Partial synchronization is an important dynamical process of coupled oscillators on various natural and artificial networks, which can remain undetected due to the system complexity. With an analogy between pairwise asynchrony of oscillators and topological defects, i.e., vortices, in the two-dimensional $XY$ model, we propose a robust and data-driven method to identify the partial synchronization on complex networks. The proposed method is based on an integer matrix whose element is pseudovorticity that discretely quantifies asynchronous phase dynamics in every two oscillators, which results in graphical and entropic representations of partial synchrony. As a first trial, we apply our method to 200 FitzHugh-Nagumo neurons on a complex small-world network. Partially synchronized chimera states are revealed by discriminating synchronized states even with phase lags. Such phase lags also appear in partial synchronization in chimera states. Our topological, graphical, and entropic method is implemented solely with measurable phase dynamics data, which will lead to a straightforward application to general oscillatory networks including neural networks in the brain.

The exact solution of the Ising model on the complete graph (CG) provides an important, though mean-field, insight for the theory of continuous phase transitions. Besides the original spin, the Ising model can be formulated in the Fortuin-Kasteleyn random cluster and the loop representation, in which many geometric quantities have no correspondence in the spin representations. Using a lifted-worm irreversible algorithm, we study the CG-Ising model in the loop representation and, based on theoretical and numerical analyses, obtain a number of exact results including volume fractal dimensions and scaling forms. Moreover, by combining with the loop-cluster algorithm, we demonstrate how the loop representation can provide an intuitive understanding to the recently observed rich geometric phenomena in the random-cluster representation, including the emergence of two configuration sectors, two length scales, and two scaling windows.

Dynamic hysteresis, viz., delay in switching of a bistable system on account of the finite sweep rate of the drive, has been extensively studied in dynamical and thermodynamic systems. Dynamic hysteresis results from slowing of the response around a saddle-node bifurcation. As a consequence, the hysteresis area increases with the sweep rate. Mean-field theory, relevant for noise-free situations, predicts power-law scaling with the area scaling exponent of $2/3$. We have experimentally investigated the dynamic hysteresis for a thermally driven metal-insulator transition in a high-quality ${\mathrm{NdNiO}}_3$ thin film and found the scaling exponent to be about $1/3$, far less than the mean-field value. To understand this, we have numerically studied Langevin dynamics of the order parameter and found that noise, which can be thought to parallel finite temperature effects, influences the character of dynamic hysteresis by systematically lowering the dynamical exponent to as small as 0.2. The power-law scaling character, on the other hand, is unaffected in the range of chosen parameters. This work rationalizes the ubiquitous power-law scaling of the dynamic hysteresis as well as the wide variation in the scaling exponent between 0.66 and 0.2 observed in different systems over the last 30 years.

Locomotion on granular inclines is a subject of high relevance in ecological physics as well as in biomimmetics and robotics. Enhancing stability on granular materials represents a huge challenge due to the fluidization transition when inclination approaches the avalanche angle. Our motivating example is the predator-prey system made of the antlion, its pit, and its prey. Recent studies have demonstrated that stability on granular inclines strongly depends on the pressure exerted on the substrate. In this work we show that for multilegged locomotion, along with pressure, the distance between the leg contacts on the substrate also plays a major role in the determination of the stability threshold. Through a set of model experiments using artificial sliders, we determine a critical distance below which stability is importantly affected by the interactions between the perturbed regions generated by each contact point. A simple model based on the Coulomb method of wedges allows us to estimate a stability criterion based on pressure, interleg distance, and substrate characteristics. Our work suggests that mass to leg-length allometric relationships, as the ones observed in ants, may be an important key in determining the locomotion success of multilegged locomotion on granular inclines.

