We present a systematic analysis of diffusion-controlled interaction and collapse of two nonidentical spatially separated $d$-dimensional $A$-particle islands in the $B$-particle sea at propagation of the sharp reaction front $A+B\to 0$ at equal species diffusivities. We show that at a sufficiently large initial distance between the centers of islands $2\ell$ and a relatively large initial ratio of island-to-sea concentrations, the evolution dynamics of the island-sea-island system demonstrates remarkable universality and, depending on the system dimension, is determined unambiguously by two dimensionless parameters $\mathrm{\Lambda }={\mathcal{N}}_0^{+}/{\mathcal{N}}_{\mathrm{\Omega }}$ and $q={\mathcal{N}}_0^{-}/{\mathcal{N}}_0^{+}$, where ${\mathcal{N}}_0^{+}$ and ${\mathcal{N}}_0^{-}$ are the initial particle numbers in the larger and smaller of the islands, respectively, and ${\mathcal{N}}_{\mathrm{\Omega }}$ is the initial number of sea particles in the volume $\mathrm{\Omega }={\left(2\ell \right)}^d$. We find that at each fixed $0<q\le 1$, there are threshold values ${\mathrm{\Lambda }}_{★}\left(q\right)$ and ${\mathrm{\Lambda }}_s\left(q\right)\ge {\mathrm{\Lambda }}_{★}\left(q\right)$ that depend on the dimension and separate the domains of individual death of each of the islands $\mathrm{\Lambda }<{\mathrm{\Lambda }}_{★}\left(q\right)$, coalescence and subsequent fragmentation (division) of a two-centered island ${\mathrm{\Lambda }}_{★}\left(q\right)<\mathrm{\Lambda }<{\mathrm{\Lambda }}_s\left(q\right)$, and collapse of a single-centered island formed by coalescence $\mathrm{\Lambda }>{\mathrm{\Lambda }}_s\left(q\right)$. We demonstrate that regardless of $d$, the trajectories of the island centers are determined unambiguously by the parameter $q$, and we reveal a detailed picture of the evolution of islands and front trajectories with an increase in $\mathrm{\Lambda }$, focusing on the scaling laws of evolution at the final collapse stage and in the vicinity of starting coalescence and fragmentation points.

Currently, much interest is drawn to the analysis of optical and matter-wave modes supported by the fractional diffraction in nonlinear media. We predict a new type of such states in the form of domain walls (DWs) in the two-component system of immiscible fields. Numerical study of the underlying system of fractional nonlinear Schrödinger equations demonstrates the existence and stability of DWs at all values of the respective Lévy index ($\alpha <2$), which determines the fractional diffraction, and at all values of the XPM/SPM ratio $\beta$ in the two-component system above the immiscibility threshold. The same conclusion is obtained for DWs in the system which includes the linear coupling, alongside the XPM interaction between the immiscible components. Analytical results are produced for the scaling of the DW's width. The DW solutions are essentially simplified in the special case of $\beta =3$, as well as close to the immiscibility threshold. In addition to symmetric DWs, asymmetric ones are constructed too, in the system with unequal diffraction coefficients and/or different Lévy indices of the two components.

Analyzing the brain in terms of organizational structures at intermediate scales provides an approach to unravel the complexity arising from interactions between its large number of components. Focusing on a wiring diagram that spans the cortex, basal ganglia, and thalamus of the macaque brain, we identify robust modules in the network that provide a mesoscopic-level description of its topological architecture. Surprisingly, we find that the modular architecture facilitates rapid communication across the network, instead of localizing activity as is typically expected in networks having community organization. By considering processes of diffusive spreading and coordination, we demonstrate that the specific pattern of inter- and intramodular connectivity in the network allows propagation to be even faster than equivalent randomized networks with or without modular structure. This pattern of connectivity is seen at different scales and is conserved across principal cortical divisions, as well as subcortical structures. Furthermore, we find that the physical proximity between areas is insufficient to explain the modular organization, as similar mesoscopic structures can be obtained even after factoring out the effect of distance constraints on the connectivity. By supplementing the topological information about the macaque connectome with physical locations, volumes, and functions of the constituent areas and analyzing this augmented dataset, we reveal a counterintuitive role played by the modular architecture of the brain in promoting global coordination of its activity. It suggests a possible explanation for the ubiquity of modularity in brain networks.

