It had been shown that the transition from a rigidly rotating spiral wave to a meandering spiral wave is via a Hopf bifurcation. Many studies have shown that these bifurcations are supercritical, but, by using simulations in a comoving frame of reference, we present numerical results which show that subcritical bifurcations are also present within FitzHugh-Nagumo. We show that a hysteresis region is present at the boundary of the rigidly rotating spiral waves and the meandering spiral waves for a particular set of parameters, a feature of FitzHugh-Nagumo that has previously not been reported. Furthermore, we present a evidence that this bifurcation is highly sensitive to initial conditions, and it is possible to convert one solution in the hysteresis loop to the other.

Turing's theory of pattern formation has provided crucial insights into the behavior of various biological, geographical, and chemical systems over the last few decades. Existing studies have focused on moving-boundary Turing systems for which the motion of the boundary is prescribed by an external agent. In this paper, we present an extension of this theory to a class of systems in which the front motion is governed by the physical processes that occur within the domain. Biological systems exhibiting apically dominant growth and corrosion of metals and alloys highlight some of the noteworthy examples of such systems. In this study, we characterize the nature of interaction between the moving front and the Turing-instability for both an activator-inhibitor and an activator-substrate model. Behavioral regimes of periodic, as well as nonperiodic (nonconstant), growth rates are obtained. Furthermore, the trends in the first show striking similarities with the cyclic-boundary-kinetics observed in experimental systems. In general, a stationary, periodic structure is also left behind the moving front. If the periodicity of the boundary kinetics agrees with the allowed range of the stable-periodic solutions, the pattern formed tends to persist. Otherwise, it evolves to a nearby energy-minimum either by peak-splitting, peak-decay, or by settling down to a spatially homogeneous state.

While particle adhesion to smooth surfaces is well understood, real surfaces are not perfectly smooth, and the effects of surface roughness on adhesion are not easily characterized. We develop a theory for the effects of surface roughness on the strength of particle adhesion due to van der Waals forces, in the Derjaguin-Muller-Toporov (DMT)-type adhesion regime. We first address a well-defined rough surface created by embedding spheres in a smooth substrate, which had been previously examined experimentally. We derive an analytic expression for the adhesive force of particles to this well-defined surface, with the key distinction from the previous work being the inclusion of interactions from surface asperities not in direct contact with the particle. We show that our theory is in good agreement with experimental results in the DMT regime. Within appropriate limits, we extend our theory to general rough surfaces and verify the theory by comparing to the exact numerical results. We show that the interactions from surface asperities not in direct contact with the particle are the dominant contribution to the adhesive force under some conditions, and our theory predicts the experimental and numerical adhesion forces very accurately.

We examine and discuss the spatial evolution of the statistical properties of mechanically generated surface gravity wave fields, initialized with unidirectional spectral energy distributions, uniformly distributed phases, and Rayleigh distributed amplitudes. We demonstrate that nonlinear interactions produce an energy cascade towards high frequency modes with a directional spread and trigger localized intermittent bursts. By analyzing the probability density function of Fourier mode amplitudes in the high frequency range of the wave energy spectrum, we show that a heavy-tailed distribution emerges with distance from the wave generator as a result of these intermittent bursts, departing from the originally imposed Rayleigh distribution, even under relatively weak nonlinear conditions.

We show the asymptotic equivalence of two forcing schemes in the lattice Boltzmann method (LBM) within second-order accuracy through the asymptotic analysis instead of the Chapman–Enskog analysis. We consider the single relaxation time LBM with the following two forcing schemes: the simplest scheme by He et al. [J. Stat. Phys. 87, 115 (1997)] (referred to as He forcing); the most popular scheme by Guo et al. [Phys. Rev. E 65, 046308 (2002)] (referred to as Guo forcing). It has been shown by using the Chapman–Enskog analysis that the He forcing leads the unphysical terms in the macroscopic equations due to the spatial and time derivatives of the body force, whereas the Guo forcing does not lead such terms. However, we find by using the asymptotic analysis that the order of the unphysical terms is comparable to or less than ${\left(\mathrm{\Delta }x\right)}^3$ for the continuity equation and ${\left(\mathrm{\Delta }x\right)}^4$ for the Navier–Stokes equations (where $\mathrm{\Delta }x$ is the lattice spacing). Therefore, not only the Guo forcing but also the He forcing give the macroscopic flow velocity and pressure for incompressible viscous fluid with relative errors of $O\left[{\left(\mathrm{\Delta }x\right)}^2\right]$. To verify the result of the asymptotic analysis, we simulate two benchmark problems in which the body force is changed in space and time: a generalized Taylor–Green problem and a natural convection problem. As a result, we find that the calculated results of macroscopic variables by the He forcing converge to those by the Guo forcing at the second-order convergence rate. Therefore, we can conclude that the He forcing and the Guo forcing are equivalent within the second-order accuracy even for the space- and time-dependent body force.