We explore the regime of operation of the modulator stage of a recently proposed laser-plasma accelerator scheme [Phys. Rev. Lett. 127, 184801 (2021)], dubbed the plasma-modulated plasma accelerator (P-MoPA). The P-MoPA scheme offers a potential route to high-repetition-rate, GeV-scale plasma accelerators driven by picosecond-duration laser pulses from, for example, kilohertz thin-disk lasers. The first stage of the P-MoPA scheme is a plasma modulator in which a long, high-energy “drive” pulse is spectrally modulated by copropagating in a plasma channel with the low-amplitude plasma wave driven by a short, low-energy “seed” pulse. The spectrally modulated drive pulse is converted to a train of short pulses, by introducing dispersion, which can resonantly drive a large wakefield in a subsequent accelerator stage with the same on-axis plasma density as the modulator. In this paper we derive the 3D analytic theory for the evolution of the drive pulse in the plasma modulator and show that the spectral modulation is independent of transverse coordinate, which is ideal for compression into a pulse train. We then identify a transverse mode instability (TMI), similar to the TMI observed in optical fiber lasers, which sets limits on the energy of the drive pulse for a given set of laser-plasma parameters. We compare this analytic theory with particle-in-cell (PIC) simulations and find that even higher energy drive pulses can be modulated than those demonstrated in the original proposal.

We present an experimental study of quasiperiodic transitions between a highly ordered square-lattice pattern and a disordered, defect-riddled state, in a circular Faraday system. We show that the transition is driven initially by a long-wave amplitude modulation instability, which excites the oscillatory transition phase instability, leading to the formation of dislocations in the Faraday lattice. The appearance of dislocations dampens amplitude modulations, which prevents further defects from being created and allows the system to relax back to its ordered state. The process then repeats itself in a quasiperiodic manner. Our experiments reveal an unexpected mechanism for temporal quasiperiodicity that results from a coupling between two distinct instabilities on the route to chaos.

We consider a system of noninteracting particles on a line with initial positions distributed uniformly with density $\rho$ on the negative half-line. We consider two different models: (i) Each particle performs independent Brownian motion with stochastic resetting to its initial position with rate $r$ and (ii) each particle performs run-and-tumble motion, and with rate $r$ its position gets reset to its initial value and simultaneously its velocity gets randomized. We study the effects of resetting on the distribution $P(Q,t)$ of the integrated particle current $Q$ up to time $t$ through the origin (from left to right). We study both the annealed and the quenched current distributions and in both cases, we find that resetting induces a stationary limiting distribution of the current at long times. However, we show that the approach to the stationary state of the current distribution in the annealed and the quenched cases are drastically different for both models. In the annealed case, the whole distribution $P_{\mathrm{an}}(Q,t)$ approaches its stationary limit uniformly for all $Q$. In contrast, the quenched distribution $P_{\mathrm{qu}}(Q,t)$ attains its stationary form for $Q<Q_{\mathrm{crit}}\left(t\right)$, while it remains time dependent for $Q>Q_{\mathrm{crit}}\left(t\right)$. We show that $Q_{\mathrm{crit}}\left(t\right)$ increases linearly with $t$ for large $t$. On the scale where $Q\sim Q_{\mathrm{crit}}\left(t\right)$, we show that $P_{\mathrm{qu}}(Q,t)$ has an unusual large deviation form with a rate function that has a third-order phase transition at the critical point. We have computed the associated rate functions analytically for both models. Using an importance sampling method that allows to probe probabilities as tiny as ${10}^{-14000}$, we were able to compute numerically this nonanalytic rate function for the resetting Brownian dynamics and found excellent agreement with our analytical prediction.

As a result of extreme weather conditions, such as heavy precipitation, natural hillslopes can fail dramatically; these slope failures can occur on a dry day, due to time lags between rainfall and pore-water pressure change at depth, or even after days to years of slow motion. While the prefailure deformation is sometimes apparent in retrospect, it remains challenging to predict the sudden transition from gradual deformation (creep) to runaway failure. We use a network science method—multilayer modularity optimization—to investigate the spatiotemporal patterns of deformation in a region near the 2017 Mud Creek, California landslide. We transform satellite radar data from the study site into a spatially embedded network in which the nodes are patches of ground and the edges connect the nearest neighbors, with a series of layers representing consecutive transits of the satellite. Each edge is weighted by the product of the local slope (susceptibility to failure) measured from a digital elevation model and ground surface deformation (current rheological state) from interferometric synthetic aperture radar (InSAR). We use multilayer modularity optimization to identify strongly connected clusters of nodes (communities) and are able to identify both the location of Mud Creek and nearby creeping landslides which have not yet failed. We develop a metric, i.e., community persistence, to quantify patterns of ground deformation leading up to failure, and find that this metric increased from a baseline value in the weeks leading up to Mud Creek's failure. These methods hold promise as a technique for highlighting regions at risk of catastrophic failure.

