The computational exploration of reactive processes is challenging due to the requirement of thorough sampling across the free energy landscape using accurate ab initio methods. To address these constraints, machine learning potentials are employed, yet their training for this kind of problem is still a laborious and tedious task. In this study, we present an efficient approach to train these potentials by cleverly using a single batch of unbiased trajectories that avoid the pitfalls of trajectories artificially biased along a suboptimal collective variable. This strategy, when integrated with current enhanced sampling techniques, allows to obtain free energy profiles and kinetic rates of ab initio quality, yet dramatically reducing the computational cost.

The ubiquitous telegrapher's equation is presented in the context of a non-local-in-time master equation on the lattice. From the exact solution of this transport equation, for different hopping models, the second moment in the infinite lattice and the time evolution of the probability in the ring have been analyzed as a function of the two characteristic timescales appearing in the memory kernel of the finite-velocity approach: the rate of energy loss and the timescale characterizing the jumping process in the lattice. We have demonstrated how these timescales characterize the constraint to find positive solutions, the time variation of entropy and therefore the approach to the disordered stationary state on the ring. This lattice model provides an analytic treatment. Thus, this result is relevant in the study of Shannon entropy, transport of information, and waves in lattices and sheds light on the functional role of the loss of energy in the finite-velocity diffusion dynamics.

Ultrafast laser radiation or beams of fast charged particles primarily excite the electronic system of a solid driving the target transiently out of thermal equilibrium. Apart from the nonequilibrium between the electrons and atoms, each subsystem may be far from equilibrium. From first principles, we derive the definition of various atomic temperatures applicable to electronically excited ensembles. It is shown that the definition of the kinetic temperature of atoms in the momentum subspace is unaffected by the excitation of the electronic system. When the electronic temperature differs from the atomic one, an expression for the configurational atomic temperature is proposed, applicable to the electronic-temperature-dependent interatomic potentials (such as ab initio molecular dynamics simulations). We study how the configurational temperature behaves during nonthermal phase transition, triggered by the evolution of the interatomic potential due to the electronic excitation. It is revealed that upon the ultrafast irradiation, the atomic system of a solid exists temporarily in a multitemperature state: separate equilibria in the momentum and configurational subspaces. Complete equilibration between the various atomic temperatures takes place at longer timescales, forming the energy equipartition. Based on these results, we propose a formulation of multitemperature heat transport equations.

We study analytically the ordering kinetics and the final metastable states in the three-dimensional long-range voter model where $N$ agents described by a Boolean spin variable $S_i$ can be found in two states (or opinion) $\pm 1$. The kinetics is such that each agent copies the opinion of another at distance $r$ chosen with probability $P\left(r\right)\propto r^{-\alpha }$ ($\alpha >0$). In the thermodynamic limit $N\to \infty$ the system approaches a correlated metastable state without consensus, namely without full spin alignment. In such states the equal-time correlation function $C\left(r\right)=\langle S_i{S}_j\rangle$ (where $r$ is the $i-j$ distance) decreases algebraically in a slow, nonintegrable way. Specifically, we find $C\left(r\right)\sim r^{-1}$, or $C\left(r\right)\sim r^{-(6-\alpha )}$, or $C\left(r\right)\sim r^{-\alpha }$ for $\alpha >5, 3<\alpha \le 5$, and $0\le \alpha \le 3$, respectively. In a finite system metastability is escaped after a time of order $N$ and full ordering is eventually achieved. The dynamics leading to metastability is of the coarsening type, with an ever-increasing correlation length $L\left(t\right)$ (for $N\to \infty$). We find $L\left(t\right)\sim t^{\frac{1}{2}}$ for $\alpha >5, L\left(t\right)\sim t^{\frac{5}{2\alpha }}$ for $4<\alpha \le 5$, and $L\left(t\right)\sim t^{\frac{5}{8}}$ for $3\le \alpha \le 4$. For $0\le \alpha <3$ there is not macroscopic coarsening because stationarity is reached in a microscopic time. Such results allow us to conjecture the behavior of the model for generic spatial dimension.

We analyze a delay differential equation model for a frequency-swept semiconductor laser and demonstrate existence of extreme events in its dynamics, with probabilities heavily dependent on the sweep rate. The extreme events appear even in absence of any noise in the system and do not exhibit significant dependence on its presence. We investigate the problem numerically and show that intensity dynamics of these events are highly localized in the filter detuning space. Overlaying it with the structure of steady-state and periodic solutions of the static system, we show that the dynamics is governed by attraction to these periodic solutions and such extreme events occur as a result of passing through the region of stable high-intensity bridge of periodic solutions.

