Fast transient growth of hydrodynamic perturbations due to nonmodal effects is shown to be possible in an ablation flow relevant to inertial confinement fusion (ICF). Likely to arise in capsule ablators with material inhomogeneities, such growths appear to be too fast to be detected by existing measurement techniques, cannot be predicted by any of the methods previously used for studying hydrodynamic instabilities in ICF, yet could cause early transitions to nonlinear regimes. These findings call for reconsidering the stability of ICF flows within the framework of nonmodal stability theory.

In this paper, a finite-volume discrete Boltzmann method based on a cell-centered scheme for inviscid compressible flows on unstructured grids is presented. In the new method, the equilibrium distribution functions are obtained from the circle function in two-dimensions (2D) and the spherical function in three-dimensions (3D). Moreover, the advective fluxes are evaluated by Roe's flux-difference splitting scheme, the gradients of the density and total energy distribution functions are computed with a least-squares method, and the Venkatakrishnan limiter is employed to prevent oscillations. To parallelize the method we use a graph-based partitioning approach that also guarantees the load balancing. The method is validated by seven benchmark problems: (a) a 2D flow pasting a bump, (b) a 2D Riemann problem, (c) a 2D flow passing the RAE2822 airfoil, (d) flows passing the NACA0012 airfoil, (e) 2D supersonic flows around a cylinder, (f) an explosion in a 3D box, and (g) a 3D flow around the ONERA M6 wing. The benchmark tests show that the results obtained by the proposed method match well with the published results, and the parallel numerical experiments show that the proposed parallel implementation has close to linear strong scalability, and parallel efficiencies of $95.31\%$ and $94.56\%$ are achieved for 2D and 3D problems on a supercomputer with up to 4800 processor cores, respectively.

We revisit the densest binary sphere packings (DBSPs) under periodic boundary conditions and present an updated phase diagram, including newly found 12 putative densest structures over the $x-\alpha$ plane, where $x$ is the relative concentration and $\alpha$ is the radius ratio of the small and large spheres. To efficiently explore the DBSPs, we develop an unbiased random search approach based on both the piling-up method to generate initial structures in an unbiased way and the iterative balance method to optimize the volume of a unit cell while keeping the overlap of hard spheres minimized. With those two methods, we have discovered 12 putative DBSPs and thereby the phase diagram is updated, while our results are consistent with those of a previous study [Hopkins et al., Phys. Rev. E 85, 021130 (2012)] with a small correction for the case of 12 or fewer spheres in the unit cell. Five of the discovered 12 DBSPs are identified in the small radius range of $0.42\le \alpha \le 0.50$, where several structures are competitive to each other with respect to packing fraction. Through the exhaustive search, diverse dense packings are discovered and, accordingly, we find that packing structures achieve high packing fractions by introducing distortion and/or combining a few local dense structural units. Furthermore, we investigate the correspondence of the DBSPs with crystals based on the space group. The result shows that many structural units in real crystals, e.g., ${\mathrm{LaH}}_{10}$ and ${\mathrm{SrGe}}_{2-\delta }$ being high-pressure phases, can be understood as DBSPs. The correspondence implies that the densest sphere packings can be used effectively as structural prototypes for searching complex crystal structures, especially for high-pressure phases.

The expressive power of artificial neural networks crucially depends on the nonlinearity of their activation functions. Though a wide variety of nonlinear activation functions have been proposed for use in artificial neural networks, a detailed understanding of their role in determining the expressive power of a network has not emerged. Here, we study how activation functions affect the storage capacity of treelike two-layer networks. We relate the boundedness or divergence of the capacity in the infinite-width limit to the smoothness of the activation function, elucidating the relationship between previously studied special cases. Our results show that nonlinearity can both increase capacity and decrease the robustness of classification, and provide simple estimates for the capacity of networks with several commonly used activation functions. Furthermore, they generate a hypothesis for the functional benefit of dendritic spikes in branched neurons.

We devise a general method to extract weak signals of unknown form, buried in noise of arbitrary distribution. Central to it is signal-noise decomposition in rank and time: only stationary white noise generates data with a jointly uniform rank-time probability distribution, $U(1,N)\times U(1,N)$, for $N$ points in a data sequence. We show that rank, averaged across jointly indexed series of noisy data, tracks the underlying weak signal via a simple relation, for all noise distributions. We derive an exact analytic, distribution-independent form for the discrete covariance matrix of cumulative distributions for independent and identically distributed noise and employ its eigenfunctions to extract unknown signals from single time series.