While the one-point height distributions (HDs) and two-point covariances of $(2+1)$ Kardar-Parisi-Zhang (KPZ) systems have been investigated in several recent works for flat and spherical geometries, for the cylindrical one the HD was analyzed for few models and nothing is known about the spatial and temporal covariances. Here, we report results for these quantities, obtained from extensive numerical simulations of discrete KPZ models, for three different setups yielding cylindrical growth. Beyond demonstrating the universality of the HD and covariances, our results reveal other interesting features of this geometry. For example, the spatial covariances measured along the longitudinal and azimuthal directions are different, with the former being quite similar to the curve for flat $(2+1)$ KPZ systems, while the latter resembles the ${\mathrm{Airy}}_2$ covariance of circular $(1+1)$ KPZ interfaces. We also argue (and present numerical evidence) that, in general, the rescaled temporal covariance $\mathcal{A}(t/t_0)$ decays asymptotically as $\mathcal{A}\left(x\right)\sim x^{-\overline{\lambda }}$ with an exponent $\overline{\lambda }=\beta +d^{*}/z$, where $d^{*}$ is the number of interface sides kept fixed during the growth (being $d^{*}=1$ for the systems analyzed here). Overall, these results complete the picture of the main statistics for the $(2+1)$ KPZ class.

Fluctuation dynamos occur in most turbulent plasmas in astrophysics and are the prime candidates for amplifying and maintaining cosmic magnetic fields. A few analytical models exist to describe their behavior, but they are based on simplifying assumptions. For instance, the well-known Kazantsev model assumes an incompressible flow that is $\delta$-correlated in time. However, these assumptions can break down in the interstellar medium as it is highly compressible and the velocity field has a finite correlation time. Using the renewing flow method developed by Bhat and Subramanian (2014), we aim to extend Kazantsev's results to a more general class of turbulent flows. The cumulative effect of both compressibility and finite correlation time over the Kazantsev spectrum is studied analytically. We derive an equation for the longitudinal two-point magnetic correlation function in real space to first order in the correlation time $\tau$ and for an arbitrary degree of compressibility (DOC). This generalized Kazantsev equation encapsulates the original Kazantsev equation. In the limit of small Strouhal numbers $\text{St}\propto \tau$ we use the Wentzel-Kramers-Brillouin approximation to derive the growth rate and scaling of the magnetic power spectrum. We find the result that the Kazantsev spectrum is preserved, i.e., $M_k\left(k\right)\sim k^{3/2}$. The growth rate is also negligibly affected by the finite correlation time; however, it is reduced by the finite magnetic diffusivity and the DOC together.

A famous consequence of the detailed fluctuation theorem (FT), $p\left(\mathrm{\Sigma }\right)/p(-\mathrm{\Sigma })=exp\left(\mathrm{\Sigma }\right)$, is the integral FT $\langle exp(-\mathrm{\Sigma })\rangle =1$ for a random variable $\mathrm{\Sigma }$ and a distribution $p\left(\mathrm{\Sigma }\right)$. When $\mathrm{\Sigma }$ represents the entropy production in thermodynamics, the main outcome of the integral FT is the second law, $\langle \mathrm{\Sigma }\rangle \ge 0$. However, a full description of the fluctuations of $\mathrm{\Sigma }$ might require knowledge of the moment generating function (MGF), $G\left(\alpha \right):=\langle exp\left(\alpha \mathrm{\Sigma }\right)\rangle$. In the context of the detailed FT, we show the MGF is lower bounded in the form $G\left(\alpha \right)\ge B(\alpha ,\langle \mathrm{\Sigma }\rangle )$ for a given mean $\langle \mathrm{\Sigma }\rangle$. As applications, we verify that the bound is satisfied for the entropy produced in the heat exchange problem between two reservoirs mediated by a weakly coupled bosonic mode and a qubit swap engine.