We analyze the three-dimensional (3D) buckling of an elastic filament in a shear flow of a viscous fluid at low Reynolds number and high Péclet number. We apply the Euler-Bernoulli beam (elastica) theoretical model. We show the universal character of the full 3D spectral problem for a small perturbation of a thin filament from a straight position of arbitrary orientation. We use the eigenvalues and eigenfunctions for the linearized elastica equation in the shear plane, found earlier by Liu et al. [Phys. Rev. Fluids 9, 014101 (2024)] with the Chebyshev spectral collocation method, to solve the full 3D eigenproblem. We provide a simple analytic approximation of the eigenfunctions, represented as Gaussian wave packets. As the main result of the paper, we derive the square-root dependence of the eigenfunction wave number on the parameter $\tilde{\chi }=-\eta sin2\varphi {sin}^2\theta$, where $\eta$ is the elastoviscous number and the filament orientation is determined by the zenith angle $\theta$ with respect to the vorticity direction and the azimuthal angle $\varphi$ relative to the flow direction. We also compare the eigenfunctions with shapes of slightly buckled elastic filaments with a non-negligible thickness with the same Young's modulus, using the bead model and performing numerical simulations with the precise hydromultipole numerical codes.

Reinforcement Learning offers a framework to learn to choose actions in order to control a system. However, at small scales Brownian fluctuations limit the control of nanomachine actuation or nanonavigation and of the molecular machinery of life. We analyze this regime using the general framework of Markov decision processes. We show that at the nanoscale, while optimal control actions should bring an improvement proportional to the small ratio of the applied force times a length scale over the temperature, the learned improvement is smaller and proportional to the square of this small ratio. Consequently, the efficiency of learning, which compares the learning improvement to the theoretical optimal improvement, drops to zero. Nevertheless, these limitations can be circumvented by using actions learned at a lower temperature. These results are illustrated with simulations of the control of the shape of small particle clusters.

The driving forces of chiral active particles and deformations of cells are often modeled by spatially inhomogeneous but temporally periodic driving forces. Such inhomogeneous oscillatory driving forces have only recently been proposed in the context of active matter, and their effects on the systems are not yet fully understood. In this work, we theoretically study the impact of spatially inhomogeneous oscillatory driving forces on continuous symmetry breaking. We first analyze the linear model for the soft modes in the ordered phase to derive the lower critical dimension of the model, and then analyze the spherical model to investigate more detailed phase behaviors. Interestingly, our analysis reveals that symmetry breaking occurs even in one and two dimensions, where the Hohenberg-Mermin-Wagner theorem prohibits continuous symmetry breaking in equilibrium. Furthermore, fluctuations of conserved quantities, such as density, are anomalously suppressed in the long-wavelength, i.e., show hyperuniformity.

Synchronization behaviors in globally coupled phase oscillators with symmetric bimodal frequency distribution and periodic coupling are studied. It is found that by a proper setting of the frequency of the periodic coupling, the synchronization propensity of the oscillators can be markedly improved. Specifically, we show that when the frequency of the periodic coupling matches the distance of the central frequencies in the distribution, the critical coupling characterizing the onset of synchronization can be substantially decreased. The mechanism behind the phenomenon of periodic-coupling-enhanced synchronization is analyzed by the methods of Ott-Antonsen ansatz and synchronization transition tree, and it is revealed that the synchronization enhancement is attributed to the resonance between the synchronization clusters and the periodic coupling.

Metastable states are identified in the Ising model with competition between the Glauber and Kawasaki dynamics. The model of interaction between magnetic moments was implemented on a network where the degree distribution follows a power law of the form $P\left(k\right)\sim k^{-\alpha }$. The evolution toward the stationary state occurred through the competition between two dynamics, driving the system out of equilibrium. In this competition, with probability $q$, the system was simulated in contact with a heat bath at temperature $T$ by the Glauber dynamics, while with probability $1-q$, the system experienced an external energy influx governed by the Kawasaki dynamics. The phase diagrams of $T$ as a function of $q$ were obtained, which are dependent on the initial state of the system, and exhibit first- and second-order phase transitions. In all diagrams, for intermediate values of $T$, the phenomenon of self-organization between the ordered phases was observed. In the regions of second-order phase transitions, we obtained the critical exponents of the order parameter $\beta$, susceptibility $\gamma$, and correlation length $\nu$. Furthermore, in the regions of first-order phase transitions, we have demonstrated the instability due to transitions between ordered phases through hysteresislike curves of the order parameter, in addition to the existence of absorbing states. We also estimated the value of tricritical points when the discontinuity in the order parameter in the phase transitions was no longer observed.

