In this paper, sufficient conditions of Turing instability are established for general delayed reaction-diffusion-chemotaxis models with no-flux boundary conditions. In particular, we address the difficulty brought about by the time delay in investigating the Turing instability. These models involve the time delay parameter $\tau$ and the general density (concentration) function in chemotaxis terms with the chemotaxis parameter $\chi$. Theoretical results reveal that the time delay parameter $\tau$ could determine the stability of positive equilibrium for ordinary differential equations, while the chemotaxis parameter $\chi$ could describe the stability of positive equilibrium for partial differential equations. In this fashion, the general conditions of Turing instability are presented. To confirm their validity, the delayed chemotaxis-type predator-prey model and the phytoplankton-zooplankton model are considered. It is found that these two models admit Turing instability, and the numerical results are in good agreement with the theoretical analysis. The obtained results are helpful in the application of the Turing pattern in models with time delay and chemotaxis.

The eigenvalue statistics are an important tool to capture localization to delocalization transition in physical systems. Recently, a $\beta \text{−}\mathrm{Gaussian}$ ensemble is being proposed as a single parameter to describe the intermediate eigenvalue statistics of many physical systems. It is critical to explore the universality of a $\beta \text{−}\mathrm{Gaussian}$ ensemble in complex networks. In this work, we study the eigenvalue statistics of various network models, such as small-world, Erdős-Rényi random, and scale-free networks, as well as in comparing the intermediate level statistics of the model networks with that of a $\beta \text{−}\mathrm{Gaussian}$ ensemble. It is found that the nearest-neighbor eigenvalue statistics of all the model networks are in excellent agreement with the $\beta \text{−}\mathrm{Gaussian}$ ensemble. However, the $\beta \text{−}\mathrm{Gaussian}$ ensemble fails to describe the intermediate level statistics of higher order eigenvalue statistics, though there is qualitative agreement till $n<4$. Additionally, we show that the nearest-neighbor eigenvalue statistics of the $\beta \text{−}\mathrm{Gaussian}$ ensemble is in excellent agreement with the intermediate higher order eigenvalue statistics of model networks.

In this study, the stochastic properties of player and team ball possession times in professional football matches are examined. Data analysis shows that player possession time follows a gamma distribution and the player count of a team possession event follows a mixture of two geometric distributions. We propose a formula for expressing team possession time in terms of player possession time and player count in a team's possession, verifying its validity through data analysis. Furthermore, we calculate an approximate form of the distribution of team possession time and study its asymptotic property.

In geometrically frustrated assemblies, equilibrium self-limitation manifests in the form of a minimum in the free energy per subunit at a finite, multisubunit size which results from the competition between the elastic costs of frustration within an assembly and the surface energy at its boundaries. Physical realizations—from ill-fitting particle assemblies to self-twisting protein superstructures—are capable of multiple mechanisms of escaping the cumulative costs of frustration, resulting in unlimited equilibrium assembly, including elastic modes of “shape flattening” and the formation of weak, defective bonds that screen intra-assembly stresses. Here we study a model of one-dimensional chain assembly of incommensurate “polybricks” and determine its equilibrium assembly as a function of temperature, concentration, degree of shape frustration, elasticity, and interparticle binding, notably focusing on how weakly cohesive, defective bonds give rise to strongly temperature-dependent assembly. Complex assembly behavior derives from the competition between multiple distinct local minima in the free-energy landscape, including self-limiting chains, weakly bound aggregates of self-limiting chains, and strongly bound, elastically defrustrated assemblies. We show that this scenario, in general, gives rise to anomalous multiple aggregation behavior, in which disperse subunits (stable at low concentration and high temperature) first exhibit a primary aggregation transition to self-limiting chains (at intermediate concentration and temperature) which are ultimately unstable to condensation into unlimited assembly of finite-chains through weak binding beyond a secondary aggregation transition (at low temperature and high concentration). We show that window of stable self-limitation is determined both by the elastic costs of frustration in the assembly as well as energetic and entropic features of intersubunit binding.

