The presence of erratic or unstable paths in standard kinetic Monte Carlo simulations significantly undermines the accurate simulation and sampling of transition pathways. While typically reliable methods, such as the Gillespie algorithm, are employed to simulate such paths, they encounter challenges in efficiently identifying rare events due to their sequential nature and reliance on exact Monte Carlo sampling. In contrast, the weighted-ensemble method effectively samples rare events and accelerates the exploration of complex reaction pathways by distributing computational resources among multiple replicas, where each replica is assigned a weight reflecting its importance, and evolves independently from the others. Here, we implement the highly efficient and robust weighted-ensemble method to model susceptible-infected-susceptible dynamics on large heterogeneous population networks, and explore the interplay between stochasticity and contact heterogeneity, which ultimately gives rise to disease clearance. Studying a wide variety of networks characterized by fat-tailed asymmetric degree distributions, we are able to compute the mean time to extinction and quasistationary distribution around it in previously inaccessible parameter regimes.

We examine anew the relationship of directed polymers in random media on traditional hypercubic versus hierarchical lattices, with the goal of understanding the dimensionality dependence of the essential scaling index $\beta$ at the heart of the Kardar-Parisi-Zhang universality class. A seemingly accurate, but entirely empirical, ansatz due to Perlsman and Schwartz, proposed many years ago, can be put in proper context by anchoring the connection between these distinct lattice types at vanishing dimensionality. We graft together complementary perturbative field-theoretic and nonperturbative real-space renormalization group tools to establish the necessary connection, thereby elucidating the central mystery underlying the ansatz's uncanny apparent success, but also revealing its intrinsic limitations. Furthermore, we perform an extensive Euler integration of the KPZ equation in $3+1$ dimensions which, bolstered by a separate directed polymer simulation, allows us an estimate for the critical exponent ${\beta }_{3+1}^{\mathrm{KPZ}}=0.1845\left(4\right)$ that greatly improves upon all previous Monte Carlo calculations in this regard and rules out the Perlsman-Schwartz value, $0.{1882}^{+}$, in that dimension. Finally, leveraging this hybrid RG partnership permits us a versatile, more potent, tool to explore the general KPZ problem across dimensions, as well as a conjecture for its key critical exponent, $\beta =\frac{1}{2}-0.22967\varepsilon ,$ as $\varepsilon \to 0,$ testable in a three-loop calculation.

We introduce a metric to quantify the fragility of chess positions using the interaction graph of pieces. This fragility score $F$ captures the tension within a position and serves as a strong indicator of tipping points in a game. In well-known games, maximum fragility often aligns with decisive moments marked by brilliant moves. Analyzing a large dataset of games, we find that fragility typically peaks around move 15, with pawns ($\approx 60\%$) and knights ($\approx 20\%$) frequently involved in high-tension positions. Comparing the Stockfish evaluation with the fragility score, we observe that the maximum fragility ply often serves as a critical turning point, where the moves made afterward can determine the outcome of the game. Remarkably, average fragility curves show a universal pattern across a wide range of players, games, and openings, with a subtle deviation observed in games played by the engine Stockfish. Our analysis reveals a gradual buildup of fragility starting around eight moves before the peak, followed by a prolonged fragile state lasting up to 15 moves. This suggests a gradual intensification of positional tension leading to decisive moments in the game. These insights offer a valuable tool for both players and engines to assess critical moments in chess.

The relation between the frequency-dependent friction of a molecule in a liquid and the hydrodynamic properties of the liquid is fundamental for molecular dynamics. We investigate this connection for a water molecule moving in liquid water using all-atomistic molecular dynamics (MD) simulations and linear hydrodynamic theory. We analytically calculate the frequency-dependent friction of a sphere with finite surface slip moving in a viscoelastic compressible fluid by solving the linear transient Stokes equation, including frequency-dependent shear and volume viscosities, both determined from MD simulations of bulk liquid water. From MD simulation trajectories, we also determine the frequency-dependent friction of a single water molecule moving in liquid water, as defined by the generalized Langevin equation. The frequency dependence of the shear viscosity of liquid water requires careful consideration of hydrodynamic finite-size effects to observe the asymptotic hydrodynamic power-law tail. By fitting the effective sphere radius and the slip length, the frequency-dependent friction and velocity autocorrelation function from the transient Stokes equation and simulations quantitatively agree. This shows that the transient Stokes equation accurately describes the important features of the frequency-dependent friction of a single water molecule in liquid water and thus applies down to molecular length and time scales, provided accurate frequency-dependent viscosities are used. In contrast, for a methane molecule moving in water, the frequency-dependent friction cannot be predicted based on a homogeneous model, which, supported by the extraction of the frequency-dependent surface slip, suggests that a methane molecule is surrounded by a finite-thickness hydration layer with viscoelastic properties that differ significantly from those of bulk water.

