We propose a generative, mechanistic model of temporally evolving hypergraphs in which hyperedges form via noisy copying of previous hyperedges. Our proposed model reproduces several stylized facts from many empirical hypergraphs, is learnable from data, and defines a likelihood over a complete hypergraph rather than ego-based or other subhypergraphs. Analyzing our model, we derive asymptotic descriptions of the node degree, edge size, and edge intersection size distributions in terms of the model parameters. We also show several features of empirical hypergraphs which are and are not successfully captured by our model. We provide a scalable stochastic expectation maximization algorithm with which we can fit our model to hypergraph data sets with millions of nodes and edges. Finally, we assess our model on a hypergraph link prediction task, finding that an instantiation of our model with just 11 parameters can achieve competitive predictive performance with large neural networks.

How do interactions between species influence their spatial distribution in an ecosystem? To answer this question, we introduce a spatially extended ecosystem of generalized Lotka-Volterra type, where species can diffuse and interactions are nonlocal. We compute the criterion for the loss of stability of the spatially homogeneous ecosystem, and we show that the stability of the uniform state crucially depends on the most abundant species, and on the interplay between space exploration during the timescale of reproduction and the interaction range. Focusing on the spectrum of the interaction matrix weighted by the species abundances, we identify a Baik-Ben Arous-Péché transition that translates into a transition in the final patterns of the species distribution. Finally assuming that the disorder is small, we exhibit an explicit solution of the dynamical mean-field equation for the species density, obtained as the fixed point of nonlocal Fisher-Kolmogorov-Petrovski-Piskounov equations. Our work paves the way of future combined approaches at the frontier of active matter and disordered systems, with the hope of better understanding complex ecosystems like bacterial communities.

The process of producing a liquid column is common in daily life and industrial applications, such as walking through a puddle and roller printing. While governed by the Navier-Stokes equation, its dynamics are often studied by numerical means, which hinders a full understanding of the rich mixture of physics behind, for instance, the competition of surface and potential energies, and how the pinch off is affected by the kinetic energy and water jet when a large cylinder is used. For pedestrians rushing out of the rain, the water column inevitably involves turbulence and defies simple theoretical analyses. As a result, this work will focus only on cases with a low Reynolds number to enable laminar flow and the existence of reversible and quasistatic stages. Combined with simple models, we elucidate the mechanism that drives the change of morphology and derive analytic expressions for the critical height and upper radius for the liquid column when transiting between three stages. Stage I is characterized by a static and reversible profile for the column whose upper radius $r_t$ equals that of the cylinder. The column becomes irreversible and $r_t$ starts shrinking upon entering stage II. It is not until $r_t$ stops shrinking that the column neck accelerates its contraction and descends toward the pool, the quantitative behavior of which is among the successful predictions of our theory. Pinch off dominates the second half of stage III without its usual signature of self-similarity. This is discussed and explained with an interesting incident involving a water jet similar to that made by a dropping stone.

This study develops a weighted-residual model for Oldroyd-B films on slippery substrates at moderate Reynolds number and large slippery length. Linear stability analysis reveals that wall slip promotes perturbation growth rates, increases cut-off wave numbers, and accelerates long-wave propagation speed, demonstrating a destabilizing effect. Two distinct families of traveling waves are sought, which demonstrate that varying the slippery length can alter the bifurcation type of traveling wave families. Particularly, large slippery length can cause the transition of drag-gravity regime into the drag-inertia regime. In the drag-gravity regime, slippery effect promotes the wave speed and height. However, in the drag-inertia regime, slippery effect can suppress the wave height even though the wave propagates faster. Interestingly, plateau-type waves are found in the Oldroyd-B film flow at large slippery length, which has not been reported previously.

This work investigates the path of gas locally injected and rising through a water-saturated porous medium. Gas migration through the pores network is modeled using a Gaussian distribution of capillary overpressure superimposed on a linear pressure gradient induced by gravity. Previous studies have shown that the superposition of individual gas pathways significantly affects the overall invasion morphology, impacting various practical applications. The originality of the present simulation lies in incorporating the effect of prior pathways on subsequent ones, thereby accounting for the system's memory. The final invasion zone morphology, shaped by multiple gas pathways, is quantified as a function of the memory effect, ranging from a diffusivelike invasion to a meandering progression when the influence of prior paths is substantial. Notably, we find that the probability of revisiting previously occupied sites, which quantifies the tendency of gas to follow an established path, follows a logistic function.