Self-propelled droplets serve as ideal model systems to delve deeper into understanding the motion of biological microswimmers by simulating their motility. Biological microorganisms are renowned for showcasing a diverse array of dynamic swimming behaviors when confronted with physical constraints. This study aims to elucidate the impact of physical constraints on swimming characteristics of biological microorganisms. To achieve this, we present observations on the individual and pairwise behavior of micellar solubilized self-propelled 4-cyano-4′-pentyl-biphenyl (5CB) oil droplets in a square capillary channel filled with a surfactant trimethyl ammonium bromide aqueous solution. To explore the effect of the underlying Péclet number of the swimming droplets, the study is also performed in the presence of additives such as high molecular weight polymer polyethylene oxide and molecular solute glycerol. The capillary confinement restricts droplet to predominantly one-dimensional motion, albeit with noticeable differences in their motion across the three scenarios. Through a characterization of the chemical and hydrodynamic flow fields surrounding the droplets, we illustrate that the modification of the droplets' chemical field due to confinement varies significantly based on the underlying differences in the Péclet number in these cases. This alteration in the chemical field distribution notably affects the individual droplets' motion. Moreover, these distinct chemical field interactions between the droplets also lead to variations in their pairwise motion, ranging from behaviors like chasing to scattering.

We consider passive Brownian particles trapped in an “imperfect” harmonic trap. The trap is imperfect because it is randomly turned off and on, and as a result particles fail to equilibrate. Another way to think about this is to say that a harmonic trap is time dependent on account of its strength evolving stochastically in time. Particles in such a system are passive and activity arises through external control of a trapping potential, thus, no internal energy is used to power particle motion. A stationary Fokker-Planck equation of this system can be represented as a third-order differential equation, and its solution, a stationary distribution, can be represented as a superposition of Gaussian distributions for different strengths of a harmonic trap. This permits us to interpret a stationary system as a system in equilibrium with quenched disorder.

We compute exactly the full distribution of the number $m$ of local minima in a one-dimensional landscape generated by a random walk or a Lévy flight. We consider two different ensembles of landscapes, one with a fixed number of steps $N$ and the other till the first-passage time of the random walk to the origin. We show that the distribution of $m$ is drastically different in the two ensembles (Gaussian in the former case, while having a power-law tail $m^{-3/2}$ in the latter case). However, the most striking aspect of our results is that, in each case, the distribution is completely universal for all $m$ (and not just for large $m$), i.e., independent of the jump distribution in the random walk. This means that the distributions are exactly identical for Lévy flights and random walks with finite jump variance. Our analytical results are in excellent agreement with our numerical simulations.

Thermally activated particle motion in disorder potentials is controlled by the large-$\mathrm{\Delta }V$ tail of the distribution of height $\mathrm{\Delta }V$ of the potential barriers created by the disorder. We employ the optimal fluctuation method to evaluate this tail for correlated quenched Gaussian potentials in one dimension in the presence of a small bias of the potential. We focus on the mean escape time (MET) of overdamped particles averaged over the disorder. We show that the bias leads to a strong (exponential) reduction of the MET in the direction along the bias. The reduction depends both on the bias and on detailed properties of the covariance of the disorder, such as its derivatives and asymptotic behavior at large distances. We verify our theoretical predictions for the large-$\mathrm{\Delta }V$ tail of the barrier height distribution, as well as earlier predictions of this tail for zero bias, by performing large-deviation simulations of the potential disorder. The simulations employ correlated random potential sampling based on the circulant embedding method and the Wang-Landau algorithm, which enable us to probe probability densities smaller than ${10}^{-1200}$.

Some exact solutions of the first-passage and first-arrival problems for the continuous-time random-walk model are obtained. On the basis of these exact solutions, the following has been revealed. First, for some jump-length distributions with a finite variance, the approximate solutions obtained in the diffusion approximation can differ significantly from the exact solutions. Second, for some waiting time distributions with a finite mean, the times of first passage and the times of first arrival can significantly depend on the ensemble under consideration. In particular, the mean first-passage time corresponding to the stationary ensemble can be significantly greater than the mean first-passage time corresponding to the nonaged ensemble. Third, for any continuous distribution of jump lengths, the probability of first arrival is zero for a point-like target. This last result is contrary to existing opinion, but it is consistent with the fact that a single point has a probability measure equal to zero in the probability space defined by a continuous distribution of jump lengths.