In this paper, a conservative phase-field based lattice Boltzmann equation (LBE) is developed to simulate gas-liquid-solid flows with large fluid density contrasts. In this model, the gas-liquid interface is captured by the conservative Allen-Cahn equation (CACE), where an additional source term is incorporated to realize the wettability of solid structure. Subsequently, a LBE is designed to solve this modified CACE (MCACE), while the two-phase flow field is resolved by using another classical incompressible LBE, and the fluid-solid interaction force is calculated by smoothed-profile method (SPM). Several classical simulations are conducted to demonstrate the capability of the present MCACE-LBE-SPM for simulating gas-liquid-solid flows, including a droplet spreading on a static wettable cylinder, a wettable cylinder floating on the gas-liquid interface without gravity, capillary interactions between two wettable cylinders under gravity, and multiple horizontal cylinders in gas-liquid channel flow. Numerical results indicate that the predictions by present MCACE-LBE-SPM are in good agreement with the theoretical or previous numerical results.

Tissues of living cells are a prime example of active fluids. There is experimental evidence that tissues generate extensile active stress even though their constituting cells are contractile. Fluctuating forces that could result from cell-substrate interactions have been proposed to be able to induce a transition from contractile to extensile active stress. We define the notion of contractile and extensile active stress in isotropic and anisotropic active matter. Through analytic calculations and numerical computations, we then show that in isotropic active fluids, nonlinearities and coupling between fluctuating forces and fluid density are necessary for such a transition to occur. Here, both transitions from extensile to contractile and vice versa are possible.

Chirality is a feature of many biological systems, and much research has been focused on understanding the origin and implications of this property. Famously, sugars and amino acids found in nature are homochiral, i.e., chiral symmetry is broken and only one of the two possible chiral states is ever observed. Certain types of cells show chiral behavior, too. Understanding the origin of cellular chirality and its effect on tissues and cellular dynamics is still an open problem and subject to much (recent) research, e.g., in the context of drosophila morphogenesis. Here, we develop a simple model to describe the possible origin of homochirality in cells. Combining the Vicsek model for collective behavior with the model of Jafarpour et al. [Phys. Rev. Lett. 115, 158101 (2015)], developed to describe the emergence of molecular homochirality, we investigate how a homochiral state might have evolved in cells from an initially symmetric state without any mechanisms that explicitly break chiral symmetry. We investigate the transition to homochirality and show how the “openness” of the system as well as noise determine if and when a globally homochiral state is reached. While hypothetical and explorative in nature, our analysis may serve as a starting point for more realistic models of chirality in flocking multicellular systems.

Telmisartan is a crucial angiotensin receptor blocker in treating high blood pressure. However, there is a wide gap between experimental measurements and theoretical calculations for telmisartan in the amorphous form. Herein, we present how to overcome this challenge via the elastically collective nonlinear Langevin equation theory. First, we utilize a hard-sphere fluid model to rapidly analyze local and nonlocal effects on the molecular dynamics of telmisartan. A nonuniversal coupling parameter is introduced to capture physicochemical complexity via dynamic fragility. Then, a chemical mapping is created to evaluate the impact of temperature on the relaxation of telmisartan. The difference between supercooled and glassy states is encoded in thermal expansion coefficients. The above strategy allows us to determine the primary relaxation time over 30 decades and its secondary counterpart over 12 decades. From there, we can satisfactorily explain previous broadband-dielectric-spectroscopy observations without fitting procedures. Our results promise to enhance the applicability of amorphous telmisartan to health protection and promotion.