Previous experimental and theoretical evidence has shown that convective flow may appear in granular fluids if subjected to a thermal gradient and gravity (Rayleigh-Bénard-type convection). In contrast to this, we present here evidence of gravity-free thermal convection in a granular gas, with no presence of external thermal gradients either. Convection is here maintained steady by internal gradients due to dissipation and thermal sources at the same temperature. The granular gas is composed by identical disks and is enclosed in a rectangular region. Our results are obtained by means of an event-driven algorithm for inelastic hard disks.

Percolation and fracture propagation in disordered solids represent two important problems in science and engineering that are characterized by phase transitions: loss of macroscopic connectivity at the percolation threshold $p_c$ and formation of a macroscopic fracture network at the incipient fracture point (IFP). Percolation also represents the fracture problem in the limit of very strong disorder. An important unsolved problem is accurate prediction of physical properties of systems undergoing such transitions, given limited data far from the transition point. There is currently no theoretical method that can use limited data for a region far from a transition point $p_c$ or the IFP and predict the physical properties all the way to that point, including their location. We present a deep neural network (DNN) for predicting such properties of two- and three-dimensional systems and in particular their percolation probability, the threshold $p_c$, the elastic moduli, and the universal Poisson ratio at $p_c$. All the predictions are in excellent agreement with the data. In particular, the DNN predicts correctly $p_c$, even though the training data were for the state of the systems far from $p_c$. This opens up the possibility of using the DNN for predicting physical properties of many types of disordered materials that undergo phase transformation, for which limited data are available for only far from the transition point.

The spin-1/2 Ising-Heisenberg model on a triangulated Husimi lattice is exactly solved in a magnetic field within the framework of the generalized star-triangle transformation and the method of exact recursion relations. The generalized star-triangle transformation establishes an exact mapping correspondence with the effective spin-1/2 Ising model on a triangular Husimi lattice with a temperature-dependent field, pair and triplet interactions, which is subsequently rigorously treated by making use of exact recursion relations. The ground-state phase diagram of a spin-1/2 Ising-Heisenberg model on a triangulated Husimi lattice, which bears a close resemblance with a triangulated kagomé lattice, involves, in total, two classical and three quantum ground states manifested in respective low-temperature magnetization curves as intermediate plateaus at 1/9, 1/3, and 5/9 of the saturation magnetization. It is verified that the fractional magnetization plateaus of quantum nature have character of either dimerized or trimerized ground states. A low-temperature magnetization curve of the spin-1/2 Ising-Heisenberg model on a triangulated Husimi lattice resembling a triangulated kagome lattice may exhibit either no intermediate plateau, a single 1/3 plateau, a single 5/9 plateau, or a sequence of 1/9, 1/3, and 5/9 plateaus depending on a character and relative size of two considered coupling constants.

We discuss the derivation and the solutions of integrodifferential equations (variable-order time-fractional diffusion equations) following as continuous limits for lattice continuous time random walk schemes with power-law waiting-time probability density functions whose parameters are position-dependent. We concentrate on subdiffusive cases and discuss two situations as examples: A system consisting of two parts with different exponents of subdiffusion, and a system in which the subdiffusion exponent changes linearly from one end of the interval to another one. In both cases we compare the numerical solutions of generalized master equations describing the process on the lattice to the corresponding solutions of the continuous equations, which follow by exact solution of the corresponding equations in the Laplace domain with subsequent numerical inversion using the Gaver-Stehfest algorithm.

