In this study, we present an oscillatory anisotropic sandpile model as an extension of the Bak, Tang, and Wiesenfeld (BTW) model. We focus on exploring the statistical properties of both local and global measures. The model introduces oscillations controlled by a time period, $T$, applied in the parallel direction, while the perpendicular direction follows the standard BTW model. Our results provide strong evidence of a directionality crossover at $T=T^{*}$: for $T$ above (below) this value, avalanches predominantly extend along the spatial parallel direction. Notably, the spanning avalanche probability (SAP) in both directions reaches zero within an interval around $T^{*}$, indicating a localization of avalanches at the crossover point. SAP shows distinct behaviors on either side of this interval. Our scaling analysis reveals an additional crossover between small and large spatial scales, each characterized by unique scaling exponents. The distribution functions for avalanche mass $m$, size $s$, and duration $D$ exhibit power-law behavior within this regime, with notable peaks at positions aligning with the crossover points; these peaks scale with $T$, introducing new scaling exponents. The scaling relations between mass, size, and linear perpendicular avalanche extent $l_{\perp }$ allow us to identify and estimate the scaling exponents ${\gamma }_{m{l}_{\perp }}=2.0\pm 0.05$ and ${\gamma }_{ms}=0.95\pm 0.03$ in the small-scale regime and ${\gamma }_{m{l}_{\perp }}=2.66\pm 0.05$ and ${\gamma }_{ms}=0.68\pm 0.03$ in the large-scale regime for all $T$ values. The mass-duration scaling exponent, ${\gamma }_{mD}=1.57\pm 0.05$, remains robust against changes in $T$.

Search processes often involve multiple agents that collectively search a randomly located target. While increasing the number of agents usually decreases the time at which the first agent finds the target, it also requires resources to create and sustain more agents. In this paper, we raise the question of the optimal timing for launching multiple agents in a search in order to reach the best compromise between minimizing the overall search time and minimizing the costs associated with launching and sustaining agents. After introducing a general formalism for independent agents in which we allow them to be launched at arbitrary times, we investigate by means of analytical calculations and numerical optimization the optimal launch strategies to optimize the quantiles of the search cost and its mean. Finally, we compare our results with the case of stochastic resetting and study the conditions under which it is preferable to launch new searchers rather than resetting the first one to its initial position.

The phenomenon of discharge mode transition in air plasmas, which refers to the selective production of reactive species under different external conditions, has been a longstanding issue and has regained major attention recently due to emerging plasma applications. In this letter, we present a novel kinetic model that incorporates both vibrational ${\mathrm{N}}_2$ kinetics and ${\mathrm{N}}_2{\mathrm{O}}_5$ dissociation reactions in plasma chemistry. This model describes the experimental results of discharge mode transition self-consistently, which has not been achieved before. It is found that both power- and temperature-triggered discharge mode transitions are directly induced by the enhanced recombination of NO and $\mathrm{N}{\mathrm{O}}_2$ to quench O and ${\mathrm{O}}_3$. Two distinct pathways for NO and $\mathrm{N}{\mathrm{O}}_2$ production are identified: high discharge powers sustaining the excitation of ${\mathrm{N}}_2$ to high vibrational levels and elevated gas temperature accelerating ${\mathrm{N}}_2{\mathrm{O}}_5$ dissociation. Essentially, both species are indispensable for enabling discharge mode transition, as their absence leads to significant deviations in transition dynamics. These results explain the origin and kinetics of discharge mode transition and contribute to further advancing plasma applications.

The stochastic gradient descent (SGD) algorithm is the algorithm we use to train neural networks. However, it remains poorly understood how the SGD navigates the highly nonlinear and degenerate loss landscape of a neural network. In this work, we show that the minibatch noise of SGD regularizes the solution towards a noise-balanced solution whenever the loss function contains a rescaling parameter symmetry. Because the difference between a simple diffusion process and SGD dynamics is the most significant when symmetries are present, our theory implies that the loss function symmetries constitute an essential probe of how SGD works. We then apply this result to derive the stationary distribution of stochastic gradient flow for a diagonal linear network with arbitrary depth and width. The stationary distribution exhibits complicated nonlinear phenomena such as phase transitions, broken ergodicity, and fluctuation inversion. These phenomena are shown to exist uniquely in deep networks, implying a fundamental difference between deep and shallow models.