Understanding the role of active fluctuations in physics is a problem in statu nascendi appearing both as a hot topic and a major challenge. The reason for this is the fact that they are inherently nonequilibrium. This feature opens a landscape of phenomena yet to be explored that are absent in the presence of thermal fluctuations alone. Recently a paradoxical effect has been briefly communicated in which a free-particle transport induced by active fluctuations in the form white Poisson shot noise can be enormously boosted when the particle is additionally subjected to a periodic potential. In this work we considerably extend the original predictions and investigate the impact of statistics of active noise on the occurrence of this effect. We construct a toy model of the jump-relaxation process that allow us to identify different regimes of the free-particle transport boost and explain their corresponding mechanisms. Moreover, we formulate and interpret the conditions for statistics of active fluctuations that are necessary for the emergence of giant enhancement of the free-particle transport induced by the periodic potential. Our results are relevant not only for microscopic physical systems but also for biological ones such as, e.g., living cells where fluctuations generated by metabolic activities are active by default.

Self-organized vegetation patterns are an amazing aspect of dryland ecosystems; in addition to being visually appealing, patterns control how these water-deprived systems react to escalating environmental stress. Although there is a wide variety of vegetation patterns, little is known about the mechanisms behind spiral patterns. The well-known models that explain other vegetation patterns such stripes, rings, and fairy circles cannot account for these spirals. Here we have adopted a modeling approach in which the interplay between herbivore grazing and vegetation is found to be the reason why spirals form. To comprehend the nonlinear dependence of grazing on the availability vegetation, we have introduced a grazing term that gets saturated when forage is abundant. To account for the impact of the spatial nonhomogeneity in vegetation layout, it is thought that grazing is dependent on mean vegetation density rather than density at a single site. Results show how the system dynamics is changed fundamentally depending on the different types of grazing response. Incorporation of nonlocality into the herbivore grazing leads to spiral-shaped vegetation patterns only in natural grazing scenarios; however, no patterning is seen in human controlled herbivory. Overall, our research points to the nonlocal, nonlinear grazing behavior of herbivores as one of the major driving forces for the development of spiral patterns.

Intermediate filaments form an essential structural network, spread throughout the cytoplasm, and play a key role in cell mechanics, intracellular organization, and molecular signaling. The maintenance of the network and its adaptation to the cell's dynamic behavior relies on several mechanisms implicating cytoskeletal crosstalk which are not fully understood. Mathematical modeling allows us to compare several biologically realistic scenarios to help us interpret experimental data. In this study we observe and model the dynamics of the vimentin intermediate filaments in single glial cells seeded on circular micropatterns following microtubule disruption by nocodazole treatment. In these conditions, the vimentin filaments move towards the cell center and accumulate before eventually reaching a steady state. In the absence of microtubule-driven transport, the motion of the vimentin network is primarily driven by actin-related mechanisms. To model these experimental findings, we hypothesize that vimentin may exist in two states, mobile and immobile, and switch between the states at unknown (either constant or nonconstant) rates. Mobile vimentin is assumed to advect with either constant or nonconstant velocity. We introduce several biologically realistic scenarios using this set of assumptions. For each scenario, we use differential evolution to find the best parameter sets resulting in a solution that most closely matches the experimental data and then the assumptions are evaluated using the Akaike information criterion. This modeling approach allows us to conclude that our experimental data are best explained by a spatially dependent trapping of intermediate filaments or a spatially dependent speed of actin-dependent transport.

We report on the rebound of a table-tennis ball impinging without any initial spin in oblique incidence on a rigid surface. We show that, below a critical incidence angle, the ball rolls without sliding when bouncing back from the surface. In that case, the reflected angular velocity acquired by the ball can be predicted without any knowledge of the properties of the contact between the ball and the solid surface. Beyond the critical incidence angle, the condition of rolling without sliding is not reached within the time of contact with the surface. In this second case, one can predict the reflected angular and linear velocities, as well as the rebound angle, provided the supplementary knowledge of the friction coefficient associated with the ball-substrate contact.