We investigated the spectra of resonances of four-vertex microwave networks simulating both quantum graphs with preserved and with partially violated time-reversal invariance before and after an edge switch operation. We show experimentally that under the edge switch operation, the spectra of the microwave networks with preserved time-reversal symmetry are level-1 interlaced, i.e., ${\nu }_{n-r}\le {\tilde{\nu }}_n\le {\nu }_{n+r}$, where $r=1$, in agreement with the recent theoretical predictions of Aizenman et al. [M. Aizenman, H. Schanz, U. Smilansky, and S. Warzel, Acta Phys. Pol. A 132, 1699 (2017)]. Here, we denote by ${\left\{{\nu }_n\right\}}_{n=1}^{\infty }$ and ${\left\{{\tilde{\nu }}_n\right\}}_{n=1}^{\infty }$ the spectra of microwave networks before and after the edge switch transformation. We demonstrate that the experimental distribution $P\left(\mathrm{\Delta }N\right)$ of the spectral shift $\mathrm{\Delta }N$ is close to the theoretical one. Furthermore, we show experimentally that in the case of the four-vertex networks with partially violated time-reversal symmetry, the spectra are level-1 interlaced. Our experimental results are supplemented by the numerical calculations performed for quantum graphs with violated time-reversal symmetry. In this case, the edge switch transformation also leads to the spectra which are level-1 interlaced. Moreover, we demonstrate that for microwave networks simulating graphs with violated time-reversal symmetry, the experimental distribution $P\left(\mathrm{\Delta }N\right)$ of the spectral shift $\mathrm{\Delta }N$ agrees, within the experimental uncertainty, with the numerical one.

Many machine learning algorithms used for dimensional reduction and manifold learning leverage on the computation of the nearest neighbors to each point of a data set to perform their tasks. These proximity relations define a so-called geometric graph, where two nodes are linked if they are sufficiently close to each other. Random geometric graphs, where the positions of nodes are randomly generated in a subset of ${\mathbb{R}}^d$, offer a null model to study typical properties of data sets and of machine learning algorithms. Up to now, most of the literature focused on the characterization of low-dimensional random geometric graphs whereas typical data sets of interest in machine learning live in high-dimensional spaces ($d\gg {10}^2$). In this work, we consider the infinite dimensions limit of hard and soft random geometric graphs and we show how to compute the average number of subgraphs of given finite size $k$, e.g., the average number of $k$ cliques. This analysis highlights that local observables display different behaviors depending on the chosen ensemble: soft random geometric graphs with continuous activation functions converge to the naive infinite-dimensional limit provided by Erdös-Rényi graphs, whereas hard random geometric graphs can show systematic deviations from it. We present numerical evidence that our analytical results, exact in infinite dimensions, provide a good approximation also for dimension $d\gtrsim 10$.

The distribution of intervals between human actions such as email posts or keyboard strokes demonstrates distinct properties at short versus long timescales. For instance, at long timescales, which are presumably controlled by complex process such as planning and decision making, it has been shown that those interevent intervals follow a scale-invariant (or power-law) distribution. In contrast, at shorter timescales—which are governed by different processes such as sensorimotor skill—they do not follow the same distribution and we know little about how they relate to the scale-invariant pattern. Here, we analyzed 9 million intervals between smartphone screen touches of 84 individuals which span several orders of magnitudes (from milliseconds to hours). To capture these intervals, we extend a priority-based generative model to smartphone touching events. At short timescale, the model is governed by refractory effects, while at longer timescales, the intertouch intervals are governed by the priority difference between smartphone tasks and other tasks. The flexibility of the model allows us to capture interindividual variations at short and long timescales, while its tractability enables efficient model fitting. According to our model, each individual has a specific power-law exponent which is tightly related to the effective refractory time constant suggesting that motor processes which influence the fast actions are related to the higher cognitive processes governing the longer interevent intervals.

Simplicial complexes are gaining increasing scientific attention as they are generalized network structures that can represent the many-body interactions existing in complex systems ranging from the brain to high-order social networks. Simplicial complexes are formed by simplicies, such as nodes, links, triangles, and so on. Cell complexes further extend these generalized network structures as they are formed by regular polytopes, such as squares, pentagons, etc. Pseudofractal simplicial and cell complexes are a major example of generalized network structures and they can be obtained by gluing two-dimensional $m$-polygons ($m=3$ triangles, $m=4$ squares, $m=5$ pentagons, etc.) along their links according to a simple iterative rule. Here we investigate the interplay between the topology of pseudofractal simplicial and cell complexes and their dynamics by characterizing the critical properties of link percolation defined on these structures. By using the renormalization group we show that the pseudofractal simplicial and cell complexes have a continuous percolation threshold at $p_c=0$. When the pseudofractal structure is formed by polygons of the same size $m$, the transition is characterized by an exponential suppression of the order parameter $P_{\infty }$ that depends on the number of sides $m$ of the polygons forming the pseudofractal cell complex, i.e., $P_{\infty }\propto pexp(-\alpha /p^{m-2})$. Here these results are also generalized to random pseudofractal cell complexes formed by polygons of different number of sides $m$.