The construction of accurate interatomic potentials, and related fields of forces, from equilibrium conformational distributions of molecules is a crucial step in coarse-grained modeling. In this work we show that in order to develop accurate laboratory-frame force fields that preserve translational and rotational diffusion of a molecule, the observed body-fixed free-energy landscape must be corrected for conformation-dependent rotational entropy to isolate the potential energy surface. We further demonstrate that even when the instantaneous effects of the correction are small, the resulting lagged correlations of the modeled force can be greatly altered and hence the correction is especially vital when parametrizing friction coefficients using modeled interatomic potentials.

This work was devoted to developing an effective spectral method for solving the Dirac equation with the singular Coulomb potential, where the fast Fourier transformation could be directly applied. In the method, the trigonometric sine functions were chosen as the basis, and a well-designed scaling function was proposed to account for the singularity of the Coulomb potential. In the spirit of the discrete variable representation, the Chebyshev-Gauss quadrature was adopted. It is found that the method could achieve spectral convergence easily to a precision around ${10}^{-32}$ with quadruple variables. Although the numerical solution of the Dirac equation is more demanding than the Schrödinger equation due to the relativistic effects, the numerical convergence of the proposed method is comparable with the best spectral method at the moment for solving the Dirac equation, the Lagrange mesh method.

The spreading dynamics of a liquid droplet impacting a solid surface depend on the surface tension of the liquid and the dissipation phenomena at work in the droplet. In this study, we investigate the final state after the impact of a granular droplet in a pendular state, i.e., a droplet composed of solid grains held together by liquid capillary bridges, where the dissipation and fragmentation processes during impact are not well understood. We measure the total surface area and perimeter of all the fragments formed after impact, as seen from above. We investigate how the final surface area and perimeter of the granular droplet after impact depend on the impact speed, grain diameter, and the properties of the interstitial liquid. Our observations show that the final perimeter and surface area of the granular droplets can be rationalized by scaling laws expressed in terms of a Weber number based on the diameter of grains that constitute the droplet. Compared with the impact of a pure liquid droplet, the impact of a granular droplet is more prone to fragmentation, which affects the evolution of the final perimeter with the Weber number. In addition, we study the number of fragments and their size distribution as a function of the Weber number and observe similarities with the fragmentation of pure liquid droplets.

We study the evolution of a system of many point particles initially concentrated in a small region in $d$ dimensions. Particles undergo overdamped motion caused by pairwise interactions through the long-ranged repulsive $r^{-s}$ potential; each particle is also subject to white Gaussian noise. When $s<d$, the expansion is governed by nonlocal hydrodynamic equations. In the one-dimensional case, we deduce self-similar solutions for all $s\in (-2,1)$. The expansion of Coulomb gases remains well-defined in the infinite-particle limit: The density is spatially uniform and inversely proportional to time, independent of the spatial dimension.

Barrier-crossing processes are often described using Markovian models, where reaction rates are quantified by mean first-passage times (MFPTs), barrier-escape times, or state-correlation functions. However, for systems exhibiting non-Markovian dynamics, where memory effects play a significant role, these metrics can differ substantially, complicating the interpretation of reaction kinetics from experimental or simulated time-series data. Here, we investigate the numerical evaluation of MFPTs and escape times in non-Markovian systems. For the MFPTs, we focus on two distinct computational approaches: one that considers only first arrivals between states, equivalent to the waiting or dwell time, and another that includes all first passages for a barrier-crossing event. Using extensive simulations of a one-dimensional generalized Langevin equation, we show that these methods yield equivalent results in the Markovian limit but diverge significantly under strong non-Markovian conditions. We derive a relationship between their respective passage-time distributions, which we validate against simulation data. Analysis of these distributions reveals that mean reaction times can be dominated either by rapid state recrossing or by slow escape dynamics. As such, our results highlight the importance of examining full kinetic distributions, rather than just mean values, to accurately characterize barrier-crossing dynamics in systems with memory.

Some questions raised by the modeling of the interactions between colloids using scattering data are examined. After a brief overview of the predictions and limitations of the basic potentials with short-range attraction, we first analyze recent data on coated silica dispersions, using a model with short-ranged repulsion and an improved treatment of the short-ranged attraction. We discuss in particular the unicity of the potential extracted from the structural data, the state dependence of the fitting parameters and their link with the characteristics of the particles, the effect of the particle size, and the density and temperature in pure components and in mixtures. The analysis of the data in the silica dispersions is next confronted with charged colloids and star polymers. Based on the prediction for the position of the main peak of the scattering intensity in six dispersions at different state points, the possible role of many-body effects in the scattering intensity is confirmed. Finally, the use of gelation data for refining the potential extraction is discussed.