We describe the full two-dimensional scattering of long-lived breathers in a model hexagonal lattice of atoms. The chosen system, representing an idealized model of mica, combines a Lennard-Jones interatomic potential with an “egg-box” harmonic potential well surface. We investigate the dependence of breather properties on the ratio of the well depths associated with the interaction and on-site potentials. High values of this ratio lead to large spatial displacements in adjacent chains of atoms and thus enhance the two-dimensional character of the quasi-one-dimensional breather solutions. This effect is further investigated during breather-breather collisions by following the constrained energy density function in time for a set of randomly excited mobile breather solutions. Certain collisions lead to ${60}^{\circ }$ scattering, and collisions of mobile and stationary breathers can generate a rich variety of states.

Many complex networks are known to exhibit sudden transitions between alternative steady states with contrasting properties. Such a sudden transition demonstrates a network's resilience, which is the ability of a system to persist in the face of perturbations. Most of the research on network resilience has focused on the transition from one equilibrium state to an alternative equilibrium state. Although the presence of nonequilibrium dynamics in some nodes may advance or delay sudden transitions in networks and give early warning signals of an impending collapse, it has not been studied much in the context of network resilience. Here we bridge this gap by studying a neuronal network model with diverse topologies, in which nonequilibrium dynamics may appear in the network even before the transition to a resting state from an active state in response to environmental stress deteriorating their external conditions. We find that the percentage of uncoupled nodes exhibiting nonequilibrium dynamics plays a vital role in determining the network's transition type. We show that a higher proportion of nodes with nonequilibrium dynamics can delay the tipping and increase networks' resilience against environmental stress, irrespective of their topology. Further, predictability of an upcoming transition weakens, as the network topology moves from regular to disordered.

Strong inhibitory input to neurons, which occurs in balanced states of neural networks, increases synaptic current fluctuations. This has led to the assumption that inhibition contributes to the high spike-firing irregularity observed in vivo. We used single compartment neuronal models with time-correlated (due to synaptic filtering) and state-dependent (due to reversal potentials) input to demonstrate that inhibitory input acts to decrease membrane potential fluctuations, a result that cannot be achieved with simplified neural input models. To clarify the effects on spike-firing regularity, we used models with different spike-firing adaptation mechanisms, and we observed that the addition of inhibition increased firing regularity in models with dynamic firing thresholds and decreased firing regularity if spike-firing adaptation was implemented through ionic currents or not at all. This fluctuation-stabilization mechanism provides an alternative perspective on the importance of strong inhibitory inputs observed in balanced states of neural networks, and it highlights the key roles of biologically plausible inputs and specific adaptation mechanisms in neuronal modeling.

Certain types of active systems can be treated as an equilibrium system with excess nonconservative forces driving some of the microscopic degrees of freedom. We derive results for how many particles having both conservative and nonconservative forces will behave. Treating nonconservative forces perturbatively, we show how the probability distribution of the microscopic degrees of freedom is modified from the Boltzmann distribution. We then derive approximate forms of this distribution through analyzing the nature of our perturbations. We compare the perturbative expansion for the microscopic probability distribution to an exactly solvable active system. Finally, we consider how the approximate forms for the microscopic distributions we have derived lead to different macroscopic states when coarse grained for two different kinds of systems, a collection of motile particles, and a system where nonconservative forces are applied in space. In the former, we are able to show that nonconservative forces lead to an effective attractive interaction between motile particles, and in the latter we note that by introducing nonconservative interactions between particles we modify densities through extra terms which couple to surfaces. In this way, we are able to recast certain active problems as the statistical mechanics of nonconservative forces.

Tactoids are pointed, spindlelike droplets of nematic liquid crystal in an isotropic fluid. They have long been observed in inorganic and organic nematics, in thermotropic phases as well as lyotropic colloidal aggregates. The variational problem of determining the optimal shape of a nematic droplet is formidable and has only been attacked in selected classes of shapes and director fields. Here, by considering a special class of admissible solutions for a bipolar droplet, we study the prevalence in the population of all equilibrium shapes of each of the three that may be optimal (tactoids primarily among them). We show how the prevalence of a shape is affected by a dimensionless measure $\alpha$ of the drop's volume and the ratios $k_{24}$ and $k_3$ of the saddle-splay constant $K_{24}$ and the bending constant $K_{33}$ of the material to the splay constant $K_{11}$. Tactoids, in particular, prevail for $\alpha ⪅16.2+0.3k_3-(14.9-0.1k_3)k_{24}$. Our class of shapes (and director fields) is sufficiently different from those employed so far to unveil a rather different role of $K_{24}$.

