We consider phase transitions, in the form of spontaneous symmetry breaking (SSB) bifurcations of solitons, in dual-core couplers with fractional diffraction and cubic self-focusing acting in each core, characterized by Lévy index $\alpha$. The system represents linearly coupled optical waveguides with the fractional paraxial diffraction or group-velocity dispersion (the latter system was used in a recent experiment [Nat. Commun. 14, 222 (2023)], which demonstrated the first observation of the wave propagation in an effectively fractional setup). By dint of numerical computations and variational approximation, we identify the SSB in the fractional coupler as the bifurcation of the subcritical type (i.e., the symmetry-breaking phase transition of the first kind), whose subcriticality becomes stronger with the increase of fractionality $2-\alpha$, in comparison with very weak subcriticality in the case of the nonfractional diffraction, $\alpha =2$. In the Cauchy limit of $\alpha \to 1$, it carries over into the extreme subcritical bifurcation, manifesting backward-going branches of asymmetric solitons which never turn forward. The analysis of the SSB bifurcation is extended for moving (tilted) solitons, which is a nontrivial problem because the fractional diffraction does not admit Galilean invariance. Collisions between moving solitons are studied too, featuring a two-soliton symmetry-breaking effect and merger of the solitons.

We study observation entropy (OE) for the quantum kicked top model, whose classical counterpart possesses different phases: regular, mixed, or chaotic, depending on the strength of the kicking parameter. We show that OE grows logarithmically with coarse-graining length beyond a critical value in the regular phase, while OE growth is much faster in the chaotic regime. In the dynamics, we demonstrate that the short-time growth rate of OE acts as a measure of the chaoticity in the system, and we compare our results with out-of-time-ordered correlators (OTOC). Moreover, we show that in the deep quantum regime, the results obtained from OE are much more robust compared to OTOC results. Finally, we also investigate the long-time behavior of OE to distinguish between saddle-point scrambling and true chaos, where the former shows large persistent fluctuations compared to the latter.

Reservoir Computing has found many potential applications in the field of complex dynamics. In this article, we explore the exceptional capability of the echo-state network (ESN) model to make it learn a unidirectional coupling scheme from only a few time series data of the system. We show that, once trained with a few example dynamics of a drive-response system, the machine is able to predict the response system's dynamics for any driver signal with the same coupling. Only a few time series data of an $A-B$ type drive-response system in training is sufficient for the ESN to learn the coupling scheme. After training, even if we replace drive system $A$ with a different system $C$, the ESN can reproduce the dynamics of response system $B$ using the dynamics of new drive system $C$ only.

We perform feedback experiments and simulations in which a colloidal dumbbell particle, acting as a particle on a ring, is followed by a repulsive optical trap controlled by a continuous-time-delayed feedback protocol. The dynamics are described by a persistent random walk similarly to that of an active Brownian particle, with a transition from predominantly diffusive to driven behavior at a critical delay time. We model the dynamics in the short and long delay regimes using stochastic delay differential equations and derive a condition for stable driven motion. We study the stochastic thermodynamic properties of the system, finding that the maximum work done by the trap coincides with a local minimum in the mutual information between the trap and the particle position at the onset of stable driven dynamics.

Molecular dynamics simulations have been performed to study the dynamics of nanodroplets impacting on a flat superhydrophobic surface and surfaces covered with nanocone structures. We present a panorama of nanodroplet behaviors for a wide range of impact velocities and different cone geometrics, and develop a model to predict whether a nanodroplet impacting onto cone-textured surfaces will touch the underlying substrate during impact. The advantages and disadvantages of applying nanocone structures to the solid surface are revealed by the investigations into restitution coefficient and contact time. The effects of nanocone structures on droplet bouncing dynamics are probed using momentum analysis rather than conventional energy analysis. We further demonstrate that a single Weber number is inadequate for unifying the dynamics of macroscale and nanoscale droplets on cone-textured surfaces, and propose a combined dimensionless number to address it. The extensive findings of this study carry noteworthy implications for engineering applications, such as nanoprinting and nanomedicine on functional patterned surfaces, providing fundamental support for these technologies.

We study the nonequilibrium Langevin dynamics of $N$ particles in one dimension with Coulomb repulsive linear interactions. This is a dynamical version of the so-called jellium model (without confinement) also known as ranked diffusion. Using a mapping to the Lieb-Liniger model of quantum bosons, we obtain an exact formula for the joint distribution of the positions of the $N$ particles at time $t$, all starting from the origin. A saddle-point analysis shows that the system converges at long time to a linearly expanding crystal. Properly rescaled, this dynamical state resembles the equilibrium crystal in a time-dependent effective quadratic potential. This analogy allows us to study the fluctuations around the perfect crystal, which, to leading order, are Gaussian. There are however deviations from this Gaussian behavior, which embody long-range correlations of purely dynamical origin, characterized by the higher-order cumulants of, e.g., the gaps between the particles, which we calculate exactly. We complement these results using a recent approach by one of us in terms of a noisy Burgers equation. In the large-$N$ limit, the mean density of the gas can be obtained at any time from the solution of a deterministic viscous Burgers equation. This approach provides a quantitative description of the dense regime at shorter times. Our predictions are in good agreement with numerical simulations for finite and large $N$.

