The motion of a colloidal probe in a complex fluid, such as a micellar solution, is usually described by the generalized Langevin equation, which is linear. However, recent numerical simulations and experiments have shown that this linear model fails when the probe is confined and that the intrinsic dynamics of the probe is actually nonlinear. Noting that the kurtosis of the displacement of the probe may reveal the nonlinearity of its dynamics also in the absence confinement, we compute it for a probe coupled to a Gaussian field and possibly trapped by a harmonic potential. We show that the excess kurtosis increases from zero at short times, reaches a maximum, and then decays algebraically at long times, with an exponent which depends on the spatial dimensionality and on the features and correlations of the dynamics of the field. Our analytical predictions are confirmed by numerical simulations of the stochastic dynamics of the probe and the field where the latter is represented by a finite number of modes.

This paper considers the motion of an object subjected to a dry friction and an external random force. The objective is to characterize the role of the correlation time of the external random force. We develop efficient stochastic simulation methods for computing the diffusivity (the linear growth rate of the variance of the displacement) and other related quantities of interest when the external random force is white or colored. These methods are based on original representation formulas for the quantities of interest, which make it possible to build unbiased and consistent estimators. The numerical results obtained with these original methods are in perfect agreement with known closed-form formulas valid in the white-noise regime. In the colored-noise regime, the numerical results show that the predictions obtained from the white-noise approximation are reasonable for quantities such as the histograms of the stationary velocity but can be wrong for the diffusivity unless the correlation time is extremely small.

The second law of thermodynamics states that entropy production cannot be negative. Recent developments concerning uncertainty relations in stochastic thermodynamics, such as thermodynamic uncertainty relations and speed limits, have yielded refined second laws that provide lower bounds of entropy production by incorporating information from current statistics or distributions. In contrast, in this study we bound the entropy production from above by terms comprising the dynamical activity and maximum transition-rate ratio. We derive two upper bounds: One applies to steady-state conditions, whereas the other applies to arbitrary time-dependent conditions. We verify these bounds through numerical simulation and identify several potential applications.

We describe a direct method to estimate the bipartite mutual information of a classical spin system based on Monte Carlo sampling enhanced by autoregressive neural networks. It enables us to study arbitrary geometries of subsystems, and it can be generalized to classical field theories. We demonstrate it on the Ising model for four partitionings, including a multiply connected even-odd division. We show that the area law is satisfied for temperatures away from the critical temperature: the constant term is universal, whereas the proportionality coefficient is different for the even-odd partitioning.

It is possible to investigate emergence in many real systems using time-ordered data. However, classical time series analysis is usually conditioned by data accuracy and quantity. A modern method is to map time series onto graphs and study these structures using the toolbox available in complex network analysis. An important practical problem to investigate the criticality in experimental systems is to determine whether an observed time series is associated with a critical regime or not. We contribute to this problem by investigating the mapping called visibility graph (VG) of a time series generated in dynamical processes with absorbing-state phase transitions. Analyzing degree correlation patterns of the VGs, we are able to distinguish between critical and off-critical regimes. One central hallmark is an asymptotic disassortative correlation on the degree for series near the critical regime in contrast with a pure assortative correlation observed for noncritical dynamics. We are also able to distinguish between continuous (critical) and discontinuous (noncritical) absorbing state phase transitions, the second of which is commonly involved in catastrophic phenomena. The determination of critical behavior converges very quickly in higher dimensions, where many complex system dynamics are relevant.

A fundamental problem in ecology is to understand how competition shapes biodiversity and species coexistence. Historically, one important approach for addressing this question has been to analyze consumer resource models using geometric arguments. This has led to broadly applicable principles such as Tilman's $R^{*}$ and species coexistence cones. Here, we extend these arguments by constructing a geometric framework for understanding species coexistence based on convex polytopes in the space of consumer preferences. We show how the geometry of consumer preferences can be used to predict species which may coexist and enumerate ecologically stable steady states and transitions between them. Collectively, these results provide a framework for understanding the role of species traits within niche theory.

