Collections of persistently moving active particles are an example of a nonequilibrium heat bath. One way to study the nature of nonequilibrium fluctuations in such systems is to follow the dynamics of an embedded probe particle. With this aim, we study the dynamics of an anisotropic inclusion embedded in a bath of active particles. By studying various statistical correlation functions of the dynamics, we show that the emergent motility of this inclusion depends on its shape as well as the properties of the active bath. We demonstrate that both the decorrelation time of the net force on the inclusion and the dwell time of bath particles in a geometrical trap on the inclusion have a nonmonotonic dependence on its shape. We also find that the motility of the inclusion is optimal when the volume fraction of the active bath is close to the value for the onset of motility induced phase separation.

Molecularly thin films of the smectic liquid crystal 4′-octyl-4-biphenylcarbonitrile (8CB) at the air-water interface phase separate into regions with different numbers of layers, in analogy with freestanding smectic liquid crystalline films. This paper reports the line tension associated with the boundary of coexisting trilayer and monolayer phases of in Langmuir films of 8CB at the air-water interface as a function of temperature and humidity and infers information on the boundary profile between the coexisting phases. Two complementary techniques are used to characterize the 8CB thin films: surface pressure–area isotherm and Brewster angle microscopy (BAM). We determine the line tension by stretching isolated domains from their equilibrium circular shape and analyzing the free relaxation with a hydrodynamic model. Then, we interpret the line tension vs temperature data in terms of an excess line entropy for the domain boundary, which requires careful consideration of the thermodynamics of inhomogeneous monolayer systems.

Proton deflectometry is used in magnetized high-energy-density plasmas to observe electromagnetic fields. We describe a reconstruction algorithm to recover the electromagnetic fields from proton fluence data in 1-D. The algorithm is verified against analytic solutions and applied to example data. Next, we study the role of source fluence uncertainty for 1-D reconstructions. We show that reconstruction boundary conditions can be used to constrain the source fluence profile and use this to develop a reconstruction using a specified pair of boundary conditions on the magnetic field. From these considerations, we experimentally demonstrate a hybrid mesh-fluence reconstruction technique where fields are reconstructed from fluence data in an interior region with boundary conditions supplied by direct mesh measurements at the boundary.

Stochastic processes have found numerous applications in science, as they are broadly used to model a variety of natural phenomena. Due to their intrinsic randomness and uncertainty, they are, however, difficult to characterize. Here, we introduce an unsupervised machine learning approach to determine the minimal set of parameters required to effectively describe the dynamics of a stochastic process. Our method builds upon an extended $\beta$-variational autoencoder architecture. By means of simulated data sets corresponding to paradigmatic diffusion models, we showcase its effectiveness in extracting the minimal relevant parameters that accurately describe these dynamics. Furthermore, the method enables the generation of new trajectories that faithfully replicate the expected stochastic behavior. Overall, our approach enables the autonomous discovery of unknown parameters describing stochastic processes, hence enhancing our comprehension of complex phenomena across various fields.

A steel ball with a density higher than that of water can bounce on a water surface when heated to a temperature well above the Leidenfrost point. In this letter, an experiment is conducted where heated steel balls are released onto a water surface. The heated steel ball descends into the liquid, thus causing the liquid to evaporate and form a vapor cushion with an upward force that lifts the steel ball. Subsequently, the steel ball bounces off the water surface, like a solid ball bouncing off an elastic surface without sinking into the water. This phenomenon is known as the inverse Leidenfrost effect. In this letter, we evaluate the various motion behaviors of spheres at different Reynolds numbers and temperatures. Additionally, we analyze the bouncing behavior of solid spheres on a free liquid surface and examine the various force components.

