We investigate the impact of noise on parameter fitting for an Ornstein-Uhlenbeck process, focusing on the effects of multiplicative and thermal noise on the accuracy of signal separation. To address these issues, we propose algorithms and methods that can effectively distinguish between thermal and multiplicative noise and improve the precision of parameter estimation for optimal data analysis. Specifically, we explore the impact of both multiplicative and thermal noise on the obfuscation of the actual signal and propose methods to resolve them. First, we present an algorithm that can effectively separate thermal noise with comparable performance to Hamilton Monte Carlo (HMC) methods, but with significantly improved speed. We then analyze multiplicative noise and demonstrate that HMC is insufficient for isolating thermal and multiplicative noise. However, we show that with additional knowledge of the ratio between thermal and multiplicative noise, we can accurately distinguish between the two types of noise when provided with a sufficiently large sampling rate or an amplitude of multiplicative noise that is smaller than the thermal noise. Thus, we demonstrate the mechanism underlying an otherwise counterintuitive phenomenon: when multiplicative noise dominates the noise spectrum, one can successfully estimate the parameters for such systems after adding additional white noise to shift the noise balance.

Anomalous transport in low dimensional spin chains is an intriguing topic that can offer key insights into the interplay of integrability and symmetry in many-body dynamics. Recent studies have shown that spin–spin correlations in spin chains, where integrability is either perfectly preserved or broken by symmetry-preserving interactions, fall in the Kardar–Parisi–Zhang (KPZ) universality class. Similarly, energy transport can show ballistic or diffusive-like behavior. Although such behavior has been studied under equilibrium conditions, no results on nonequilibrium spin transport in classical spin chains has been reported so far. In this work, we investigate both spin and energy transport in classical spin chains (integrable and nonintegrable) when coupled to two reservoirs at two different temperatures/magnetizations. In both the integrable case and the broken-integrability (but spin-symmetry preserving) case, we report anomalous scaling of spin current with system size (${\mathbb{J}}^s\propto L^{-\mu }$), with an exponent value that, within error bars, is close to the KPZ universality class value $\mu \approx 2/3$. On the other hand, it is noteworthy that the energy current remains ballistic (${\mathbb{J}}^e\propto L^{-\eta }$ with $\eta \approx 0$) in the purely integrable case while there is departure from ballistic behavior ($\eta >0$) when integrability is broken regardless of spin-symmetry. We also present results on other interesting observables in the nonequilibrium steady state such as the spatial profiles of magnetization and energy, and spin–spin correlations.

We compute the connected two-time correlator of the maximum $M_N\left(t\right)$ of $N$ independent Gaussian stochastic processes (GSPs) characterized by a common correlation coefficient $\rho$ that depends on the two times $t_1$ and $t_2$. We show analytically that this correlator, for fixed times $t_1$ and $t_2$, decays for large $N$ as a power law $N^{-\gamma }$ (with logarithmic corrections) with a decorrelation exponent $\gamma =(1-\rho )/(1+\rho )$ that depends only on $\rho$, but otherwise is universal for any GSP. We study several examples of physical processes including the fractional Brownian motion (fBm) with Hurst exponent $H$ and the Ornstein-Uhlenbeck process (OUP). For the fBm, $\rho$ is only a function of $\tau =\sqrt{t_1/t_2}$ and we find an interesting freezing transition at a critical value $\tau ={\tau }_c=(3-\sqrt{5})/2$. For $\tau <{\tau }_c$, there is an optimal $H^{*}\left(\tau \right)>0$ that maximizes the exponent $\gamma$ and this maximal value freezes to $\gamma =1/3$ for $\tau >{\tau }_c$. For the OUP, we show that $\gamma =\tanh \left(\mu \right|t_1-t_2|/2)$, where $\mu$ is the stiffness of the harmonic trap. Numerical simulations confirm our analytical predictions.