We consider a class of nonstandard, two-dimensional Hamiltonian models that may show features of active particle dynamics, and therefore, we refer to these models as active Hamiltonian (AH) systems. The idea is to consider a spin fluid where—on top of spin-spin and particle-particle interactions—spins are coupled to the particle's velocities via a vector potential. Continuous spin variables interact with each other as in a standard $XY$ model. Typically, the AH models exhibit nonstandard thermodynamic properties (e.g., for temperature and pressure) and equations of motion with nonstandard forces. This implies that the derivation of symplectic algorithms to solve Hamilton's equations of motion numerically, as well as the thermostatting for these systems, is not straightforward. Here, we derive a symplectic integration scheme and propose a Nosé-Poincaré thermostat, providing a correct sampling in the canonical ensemble. The expressions for AH systems that we find for temperature and pressure might have parallels with the ongoing debate about the definition of pressure and the equation of state in active matter systems. For a specific AH model, recently proposed by Casiulis et al. [Phys. Rev. Lett. 124, 198001 (2020)], we rationalize the symplectic algorithm and the proposed thermostatting, and investigate the transition from a fluid at high temperature to a cluster phase at low temperature where, due to the coupling of velocities and spins, the cluster phase shows a collective motion that is reminiscent to that observed in a variety of active systems.

In this article, we perform a systematic study of the global entanglement and exciton coherence length dynamics in natural light-harvesting system Fenna-Matthews-Olson (FMO) complex across various parameters of a dissipative environment from low to high temperatures, weak to strong system-environment coupling, and non-Markovian environments. A nonperturbative numerically exact hierarchical equations of motions method is employed to obtain the dynamics of the system. We found that entanglement is driven primarily by the strength of interaction between the system and environment, and it is modulated by the interplay between temperature and non-Markovianity. In contrast, coherence length is found to be insensitive to non-Markovianity. In agreement with previous studies, we do not observe a direct correlation between global entanglement and the efficiency of the excitation energy transfer in the FMO complex. As a new result, we found that the coherence length dynamics is correlated with the excitation energy transfer dynamics.

We study a one-dimensional run-and-tumble particle (RTP), which is a prototypical model for active systems, moving within an arbitrary external potential. Using backward Fokker-Planck equations, we derive the differential equation satisfied by its mean first-passage time (MFPT) to an absorbing target, which, without any loss of generality, is placed at the origin. Depending on the shape of the potential, we identify four distinct “phases,” with a corresponding expression for the MFPT in every case, which we derive explicitly. To illustrate these general expressions, we derive explicit formulas for two specific cases which we study in detail: a double-well potential and a logarithmic potential. We then present different applications of these general formulas to (1) the generalization of the Kramers escape law for an RTP in the presence of a potential barrier, (2) the “trapping” time of an RTP moving in a harmonic well, and (3) characterizing the efficiency of the optimal search strategy of an RTP subjected to stochastic resetting. Our results reveal that the MFPT of an RTP in an external potential exhibits a far more complex and, at times, counterintuitive behavior compared to that of a passive particle (e.g., Brownian) in the same potential.

The method of self-consistent expansions is a powerful tool for handling strong coupling problems that might otherwise be beyond the reach of perturbation theory, providing surprisingly accurate approximations even at low order. First applied in its embryonic form to fully-developed turbulence, it has subsequently been successfully applied to a variety of problems that include polymer statistics, interface dynamics, and high-order perturbation theory for the anharmonic oscillator. Here, we show that the self-consistent expansion can be applied to singular perturbation problems arising in the theory of partial differential equations in conjunction with renormalization group methods. We demonstrate its application to Barenblatt's nonlinear diffusion equation for porous media filtration, where the long-time asymptotics exhibits anomalous dimensions that can be systematically calculated using the perturbative renormalization group. We find that even the first-order self-consistent expansion, when combined with the Callan-Symanzik equation, improves the approximation of the anomalous dimension obtained by the first-order perturbative renormalization group, especially in the strong coupling regime. We also develop a field-theoretic framework for deterministic partial differential equations to facilitate the application of self-consistent expansions to other dynamic systems and illustrate its application using the example of Barenblatt's equation. The scope of our results on the application of renormalization group and self-consistent expansions is limited to partial differential equations whose long-time asymptotics is controlled by incomplete similarity. However, our work suggests that these methods could be applied to a broader suite of singular perturbation problems such as boundary layer theory, multiple scales analysis, and matched asymptotic expansions, for which excellent approximations using renormalization group methods alone are already available.