It has become standard practice to describe systems that remain far from equilibrium even in their steady state by Langevin equations with colored noise which is chosen independently from the friction contribution. Since these Langevin equations are typically not derived from first-principle Hamiltonian dynamics, it is not clear whether they correspond to physically realizable scenarios. By exact Mori projection in phase space we derive the nonequilibrium generalized Langevin equation (GLE) for an arbitrary phase-space dependent observable $A$ from a generic many-body Hamiltonian with a time-dependent external force $h\left(t\right)$ acting on the same observable $A$. This is the same Hamiltonian from which the standard fluctuation-dissipation theorem is derived, which reflects the generality of our approach. The observable $A$ could, for example, be the position of an atom, of a molecule or of a macroscopic object, the distance between two such entities or a more complex phase-space function such as the reaction coordinate of a chemical reaction or of the folding of a protein. The Hamiltonian could, for example, describe a fluid, a solid, a viscoelastic medium, or even a turbulent inhomogeneous environment. The GLE, which is a closed-form equation of motion for the observable $A$, is obtained in explicit form to all orders in $h\left(t\right)$ and without restrictions on the type of many-body Hamiltonian or the observable $A$. If the dynamics of the observable $A$ corresponds to a Gaussian process, the resultant GLE has a similar form as the equilibrium Mori GLE, and in particular the friction memory kernel is given by the two-point autocorrelation function of the sum of the complementary and the external force $h\left(t\right)$. This is a nontrivial and useful result, as many observables that characterize nonequilibrium systems display Gaussian statistics. For non-Gaussian nonequilibrium observables correction terms appear in the GLE and in the relation between the force autocorrelation and the friction memory kernel, which are explicitly given in terms of cubic correlation functions of $A$. Interpreting the external force $h\left(t\right)$ as a stochastic process, we derive nonequilibrium corrections to the fluctuation-dissipation theorem and present methods to extract all GLE parameters from experimental or simulation time-series data, thus making our nonequilibrium GLE a practical tool to study and model general nonequilibrium systems.

Stochastic reaction-diffusion models are employed to represent many complex physical, biological, societal, and ecological systems. The macroscopic reaction rates describing the large-scale, long-time kinetics in such systems are effective, scale-dependent renormalized parameters that need to be either measured experimentally or computed by means of a microscopic model. In a Monte Carlo simulation of stochastic reaction-diffusion systems, microscopic probabilities for specific events to happen serve as the input control parameters. To match the results of any computer simulation to observations or experiments carried out on the macroscale, a mapping is required between the microscopic probabilities that define the Monte Carlo algorithm and the macroscopic reaction rates that are experimentally measured. Finding the functional dependence of emergent macroscopic rates on the microscopic probabilities (subject to specific rules of interaction) is a very difficult problem, and there is currently no systematic, accurate analytical way to achieve this goal. Therefore, we introduce a straightforward numerical method of using lattice Monte Carlo simulations to evaluate the macroscopic reaction rates by directly obtaining the count statistics of how many events occur per simulation time step. Our technique is first tested on well-understood fundamental examples, namely, restricted birth processes, diffusion-limited two-particle coagulation, and two-species pair annihilation kinetics. Next we utilize the thus gained experience to investigate how the microscopic algorithmic probabilities become coarse-grained into effective macroscopic rates in more complex model systems such as the Lotka-Volterra model for predator-prey competition and coexistence, as well as the rock-paper-scissors or cyclic Lotka-Volterra model and its May-Leonard variant that capture population dynamics with cyclic dominance motifs. Thereby we achieve a more thorough and deeper understanding of coarse graining in spatially extended stochastic reaction-diffusion systems and the nontrivial relationships between the associated microscopic and macroscopic model parameters, with a focus on ecological systems. The proposed technique should generally provide a useful means to better fit Monte Carlo simulation results to experimental or observational data.

Understanding the entropy production of systems strongly coupled to thermal baths is a core problem of both quantum thermodynamics and mesoscopic physics. While many techniques exist to accurately study entropy production in such systems, they typically require a microscopic description of the baths, which can become numerically intractable to study for large systems. Alternatively an open-systems approach can be employed with all the nuances associated with various levels of approximation. Recently, the mesoscopic leads approach has emerged as a powerful method for studying such quantum systems strongly coupled to multiple thermal baths. In this method, a set of discretized lead modes, each locally damped, provide a Markovian embedding. Here we show that this method proves extremely useful to describe entropy production of a strongly coupled open quantum system. We show numerically, for both noninteracting and interacting setups, that a system coupled to a single bath exhibits a thermal fixed point at the level of the embedding. This allows us to use various results from the thermodynamics of quantum dynamical semigroups to infer the nonequilibrium thermodynamics of the strongly coupled, non-Markovian central systems. In particular, we show that the entropy production in the transient regime recovers the well-established microscopic definitions of entropy production with a correction that can be computed explicitly for both the single- and multiple-lead cases.