Plagioclase is a principal component of the Earth's crust, whose compositional and structural analysis is vital for understanding the crust's construction and evolution. Accurate identification of extinction angle features plays an important role in determining the sodium-calcium content in plagioclase. Manual evaluation of these extinction angle features is tedious and dependent on human expertise. Additionally, current image recognition methods for identifying plagioclase extinction angles face challenges such as information loss, weak stripe features, and difficulty in capturing long-range spatiotemporal features. To address these challenges, we propose an extinction angle identification neural network called AFI-Net, which utilizes polarized image sequences for the accurate detection of plagioclase's extinction angle features. AFI-Net combines a 2D convolutional neural network with a Transformer. Initially, a stripe attention module is developed to enhance the network's ability to detect stripe features. Building upon this module, a 2D backbone network is designed to efficiently extract spatial features from polarized images. The spatial features are then fed into a customized Transformer-based module to extract spatiotemporal features. Ultimately, these spatiotemporal features are used to accurately identify the extinction angle features of plagioclase. Extensive quantitative and qualitative experimental results demonstrate that AFI-Net achieves high accuracy and stability in recognizing the extinction angle features of plagioclase, showing significant superiority over current advanced recognition methods.

We study stochastic thermodynamics of overdamped Brownian motion in a flowing fluid. Unlike some previous papers, we treat the effects of the flow field as a nonconservational driving force acting on the Brownian particle. This allows us to apply the theoretical formalism developed in a recent paper for general nonconservative Langevin dynamics. We define heat and work both at the trajectory level and at the ensemble level, and prove the second law of thermodynamics explicitly. The entropy production is decomposed into a housekeeping part and an excess part, both of which are non-negative at the ensemble level. Fluctuation theorems are derived for the housekeeping work, the excess work, and the total work, which are further verified using numerical simulations. A comparison between our theory and an earlier theory by Speck et al. [Phys. Rev. Lett. 100, 178302 (2008)] is also carried out.

Entropy production is an essential aspect of creating and maintaining nonequilibrium systems. Despite their ubiquity, calculation of entropy production rates is challenging for high-dimensional systems, so it has only been reported for simple (i.e., l-particle) systems. Moreover, there is a dearth of nontrivial experimental systems where precise measurements of entropy production rate and characterization of the nonequilibrium steady state (NESS) are simultaneously possible. We report an approach to calculate the entropy production rate of overdamped, nonconservative, $N$-body systems and demonstrate this on a six-particle triangle optical matter (OM) system as a nontrivial example. OM systems consist of (nano-)particles organized into ordered arrays that are bound by electrodynamic interactions associated with the scattering and interference of light, and the associated induced-polarizations in and among the particles in coherent optical beams. The flux of laser light in OM systems in a solution environment necessitates that they dissipate energy, produce entropy, and relax to a NESS. The NESS may have several ordered particle configurations (i.e., isomers) that can interchange by barrier crossing processes. Understanding the power dissipation and entropy production rate of a NESS in an OM system along different (collective) modes of motion can advance understanding of the relative stability of the NESSs as well as inform design and control of OM structures. Therefore, we compute the components of the entropy production rate and power dissipation along the collective coordinates of the 6 Ag nanoparticle triangle OM system from OM NESS trajectory data and verify the Seifert relation [U. Seifert, Rep. Prog. Phys. 75, 126001 (2012)] for these complex systems with a nuanced interpretation.

We investigate hydrodynamic fluctuations in the flow past a circular cylinder near the critical Reynolds number ${\mathrm{Re}}_c$ for the onset of vortex shedding. Starting from the fluctuating Navier-Stokes equations, we perform a perturbation expansion around ${\mathrm{Re}}_c$ to derive analytical expressions for the statistics of the fluctuating lift force. Molecular-level simulations using the direct simulation Monte Carlo method support the theoretical predictions of the lift power spectrum and amplitude distribution. Notably, we have been able to collect sufficient statistics at distances $\mathrm{Re}/{\mathrm{Re}}_c-1=O\left({10}^{-3}\right)$ from the instability that confirm the appearance of non-Gaussian fluctuations, and we observe that they are associated with intermittent vortex shedding. These results emphasize how unavoidable thermal-noise-induced fluctuations become dramatically amplified in the vicinity of oscillatory flow instabilities and that their onset is fundamentally stochastic.

The development of new algorithms for simulations in physics is as important as the development of new analytical methods. In this paper, we present a comparison of the recently developed microcanonical population annealing (MCPA) algorithm with the rather mature Wang-Landau algorithm. The comparison is performed on two cases of the Potts model that exhibit a first-order phase transition. We compare the simulation results of both methods with exactly known results, including the finite-dimensional dependence of the maximum of the specific heat capacity. We evaluate the Binder cumulant minimum, the ratio of peaks in the energy distribution at the critical temperature, the energies of the ordered and disordered phases, and interface tension. Both methods exhibit similar accuracy at selected sets of modeling parameters.

