Excitable media, particularly cardiac tissue, exhibit diverse spatiotemporal wave patterns, among which abnormal waves (e.g., focal activity, rotational activity) can induce life-threatening cardiac arrhythmias. Locating and classifying the sources of these abnormal waves is crucial for guiding clinical treatment. Nevertheless, existing methods mostly only identify phase singularities (PSs) of spiral waves and fail to cover other important sources of target waves and waves rotating around obstacles. To overcome this, we propose a method that can identify spiral waves, target waves, and waves rotating around obstacles, as well as accurately locate their sources. The method involves two steps: (1) the computation of the transmembrane potential velocity field using optical flow techniques, with the zero-velocity fixed points identified as potential wave sources, and (2) the classification of the types of these fixed points via the Jacobian matrix analysis. Validation using simulated datasets generated by the Luo-Rudy model demonstrates the method's effectiveness: it robustly and accurately identifies wave types and locates their sources even in complex scenarios involving obstacles or background noise.

We study the aspects of quantum chaos in mushroom billiards introduced by Bunimovich. This family of billiards classically has the property of mixed phase space with precisely one entirely regular and one fully chaotic (ergodic) component, whose size depends on the width w of the stem, and has two limiting geometries, namely the circle (as the integrable system) and stadium (as the fully chaotic system). Therefore, this one-parameter system is ideal to study the semiclassical behavior of the quantum counterpart. Here, in paper I, we study the spectral statistics as a function of the geometry defined by w and as a function of the semiclassical parameter k, which in this case is just the wave number k. We show that at sufficiently large k the level spacing distribution is excellently described by the Berry-Robnik distribution (without fitting). At lower k the small deviations from it can be well described by the Berry-Robnik-Brody distribution, which captures the effects of weak dynamical localization of Poincaré-Husimi functions. We also employ the analytical theory of the level spacing ratios distribution P(r) for mixed-type systems, recently obtained by Yan [Phys. Rev. E 111, 054213 (2025)2470-004510.1103/PhysRevE.111.054213], which does not require a spectral unfolding procedure, and show excellent agreement with numerics in the semiclassical limit of large k. In paper II [M. Orel and M. Robnik, Phys. Rev. E 113, 044218 (2026)10.1103/rwq2-rydx] we shall analyze the eigenstates by means of Poincaré-Husimi functions.

The generation of skin friction in a spatially evolving turbulent boundary layer at a Mach number Ma_{∞}=2.9 is analyzed using direct numerical simulation (DNS). Particular attention is paid to clarifying the impact of the turbulent/nonturbulent interface (TNTI) height on the skin friction. In contrast to the RD identity N. Renard et al. [J. Fluid Mech. 790, 339 (2016)0022-112010.1017/jfm.2016.12] and its extension to compressible flow W.P. Li et al. [J. Fluid Mech. 875, 101 (2019)0022-112010.1017/jfm.2019.499] we decompose the instantaneous skin friction into four physics-informed contributions. Taking advantage of this novel decomposition method, the conditional statistics contributing to the skin friction near the TNTI can be analyzed. The instantaneous height of the TNTI follows a Gaussian distribution. At a moderate Reynolds number, the height of the TNTI shows no statistical correlation with the skin friction. More specifically, in the vicinity of the TNTI, the contributions of the viscous dissipation and the spanwise inhomogeneity are close to zero. Both the material derivative term and the streamwise inhomogeneity term are mainly determined by the production of the pressure gradient and the streamwise velocity, but these two terms approximately counterbalance each other. This numerical study contributes to understanding the generation of the skin friction in a supersonic turbulent boundary layer, which is crucial in controlling aerodynamics drag in aerospace engineering.

We have simulated an automaton version of the quenched Kardar-Parisi-Zhang (qKPZ) equationin one and two dimensions in order to study the scaling properties of the interface at the depinning transition. Specifically, the α,β,θ, and δ critical exponents characterizing the surface kinetic roughening and depinning behaviors have been directly computed from the simulations. In addition, by studying the height-difference correlation function in real space, we have also been able to directly compute the dynamic correlation length and its associated dynamic critical exponent z. The full sets of scaling exponents are largely compatible with those of the directed percolation depinning universality class for one- and two-dimensional interfaces. Furthermore, we have numerically computed the probability density function (PDF) of the front fluctuations in the growth regime, finding its asymptotic form in one and two dimensions. While the PDF features strongly non-Gaussian skewness and kurtosis values, it also differs from the PDF of the KPZ equationwith time-dependent noise for physical substrate dimensions, both in the central part and at the tails of the distribution.

In this paper, we explore the features of a genetic network where the transcription factors, namely, activators and repressors bind to the promoter in a competitive way. We have developed an analytical method to find the most probable set of parameter values that are unavailable in experiments. We study the behavior of intrinsic noise of the circuit and compare the profile with the network where the activator and the repressor bind the promoter noncompetitively. We observe that the noise found in the super-Poissonian region of the competitive genetic circuit is higher than the noise obtained in the same from a noncompetitive one. We further notice that, due to the effect of transcriptional reinitiation in the presence of the activator and repressor molecules, there exist some anomalous characteristic features in the mean expressions and noise profiles. On top of that, we find low noise in the transcriptional level and high noise in the translational level in presence of reinitiation than in absence of the same. In addition, we find out the method to reduce the noise further below the Poissonian level in competitive circuit than the noncompetitive one with the help of some noise-reducing factors. We also notice that the effect of extrinsic noise due to the environmental fluctuation on the competitive activator-repressor system is insignificant in the low noise limit.