We consider nonlinear wave structures described by the modified Korteweg–de Vries equation, taking into account a small Burgers viscosity for the case of steplike initial conditions. The Whitham modulation equations are derived, which include the small viscosity as a perturbation. It is shown that for a long enough time of evolution, this small perturbation leads to the stabilization of cnoidal bores, and their main characteristics are obtained. The applicability conditions of this approach are discussed. Analytical theory is compared with numerical solutions and good agreement is found.

Shot-to-shot electron beam pointing instability in the plasma bubble, defined here as electron beam pointing jitter (EBJ), is a long-standing problem that limits the potential of the laser wakefield accelerator (LWFA) in a range of demanding applications. In general, EBJ is caused by variations in laser and plasma parameters from shot to shot, although the exact physical mechanism by which EBJ grows in the plasma wave remains unclear. In this work we theoretically investigate the fundamental physics of EBJ inside the plasma bubble and show how the intrinsic betatron oscillation can act as an amplifier to enhance EBJ growth. The analytical formulas for electron trajectory, pointing angle, and EBJ are derived from the basic momentum equation of an electron and verified numerically. It is shown that the shot-to-shot fluctuations of the laser and plasma parameters, such as laser strength, focus, and carrier-envelope phase, as well as the ambient plasma density and profile, lead to EBJ. The evolution of EBJ is dictated by the dynamics of the plasma bubble. Two amplification processes of the betatron oscillation are found in the rapidly evolving bubbles and play important roles in EBJ growth. The first is driven by a linear resonance in the wobbling bubble due to the coupling of the betatron oscillation and the bubble centroid oscillation. The second is a parametric resonance seen in the breathing bubble, where EBJ grows exponentially due to the strong frequency modulation of the betatron oscillation. Their characteristic functions, growth rates, and resonance conditions are deduced analytically and validated numerically. Finally, we also studied how radiation reaction affects EBJ. Our research provides a clear understanding of the basics of EBJ dynamics in LWFA and will help improve the use of LWFA in demanding applications.

A common approach to assess the nature of energy conversion in a classical fluid or plasma is to compare power densities of the various possible energy conversion mechanisms. A leading research area is quantifying energy conversion for systems that are not in local thermodynamic equilibrium (LTE), as is common in a number of fluid and plasma systems. Here we introduce the “higher-order nonequilibrium term” (HORNET) effective power density, which quantifies the rate of change of departure of a phase space density from LTE. It has dimensions of power density, which allows for quantitative comparisons with standard power densities. We employ particle-in-cell simulations to calculate HORNET during two processes, magnetic reconnection and decaying kinetic turbulence in collisionless magnetized plasmas, that inherently produce non-LTE effects. We investigate the spatial variation of HORNET and the time evolution of its spatial average. By comparing HORNET with power densities describing changes to the internal energy (pressure dilatation, $\mathrm{Pi}-\mathrm{D}$, and divergence of the vector heat flux density), we find that HORNET can be a significant fraction of these other measures (8% and 35% for electrons and ions, respectively, for reconnection; up to 67% for both electrons and ions for turbulence), meaning evolution of the system towards or away from LTE can be dynamically important. Applications to numerous plasma phenomena are discussed.

The study of thermodynamic properties of microscopic systems, such as a colloid in a fluid, has been of great interest to researchers since the discovery of the fluctuation theorem and associated laws of stochastic thermodynamics. However, most of these studies confine themselves to systems where effective fluctuations acting on the colloid are in the form of delta-correlated Gaussian white noise (GWN). In this study, instead, we look into the work distribution function when a colloid trapped in a harmonic potential moves from one position to another in a fluid medium with an elongational flow field where the effective fluctuations are given by the Ornstein-Uhlenbeck noise, a type of colored noise. We use path integrals to calculate this distribution function and compare and contrast its properties to the case with GWN. We find that the work distribution function turns out to be non-Gaussian as a result of the elongational flow field but continues to obey the fluctuation theorem in both types of noise. Further, we also look into the effects of the various system parameters on the behavior of work fluctuations and find that although the distribution tends to broaden with increasing noise intensity, increased correlation in fluctuations acts to oppose this effect. Additionally, the system is found to consume heat from the surroundings at early times and dissipate it into the media at later times. This study, therefore, is a step towards gaining a better understanding of the thermodynamic properties of colloidal systems under nonlinear complex flows that also display correlated fluctuations.