Recent developments in distributed computing architecture are slowly changing the way we develop partial differential equation solvers for simulating complex industrial and natural systems. Since achieving perfect parallelization of implicit temporal schemes is quite challenging, there is a growing interest in using explicit procedures with enhanced stability limits. The current work focuses on one such enhancement obtained by modifying an asynchronous delayed difference method. The proposed scheme, called the weighted difference scheme, is obtained as a weighted average of the delayed and conventional explicit schemes. This method exhibits an improved stability limit of 1.5 and also helps overcome the checkerboard instability associated with the delayed difference scheme. In the current paper, we discuss the different attributes of the proposed weighted scheme using a series of numerical analyses.

Classical first passage under resetting is a paradigm in the search process. Despite its multitude of applications across interdisciplinary sciences, experimental realizations of such resetting processes posit practical challenges in calibrating these zero time irreversible transitions. Here, we consider a strategy in which resetting is performed using finite-time return protocols in lieu of instantaneous returns. These controls could also be accompanied with random fluctuations or errors allowing target detection even during the return phase. To better understand the phenomena, we develop a unified renewal approach that can encapsulate arbitrary search processes centered around home in a fairly general topography containing targets, various resetting times, and return mechanisms in arbitrary dimensions. While such finite-time protocols would apparently seem to prolong the overall search time in comparison to the instantaneous resetting process, we show on the contrary that a significant speed-up can be gained by leveraging the stochasticity in home returns. The formalism is then explored to reveal a universal criterion distilling the benefits of this strategy. We demonstrate how this general principle can be utilized to improve overall performance of a one-dimensional diffusive search process reinforced with experimentally feasible parameters. We believe that such strategies designed with inherent randomness can be made optimal with precise controllability in complex search processes.

Network scientists often use complex dynamic processes to describe network contagions, but tools for fitting contagion models typically assume simple dynamics. Here, we address this gap by developing a nonparametric method to reconstruct a network and dynamics from a series of node states, using a model that breaks the dichotomy between simple pairwise and complex neighborhood-based contagions. We then show that a network is more easily reconstructed when observed through the lens of complex contagions if it is dense or the dynamic saturates, and that simple contagions are better otherwise.

Energy cascades lie at the heart of the dynamics of turbulent flows. In a recent study of turbulence in fluids with odd viscosity X. M. de Wit et al. [Nature (London) 627, 515 (2024)], the two dimensionalization of the flow at small scales leads to the arrest of the energy cascade and selection of an intermediate scale, between the forcing and the viscous scales. To demonstrate the generality of the phenomenon and its existence for a wide class of turbulent systems, we study a shell model that is carefully constructed to have three-dimensional turbulent dynamics at small wave numbers and two-dimensional turbulent dynamics at large wave numbers. The large scale separation that we can achieve in our shell model allows us to examine clearly the interplay between these dynamics, which leads to an arrest of the energy cascade at a transitional wave number and an associated accumulation of energy at the same scale. Such pile-up of energy around the transitional wave number is reminiscent of the formation of condensates in two-dimensional turbulence, but, in contrast, it occurs at intermediate wave numbers instead of the smallest wave number.

The problem of free-riding arises when individuals benefit from a shared resource, service, or public good without contributing proportionately to its provision. This conduct often leads to a collective action problem, as individuals pursue personal gains while relying on the contributions of others. In this study, we present a Bayesian inference model to elucidate the behavior of participants in a public goods game, a conceptual framework that captures the essence of the free-riding problem. Here, individuals possess information on the distribution of group donations to the public good. Our model is grounded in the premise that individuals strive to harmonise their actions with the group's donation patterns. Our model is able to replicate behavioral patterns that resemble those observed in experiments with midsized groups (100 people), but fails to replicate those for larger scales (1000 people). Our results suggest that, in these scenarios, humans prefer imitation and convergence behaviors over profit optimization. These insights contribute to understanding how cooperation is achieved through alignment with group behavior.