In geotechnics as well as in planetary science, it is important to find a means by which to protect a base from impacts of micrometeoroids. In the moon, for example, covering a moon base with regolith, and housing such regolith by movable bounding walls, could work as a stress-leaking shield. Using a numerical model, by performing impacts on a granular material housed in a rectangular container made with one movable sidewall, it is found that such wall mobility serves as a good means for controlling the maximum force exerted at the container's base. We show that the force exerted at the container's base decreases as the movable wall decreases in mass, and it follows a Janssen-like trend. Moreover, by making use of a dynamically defined redirecting coefficient $K\left(X\right)$, proposed by Windows-Yule et al. [Phys. Rev. E 100, 022902 (2019)], which depends on the container's width $X$, we propose a model for predicting the maxima measured at the container's base. The model depends on the projectile and granulate properties, and the container's geometry.

The subharmonic acoustic emission of a stable oscillating bubble inside a rigid tube is investigated by direct numerical simulation. The mechanisms of bubble-tube interaction on the acoustic wave emitted by the bubble are clarified. When the bubble is small compared to the tube diameter, a critical threshold for the pressure amplitude appears beyond the point which nonspherical effects become important and bubble breaks. For a finite tube diameter, the scattered wave by the bubble is shown to generate a plane wave where the intensity of the subharmonic component becomes maximum for an optimal distance between the bubble and the tube wall. This effect seems to be directly related to the appearance of local resonance phenomena and a bubble resonance shift where liquid's compressibility plays a major role.

Leveraging on analyses of Hamiltonian dynamics to examine the ion motion, we explicitly demonstrate that the proton sheet crossing and plateau-type energy spectrum are two intrinsic features of the effectively accelerated proton beams driven by a drift quasistatic longitudinal electric field. Via two-dimensional particle-in-cell simulations, we show the emergence of proton sheet crossing in a relativistically transparent plasma foil irradiated by a linearly polarized short pulse with the power of one petawatt. Instead of successively blowing the whole foil forward, the incident laser pulse readily penetrates through the plasma bulk, where the proton sheet crossing takes place and the merged self-generated longitudinal electric field traps and reflects the protons to yield a group of protons with plateau-type energy spectrum.

We consider the symmetric two-state 16-vertex model on the square lattice whose vertex weights are invariant under any permutation of adjacent edge states. The vertex-weight parameters are restricted to a critical manifold which is self-dual under the gauge transformation. The critical properties of the model are studied numerically with the Corner Transfer Matrix Renormalization Group method. Accuracy of the method is tested on two exactly solvable cases: the Ising model and a specific version of the Baxter eight-vertex model in a zero field that belong to different universality classes. Numerical results show that the two exactly solvable cases are connected by a line of critical points with the polarization as the order parameter. There are numerical indications that critical exponents vary continuously along this line in such a way that the weak universality hypothesis is violated.

Transient regimes, often difficult to characterize, can be fundamental in establishing final steady states features of reaction-diffusion phenomena. This is particularly true in ecological problems. Here, through both numerical simulations and an analytic approximation, we analyze the transient of a nonequilibrium superdiffusive random search when the targets are created at a certain rate and annihilated upon encounters (a key dynamics, e.g., in biological foraging). The steady state is achieved when the number of targets stabilizes to a constant value. Our results unveil how key features of the steady state are closely associated to the particularities of the initial evolution. The searching efficiency variation in time is also obtained. It presents a rather surprising universal behavior at the asymptotic limit. These analyses shed some light into the general relevance of transients in reaction-diffusion systems.

I study the statistical description of a small quantum system, which is coupled to a large quantum environment in a generic form and with a generic interaction strength, when the total system lies in an equilibrium state described by a microcanonical ensemble. The focus is on the difference between the reduced density matrix (RDM) of the central system in this interacting case and the RDM obtained in the uncoupled case. In the eigenbasis of the central system's Hamiltonian, it is shown that the difference between diagonal elements is mainly confined by the ratio of the maximum width of the eigenfunctions of the total system in the uncoupled basis to the width of the microcanonical energy shell; meanwhile, the difference between off-diagonal elements is given by the ratio of certain property of the interaction Hamiltonian to the related level spacing of the central system. As an application, a sufficient condition is given, under which the RDM may have a canonical Gibbs form under system-environment interactions that are not necessarily weak; this Gibbs state usually includes certain averaged effect of the interaction. For central systems that interact locally with many-body quantum chaotic systems, it is shown that the RDM usually has a Gibbs form. I also study the RDM which is computed from a typical state of the total system within an energy shell.