Random sequential adsorption of extended objects deposited on two-dimensional regular lattices is studied. The depositing objects are chains formed by occupying adsorption sites on the substrate through a self-avoiding walk of $k$ lattice steps; these objects are also called “tortuous $k$-mers.” We study how the jamming coverage, ${\theta }_{j,k}$, depends on $k$ for lattices with different connectivity (honeycomb, square, and triangular). The dependence can be fitted by the function ${\theta }_{j,k}={\theta }_{j,k\to \infty }+B/k+C/k^2$, where $B$ and $C$ are found to be shared parameters by the three lattices and ${\theta }_{j,k\to \infty }$ ($>0$) is the jamming coverage for infinitely long $k$-mers for each of them. The jamming coverage is found to have a growing behavior with the connectivity of the lattice. In addition, ${\theta }_{j,k}$ is found to be higher for tortuous $k$-mers than for the previously reported for linear $k$-mers in each lattice. The results were obtained by means of numerical simulation through an efficient algorithm whose characteristics are discussed in detail. The computational method introduced here also allows us to investigate the full-time kinetics of the surface coverage ${\theta }_k\left(t\right)$ $[{\theta }_{j,k}\equiv {\theta }_k(t\to \infty )]$. Along this line, different time regimes are identified and characterized.

As phenomena that necessarily emerge from the collective behavior of interacting particles, phase transitions continue to be difficult to predict using statistical thermodynamics. A recent proposal called the topological hypothesis suggests that the existence of a phase transition could perhaps be inferred from changes to the topology of the accessible part of the configuration space. This paper instead suggests that such a topological change is often associated with a dramatic change in the configuration space geometry, and that the geometric change is the actual driver of the phase transition. More precisely, a geometric change that brings about a discontinuity in the mixing time required for an initial probability distribution on the configuration space to reach the steady state is conjectured to be related to the onset of a phase transition in the thermodynamic limit. This conjecture is tested by evaluating the diffusion diameter and $\epsilon$-mixing time of the configuration spaces of hard-disk and hard-sphere systems of increasing size. Explicit geometries are constructed for the configuration spaces of these systems and numerical evidence suggests that a discontinuity in the $\epsilon$-mixing time coincides with the solid-fluid phase transition in the thermodynamic limit.

Synchronization and desynchronization of coupled oscillators appear to be the key property of many physical systems. It is believed that to predict a synchronization (or desynchronization) event, the knowledge on the exact structure of the oscillatory network is required. However, natural sciences often deal with observations where the coupling coefficients are not available. In the present paper we suggest a way to characterize synchronization of two oscillators without the reconstruction of coupling. Our method is based on the Kuramoto chain with three oscillators with constant but nonidentical coupling. We characterize coupling in this chain by two parameters: the coupling strength $s$ and disparity $\sigma$. We give an analytical expression of the boundary $s_{\text{max}}$ of synchronization occurred when $s>s_{\text{max}}$. We propose asymmetry $A$ of the generalized order parameter induced by the coupling disparity as a new characteristic of the synchronization between two oscillators. For the chain model with three oscillators we present the self-consistent inverse problem. We explore scaling properties of the asymmetry $A$ constructed for the inverse problem. We demonstrate that the asymmetry $A$ in the chain model is maximal when the coupling strength in the model reaches the boundary of synchronization $s_{\text{max}}$. We suggest that the asymmetry $A$ may be derived from the phase difference of any two oscillators if one pretends that they are edges of an abstract chain with three oscillators. Performing such a derivation with the general three-oscillator Kuramoto model, we show that the crossover from the chain to general network of oscillators keeps the interrelation between the asymmetry $A$ and synchronization. Finally, we apply the asymmetry $A$ to describe synchronization of the solar magnetic field proxies and discuss its potential use for the forecast of solar cycle anomalies.