The present study is dedicated to investigating the nonlinear optical response of thermal origin of lyotropic chromonic liquid-crystal phases composed of sunset yellow azo dye and water. Using time-resolved Z-scan and two-dimensional x-ray diffraction (XRD) techniques, the influence of molecular organization on the thermal responses of the isotropic and nematic phases is analyzed. The results indicate that the nonlinear optical response is strongly dependent on the dye concentration and on the selective light absorption by the system, highlighting the interaction between molecular aggregation and heat transfer. The structural analysis by XRD reveals significant changes in the organization of the molecular aggregates across the isotropic and nematic phases, directly affecting the amplitude of the phase distortion observed in the Z-scan experiments. The correlation between structural and optical data suggests that the supramolecular organization plays a crucial role in the thermal response of the mixture, influencing its nonlinear optical properties. These findings provide profound insights into the thermal mechanisms of chromonic liquid crystals.

The spring network model constitutes the backbone in the representations of a host of physical systems. In this work, we report the disturbance-driven microscopic dynamics of an isolated, closed spring network of spherical topology in mechanical equilibrium. The system permits self-intersection. We first show the lowest-energy configurations of the closed spring networks as packings of regular triangles. The dynamics of the disturbed spring network is analyzed from the multiple perspectives of energetics, structural instability, and speed distribution. We reveal the crumpling transition of strongly disturbed spring networks and the rapid convergence of the speed distribution toward the Maxwell-Boltzmann distribution. This work demonstrates the rich physics arising from the interplay of flexibility and dynamics. The results may yield insights into the shape fluctuation and structural instability of deformable membranes from the dynamical perspective.

Non-dyadic higher-order interactions affect collective behavior in various networked dynamical systems. Here, we discuss the properties of a novel Ising model with higher-order interactions and characterize its phase transitions between the ordered and the disordered phase. By a mean-field treatment, we show that the transition is continuous when only three-body interactions are considered, but becomes abrupt when interactions of higher orders are introduced. Using a Georges-Yedidia expansion to go beyond a naïve mean-field approximation, we reveal a quantitative shift in the critical point of the phase transition, which does not affect the universality class of the model. Finally, we compare our results with traditional $p$-spin models with many-body interactions. Our work unveils new collective phenomena on complex interacting systems, revealing the importance of investigating higher-order systems beyond three-body interactions.

Ergotropy serves as a key indicator for assessing the performance of quantum batteries (QBs). Using the Redfield master equation, we investigate ergotropy dynamics in a non-Markovian QB composed of an $N$-spin chain embedded in a microcavity. Distinct from the Markovian charging process, the thermal charging process exhibits a distinct oscillatory behavior in the extracted ergotropy. We show that these oscillations can be effectively suppressed through coordinated tuning of coherent driving, cavity parameters, and spin-spin couplings. In addition, we analyze the influence of various system and environmental parameters on the time evolution of ergotropy, revealing rich dynamical features. Our results offer insights into the control of energy extraction in QBs and may inform future designs of practical battery architectures.

The celebrated Lindblad equation governs the nonunitary time evolution of density operators used in the description of open quantum systems. It is usually derived from the von Neumann equation for a large system, at given physical conditions, when a small subsystem is explicitly singled out and the rest of the system acts as an environment whose degrees of freedom are traced out. In the specific case of a subsystem with variable particle number, the equilibrium density operator is given by the well-known grand canonical Gibbs state. Consequently, solving the Lindblad equation in this case should automatically yield, without any additional assumptions, the corresponding density operator in the limiting case of statistical equilibrium. Current studies of the Lindblad equation with varying particle number assume, however, the grand canonical Gibbs state a priori: the chemical potential is externally imposed rather than derived from first principles, and hence the corresponding density operator is not obtained as a natural solution of the equation. In this work, we investigate the compatibility of grand canonical statistical mechanics with the derivation of the Lindblad equation. We propose an alternative and complementary approach to the current literature that consists in using a generalized system Hamiltonian which includes a term $\mu N$. In a previous paper, this empirically well-known term has been formally derived from the von Neumann equation for the specific case of equilibrium. Including $\mu N$ in the system Hamiltonian leads to a modified Lindblad equation which yields the grand canonical state as a natural solution, meaning that all the quantities involved are obtained from the physics of the system without any external assumptions.

This article presents a hybrid lattice Boltzmann method for simulating multiphase. Mean mass and momentum are solved using a lattice Boltzmann method, while an order parameter, indicating whether the fluid is gaseous or liquid, is solved by a classical finite volume scheme. The lattice Boltzmann scheme is adapted from existing methods using an equilibrium formulation, as well as macroscopic reconstructions. The consistency of the resulting scheme is confirmed analytically. Validations are then presented for canonical academic cases, as well as 2D liquid jet simulations yielding different breakup covering dripping, sinuous, and atomization regimes.