Rocks famously have scale-dependent strength, yet the actual dependence is notoriously hard to measure or incorporate into any theoretical framework. Natural rough surfaces present an opportunity to solve the problem. Surfaces sliding in shear evolve as protrusions collide. These asperities can deform or break, thus creating a new surface shape. In particular, natural surfaces have roughness at all scales as well as scale-dependent strength. Based on a scaling analysis, we have previously suggested that the scale-dependent aspect ratio of steady-state surfaces should be proportional to the scale-dependent shear strain at yield. If true, scale-dependent strength could easily be inferred from natural surfaces. Thus, moving beyond the scaling argument to a rigorous treatment of scale-dependent strength for multiscale rough surfaces in shear is important. However, analytic frameworks for analyzing multiscale problems are challenging, as conventional continuum mechanics typically involves a single value for a material property across scales. Here, we build on the formalism of Persson (2001) that presents a method to compute contact area for rough surfaces with a prescribed topographic spectrum using a stochastic differential equation. The Persson formalism allows for plastic yield under normal loading of otherwise elastic materials and leaves open the possibility of scale-dependent yield stress. In this study, we pursue this route to develop a theory and numerical results for the yielding of a rough, elastoplastic surface with scale-dependent yield stress. Here, we examine surfaces for which the power spectrum of the topography $C$ and yield stress $Y$ follow power laws as a function of scale $\lambda$, such that $C\sim {\lambda }^{-m}$ and $Y\sim {\lambda }^{-n}$, respectively. In this formal treatment of the problem, we focus on surfaces in contact and the resulting yield and do not impose shear. Numerical solutions show that the deviation from the elastic scaling solution is bounded as expected by the prior 1D heuristic scaling argument that anticipates the Hurst exponent as $1-n$. We also show that the plasticity is expected to erode the contacts if $m$ is lower than $n-3$, which corresponds to a Hurst exponent lower than $1-n/2$. This result is rigorously sound for 2D, i.e., realistic surfaces, and quantitatively different than the prior scaling argument. The theory now permits a correspondingly quantitative approach to interpreting natural surfaces.

Power-law precursory acceleration of observable quantities has been accepted as an effective way to predict time to failure in both materials and structures. However, the form of the power-law exponent is seldom known a priori and is a key challenge in blind prediction. We report a linear relation with respect to time $t$ of the estimated failure times $t_{*}$ that are calculated step by step using the most recent updates of the monitored quantity. Our findings indicate that the monitored quantity can be defined as any power of the inverse rate. All projections of $t_{*}$ for any exponent universally intersect with the straight line of $t=t_{*}$, with the intersection uniquely defining the failure time. The method is validated against synthetic data, laboratory experiments (materials failure), and volcanic eruption data (structural failure). Our work provides the basis for a significant improvement in time to failure forecasting where the controlling power-law exponent is not known in advance.

A complete analysis of classical periodic orbits (POs) and their bifurcations was conducted in spherical harmonic oscillator system with spin-orbit coupling. The motion of the spin is explicitly considered using the spin canonical variables derived by semiclassical approximation to the spin coherent state path-integral representation. In addition to the diametric and two circular PO families with frozen spin, solutions that bridge two circular POs are found in which orbital motion is coupled to spin precession. In addition, each bridge encounters a secondary bifurcation on the way from one circular PO to the other and generates a new PO that survives at higher energies while maintaining a constant period. The generic expressions for those POs are obtained explicitly, and all the above peculiar bifurcation scenarios are described fully analytically.