We investigate three-dimensional quantum turbulence as described by the Gross-Pitaevskii model using the analytical method exploited in the Onsager “ideal turbulence” theory. We derive the scale independence of the scale-to-scale kinetic energy flux and establish a double-cascade scenario: At scales much larger than the mean intervortex ${\ell }_i$, the Richardson cascade becomes dominant, whereas at scales much smaller than ${\ell }_i$, another type of cascade is induced by quantum stress. We then evaluate the corresponding velocity power spectrum using a phenomenological argument. The relation between this cascade, which we call quantum stress cascade, and the Kelvin-wave cascade is also discussed.

The nonlinear Fourier transform (NFT) is used to characterize the optical combs in the Lugiato-Lefever equation with both anomalous and normal dispersion. We demonstrate that the NFT signal processing technique can simplify analysis of the formation of dissipative dark solitons and regimes exploiting modulation instability for a generation of coherent structures, by approximating the comb with several discrete eigenvalues, providing a platform for the analytical description of dissipative coherent structures.

We investigate the occurrence of synchronous population activities in a neuronal network composed of both excitatory and inhibitory neurons and equipped with short-term synaptic plasticity. The collective firing patterns with different macroscopic properties emerge visually with the change of system parameters, and most long-time collective evolution also shows periodic-like characteristics. We systematically discuss the pattern-formation dynamics on a microscopic level and find a lot of hidden features of the population activities. The bursty phase with power-law distributed avalanches is observed in which the population activity can be either entire or local periodic-like. In the purely spike-to-spike synchronous regime, the periodic-like phase emerges from the synchronous chaos after the backward period-doubling transition. The local periodic-like population activity and the synchronous chaotic activity show substantial trial-to-trial variability, which is unfavorable for neural code, while they are contrary to the stable periodic-like phases. We also show that the inhibitory neurons can promote the generation of cluster firing behavior and strong bursty collective firing activity by depressing the activities of postsynaptic neurons partially or wholly.

The robustness of complex networks against attack has been an important issue for decades. Most of the previous studies focused on targeted attack (TA) and random attack (RA), while recently localized attack (LA) has drawn the attention of researchers. However, the existing studies related to LA mainly aim to reveal the properties on various network topologies so that the strategy to enhance network robustness against LA is still not well studied. In this paper, we propose a global disassortative rewiring strategy to enhance the robustness of scale-free networks against LA without changing the degree distribution. The validations are conducted on simulated scale-free networks and two real-life networks. As global disassortative rewiring strategy outperforms the other strategies, it can be proved effective in enhancing network robustness against LA and may contribute to future network risk reduction. In addition, by avoiding calculating and comparing the localized-robustness measurement within each rewire operation, our strategy offers a significant advantage in computational efficiency.

Hodgkin and Huxley's seminal neuron model describes the propagation of voltage spikes in axons, but it cannot explain certain full-neuron features crucial for understanding the neural code. We consider channel current fluctuations in a trisection of the Hodgkin-Huxley model, allowing an analytic-mechanistic explanation of these features and yielding consistently excellent matches with in vivo recordings of cerebellar Purkinje neurons, which we use as model systems. This shows that the neuronal encoding is described conclusively by a soft-thresholding function having just three parameters.

We investigate the mechanical response of jammed packings of repulsive, frictionless spherical particles undergoing isotropic compression. Prior simulations of the soft-particle model, where the repulsive interactions scale as a power law in the interparticle overlap with exponent $\alpha$, have found that the ensemble-averaged shear modulus $\langle G\left(P\right)\rangle$ increases with pressure $P$ as $\sim P^{(\alpha -3/2)/(\alpha -1)}$ at large pressures. $\langle G\rangle$ has two key contributions: (1) continuous variations as a function of pressure along geometrical families, for which the interparticle contact network does not change, and (2) discontinuous jumps during compression that arise from changes in the contact network. Using numerical simulations, we show that the form of the shear modulus $G^f$ for jammed packings within near-isostatic geometrical families is largely determined by the affine response $G^f\sim G_a^f$, where $G_a^f/G_{a0}={(P/P_0)}^{(\alpha -2)/(\alpha -1)}-P/P_0, P_0\sim N^{-2(\alpha -1)}$ is the characteristic pressure at which $G_a^f=0, G_{a0}$ is a constant that sets the scale of the shear modulus, and $N$ is the number of particles. For near-isostatic geometrical families that persist to large pressures, deviations from this form are caused by significant nonaffine particle motion. We further show that the ensemble-averaged shear modulus $\langle G\left(P\right)\rangle$ is not simply a sum of two power laws, but $\langle G\left(P\right)\rangle \sim {(P/P_c)}^a$, where $a\approx (\alpha -2)/(\alpha -1)$ in the $P\to 0$ limit and $\langle G\left(P\right)\rangle \sim {(P/P_c)}^b$, where $b\gtrsim (\alpha -3/2)/(\alpha -1)$, above a characteristic pressure that scales as $P_c\sim N^{-2(\alpha -1)}$.