In this work, we study the existence and stability of constant density (flat-top) solutions to the Gross-Pitaevskii equation (GPE) in confining potentials. These are constructed by using the “inverse problem” approach which corresponds to the identification of confining potentials that make flat-top waveforms exact solutions to the GPE. In the one-dimensional case, the exact solution is the sum of stationary kink and antikink solutions, and in the overlapping region, the density is constant. In higher spatial dimensions, the exact solutions are generalizations of this wave function. In the absence of self-interactions, the confining potential is similar to a smoothed-out finite square well with minima also at the edges. When self-interactions are added, terms proportional to $\pm g{\psi }^{*}\psi$ and $\pm gM$ with $M$ representing the mass or number of particles in Bose-Einstein condensates get added to the confining potential and total energy, respectively. In the realm of stability analysis, we find (linearly) stable solutions in the case with repulsive self-interactions which also are stable to self-similar deformations. For attractive interactions, however, the minima at the edges of the potential get deeper and a barrier in the center forms as we increase the norm. This leads to instabilities at a critical value of $M$. Comparing the stability criteria from Derrick's theorem with Bogoliubov-de Gennes (BdG) analysis stability results, we find that both predict stability for repulsive self-interactions and instability at a critical mass $M$ for attractive interactions. However, the numerical analysis gives a much lower critical mass. This is due to the emergence of symmetry-breaking instabilities that were detected by the BdG analysis and violate the symmetry $x\to -x$ assumed by Derrick's theorem.

Information and individual activities often spread globally through the network of social ties. While social contagion phenomena have been extensively studied within the framework of threshold models, it is common to make an assumption that may be violated in reality: each individual can observe the neighbors' states without error. Here, we analyze the dynamics of global cascades under uncertainty in an otherwise standard threshold model. Each individual uses statistical inference to estimate the probability distribution of the number of active neighbors when deciding whether to be active, which gives a probabilistic threshold rule. Unlike the deterministic threshold model, the spreading process is generally nonmonotonic, as the inferred distribution of neighbors' states may be updated as a new signal arrives. We find that social contagion may occur as a self-fulfilling event in that misperception may trigger a cascade in regions where cascades would never occur under certainty.

We investigated the dynamical behaviors of bimodular continuous attractor neural networks, each processing a modality of sensory input and interacting with each other. We found that when bumps coexist in both modules, the position of each bump is shifted towards the other input when the intermodular couplings are excitatory and is shifted away when inhibitory. When one intermodular coupling is excitatory while another is moderately inhibitory, temporally modulated population spikes can be generated. On further increase of the inhibitory coupling, momentary spikes will emerge. In the regime of bump coexistence, bump heights are primarily strengthened by excitatory intermodular couplings, but there is a lesser weakening effect due to a bump being displaced from the direct input. When bimodular networks serve as decoders of multisensory integration, we extend the Bayesian framework to show that excitatory and inhibitory couplings encode attractive and repulsive priors, respectively. At low disparity, the bump positions decode the posterior means in the Bayesian framework, whereas at high disparity, multiple steady states exist. In the regime of multiple steady states, the less stable state can be accessed if the input causing the more stable state arrives after a sufficiently long delay. When one input is moving, the bump in the corresponding module is pinned when the moving stimulus is weak, unpinned at intermediate stimulus strength, and tracks the input at strong stimulus strength, and the stimulus strengths for these transitions increase with the velocity of the moving stimulus. These results are important to understanding multisensory integration of static and dynamic stimuli.

The spatial spread of an epidemic is investigated in the case of a bistable dynamics, where the effective transmission rate depends on the fraction of infected and the state of no epidemic is linearly stable. The front propagation phenomenon is investigated both numerically and theoretically, by an analysis in a four-dimensional phase plane. A good agreement between numerical and theoretical results has been found both for the front profiles and for the speed of invasion. We discovered a novel phenomenon of front stoppage: In some regime of parameters, the front solution ceases to exist, and the propagating pulse of infection decays despite the initial outbreak.

The primary visual cortex (V1) is the first cortical area that processes visual information relayed from the thalamus. The topologies permitted in joint ocular dominance (OD), orientation preference (OP), and direction preference (DP) maps in V1 are considered, with the aim of finding a maximally symmetric periodic case that can serve as the basis for perturbations toward natural realizations. It is shown that mutual consistency of the maps selects just two possible such lattice structures, and that one of these is much closer to experiment than the other. This comprises a hexagonal lattice of alternating positive and negative OP singularities, with each unit cell or hypercolumn containing four such singularities, each of which radiates three DP discontinuities that follow OP contours and end at OP singularities of opposite sign. Other DP discontinuities emanate at 90 degrees to the midpoints of the ones that link OP singularities, and cross OP contours perpendicularly. These features explain experimentally observed relationships between DP discontinuities and OP contours, including sudden approximately 90-degree changes of direction in the former.