The Hamiltonian mean-field (HMF) model is a long-range interaction system that exhibits quasistationary states (QSS), which persist for long times before reaching thermodynamic equilibrium. These states are traditionally characterized by homogeneous/demagnetized or nonhomogeneous/magnetized phase-space structures, separated by an out-of-equilibrium phase transition that depends on the initial energy $u_0$ and magnetization $M_0$ of the system. However, the magnetization also exhibits fluctuations around its mean value in time, which can provide additional insights into the nature of the QSS. In this study, the permutation entropy $H$ and the statistical complexity $C$ are used as tools to characterize the dynamical properties of these magnetization fluctuations. It is found that most data points lie above the entropy-complexity curve for stochastic processes with a power-law spectrum ($k$ noise), suggesting that the magnetization retains more structure than purely stochastic processes. As the initial energy $u_0$ increases, both $H$ and $C$ exhibit global minima that align closely with the critical energy $u^{*}$ separating magnetized and demagnetized QSSs. This agreement is particularly strong for $M_0\lesssim 0.4$, where a first-order out-of-equilibrium phase transition has been reported for the HMF model. Below this transition, magnetized QSSs are associated with more ordered fluctuations, exhibiting fewer correlated structures. Above this transition, demagnetized QSSs are characterized by fluctuations that shift toward more complex and more disordered dynamics, with an increasing number of correlated structures as $u_0$ increases.

The anticipating synchronization in an ensemble of electrochemical cell oscillators exhibiting chaotic dynamics is analyzed. Using a setup up of up to three oscillators, it is observed that when such systems are coupled by unidirectional delayed time terms, the slave system can anticipate the dynamics of the master system by an anticipation time of $\tau$. This anticipating time has an upper limit (critical $\tau$) beyond which the slave system can no longer predict the master's chaotic dynamics due to Lyapunov instability. In order to enhance the anticipating time, we used a chain of oscillators in a master-slave configuration (i.e., via unidirectional coupling). The experimental observations were verified by numerical simulations using appropriate model systems. These results indicate that this specific type of synchronization is prevalent in a group of coupled electrochemical oscillators despite the inherent heterogeneities and drift phenomena, making them relevant for possible applications in biological systems.

Computational scientists have long been developing a diverse portfolio of methodologies to characterize condensed matter systems. Most of the descriptors resulting from these efforts are ultimately based on the spatial configurations of particles, atoms, or molecules within these systems. Noteworthy examples include symmetry functions and the smooth overlap of atomic positions (SOAP) descriptors, which have significantly advanced the performance of predictive machine learning models for both condensed matter and small molecules. However, while graph-based descriptors are frequently employed in machine learning models to predict the functional properties of small molecules, their application in the context of condensed matter has been limited. In this paper, we put forward a number of graph-based descriptors (such as node centrality and local clustering coefficients) traditionally utilized in network science as alternative representations for condensed matter systems. We apply this graph-based formalism to investigate the dynamical properties and phase transitions of the prototypical Lennard-Jones system. We find that our graph-based formalism outperforms symmetry function descriptors in predicting the dynamical properties and phase transitions of this system. These results demonstrate the broad applicability of graph-based features in representing condensed matter systems, paving the way for exciting advancements in the field of condensed matter through the integration of network science concepts.

The structures of fiber networks can vary greatly due to fiber interactions during formation. We have modified the steps of generating Mikado networks to create two model classes by altering the spatial distribution and relative orientation of their fibers to mimic the structures of self-assembling peptide hydrogels (SAPHs), whose physical properties depend strongly on their fibers' interactions. The results of our models and experiments on a set of beta-sheet forming SAPHs show that modifying a network's structure affects the percolation threshold and the mechanical behavior of the material, both near percolation and at higher densities.

We investigate with particle-in-cell simulation the transport of fast electrons of MeV under a kT-level magnetic field produced by a circular coil target, where the fast electrons are generated by a picosecond laser pulse with typical intensity of $5\times {10}^{19}\mathrm{W}/{\mathrm{cm}}^2$ adopted in fast ignition. The fast electrons can be well collimated when the coil diameter is about $200\mu \mathrm{m}$ in the fast ignition or double-cone ignition scheme of laser fusion when the current in the coil is taken as around 200 kA according to typical experimental results. The optimized coil diameter results from the competition between the strength enhancement and the nonuniformity growth of the magnetic field as the reduction of the coil diameter. Here the nonuniformity growth can induce the magnetic mirror effect, which causes the reflection of some transporting fast electrons. In particular, when the coil diameter is larger than $500\mu \mathrm{m}$, the fast-electron transport under the produced magnetic field is very close to the case with a uniform magnetic field. We also find shifting the coil longitudinal position along the laser progapagation can change the electron transport range within the convergent or divergent magnetic field lines, and placing the coil tens of micrometers away from the electron generation position is favorable for the electron transport. This work could be applied not only in fast ignition and double-cone ignition schemes, but also to ion acceleration and radiation sources based on laser-driven fast electrons.