This study investigates the impact of external forces on the movement of particles, specifically focusing on a type of box piecewise linear map that generates normal diffusion akin to Brownian motion. Through numerical methods, the research delves into the effects of two distinct external forces: linear forces linked to the particle's current position and periodic sinusoidal forces related to time. The results uncover anomalous dynamical behavior characterized by nonlinear growth in the ensemble-averaged mean-squared displacement (EAMSD), aging, and ergodicity breaking. Notably, the diffusion pattern of particles under linear external forces resembles an Ehrenfest double urn model, with its asymptotic EAMSD coinciding with the Langevin equation under linear potential. Meanwhile, particle movement influenced by periodic sinusoidal forces corresponds to an inhomogeneous Markov chain, with its external force amplitude and diffusion coefficient function exhibiting a “multipeak” fractal structure. The study also provides insights into the formation of this structure through the turnstiles dynamics.

In this paper, we propose an application of the basin stability tool which allows us to update the information on the system properties under parameter uncertainties. The concept is presented using a classical mechanical setup of coupled pendula, exchanging the energy via the supporting structure. Depending on the support parameters, the model can exhibit different types of coexisting synchronous patterns as well as remaining desynchronized. We calculate basin stability maps of particular behaviors and combine them with prior parameter distributions using Bayesian inference. The obtained posterior distributions, based on the attractor occurrence, update our knowledge on the system properties in the terms of probabilities. We also underline the problem of evaluating basin stability close to the existence borders, comparing the classical approach of fixed parameters with the one involving variations. The differences between the estimation methods can have a crucial meaning for the discussed application and should be considered carefully. The results presented in this paper uncover ways of applying the basin stability concept, which can be used to study the properties of complex dynamical systems from a probability perspective.

We experimentally investigate the undirected open microwave network $\mathrm{\Gamma }$ with internal absorption composed of two coupled directed halves, unidirectional networks ${\mathrm{\Gamma }}_{+}$ and ${\mathrm{\Gamma }}_{-}$, corresponding to two possible directions of motion on their edges. The two-port scattering matrix of the network $\mathrm{\Gamma }$ is measured and the spectral statistics and the elastic enhancement factor of the network are evaluated. The comparison of the number of experimental resonances with the theoretical one predicted by the Weyl's law shows that within the experimental resolution the resonances are doubly degenerate. This conclusion was also corroborated by the numerical calculations. Though the network is characterized by the time-reversal symmetry, the missing level spectral statistics and the elastic enhancement factor are rather close to the Gaussian unitary ensemble predictions in random matrix theory. We used numerical calculations for the open nondissipative quantum graph possessing the same structure as the microwave network $\mathrm{\Gamma }$ to investigate the doublet structures in the spectrum which otherwise would not be experimentally resolved. We show that the doublet size distribution is close to the Poisson distribution.

Purcell's planar three-link microswimmer is a classic model of swimming in low-Reynolds-number fluid, inspired by motion of flagellated microorganisms. Many works analyzed this model, assuming that the two joint angles are directly prescribed in phase-shifted periodic inputs. In this work, we study a more realistic scenario by considering an extension of this model which accounts for joints' elasticity and mechanical actuation of periodic torques so that the joint angles are dynamically evolving. Numerical analysis of the swimmer's dynamics reveals multiplicity of periodic solutions, depending on parameters of the inputs—frequency and amplitude of excitation, joints' stiffness ratio, as well as joint's activation. We numerically study swimming direction reversal, as well as bifurcations, stability transitions, and symmetry breaking of the periodic solutions, which represent the effect of buckling instability observed in swimming microorganisms. The results demonstrate that this variant of Purcell's simple model displays rich nonlinear dynamic behavior with actuated-elastic joints. Similar results are also obtained when studying an extended model of a six-link microswimmer.