Adaptation is used by biological sensory systems to respond to a wide range of environmental signals, by adapting their response properties to the statistics of the stimulus in order to maximize information transmission. We derive rules of optimal adaptation to changes in the mean and variance of a continuous stimulus in terms of Bayesian filters and map them onto stochastic equations that couple the state of the environment to an internal variable controlling the response function. We calculate numerical and exact results for the speed and accuracy of adaptation and its impact on information transmission. We find that, in the regime of efficient adaptation, the speed of adaptation scales sublinearly with the rate of change of the environment. Finally, we exploit the mathematical equivalence between adaptation and stochastic thermodynamics to quantitatively relate adaptation to the irreversibility of the adaptation time course, defined by the rate of entropy production. Our results suggest a means to empirically quantify adaptation in a model-free and nonparametric way.

We report the numerical evidence of a new state of bacterial turbulence in confined domains. By means of extensive numerical simulations of the Toner-Tu-Swift-Hohenberg model for dense bacterial suspensions in circular geometry, we discover the formation a stable, ordered state in which the angular momentum symmetry is broken. This is achieved by self-organization of a turbulent-like flow into a single, giant vortex of the size of the domain. The giant vortex is surrounded by an annular region close to the boundary, characterized by small-scale, radial vorticity streaks. The average radial velocity profile of the vortex is found to be in agreement with a simple analytical prediction. We also provide an estimate of the temporal and spatial scales of a suitable experimental setup comparable with our numerical findings.

We explore the generalization properties of an echo state network applied as a reduced-order model to predict flux-driven two-dimensional turbulent convection. To this end, we consider a convection domain with constant height with a variable ratio of buoyancy fluxes at the top and bottom boundaries, which break the top-down symmetry in comparison to the standard Rayleigh-Bénard case, thus leading to highly asymmetric mean and fluctuation profiles across the layer. Our direct numerical simulation model describes a convective boundary layer in a simple way. The data are used to train and test a recurrent neural network in the form of an echo state network. The input of the echo state network is obtained in two different ways, either by a proper orthogonal decomposition or by a convolutional autoencoder. In both cases, the echo state network reproduces the turbulence dynamics and the statistical properties of the buoyancy flux, and is able to model unseen data records with different flux ratios.

Pore-scale modeling based on the 3D structural information of porous materials has enormous potential in assessing physical properties beyond the capabilities of laboratory methods. Such capabilities are pricey in terms of computational expenses, and this limits the applicability of the direct simulations to a small volume and requires high-performance computational resources, especially for multiphase flow simulations. The only pore-scale technique capable of dealing with large representative volumes of porous samples is pore-network (PNM) based modeling. The problem of the PNM approach is that 3D pore geometry first needs to be simplified into a graph of pores and throats that conserve topological and geometrical properties of the original 3D image. While significant progress has been achieved in terms of geometry representation, no methodology provides full conservation of the topological features of the pore structure. In this paper we present a pore-network extraction algorithm for binary 3D images based on discrete Morse theory and persistent homology that by design targets topology preservation. In addition to methodological developments, we also clarify the relationship between topological characteristics of constructed Morse chain complex and pore-network elements. We show that the Euler numbers calculated for PNMs based on our methodology coincide with those obtained using the direct topological analysis. The characteristics of the extracted pore network are calculated for several 3D porous binary images and compared with the results of maximum inscribed balls-based and watershed-based approaches as well as a hybrid approach to support our methodology.

In this paper, a multiple-distribution-function lattice Boltzmann method (MDF-LBM) with a multiple-relaxation-time model is proposed for incompressible Navier-Stokes equations which are considered as coupled convection-diffusion equations. Through direct Taylor expansion analysis, we show that the Navier-Stokes equations can be recovered correctly from the present MDF-LBM, and additionally, it is also found that the velocity and pressure can be directly computed through the zero and first-order moments of the distribution function. Then in the framework of the present MDF-LBM, we develop a locally computational scheme for the velocity gradient in which the first-order moment of the nonequilibrium distribution is used; this scheme is also extended to calculate the velocity divergence, strain rate tensor, shear stress, and vorticity. Finally, we also conduct some simulations to test the MDF-LBM and find that the numerical results not only agree with some available analytical and numerical solutions but also have a second-order convergence rate in space.

