorous jamming test is superior to standard ways to ascertain jamming, including the so-called “pressure-leak” test. We find that various standard packing protocols struggle to reliably create packings that are jammed for even modest system sizes of $N\approx {10}^3$ bidisperse disks in two dimensions; importantly, these packings have a high reduced pressure that persists over extended amounts of time, meaning that they appear to be jammed by conventional tests, though rigorous jamming tests reveal that they are not. We present evidence that suggests that deviations from hyperuniformity in putative maximally random jammed (MRJ) packings can in part be explained by a shortcoming of the numerical protocols to generate exactly jammed configurations as a result of a type of “critical slowing down” as the packing's collective rearrangements in configuration space become locally confined by high-dimensional “bottlenecks” from which escape is a rare event. Additionally, various protocols are able to produce packings exhibiting hyperuniformity to different extents, but this is because certain protocols are better able to approach exactly jammed configurations. Nonetheless, while one should not generally expect exact hyperuniformity for disordered packings with rattlers, we find that when jamming is ensured, our packings are very nearly hyperuniform, and deviations from hyperuniformity correlate with an inability to ensure jamming, suggesting that strict jamming and hyperuniformity are indeed linked. This raises the possibility that the ideal MRJ packings have no rattlers. Our work provides the impetus for the development of packing algorithms that produce large disordered strictly jammed packings that are rattler free, which is an outstanding, challenging task.

Quantum work is usually determined from two projective measurements of the energy at the beginning and at the end of a thermodynamic process. However, this paradigm cannot be considered thermodynamically consistent as it does not account for the thermodynamic cost of these measurements. To remedy this conceptual inconsistency we introduce a paradigm that relies only on the expected change of the average energy given the initial energy eigenbasis. In particular, we completely omit quantum measurements in the definition of quantum work, and hence quantum work is identified as a thermodynamic quantity of only the system. As main results we derive a modified quantum Jarzynski equality and a sharpened maximum work theorem in terms of the information free energy. A comparison of our results with the standard approach allows one to quantify the informational cost of projective measurements.

It is shown that direct-drive implosions on the OMEGA laser have achieved core conditions that would lead to significant alpha heating at incident energies available on the National Ignition Facility (NIF) scale. The extrapolation of the experimental results from OMEGA to NIF energy assumes only that the implosion hydrodynamic efficiency is unchanged at higher energies. This approach is independent of the uncertainties in the physical mechanism that degrade implosions on OMEGA, and relies solely on a volumetric scaling of the experimentally observed core conditions. It is estimated that the current best-performing OMEGA implosion [Regan et al., Phys. Rev. Lett. 117, 025001 (2016)] extrapolated to a 1.9 MJ laser driver with the same illumination configuration and laser-target coupling would produce 125 kJ of fusion energy with similar levels of alpha heating observed in current highest performing indirect-drive NIF implosions.

Statistical systems composed of atoms interacting with each other trough nonintegrable interaction potentials are considered. Examples of these potentials are hard-core potentials and long-range potentials, for instance, the Lennard-Jones and dipolar potentials. The treatment of such potentials is known to confront several problems, e.g., the impossibility of using the standard mean-field approximations, such as Hartree and Hartree-Fock approximations, the impossibility of directly introducing coherent states, the difficulty in breaking the global gauge symmetry, which is required for describing Bose-Einstein condensed and superfluid systems, the absence of a correctly defined Fourier transform, which hampers the description of uniform matter as well as the use of local-density approximation for nonuniform systems. A novel iterative procedure for describing such systems is developed, starting from a correlated mean-field approximation, allowing for a systematic derivation of higher orders, and meeting no problems listed above. The procedure is applicable to arbitrary systems, whether equilibrium or nonequilibrium. The specification for equilibrium systems is presented. The method of extrapolating the expressions for observable quantities from weak coupling to strong coupling is described.