We report computer simulations on the adhesive loose packing (ALP) limit of monodisperse axisymmetric ellipsoids, spherocylinders, and polymers by the random ballistic deposition method with the hit-stick-freeze assumption. The mean-field results demonstrate that the global packing fraction reaches a maximum value of 0.1469 for spheres, and it is nicely correlated with the aspect ratio in the 1 and -2 power-law relations for extremely oblate and prolate particles, respectively. For a given aspect ratio λ, the density follows the sequence of decreasing packing fraction: spheres > prolate ellipsoids > spherocylinders > polymers for λ<3, or spheres > spherocylinders > prolate ellipsoids > polymers for λ≥3. In addition, we highlight that the local coordination number excellently follows the normal distribution with a universal mean value of 2.001, regardless of the particle type and aspect ratio. The standard deviation is 0.730 for spheres, which increasingly approaches the asymptotic values of 0.850 for λ→0 and 1.112 for λ→+∞. Furthermore, we find that the radial distribution function is dominantly governed by the first contact shell with three distinct features, corresponding to the local minor-to-minor, minor-to-major, and major-to-major contacts between two particles. Finally, we present the universal correlation forms for both the global packing fraction and the standard deviation of coordination number, covering the wide aspect ratio range of 0.003-60 for ellipsoids and 1-60 for spherocylinders and polymers. We emphasize that the ALP limit represents the minimum-density state achievable via random ballistic deposition of strongly adhesive particles, while looser structures may be obtained by other cluster aggregation processes.

We study the genetic interfaces between two species of an expanding colony that consists of individual microorganisms that reproduce and undergo diffusion, both at the frontier and in the interior. Within the bulk of the colony, the genetic interface is controlled in a simple way via interspecies interactions. However, at the frontier of the colony, the genetic interface width saturates at finite values for long times, for both neutral strains and interspecies interactions such as antagonism. This finite width arises from geometric effects: genetic interfaces drift toward local minima at an undulating colony frontier, where a focusing mechanism induced by curvature impedes diffusive mixing. Numerical simulations support a logarithmic dependence of the genetic interface width on the strength of the number fluctuations.

We investigate the influence of an anonymous leader on a collective of self-propelled robots using Kilobot experiments and numerical simulations. Each robot possesses a binary internal state that determines the direction of its intrinsic rotational motion, leading to clockwise or counterclockwise circular trajectories. A single leader alternates deterministically between these two internal chiral states, while the other robots update their internal state through a stochastic majority rule based on local communication. The leader induces correlations with the collective response that peak at intermediate perturbation levels, resembling stochastic resonance. Numerical simulations confirm that this resonance arises when the leader's reversal period matches the mean residence time of the leaderless system. Our results contribute to understanding decision-making in active matter and suggest general principles for steering robotic swarms with minimal and anonymous leadership.

Plants often exhibit regular arrangements of seeds or leaves, known as phyllotaxis, and can famously exhibit Fibonacci spirals, as in sunflower heads or on pine cones. While there are many models which can reproduce a spiral formation, the actual mechanism of arrangement remains unclear. Here, we test a more general class of model, based on the Keller-Segel model, in which a diffusing chemical signal produces its own transport signal and can form local instabilities. By modeling the plant as a disk with a signal source at the center and radial growth, we show that we can reproduce both Fibonacci spirals and alternating patterns, depending on a balance between growth and source. Finally, using linear stability analysis, we show how the pattern arises due to a balance between the growth of instabilities and the growth of the plant. Overall, this work demonstrates how the Keller-Segel model can reproduce a wide range of observed patterns, and may act as a phenomenological description of a number of processes in plants.

For high-efficiency inertial confinement fusion implosions, it is predicted that a burning hot spot will successfully encompass all surrounding fuel and then transition into a thermal runaway where the internal energy increase from fusion occurs on a timescale faster than the expansion of the fuel is able to quench the fusion chain reaction after ignition occurs. Observation of this dynamic phase transition would indicate distinct burn properties and indicate an implosion's robustness. A technique for diagnosing the presence of thermal runaway from measurements of nuclear reaction history is presented. The technique is based on taking the logarithmic derivative of the nuclear reaction history, called the α curve, and allowing a mathematical decoupling of the mass, volume, and thermal reactivity in the fusion reaction rate equation. During thermal runaway, where the thermal temperature dominates the burn dynamics, a maximum in the α curve is found where there is a maximum in the first derivative of the thermal fusion reactivity, an effect to the deuterium-tritium (DT) fusion cross-section resonance. This provides a distinct signature related to the fundamental nature of the DT fusion nuclear resonance and signifies the transition into the fusion thermal instability. Impacts of charged particle transport on the effect are also assessed and the analytical formulas are compared and found to be in agreement with radiation hydrodynamic codes.