Nonreversible Markov chains can outperform reversible chains in the Markov chain Monte Carlo method. Lifting is a versatile approach to introducing net stochastic flow in state space and constructing a nonreversible Markov chain. We present here an application of the lifting technique to the directed-worm algorithm. The transition probability of the worm update is optimized using the geometric allocation approach; the worm backscattering probability is minimized, and the stochastic flow breaking the detailed balance is maximized. We demonstrate the performance improvement over the previous worm and cluster algorithms for the four-dimensional hypercubic lattice Ising model. The sampling efficiency of the present algorithm is approximately 80, 5, and 1.7 times as high as those of the standard worm algorithm, the Wolff cluster algorithm, and the previous lifted worm algorithm, respectively. We estimate the dynamic critical exponent of the hypercubic lattice Ising model to be $z\approx 0$ in the worm and the Wolff cluster updates. The lifted version of the directed-worm algorithm can be applied to a variety of quantum systems as well as classical systems.

We study the thermodynamics and critical behavior of $\mathrm{su}\left(m\right)$ spin chains of Haldane-Shastry type at zero chemical potential, both in the ${\mathrm{A}}_{N-1}$ and ${\text{BC}}_N$ cases. We evaluate in closed form the free energy per spin for arbitrary values of $m$, from which we derive explicit formulas for the energy, entropy, and specific heat per spin. In particular, we find that the specific heat features a single Schottky peak, whose temperature is well approximated for $m\lesssim 10$ by the corresponding temperature for an $m$-level system with uniformly spaced levels. We show that at low temperatures the free energy per spin of the models under study behaves as that of a one-dimensional conformal field theory with central charge $c=m-1$ (with the only exception of the Frahm-Inozemtsev chain at zero value of its parameter). However, from a detailed study of the ground-state degeneracy and the low-energy excitations, we conclude that these models are only critical in the antiferromagnetic case, with a few exceptions that we fully specify.

Recent numerical explorations of extremely intense circulation fluctuations at high Reynolds number flows have brought to light novel aspects of turbulent intermittency. Vortex gas modeling ideas, which are related to a picture of turbulence as a dilute system of vortex tube structures, have been introduced alongside such developments, leading to accurate descriptions of the core and the intermediate tails of circulation probability distribution functions (cPDFs), as well as the scaling exponents associated to statistical moments of circulation. We extend the predictive reach of the vortex gas picture of turbulence by emphasizing that multifractality breaking, one of its salient phenomenological ingredients, is the key concept to disclose the asymptotic form of cPDF tails. A remarkable analytical agreement is found with previous results derived within the framework of the instanton approach to circulation intermittency, a functional formalism devised to single out the statistically dominant velocity configurations associated to extreme circulation events.

Lévy stochastic processes, with noise distributed according to a Lévy stable distribution, are ubiquitous in science. Focusing on the case of a particle trapped in an external harmonic potential, we address the problem of finding “shortcuts to adiabaticity”: After the system is prepared in a given initial stationary state, we search for time-dependent protocols for the driving external potential, such that a given final state is reached in a given, finite time. These techniques, usually employed for stochastic processes with additive Gaussian noise, are typically based on a inverse-engineering approach allowing to find exact analytical solutions for the required protocol. We generalize the approach to the wider class of Lévy stochastic processes, both in the overdamped and (for pure translations) in the underdamped regime, by finding exact equations for the relevant characteristic functions in Fourier space.

Long-range interacting systems irreversibly relax as a result of their finite number of particles, $N$. At order $1/N$, this process is described by the inhomogeneous Balescu-Lenard equation. Yet, this equation exactly vanishes in one-dimensional inhomogeneous systems with a monotonic frequency profile and sustaining only 1:1 resonances. In the limit where collective effects can be neglected, we derive a closed and explicit $1/N^2$ collision operator for such systems. We detail its properties, highlighting in particular how it satisfies an $H$ theorem for Boltzmann entropy. We also compare its predictions with direct $N$-body simulations. Finally, we exhibit a generic class of long-range interaction potentials for which this $1/N^2$ collision operator exactly vanishes.

We study the dynamics of solitary waves traveling in a one-dimensional chain of bistable elements in the presence of a local inhomogeneity (“defect”). Numerical simulations reveal that depending upon its initial speed, an incoming solitary wave can get transmitted, captured, or reflected upon interaction with the defect. The dynamics are dominated by energy exchange between the wave and a breather mode localized at the defect. We derive a reduced-order two degree of freedom Hamiltonian model for wave-breather interaction and analyze it using dynamical systems techniques. Lobe dynamics analysis reveals the fine structure of phase space that leads to the complicated dynamics in this system. This work is a step toward developing a rational approach to defect engineering for manipulating nonlinear waves in mechanical metamaterials.