We generalize the Kuramoto model by interpreting the $N$ variables on the unit circle as eigenvalues of a $N$-dimensional unitary matrix $U$ in three versions: general unitary, symmetric unitary, and special orthogonal. The time evolution is generated by $N^2$ coupled differential equations for the matrix elements of $U$, and synchronization happens when $U$ evolves into a multiple of the identity. The Ott-Antonsen ansatz is related to the Poisson kernels that are so useful in quantum transport, and we prove it in the case of identical natural frequencies. When the coupling constant is a matrix, we find some surprising new dynamical behaviors.

Spiral waves in cardiac tissue have been identified as a significant factor leading to life-threatening arrhythmias and ventricular fibrillation. Consequently, understanding the mechanisms underlying the dynamics of such waves and exploring strategies for their elimination have garnered substantial interest and emerged as crucial research objectives. Spiral waves often become pinned (trapped) at anatomical obstacles in cardiac tissue, resulting in increased stability and posing challenges for their elimination. The unpinning of spiral waves can be achieved through the application of an external electric field and has been the subject of previous research. Recently, optogenetics has emerged as an alternative method to modulate electrical activity by illumination of cardiac tissue. In this paper, we employ mathematical modeling to investigate the potential of utilizing local illumination to unpin and eliminate spiral waves in cardiac tissue. We also extend this methodology to explore the effects of more complex turbulent excitation patterns. We conduct simulations using low-dimensional (Barkley) and ionic (Fenton-Karma) models of cardiac tissue, incorporating optogenetical channels. Our findings demonstrate that local suprathreshold illumination can successfully unpin spiral waves in $100\%$ of cases. Notably, unlike unpinning by electrical field stimulation, this approach does not necessitate precise timing of stimulus application during a specific phase of rotation. Additionally, we demonstrate that periodic optogenetical stimulation can effectively eliminate both unpinned spiral waves and turbulence by moving them toward the boundary via an antitachycardia pacing mechanism.

This study introduces a simulated active matter system, applying the pedestrian collision avoidance paradigm, which involves dynamically adjusting the desired velocity. We present a human-zombie game set within a closed geometry, combining predator-prey behavior with a one-way contagion process that transforms prey into predators. The system demonstrates varied responses in our implemented model: with agents having the same maximum speeds, a single zombie always captures a human, whereas two zombies never capture a single human agent. As the number of human agents increases, observables such as the final fraction of zombie agents and total conversion times exhibit significant changes in the system's behavior at intermediate density values. Most notably, there is evidence of a first-order phase transition when analyzing the mean population speed as an order parameter.

Taking advantage of the competition between elasticity and capillarity has proven to be an efficient way to design structures by folding, bending, or assembling elastic objects in contact with liquid interfaces. Elastocapillary effects often occur at scales where gravity does not play an important role, such as in microfabrication processes. However, the influence of gravity can become significant at the desktop scale, which is relevant for numerous situations including model experiments used to provide a fundamental physics understanding, working at easily accessible scales. We focus here on the case of elastic ribbons placed in two-dimensional bubble columns: by introducing an elastic ribbon inside the central soap films of a staircase bubble structure in a square cross-section column, the deviation from Plateau's laws (capillarity-dominated case dictating the shape of usual foams) can be quantified as a function of the rigidity of the ribbon. For long ribbons, gravity cannot be neglected. We provide a detailed theoretical analysis of the ribbon profile, taking into account capillarity, elasticity, and gravity. We compute the total energy of the system and perform energy minimization under constraints, using Lagrangian mechanics. The model is then validated via a comparison with experiments with three different ribbon thicknesses.

We consider boundary-layer structures that arise in connection with the transport of neutral particles (e.g., photons or neutrons) through a participating medium. Such boundary-layer structures were previously identified by the authors in certain particular cases [Phys. Rev. E 104, L032801 (2021)]. Extending the previous work to anisotropic scattering and general Fresnel boundary conditions, this contribution presents computational algorithms which (1) resolve the aforementioned layers as well as previously unreported boundary layers associated with Fresnel boundary transmission and reflection, and (2) yield accurate simulations at fixed computational cost for transport under phase functions with arbitrarily strong anisotropy. The present paper additionally includes (3) Mathematical proofs which justify the numerical methods proposed for resolution of boundary-layer structures. The impact of the new theory on algorithmic performance is demonstrated through a series of 1D computational benchmarks that emulate typical photon- and neutron-transport applications such as, e.g., optical tomography, and nuclear reactor analysis and design. Experimental results for transmission of photons through turbid media are presented, exhibiting close agreement between simulated and experimental data. As illustrated by means of a variety of numerical results, the proposed boundary-layer-based approach tackles transport problems with unprecedented accuracy and efficiency.