Physical review. E最新文献

Immiscible two-phase flow in porous media occurs in many processes, such as enhanced oil recovery (EOR), as well as oil spill and soil remediation. These processes involve a fluid displacing another immiscible fluid within the confines of a heterogeneous porous structure. The invasion pattern generally remains the same under constant conditions but can also evolve over time in the presence of surfactants, which alter the interfacial tension (IFT) and surface wettability. The dynamics under such conditions extend beyond the usual way in which such immiscible displacement is modeled. Here, we develop a time-dependent pore network model (PNM) to simulate the effects of surfactant-induced IFT reduction on immiscible displacement driven by constant inlet pressure, with pressure drops across the network calculated using a random resistor network and mass conservation equations. Node-specific flux and velocity are derived using the Hagen-Poiseuille equation, and surfactant adsorption is modeled using the Langmuir isotherm, capturing its impact on fluid-fluid and solid-fluid interfaces within the invaded path. Since the evolution of the invasion pattern comprises the cooperative mechanisms of surfactant mass transfer to the interfaces and the resulting changes in capillary and Laplace pressures, we employ two strategies to quantify this complex feedback behavior: mass transfer based, introducing a mass transfer timescale, and Laplace pressure based, scaling with the inlet pressure. Results reveal that heavy-tailed pore throat distribution accelerates the onset of secondary invasions, which enhances the dominance of Laplace pressure. As the distribution becomes more symmetric or Gaussian, mass transfer becomes the dominant mechanism. This interplay highlights the intricate balance between mass transfer and capillary effects in governing the spatiotemporal evolution of immiscible fluid invasion.

We study the statistical mechanics of two-dimensional "super-Coulombic" plasmas, namely, neutral plasmas with power-law interactions longer ranged than Coulomb. To that end, we employ numerically exact large-scale Monte Carlo simulations. Contrary to naive energy-entropy arguments, we observe a charge confinement-deconfinement transition as a function of temperature. Remarkably, the transition lies in the Berezinskii-Kosterlitz-Thouless (BKT) universality class. Our results corroborate recent dielectric medium and renormalization group calculations predicting effective long-scale Coulomb interactions in microscopically super-Coulombic gases. We explicitly showcase this novel dielectric screening phenomenon, capturing the emergent Coulomb potential and the associated crossover length scale. This is achieved by utilizing a new test charge based methodology for determining effective inter-particle interactions. Lastly, we show that this Coulomb emergence and the associated BKT transition occur universally across generic interactions and densities.

Speed-accuracy tradeoffs are a common feature in several physical and biological systems. Here, we demonstrate analogous speed-performance tradeoffs in the game of cricket, where batters score runs off the balls delivered by bowlers. Leveraging extensive data from cricket, we show that a batter's run-scoring rate and probability of dismissal are related, and this relation can be approximated by a power law. Similar relation is observed for bowlers as well that links their run-conceding rate and wicket taking abilities. The exponents in these power-law relations quantify player adaptability under varying conditions and serve as a robust performance indicator. Using a drift-diffusion-decay model for run scoring and conceding, we find that players with extreme exponent values are better suited to specific game formats and match conditions than those with moderate values. These findings provide a quantitative framework for evaluating player potential, optimizing team strategy, and extending the analysis to other systems exhibiting similar speed-accuracy or performance tradeoffs.

This study analyzes pass networks in football (soccer) using a stochastic model known as the Pólya urn. By focusing on preferential selection, it theoretically demonstrates that the time evolution of networks can be characterized by a single parameter. Building on this result, a data analysis method is proposed and applied to a large-scale public dataset of professional football matches. The statistical properties of the preferential-selection parameter are examined, demonstrating its correlation with pass accuracy and with mean pass difficulty. This method is applicable to various evolving networks.

We use the Kac-Rice formula and results from random matrix theory to obtain the average number of critical points of a family of high-dimensional empirical loss functions, where the data are correlated d-dimensional Gaussian vectors, whose number has a fixed ratio with their dimension. The correlations are introduced to model the existence of structure in the data, as is common in current machine learning systems. Under a technical hypothesis, our results are exact in the large-d limit, and characterize the annealed landscape complexity, namely the logarithm of the expected number of critical points at a given value of the loss. We first address in detail the landscape of the loss function of a single perceptron and then generalize it to the case where two competing datasets with different covariance matrices are present, with the perceptron seeking to discriminate between them. The latter model can be applied to understand the interplay between adversity and nontrivial data structures. For completeness, we also treat the case of a loss function used in training generalized linear models in the presence of correlated input data.