Friction reduction is a major issue in multiple domains, and lubrication is often used in order to achieve it. Gas lubrication is a very efficient way to increase slipperiness, reducing the friction coefficient to almost zero. The main challenge with gas lubrication is to keep the gas inside the contact area due to the fact that it is easily squeezed out because of its low viscosity. Here we use the Leidenfrost effect to form a lubricating gas layer in between a disk of dry ice and a substrate, thus leading to lubricated friction. The gas is continuously provided by sublimation due to the temperature difference between dry ice and substrate. We perform different experiments on dry ice, measuring friction and parameters inside the gas layer. We then chart the crossover from high to low friction as a function of pressure and temperature, and we reveal the role of gas layer thickness. The substrate temperature and macroscopic pressure are found to strongly affect the friction, and very low friction is reached only in particular conditions. These conditions are easily controlled through external parameters, which allows us to use the Leidenfrost effect to efficiently modify friction.

A 1-mm-size cluster composed of 10 dust particles immersed in plasma is rotated by the torque of a pulsed electron beam with energy in the range 8–12 keV. The dust particles are electrically charged spheres with radius 5.9 $\mu \mathrm{m}$ and are levitated in the plasma sheath, forming a round, planar, Coulomb-coupled cluster. The electron beam irradiates the dust cluster passing slightly off its center, and sets the particles in motion by the action of the electron drag force. The total torque at 12 keV is $4.9\pm 0.2\times {10}^{-11}$ Nm at an angular speed $1.41\pm 0.05$ rad ${\mathrm{s}}^{-1}$. The main dynamical features of the cluster such as intershell rotation and itinerancy of the dust particles inside the cluster are simulated by using a molecular dynamics code.

Molecular expressions for thermodynamic properties and derivatives of the Gibbs energy up to third order in the isobaric-isothermal ($NpT$) ensemble are systematically derived using the methodology developed by Lustig for the microcanonical and canonical ensembles [J. Chem. Phys. 100, 3048 (1994); Mol. Phys. 110, 3041 (2012)]. They are expressed by phase-space functions, which represent derivatives of the Gibbs energy with respect to temperature and pressure. Additionally, expressions for the phase-space functions for temperature-dependent potentials are provided, which, for example, are required when quantum corrections, e.g., Feynman-Hibbs corrections, are applied in classical simulations. The derived expressions are validated by Monte Carlo simulations for the simple Lennard-Jones model fluid at three selected state points. A unique result is that the phase-space functions contain only ensemble averages of combinations of powers of enthalpy and volume. Thus, the calculation of thermodynamic properties in the $NpT$ ensemble does not require volume derivatives of the potential energy. This is particularly advantageous in Monte Carlo simulations when the interactions between molecules are described by empirical force fields or very accurate ab initio pair and nonadditive three-body potentials.

We study the nonequilibrium steady-state (NESS) dynamics of two-dimensional Brownian gyrators under harmonic and nonharmonic potentials via computer simulations and analyses based on the Fokker-Planck equation, while our nonharmonic cases feature a double-well potential and an isotropic quartic potential. In particular, we report two simple methods that can help understand gyrating patterns. For harmonic potentials, we use the Fokker-Planck equation to survey the NESS dynamical characteristics; i.e., the NESS currents gyrate along the equiprobability contours and the stationary point of flow coincides with the potential minimum. As a contrast, the NESS results in our nonharmonic potentials show that these properties are largely absent, as the gyrating patterns are very distinct from those of corresponding probability distributions. Furthermore, we observe a critical case of the double-well potential, where the harmonic contribution to the gyrating pattern becomes absent, and the NESS currents do not circulate about the equiprobability contours near the potential minima even at low temperatures.