In this work, the calculation of Casimir forces across thin DNA films is carried out based on the Lifshitz theory. The variations of Casimir forces due to the DNA thicknesses, volume fractions of containing water, covering media, and substrates are investigated. For a DNA film suspended in air or water, the Casimir force is attractive, and its magnitude increases with decreasing thickness of DNA films and the water volume fraction. For DNA films deposited on a dielectric (silica) substrate, the Casimir force is attractive for the air environment. However, the Casimir force shows unusual features in a water environment. Under specific conditions, switching sign of the Casimir force from attractive to repulsive can be achieved by increasing the DNA-film thickness. Finally, the Casimir force for DNA films deposited on a metallic substrate is investigated. The Casimir force is dominated by the repulsive interactions at a small DNA-film thickness for both the air and water environments. In a water environment, the Casimir force turns out to be attractive for a large DNA-film thickness, and a stable Casimir equilibrium can be found. The influences of electrolyte screening on the Casimir pressure of DNA films are also discussed at the end. In addition to the adhesion stability, our finding could be applicable to the problems of condensation and decondensation of DNA, due to fluctuation-induced dispersion forces.

Stochastic heating is a well-known mechanism through which magnetized particles may be energized by low-frequency electromagnetic waves. In its simplest version, under spatially homogeneous conditions, it is known to be operative only above a threshold in the normalized wave amplitude, which may be a demanding requisite in actual scenarios, severely restricting its range of applicability. In this paper we show, by numerical simulations supported by inspection of the particle Hamiltonian, that allowing for even a very weak spatial inhomogeneity completely removes the threshold, trading the requirement upon the wave amplitude with a requisite upon the duration of the interaction between the wave and particle. The thresholdless chaotic mechanism considered here is likely to be applicable to other inhomogeneous systems.

When two intense laser beams cross at a small angle, the interference in the crossing area results in a finite intensity grating. We consider femtosecond laser filamentation in such a grating, in a situation when the process is largely confined to the grating maxima and leads to formation of a structured filament wake channel. In a dense gas, electron impact processes during the laser pulse cause a copious excitation of neutral atoms, resulting in formation of a finite grating of the density of excited atoms. Numerically solving the equations of laser-driven kinetics, we obtain the properties of this grating, as depending on the characteristics of the interfering beams and especially on the interbeam phase delay. The excitation gratings thus formed give rise to a hallmark effect of Rabi sideband emission when probed by a picosecond 800 nm laser pulse, which couples with transitions in the excited states manifold. Spectral and spatial interference of the emitted radiation forms four-dimensional spatial-spectral fringe patterns accessible for observation on a remote screen. The patterns are indicative of the excitation grating structure; their sensitivity to the phase delay between the crossing pump pulses warrants experimental verification.

As has long been known to computer scientists, the performance of probabilistic algorithms characterized by relatively large runtime fluctuations can be improved by applying a restart, i.e., episodic interruption of a randomized computational procedure followed by initialization of its new statistically independent realization. A similar effect of restart-induced process acceleration could potentially be possible in the context of enzymatic reactions, where dissociation of the enzyme-substrate intermediate corresponds to restarting the catalytic step of the reaction. To date, a significant number of analytical results have been obtained in physics and computer science regarding the effect of restart on the completion time statistics in various model problems, however, the fundamental limits of restart efficiency remain unknown. Here we derive a range of universal statistical inequalities that offer constraints on the effect that restart could impose on the completion time of a generic stochastic process. The corresponding bounds are expressed via simple statistical metrics of the original process such as harmonic mean $h$, median value $m$, and mode $M$, and, thus, are remarkably practical. We test our analytical predictions with multiple numerical examples, discuss implications arising from them and important avenues of future work.

We use a subdiffusion equation with fractional Caputo time derivative with respect to another function $g$ ($g$-subdiffusion equation) to describe a smooth transition from ordinary subdiffusion to superdiffusion. Ordinary subdiffusion is described by the equation with the “ordinary” fractional Caputo time derivative, superdiffusion is described by the equation with a fractional Riesz-type spatial derivative. We find the function $g$ for which the solution (Green's function, GF) to the $g$-subdiffusion equation takes the form of GF for ordinary subdiffusion in the limit of small time and GF for superdiffusion in the limit of long time. To solve the $g$-subdiffusion equation we use the $g$-Laplace transform method. It is shown that the scaling properties of the GF for $g$-subdiffusion and the GF for superdiffusion are the same in the long time limit. We conclude that for a sufficiently long time the $g$-subdiffusion equation describes superdiffusion well, despite a different stochastic interpretation of the processes. Then, paradoxically, a subdiffusion equation with a fractional time derivative describes superdiffusion. The superdiffusive effect is achieved here not by making anomalously long jumps by a diffusing particle, but by greatly increasing the particle jump frequency which is derived by means of the $g$-continuous-time random walk model. The $g$-subdiffusion equation is shown to be quite general, it can be used in modeling of processes in which a kind of diffusion change continuously over time. In addition, some methods used in modeling of ordinary subdiffusion processes, such as the derivation of local boundary conditions at a thin partially permeable membrane, can be used to model $g$-subdiffusion processes, even if this process is interpreted as superdiffusion.