Using discrete element simulations based on molecular dynamics, we investigate the mechanical behavior of two-dimensional sheared, dry, frictional granular media in the "dense" and "critical" regimes. We find that this behavior is partitioned between transient stages and a final stationary stage. While the latter is macroscopically consistent with the predictions of the viscous μ(I) rheology, both the macroscopic behavior during the transient stages and the overall microscopic behavior suggest a more complex picture. Indeed, the simulated granular medium exhibits a finite elastic stiffness throughout its entire shear deformation history, although topological rearrangements of the grains at the microscale translate into a partial degradation of this stiffness, which can be interpreted as a form of elastic damage. When letting the system relax under constant volume at different stages of shear deformation, the relaxation of stresses follows a compressed exponential, also highlighting the role of elastic interactions in the medium, with residual stresses that depend on the level of elastic damage. The relations we establish between elastic and relaxation properties point to a complex rheology, characterized by a damage-dependent transition between a viscoelastoplastic and a viscous behavior.

How do neural language models acquire a language's structure when trained for next-token prediction? We address this question by deriving theoretical scaling laws for neural network performance on synthetic datasets generated by the random hierarchy model (RHM)-an ensemble of probabilistic context-free grammars designed to capture the hierarchical structure of natural language while remaining analytically tractable. Previously, we developed a theory of representation learning based on data correlations that explains how deep learning models capture the hierarchical structure of the data sequentially, one layer at a time. Here, we extend our theoretical framework to account for architectural differences. In particular, we predict and empirically validate that convolutional networks, whose structure aligns with that of the generative process through locality and weight sharing, enjoy a faster scaling of performance compared to transformer models, which rely on global self-attention mechanisms. This finding clarifies the architectural biases underlying neural scaling laws and highlights how representation learning is shaped by the interaction between model architecture and the statistical properties of data.

Tipping points (TP) are abrupt transitions between metastable states in complex systems, most often described by a bifurcation or crisis of a multistable system induced by a slowly changing control parameter. An avenue for predicting TPs in real-world systems is critical slowing down (CSD), which is a decrease in the relaxation rate after perturbations prior to a TP that can be measured by statistical early warning signals (EWS) in the autocovariance of observational time series. In high-dimensional systems, we cannot expect a priori chosen scalar observables to show significant EWS, and some may even show an opposite signal. Thus, to avoid false negative or positive early warnings, it is desirable to monitor fluctuations only in observables that are designed to capture CSD. Here we propose that a natural observable for this purpose can be obtained by a data-driven approximation of the first nontrivial eigenfunction of the backward Fokker-Planck (or Kolmogorov) operator, using the diffusion map algorithm.

Over the past seven decades, the classical Monte Carlo method has played a huge role in the fields of rarefied gas flow and micro/nanoscale heat transfer, but it also has shortcomings: the time step and cell size are limited by the relaxation time and mean free path, making it difficult to efficiently simulate multiscale heat and mass transfer problems from the ballistic to diffusion limit. To overcome this drawback, a unified gas-kinetic wave-particle (UGKWP) method is developed for solving the phonon Boltzmann transport equation (BTE) in all regimes covering both ballistic and diffusive limits. This method is built upon the space-time coupled evolution model of the phonon BTE, which provides the framework for constructing a multiscale flux at the cell interfaces. At the same time, in order to capture nonequilibrium transport efficiently, the multiscale flux comprises two distinct components: a deterministic part for capturing the near-equilibrium or diffusive transport, and a statistical particle part for recovering nonequilibrium or ballistic transport phenomena. The UGKWP method exhibits remarkable multiscale adaptability and versatility, seamlessly bridging the gap between the diffusive and ballistic transport phenomena. In the diffusive limit, the present method naturally converges to Fourier's law, with the diminishing particle contribution, whereas in the ballistic limit, the nonequilibrium flux is fully described by the free-streaming particles. This inherent adaptability not only allows for precise capturing of both equilibrium and nonequilibrium heat transfer processes, but it also guarantees that the model adheres strictly to the underlying physical laws in each phonon transport regime. A series of numerical tests fully demonstrate the excellent performance of the UGKWP method in all Knudsen regimes, where the time step and cell size are not constrained by the relaxation time and mean free path in the diffusive regime. The present method is an efficient and accurate computational tool for simulating multiscale nonequilibrium heat transfer, and offering significant advantages over traditional methods in terms of numerical performance and physical applicability.

We focus on the Feigenbaum-Coullet-Tresser point of the dissipative one-dimensional z-logistic map x_{t+1}=1-a|x_{t}|^{z}(z≥1). We show that sums of iterates converge to q-Gaussian distributions P_{q}(y)=P_{q}(0)exp_{q}(-β_{q}y^{2})=P_{q}(0)[1+(q-1)β_{q}y^{2}]^{1/(1-q)}(q≥1;β_{q}>0), which optimize the nonadditive entropic functional S_{q} under simple constraints. We propose and justify heuristically a closed-form prediction for the entropic index, q(z)=1+2/(z+1), and validate it numerically via data collapse for typical z values. The formula captures how the limiting law depends on the nonlinearity order and implies finite variance for z>2 and divergent variance for 1≤z≤2. These results extend edge-of-chaos central limit behavior beyond the standard (z=2) case and provide a simple predictive law for unimodal maps with varying maximum order.