Reservoir computing (RC) has been widely applied to predict the chaotic dynamics in many systems. Yet much broader areas related to nonsmooth dynamics have seldom been touched by the RC community which have great theoretical and practical importance. The generalization of RC to this kind of system is reported in this paper. The numerical work shows that the conventional RC with a hyperbolic tangent activation function is not able to predict the dynamics of nonsmooth systems very well, especially when reconstructing attractors (long-term prediction). A nonsmooth activation function with a piecewise nature is proposed. A kind of physics-informed RC scheme is established based on this activation function. The feasibility of this scheme has been proven by its successful application to the predictions of the short- and long-term (reconstructing chaotic attractor) dynamics of four nonsmooth systems with different complexity, including the tent map, piecewise linear map with a gap, both noninvertible and discontinuous compound circle maps, and Lozi map. The results show that RC with the new activation function is efficient and easy to run. It can make perfectly both short- and long-term predictions. The precision of reconstructing attractors depends on their complexity. This work reveals that, to make efficient predictions, the activation function of an RC approach should match the smooth or nonsmooth nature of the dynamical systems.

The problem of finding various discrete breathers (DBs) in the $\beta$-Fermi-Pasta-Ulam-Tsingou simple cubic lattice is addressed. DBs are obtained by imposing localizing functions on delocalized nonlinear vibrational modes (DNVMs) having frequencies above the phonon spectrum of the lattice. Among 27 DNVMs with the wave vector at the boundary of the first Brillouin zone there are three satisfying this condition. Seven robust DBs of different symmetries are found using this approach.

We present a detailed mathematical study of a truncated normal form relevant to the bifurcations observed in wake flow past axisymmetric bodies, with and without thermal stratification. We employ abstract normal form analysis to identify possible bifurcations and the corresponding bifurcation diagrams in parameter space. The bifurcations and the bifurcation diagrams are interpreted in terms of symmetry considerations. Particular emphasis is placed on the presence of attracting robust heteroclinic cycles in certain parameter regimes. The normal form coefficients are computed for several examples of wake flows behind buoyant disks and spheres, and the resulting predictions compared with the results of direct numerical flow simulations. In general, satisfactory agreement is obtained.

We experimentally investigate the dynamics of a sphere rolling up a granular slope. During the rolling-up motion, the sphere experiences slipping and penetration (groove formation) on the surface of the granular layer. The former relates to the stuck motion of the rolling sphere, and the latter causes energy dissipation due to the deformation of the granular surface. To characterize these phenomena, we measured the motion of a sphere rolling up a granular slope of angle $\alpha$. The initial velocity $v_0$, initial angular velocity ${\omega }_0$, angle of slope $\alpha$, and density of the sphere ${\rho }_s$ were varied. As a result, the penetration depth can be scaled solely by the density ratio between the sphere and granular layer. By considering the rotational equation of motion, we estimate the friction due to the slips. Besides, by considering energy conservation, we define and estimate the friction due to groove formation. Moreover, the translational friction is proportional to the penetration depth. Using these results, we can quantitatively predict the sphere's motion including stuck behavior.

Birth and death Markov processes can model stochastic physical systems from percolation to disease spread and, in particular, wildfires. We introduce and analyze a birth-death-suppression Markov process as a model of controlled culling of an abstract, dynamic population. Using analytic techniques, we characterize the probabilities and timescales of outcomes like absorption at zero (extinguishment) and the probability of the cumulative population (burned area) reaching a given size. The latter requires control over the embedded Markov chain: this discrete process is solved using the Pollazcek orthogonal polynomials, a deformation of the Gegenbauer/ultraspherical polynomials. This allows analysis of processes with bounded cumulative population, corresponding to finite burnable substrate in the wildfire interpretation, with probabilities represented as spectral integrals. This technology is developed to lay the foundations for a dynamic decision support framework. We devise real-time risk metrics and suggest future directions for determining optimal suppression strategies, including multievent resource allocation problems and potential applications for reinforcement learning.