We examine a possibility to exploit the nonlinear lens effect—the initial stage of self-focusing to localize initially broad field distribution into the small central area where wave collapse is arrested—the nonlinear beam tapering. We describe two-dimensional localized solitary waves (ring solitons) in a physical system that presents a linear medium in the central core, surrounded by the cladding with the focusing Kerr nonlinearity. The standard variational analysis demonstrates that such solitons correspond to the minimum of the Hamiltonian.

In the past decade, geometric network models have received vast attention in the literature. These models formalize the natural idea that similar vertices are likely to connect. Because of that, these models are able to adequately capture many common structural properties of real-world networks, such as scale invariance and high clustering. Indeed, many real-world networks can be accurately modeled by positioning vertices of a network graph in hyperbolic spaces. Nevertheless, if one observes only the network connections, the presence of geometry is not always evident. Currently, triangle counts and clustering coefficients are the standard statistics to signal the presence of geometry. In this paper we show that triangle counts or clustering coefficients are insufficient because they fail to detect geometry induced by hyperbolic spaces. We, therefore, introduce a differerent statistic, weighted triangles, which weighs triangles based on their evidence for geometry. We show analytically, as well as on synthetic and real-world data, that weighted triangles are a powerful statistic to detect hyperbolic geometry in networks.

Motivated by the recent observation of liquid glass in suspensions of ellipsoidal colloids, we examine the structure of (asymptotically) saturated RSA ellipse packings. We determine the packing fractions ${\varphi }_{\mathrm{s}}\left(\alpha \right)$ to high precision, finding an empirical analytic formula that predicts ${\varphi }_{\mathrm{s}}\left(\alpha \right)$ to within less than $0.1\%$ for all $\alpha \le 10$. Then we explore how these packings' positional-orientational order varies with $\alpha$. We find a transition from tip/side- to side/side-contact-dominated structure at $\alpha ={\alpha }_{\mathrm{TS}}\simeq 2.4$. At this aspect ratio, the peak value $g_{\max }$ of packings' positional-orientational pair correlation functions is minimal, and systems can be considered maximally locally disordered. For smaller (larger) $\alpha , g_{\max }$ increases exponentially with deceasing (increasing) $\alpha$. Local nematic order and structures comparable to the precursor domains observed in experiments gradually emerge as $\alpha$ increases beyond three. For $\alpha \gtrsim 5$, single-layer lamellae become more prominent and long-wavelength density fluctuations increase with $\alpha$ as packings gradually approach the rodlike limit.

The weakly nonlinear and dispersive electrostatic ion cyclotron wave dynamics in the presence of Schamel distributed trapped electrons is studied in collisionless plasmas. The dynamics of the nonlinear wave is shown to be governed by a Schamel-Ostrovsky type equation. Analytical and numerical solutions of this equation reveal the collapse of a solitary (localized) pulse at a critical time that depends on the trapping parameter and the strength of the magnetic field. The time-dependent computational result is noteworthy, which predicts the formation of wave packets (wave group) beyond the critical time. The results are in good agreement with the astrophysical observations in auroral plasmas.

We report on measurements of the ion-electron energy-transfer cross section utilizing low-velocity ion stopping in high-energy-density plasmas at the OMEGA laser facility. These measurements utilize a technique that leverages the close relationship between low-velocity ion stopping and ion-electron equilibration. Shock-driven implosions of capsules filled with $\mathrm{D}{}^3\mathrm{He}$ gas doped with a trace amount of argon are used to generate densities and temperatures in ranges from $1\times {10}^{23}$ to $2\times {10}^{24} {\mathrm{cm}}^{-3}$ and from 1.4 to 2.5 keV, respectively. The energy loss of 1-MeV DD tritons and 3.7-MeV $\mathrm{D}{}^3\mathrm{He}$ alphas that have velocities lower than the average velocity of the thermal electrons is measured. The energy loss of these ions is used to determine the ion-electron energy-transfer cross section, which is found to be in excellent agreement with quantum-mechanical calculations in the first Born approximation. This result provides an experimental constraint on ion-electron energy transfer in high-energy-density plasmas, which impacts the modeling of alpha heating in inertial confinement fusion implosions, magnetic-field advection in stellar atmospheres, and energy balance in supernova shocks.