Discrete- and continuous-time approaches are frequently used to model the role of heterogeneity on dynamical interacting agents on the top of complex networks. While, on the one hand, one does not expect drastic differences between these approaches, and the choice is usually based on one's expertise or methodological convenience, on the other hand, a detailed analysis of the differences is necessary to guide the proper choice of one or another approach. We tackle this problem by investigating both discrete- and continuous-time mean-field theories for the susceptible-infected-susceptible (SIS) epidemic model on random networks with power-law degree distributions. We compare the discrete epidemic link equations (ELE) and continuous pair quenched mean-field (PQMF) theories with the corresponding stochastic simulations, both theories that reckon pairwise interactions explicitly. We show that ELE converges to the PQMF theory when the time step goes to zero. We performed an epidemic localization analysis considering the inverse participation ratio (IPR). Both theories present the same localization dependence on network degree exponent $\gamma$: for $\gamma <5/2$ the epidemics are localized on the maximum $k$-core of networks with a vanishing IPR in the infinite-size limit while, for $\gamma >5/2$, the localization happens on hubs that do not form a densely connected set and leads to a finite value of the IPR. However, the IPR and epidemic threshold of ELE depend on the time-step discretization such that a larger time step leads to more localized epidemics. A remarkable difference between discrete- and continuous-time approaches is revealed in the epidemic prevalence near the epidemic threshold, in which the discrete-time stochastic simulations indicate a mean-field critical exponent $\theta =1$ instead of the value $\theta =1/(3-\gamma )$ obtained rigorously and verified numerically for the continuous-time SIS on the same networks.

The idea that rodlike molecules possessing an electric dipole moment could exhibit a ferroelectric nematic phase was suggested more than a century ago. However, only recently such a phase has been reported for two quite different liquid crystals: RM734 [4-[(4-nitrophenoxy)carbonyl)]phenyl 2,4-dimethoxybenzoate] and DIO [2.3′,4′,5′-tetrafluoro[1,1′-biphenyl]-4-yl 2.6-difluoro-4-(5-propyl-1,3-dioxan-2-yl) benzoate]. For RM734 a direct ferroelectric nematic ($N_F$) to classical nematic $N$ transition was reported, whereas for DIO an intermediate phase $N_x$ was discovered between the $N_F$ and the $N$ phases. Here we present high-resolution calorimetric evidence that an intermediate $N_x$ phase also exists in RM734 along a narrow temperature range between the $N_F$ and the $N$ phases.

The relationship between the polymer orientation and the chaotic flow, in a dilute solution of rigid rodlike polymers at low Reynolds number, is investigated by means of direct numerical simulations. It is found that the rods tend to align with the velocity field in order to minimize the friction with the solvent fluid, while regions of rotational disorder are related to strong vorticity gradients, and therefore to the chaotic flow. The “turbulent-like” behavior of the system is therefore associated with the emergence and interaction of topological defects of the mean director field, similarly to active nematic turbulence. The analysis has been carried out in both two and three spatial dimensions.

In this work, we develop a phase-field-based lattice Boltzmann (LB) method for a two-scalar model of the two-phase flows with interfacial mass or heat transfer. Through the Chapman-Enskog analysis, we show that the present LB method can correctly recover the governing equations for phase field, flow field, and concentration or temperature field. In particular, to derive the two-scalar equations for the mass or heat transfer, we propose a new LB model with an auxiliary source distribution function to describe the extra flux terms, and the discretizations of some derivative terms can be avoided. The accuracy and efficiency of the present LB method are also tested through several benchmark problems, and the influence of mass or heat transfer on the fluid viscosity is further considered by introducing an exponential relation. The numerical results show that the present LB method is suitable for the two-phase flows with interfacial mass or heat transfer.