We develop an unsupervised machine learning approach to classify disordered patterns in a system of oppositely charged colloids. In this system, the interplay between Coulomb and van der Waals interactions leads to transitions in local structures, while the global structure remains disordered. Our method involves representing the local structures of the system as high-dimensional vectors and applying principal component analysis to identify distinct features of each pattern. We demonstrate that our method results in a reasonable classification of disordered patterns, which is consistent with that obtained from radial distribution functions. The interpretability of the method reveals the key characteristics of each pattern and provides valuable insights into the mechanisms underlying the unconventional phase transitions between disordered patterns.

We present a systematic procedure to derive a quantum master equation for thermal relaxation in real scalar field theory, expanding on the method proposed in Koide and Nicacio [Phys. Lett. A 494, 129277 (2024)]. We begin by introducing a generalized model for a classical scalar field interacting with a Brownian thermostat, consistent with stochastic thermodynamics. Applying canonical quantization to this model, we derive the corresponding quantum master equation, which is applicable to any form of the scalar field Hamiltonian. While its evolution is generally non-CPTP (completely positive and trace preserving), it can be adjusted to describe a CPTP evolution, such as those found in the Gorini-Kossakowski-Sudarshan-Lindblad equation by appropriately tuning the parameters of the model. In this framework, we define heat, work, and entropy in a way that satisfies the first and second laws of quantum thermodynamics. This suggests that the quantum-classical correspondence extends beyond closed systems governed by unitary time evolution to open systems as well. We further investigate the relation between the second law in quantum thermodynamics and relative entropy, providing insights into the study of quantum fluctuations through information-theoretical techniques in quantum field theory.

We consider a Brownian particle performing an overdamped motion in a power-law repulsive potential. If the potential grows with the distance faster than quadratically, the particle escapes to infinity in a finite time. We determine the average blowup time and study the probability distribution of the blowup time. In particular, we show that the long-time tail of this probability distribution decays purely exponentially, while the short-time tail exhibits an essential singularity. These qualitative features turn out to be quite universal, as they occur for all rapidly growing power-law potentials in arbitrary spatial dimensions. The quartic potential is especially tractable, and we analyze it in more detail.

Understanding the mechanisms that sustain high biodiversity remains a central challenge. MacArthur's classical consumer-resource model (MCRM) suggests that consumer diversity is limited by the number of available resources, yet empirical observations often exceed this bound. To address this, we extend the generalized consumer-resource model by incorporating intraspecific suppression and analyze its effects using the dynamical mean-field theory. Our results show that intraspecific suppression promotes biodiversity by preventing the emergence of dominant species and enabling more species to coexist, particularly in resource-rich environments. Furthermore, our results provide analytical bounds on relative diversity, demonstrating that the number of coexisting consumer species can exceed the number of resource kinds. This highlights the critical role of intraspecific suppression and environmental factors in promoting coexistence.

Bacteria can enter dormancy triggered by stress, such as starvation. When stress is removed, a large part of the population will exhibit some lag time before regrowth. It has been observed that even under stress-free conditions that allow for exponential growth, a small subpopulation can spontaneously enter dormancy temporarily. The dormant population often survives antibiotic application because many types of antibiotics target the cell growth and division process. If bacteria are in an environment where antibiotics are sometimes applied, the population can evolve to adjust their dormancy frequency to better survive antibiotics without losing too much of the population growth. Here, we consider the situation in which antibiotics are applied stochastically during repeated feast-famine cycles. We analyze the best strategy for long-term growth when the bacteria are allowed to tune both the lag time at the start of the feast period and the spontaneous dormancy in the feast period. We show that spontaneous dormancy can provide an advantage only when the antibiotic application and the start of the feast period are decoupled. When the triggered dormant and spontaneous dormant states are treated as different states and the antibiotic addition time is fixed, the optimal strategy is either triggered or spontaneous dormancy. Exhibiting both types of dormancy is optimal only when there is a certain level of stochastic fluctuation in the antibiotic application timing.

The observed Maxwellian velocity distribution functions in plasmas and the fact that the rate of elastic electron-electron collisions is many orders of magnitude smaller than the electron plasma frequency have been a long-standing puzzle. Here, we present a mechanism for efficient thermalization in collision-poor unmagnetized plasmas, which resolves this puzzle. The competition between the momentum losses of plasma particles by spontaneously emitting high-frequency non-collective fluctuations and the momentum diffusion of these particles in their self-generated fluctuating electric field fluctuations provides the Maxwellian particle distribution function. The mechanism is self-regulating, providing electron temperatures of about ${10}^7\mathrm{K}$, and it is applicable to fully ionized plasmas with electron densities below ${10}^{27}{\mathrm{cm}}^{-3}$.