Previous studies on oscillator populations with two-simplex interaction have reported novel phenomena such as discontinuous desynchronization transitions and multistability of synchronized states. However, the noise effect is not well understood. Here, we study a higher-order network of noisy oscillators with generic interactions consisting of one-simplex and two types of two-simplex interactions. We observe that when a type of two-simplex interaction is dominant, synchrony is eroded and eventually disappears even for infinitesimally weak noise. Nevertheless, synchronized states may persist for extended periods, with the lifetime increasing approximately exponentially with the strength of the two-simplex interaction. When one-simplex or another type of two-simplex interaction is sufficiently strong, noise erosion is prevented, and synchronized states become persistent. A weakly nonlinear analysis reveals that as one-simplex coupling increases, the synchronized state appears supercritically or subscritically, depending on the interaction strength. Furthermore, assuming weak noise and using Kramers' rate theory, we derive a closed dynamical equation for the Kuramoto order parameter, from which the time scale of the erosion process is derived. Our study elucidates the synchronization and desynchronization of oscillator assemblies in higher-order networks and is expected to provide insights into such systems' design and control principles.

Atmospheric pressure helium plasmas are investigated through molecular dynamics simulations at room temperature (300 K) for various ionization fractions (${\chi }_i={10}^{-1}-{10}^{-5}$) in the strongly coupled regime (ion coupling parameter, ${\mathrm{\Gamma }}_i\sim 1-10$) employing Coulomb and Yukawa interaction potentials. The role of electron screening in ion dynamics and energetics is examined through ion and gas temperatures, mean squared displacement of ions, ion coupling parameter, and radial distribution function of the system. It is found that electron screening in the Yukawa potential significantly limits the disorder-induced heating (DIH) mechanism for strongly ionized plasmas (${\chi }_i\ge {10}^{-3}$). Whereas, ions show a prominent subdiffusive behavior associated with the DIH during the nonequilibrium phase for the Coulomb potential. The DIH mechanism is explained using a model based upon the conservation of energy. However, for weakly ionized plasmas (${\chi }_i\le {10}^{-4}$), the maximum ion temperatures are almost similar for both potentials. Furthermore, electron screening affects the separation distance and arrangement of the ion-neutral pairs for all the values of ${\chi }_i$. In general, Yukawa potential results in a lower mean potential energy of the interacting particles, which is energetically favorable for the stability of the system.

In this Letter, we report on the induction of aluminum combustion within supercritical water, facilitated by an underwater explosion bubble. This bubble, initiated using an aluminum-wire electrical discharge in a water-filled tank, typically spans tens of centimeters and undergoes oscillatory dynamics characterized by expansions and compression. When significantly compressed, the bubble reaches conditions of elevated temperature and pressure, sufficient to induce a phase transition of water from its normal to a supercritical state, which provokes the vigorous ignition of micro-sized aluminum particles. We analyze its dynamics by recording the oscillation of the bubble's radius and the corresponding light emission from combustion. Additionally, we observe the cessation of luminescent emissions that last for nearly a millisecond and are attributed to turbulence at the vapor-liquid interface, instigated by hydrodynamic instabilities. These observations elucidate the combustion dynamics of metals in hydrodynamic environments under extreme conditions and pave the way for advanced studies of complex reactive systems.

Generative artificial intelligence methods are employed for the first time to construct a surrogate model for plasma turbulence that enables long-time transport simulations. The proposed GAIT (Generative Artificial Intelligence Turbulence) model is based on the coupling of a convolutional variational autoencoder that encodes precomputed turbulence data into a reduced latent space, and a recurrent neural network and decoder that generate new turbulence states 400 times faster than the direct numerical integration. The model is applied to the Hasegawa-Wakatani (HW) plasma turbulence model, which is closely related to the quasigeostrophic model used in geophysical fluid dynamics. Very good agreement is found between the GAIT and the HW models in the spatiotemporal Fourier and Proper Orthogonal Decomposition spectra, and the flow topology characterized by the Okubo-Weiss decomposition. The GAIT model also reproduces Lagrangian transport including the probability distribution function of particle displacements and the effective turbulent diffusivity.