We theoretically investigate the extractable work in single molecule unfolding-folding experiments with applied feedback. Using a simple two-state model, we obtain a description of the full work distribution from discrete to continuous feedback. The effect of the feedback is captured by a detailed fluctuation theorem, accounting for the information aquired. We find analytical expressions for the average work extraction as well as an experimentally measurable bound thereof, which becomes tight in the continuous feedback limit. We further determine the parameters for maximal power or rate of work extraction. Although our two-state model only depends on a single effective transition rate, we find qualitative agreement with Monte Carlo simulations of DNA hairpin unfolding-folding dynamics.

Suitable cluster definitions have allowed researchers to describe many ordering transitions in spin systems as geometric phenomena related to percolation. For spin glasses and some other systems with quenched disorder, however, such a connection has not been fully established, and the numerical evidence remains incomplete. Here we use Monte Carlo simulations to study the percolation properties of several classes of clusters occurring in the Edwards-Anderson Ising spin-glass model in two dimensions. The Fortuin-Kasteleyn–Coniglio-Klein clusters originally defined for the ferromagnetic problem do percolate at a temperature that remains nonzero in the thermodynamic limit. On the Nishimori line, this location is accurately predicted by an argument due to Yamaguchi. More relevant for the spin-glass transition are clusters defined on the basis of the overlap of several replicas. We show that various such cluster types have percolation thresholds that shift to lower temperatures by increasing the system size, in agreement with the zero-temperature spin-glass transition in two dimensions. The overlap is linked to the difference in density of the two largest clusters, thus supporting a picture where the spin-glass transition corresponds to an emergent density difference of the two largest clusters inside the percolating phase.

We consider an infinite system of particles on a line performing identical Brownian motions and interacting through the ${|x-y|}^{-s}$ Riesz potential, causing the overdamped motion of particles. We investigate fluctuations of the integrated current and the position of a tagged particle. We show that for $0<s<1$, the standard deviations of both quantities grow as $t^{\frac{s}{2(1+s)}}$. When $s>1$, the interactions are effectively short-ranged, and the universal subdiffusive $t^{\frac{1}{4}}$ growth emerges with only amplitude depending on the exponent $s$. We also show that the two-time correlations of the tagged-particle position have the same form as for fractional Brownian motion.

Anisotropic colloidal particles exhibit complex dynamics which play a crucial role in their functionality, transport, and phase behavior. In this Letter, we investigate the two-dimensional diffusion of smoothly curved colloidal rods—also known as colloidal bananas—as a function of their opening angle $\alpha$. We measure the translational and rotational diffusion coefficients of the particles with opening angles ranging from $0^{\circ }$ (straight rods) to nearly ${360}^{\circ }$(closed rings). In particular, we find that the anisotropic diffusion of the particles varies nonmonotonically with their opening angle and that the axis of fastest diffusion switches from the long to the short axis of the particles when $\alpha >{180}^{\circ }$. We also find that the rotational diffusion coefficient of nearly closed rings is approximately an order of magnitude higher than that of straight rods of the same length. Finally, we show that the experimental results are consistent with slender body theory, indicating that the dynamical behavior of the particles arises primarily from their local drag anisotropy. These results highlight the impact of curvature on the Brownian motion of elongated colloidal particles, which must be taken into account when seeking to understand the behavior of curved colloidal particles.

Mechanically quenching a thin film of smectic-$C$ liquid crystal results in the formation of a dense array of thousands of topological defects in the director field. The subsequent rapid coarsening of the film texture by the mutual annihilation of defects of opposite sign has been captured using high-speed, polarized light video microscopy. The temporal evolution of the texture has been characterized using an object-detection convolutional neural network to determine the defect locations, and a binary classification network customized to evaluate the brush orientation dynamics around the defects in order to determine their topological signs. At early times following the quench, inherent limits on the spatial resolution result in undercounting of the defects and deviations from expected behavior. At intermediate to late times, the observed annihilation dynamics scale in agreement with theoretical predictions and simulations of the $2\mathrm{D} XY$ model.