By introducing a simple competition mechanism for bond insertion in random graphs, explosive percolation exhibits a sharp phase transition with rich critical phenomena. We investigate high-order connectivity in explosive percolation using an event-based ensemble, focusing on biconnected clusters, where any two sites are connected by at least two independent paths. Our numerical analysis confirms that explosive percolation with different intracluster bond competition rules shares the same percolation threshold and universality, with biconnected clusters percolating simultaneously with simply connected clusters. However, the volume fractal dimension $d_f^{\prime }$ of biconnected clusters varies depending on the competition rules of intracluster bonds. The size distribution of biconnected clusters exhibits double-scaling behavior: large clusters follow the standard Fisher exponent derived from the hyperscaling relation ${\tau }^{\prime }=1+1/d_f^{\prime }$, while small clusters display a modified Fisher exponent ${\tau }_0<{\tau }^{\prime }$. These findings provide insights into the intricate nature of connectivity in explosive percolation.

Polymer loop structure commonly appears in biological phenomena, such as DNA looping and DNA denaturation. When a chain forms a loop, its elastic behavior differs from that of an open chain due to the loss of entropy. In the case of reversible loop formation, interesting behavior emerges related to the multistate nature of the conformations. In this study, we model a multistate reversible loop as a looping Gaussian chain, which can bind (close) reversibly at one or several points to form a loop, or a zipping Gaussian loop, which can zip reversibly to form a double-stranded chain. For each model, we calculate the force-extension relations in the fixed-extension (Helmholtz) and the fixed-force (Gibbs) statistical ensembles. Unlike the single Gaussian chain or loop, the multilevel systems demonstrate qualitatively distinct tensile elasticity and ensemble inequivalence. In addition, we investigate a Gaussian necklace consisting of reversible alternating blocks of the zipped chain and loop and obtain the force-temperature phase diagram. The phase diagram implies a force-induced phase transition from a completely looped (denatured) state to a mixed (bound) state.

When bubbles collapse near a wall, they typically experience an asymmetric deformation. This collapse leads to the creation of a jet that strikes the bubble interface, causing the formation of a toroidal bubble and the subsequent release of a water-hammer shock. In this study, we present a systematic analysis of the collapse of a toroidal bubble in an open field or adjacent to a flat wall using high-fidelity numerical simulation. To maintain the sharpness of the interface, we employ the interface compression technique and the boundary variation diminishing approach within the two-phase model. Our findings demonstrate that shock waves emitted from the toroidal bubble consistently propagate toward the central axis of the torus, resulting in significant pressure shocks along the axis, similar to the water-hammer shock formed during the collapse of a spherical bubble. In contrast, weak pressure waves are generated in the transverse directions, leading to relatively weaker pressure peaks. Furthermore, the wall-pressure peak induced by the toroidal bubble is approximately three times higher than that induced by the spherical bubble. Based on the directional characteristics of pressure wave propagation from collapsing toroidal bubbles, toroidal-shaped pressure vessels can be designed as buoyancy materials for deep submersibles. This design enables the focused release of energy in a specific direction, effectively minimizing the destructive chain reaction caused by the implosion.

Deriving closed-form analytical expressions for reduced-order models, and judiciously choosing the closures leading to them, has long been the strategy of choice for studying phase- and noise-induced transitions for agent-based models (ABMs). In this paper, we propose a data-driven framework that pinpoints phase transitions for an ABM—the Desai-Zwanzig model—in its mean-field limit, using a smaller number of variables than traditional closed-form models. To this end, we use the manifold learning algorithm Diffusion Maps to identify a parsimonious set of data-driven latent variables, and we show that they are in one-to-one correspondence with the expected theoretical order parameter of the ABM. We then utilize a deep learning framework to obtain a conformal reparametrization of the data-driven coordinates that facilitates, in our example, the identification of a single parameter-dependent ordinary differential equation (ODE) in these coordinates. We identify this ODE through a residual neural network inspired by a numerical integration scheme (forward Euler). We then use the identified ODE—enabled through an odd symmetry transformation—to construct the bifurcation diagram exhibiting the phase transition.