The visible dynamics of small-scale systems are strongly affected by unobservable degrees of freedom, which can belong to either external environments or internal subsystems and almost inevitably induce memory effects. Formally, such inaccessible degrees of freedom can be systematically eliminated from essentially any microscopic model through projection operator techniques, which result in nonlocal time evolution equations. This article investigates how and under what conditions locality in time can be rigorously restored beyond the standard Markov approximation, which generally requires the characteristic timescales of accessible and inaccessible degrees of freedom to be sharply separated. Specifically, we consider nonlocal time evolution equations that are autonomous and linear in the variables of interest. For this class of models, we prove a mathematical theorem that establishes a well-defined weak-memory regime, where faithful local approximations exist, even if the relevant timescales are of comparable order of magnitude. The generators of these local approximations, which become exact in the long-time limit, are time independent and can be determined to arbitrary accuracy through a convergent perturbation theory in the memory strength, where the Markov generator is recovered in first order. For illustration, we work out three simple, yet instructive, examples covering coarse-grained Markov jump networks, semi-Markov jump processes, and generalized Langevin equations.

The optional public goods game (OPGG) is a three-strategy model in which individuals can cooperate, defect, or not participate. Despite its simplicity, this model effectively captures various social dilemmas, including those involving public services, environmental sustainability, and broader societal issues. In this study, we investigate how the reward ($r$) and group size of potential players ($S$) of public goods games influence the steady-state coexistence of these strategies or the alternation of their dominance in a rock-paper-scissors dynamic. The OPGG is simulated using Monte Carlo in a nonspatial scenario, meaning there is no topology connecting the agents, allowing any player to interact with any other player. We show that under sufficiently noisy conditions, the system consistently evolves to an absorbing state, with the prevailing strategy determined by the values of $r$ and $S$. In the range $2\le r\le S$, the system shows multiple stable absorbing states, with groups of size $S=4$ exhibiting more pronounced and transient rock-paper-scissors dynamics with longer average absorbing times. We present a thorough analysis of our results in terms of the fraction of time the system spends in rock-paper-scissor cycles, the number of cycles, and the average probability that the system relaxes to each possible absorbing state, including scenarios where the system does not reach an absorbing state at all.

Energy exchange statistics between two bodies at different thermal equilibria obey the Jarzynski-Wójcik fluctuation theorem. The corresponding energy scale factor is the difference of the inverse temperatures associated to the bodies at equilibrium. In this work, we consider a dissipative quantum dynamics leading the quantum system towards a possibly nonthermal, asymptotic state. To generalize the Jarzynski-Wójcik theorem to nonthermal states, we identify a sufficient condition $\mathcal{I}$ for the existence of an energy scale factor ${\eta }^{*}$ that is unique, finite, and time independent, such that the characteristic function of the energy exchange distribution becomes identically equal to 1 for any time. This ${\eta }^{*}$ plays the role of the difference of inverse temperatures. We discuss the physical interpretation of the condition $\mathcal{I}$, showing that it amounts to an almost complete memory loss of the initial state. The robustness of our results against quantifiable deviations from the validity of $\mathcal{I}$ is evaluated by experimental studies on a single nitrogen-vacancy center subjected to a sequence of laser pulses and dissipation.

We explore the scattering dynamics of classical Coulomb-interacting clusters of ions confined to a helical geometry. Ion clusters of equally charged particles constrained to a helix can form many-body bound states; i.e., they exhibit stable motion of Coulomb-interacting identical ions. We analyze the scattering and fragmentation behavior of two ion clusters, thereby understanding the rich phenomenology of their dynamics. The scattering dynamics is complex in the sense that it exhibits cascades of decay processes involving strongly varying cluster sizes. These processes are governed by the internal energy flow and the underlying oscillatory many-body potential. We specifically focus on the impact of the collision energy on the dynamics of individual ions during and immediately after the collision of two clusters and on the internal dynamics of ion clusters that are excited during a cluster collision.