We study the nonequilibrium stationary state of a one-dimensional inertial run-and-tumble particle (IRTP) trapped in a harmonic potential. We find that the presence of inertia leads to two distinct dynamical scenarios, namely, overdamped and underdamped, characterized by the relative strength of the viscous and the trap timescales. We also find that inertial nature of the active dynamics leads to the particle being confined in specific regions of the phase plane in the overdamped and underdamped cases, which we compute analytically. Moreover, the interplay of the inertial and active timescales gives rise to several subregimes, which are characterized by very different behavior of position and velocity fluctuations of the IRTP. In particular, in the underdamped regime, both the position and velocity undergo transitions from a novel multipeaked structure in the strongly active limit to a single-peaked Gaussian-like distribution in the passive limit. On the other hand, in the overdamped scenario, the position distribution shows a transition from a U shape to a dome shape, as activity is decreased. Interestingly, the velocity distribution in the overdamped scenario shows two transitions—from a single-peaked shape with an algebraic divergence at the origin in the strongly active regime to a double-peaked one in the moderately active regime to a dome-shaped one in the passive regime.

The exploration of chimera-inspired dynamics in nonlocally coupled networks of Kuramoto oscillators with higher-order interactions is still in its nascent stages. Concurrently, the investigation of collective phenomena in higher-order interaction networks is gaining attraction. Here, we observe that hypergraph networks tend to synchronize through lower-order interactions, whereas simplicial complex networks exhibit a preference for higher-order interactions. This observation suggests that higher-order representations manifest substantial differences in chimera-inspired synchronization regions. Moreover, we introduce an explicit expression for identifying the chimera state. With a comprehensive basin stability analysis and the interplay of pairwise and higher-order interaction strengths, the emergence of the chimera state is inherent in high-order interaction networks. Our findings contribute to the understanding of chimera-inspired dynamics in higher-order interaction networks.

A paraffin droplet containing camphor and oil red O (dye) floating on the water surface shows spontaneous motion and deformation generated by the surface tension gradient around the droplet. We focused on the intermittent motion with a pronounced deformation into a crescent shape observed at specific concentrations of camphor and oil red O. We quantitatively analyzed the time changes in the droplet deformation and investigated the role of the oil red O by measuring the time-dependent paraffin-water interfacial tension with the pendant drop method. The observed effect can be explained by the active role of the oil red O molecules at the paraffin-water interface. The interfacial tension decreases gradually after the interface formation, allowing for the dynamic deformation of the droplet. The combination of the decrease in interfacial tension and the reduction in driving force related to camphor outflow generates intermittent motion with dynamic deformation into a crescent shape.

The dynamics of a system composed of elastic hard particles confined by an isotropic harmonic potential are studied. In the low-density limit, the Boltzmann equation provides an excellent description, and the system does not reach equilibrium except for highly specific initial conditions: it generically evolves toward and stays in a breathing mode. This state is periodic in time, with a Gaussian velocity distribution, an oscillating temperature, and a density profile that oscillates as well. We characterize this breather in terms of initial conditions and constants of the motion. For low but finite densities, the analysis requires taking into account the finite size of the particles. Under well-controlled approximations, a closed description is provided, which shows how equilibrium is reached at long times. The (weak) dissipation at work erodes the breather's amplitude, while concomitantly shifting its oscillation frequency. An excellent agreement is found between molecular dynamics simulation results and the theoretical predictions for the frequency shift. For the damping time, the agreement is not as accurate as for the frequency and the origin of the discrepancies is discussed.

We present a method for predicting hyperchaotic time series using a complex network-based forecasting model. We first construct a network from a given time series, which serves as a coarse-grained representation of the underlying attractor. This network facilitates multistep forecasting by capturing the local nonlinearity of the dynamics and offers superior accuracy over more extended periods than traditional methods. The network is formed by converting the patterns of local oscillations into sequences of numerical symbols, which are then used to create nodes and edges in a network, capturing the system's dynamical behavior at a reduced resolution. The network allows predictions up to several steps ahead without the exponential error increase usually associated with linear first-order methods. The improved predictions result from the unique ability of the network to collect identical pattern transitions in the orbit dynamics into a system of neighborhoods in the network. The effectiveness of this approach is demonstrated through its application to several high-dimensional hyperchaotic systems, where it outperforms both the linear first-order and other network-based methods in terms of prediction accuracy and horizon. Besides enhancing the predictability of chaotic systems, this methodology also outlines a procedure to develop a discrete model flow within an attractor.