We analyze the percolation threshold of square lattices comprising a combination of sites with regular and extended neighborhoods. We found that the percolation threshold of these composed systems smoothly decreases with the fraction of sites with extended neighbors. This behavior can be well-fitted by a Tsallis $q$-Exponential function. We found a relation between the fitting parameters and the differences in the gyration radius among neighborhoods. We also compared the percolation threshold with the critical susceptibility of nearest and next-to-nearest neighbor monoculture plantations vulnerable to the spread of phytopathogen. Notably, the critical susceptibility in monoculture plantations can be described as a linear combination of two composite systems. These results allow the refinement of mathematical models of phytopathogen propagation in agroecology. In turn, this improvement facilitates the implementation of more efficient computational simulations of agricultural epidemiology that are instrumental in testing and formulating control strategies.

It is well established that when multivalent counterions or salts are added to a solution of highly charged polyelectrolytes (PEs), correlation effects can cause charge inversion of the PE, leading to electrophoretic mobility (EM) reversal. In this work, we use coarse-grained molecular-dynamics simulations to unravel the less understood effect of coion valency on EM reversal for rigid DNA-like PEs. We find that EM reversal induced by multivalent counterions is suppressed with increasing coion valency in the salt added and eventually vanishes. Further, we find that EM is enhanced at fixed low salt concentrations for salts with monovalent counterions when multivalent coions with increasing valency are introduced. However, increasing the salt concentration causes a crossover that leads to EM reversal which is enhanced by increasing coion valency at high salt concentration. Remarkably, this multivalent coion-induced EM reversal persists even for low values of PE linear charge densities where multivalent counterions alone cannot induce EM reversal. These results facilitate tuning PE-PE interactions and self-assembly with both coion and counterion valencies.

The rational function approximation provides a natural and interpretable representation of response functions such as the many-body spectral functions. We apply the vector fitting (VFIT) algorithm to fit a variety of spectral functions calculated from the Holstein model of electron-phonon interactions. We show that the resulting rational functions are highly efficient in their fitting of sharp features in the spectral functions, and could provide a means to infer physically relevant information from a spectral data set. The position of the peaks in the approximated spectral function are determined by the location of poles in the complex plane. In addition, we developed a variant of VFIT that incorporates regularization to improve the quality of fits. With this procedure, we demonstrate it is possible to achieve accurate spectral function fits that vary smoothly as a function of physical conditions.

We analytically calculate the scaling exponents of a two-dimensional KPZ-like system: coherently moving incompressible polar active fluids. Using three different renormalization group approximation schemes, we obtain values for the roughness exponent $\chi$ and anisotropy exponent $\zeta$ that are extremely near the known exact results. This implies our prediction for the previously unknown dynamic exponent $z$ is likely to be quantitatively accurate.

Thermokinetic relations bound thermodynamic quantities, such as entropy production of a physical system over a certain time interval, with statistics of kinetic (or dynamical) observables, such as mean total variation of the observable over the time interval. We introduce a thermokinetic relation to bound the entropy production or the nonadiabatic (or excess) entropy production for overdamped Markov jump processes, possibly with time-varying rates and nonstationary distributions. For stationary cases, this bound is akin to a thermodynamic uncertainty relation, only involving absolute fluctuations rather than the mean square, thereby offering a better lower bound far from equilibrium. For nonstationary cases, this bound generalizes (classical) speed limits, where the kinetic term is not necessarily the activity (number of jumps) but any trajectory observable of interest. As a consequence, in the task of driving a system from a given probability distribution to another, we find a tradeoff between nonadiabatic entropy production and housekeeping entropy production: the latter can be increased to decrease the former, although to a limited extent. We also find constraints specific to constant-rate Markov processes. We illustrate our thermokinetic relations on simple examples from biophysics and computing devices.