Chemical reactions are usually studied under the assumption that both substrates and catalysts are well-mixed (WM) throughout the system. Although this is often applicable to test-tube experimental conditions, it is not realistic in cellular environments, where biomolecules can undergo liquid-liquid phase separation (LLPS) and form condensates, leading to important functional outcomes, including the modulation of catalytic action. Similar processes may also play a role in protocellular systems, like primitive coacervates, or in membrane-assisted prebiotic pathways. Here we explore whether the demixing of catalysts could lead to the formation of microenvironments that influence the kinetics of a linear (multistep) reaction pathway, as compared to a WM system. We implemented a general lattice model to simulate LLPS of a collection of different catalysts and extended it to include diffusion and a sequence of reactions of small substrates. We carried out a quantitative analysis of how the phase separation of the catalysts affects reaction times depending on the affinity between substrates and catalysts, the length of the reaction pathway, the system size, and the degree of homogeneity of the condensate. A key aspect underlying the differences reported between the two scenarios is that the scale invariance observed in the WM system is broken by condensation processes. The main theoretical implications of our results for mean-field chemistry are drawn, extending the mass action kinetics scheme to include substrate initial “hitting times” to reach the catalysts condensate. We finally test this approach by considering open nonlinear conditions, where we successfully predict, through microscopic simulations, that phase separation inhibits chemical oscillatory behavior, providing a possible explanation for the marginal role that this complex dynamic behavior plays in real metabolisms.

The flow of elliptical particles out of a two-dimensional silo when extracted with a conveyor belt is analyzed experimentally. The conveyor belt—placed directly below the silo outlet—reduces the flow rate, increases the size of the stagnant zone, and it has a very strong influence on the relative velocity fluctuations as they strongly increase everywhere in the silo with decreasing belt speed. In other words, instead of slower but smooth flow, flow reduction by belt leads to intermittent flow. Interestingly, we show that this intermittency correlates with a strong reduction of the orientational order of the particles at the orifice region. Moreover, we observe that the average orientation of the grains passing through the outlet is modified when they are extracted with the belt, a feature that becomes more evident for large orifices.

We report on reentrance in the random-field Ising and Blume-Capel models, induced by an asymmetric bimodal random-field distribution. The conventional continuous line of transitions between the paramagnetic and ferromagnetic phases, the $\lambda$-line, is wiped away by the asymmetry. The phase diagram, then, consists of only first-order transition lines that always end at ordered critical points. We find that, while for symmetric random-field distributions there is no reentrance, the asymmetry in the random-field results in a range of temperatures for which magnetization shows reentrance. While this does not give rise to an inverse transition in the Ising model, for the Blume-Capel model, however, there is a line of first-order inverse phase transitions that ends at an inverse-ordered critical point. We show that the location of the inverse transitions can be inferred from the ground-state phase diagram of the model.

The main point we address in this paper is the question of thermodynamic stability for phase-separating systems, at coexistence in equilibrium. It has long been known that numerical simulations of different statistical models may yield “Van der Waals-like” isotherms in the coexistence region. Such “inverted” convexity segments of thermodynamic fields, known as unstable, are forbidden by the second law of thermodynamics on entropy, and their presence is not justified in exact results. In numerical experiments, their origin has been associated with the interface between the two coexisting phases. Nonetheless, the violation of the second law by entropy has not yet, to our knowledge, been rationalized. In this work, we introduce the thermodynamics of the interface between coexisting phases and give an alternative interpretation to the theory developed by Hill in the 1960s. Our approach points to a misinterpretation of the usual measurements of thermodynamic potentials in simulations. Correct interpretation eliminates the unstable regions of the true potentials. Our adapted theory is verified for the 2D lattice gas through carefully planned simulations. The thermodynamic description of the interface behavior inside the coexistence region restores the proper convexity of the true chemical potential isotherms. As a bonus, our interpretation allows direct calculation of surface tension in very good accordance with Onsager's analytic prediction.

The area enclosed by the two-dimensional Brownian motion in the plane was studied by Lévy, who found the characteristic function and probability density of this random variable. For other planar processes, in particular ergodic diffusions described by linear stochastic differential equations (SDEs), only the expected value of the stochastic area is known. Here we calculate the generating function of the stochastic area for linear SDEs, which can be related to the integral of the angular momentum, and extract from the result the large deviation functions characterizing the dominant part of its probability density in the long-time limit, as well as the effective SDE describing how large deviations arise in that limit. In addition, we obtain the asymptotic mean of the stochastic area, which is known to be related to the probability current, and the asymptotic variance, which is important for determining from observed trajectories whether or not a diffusion is reversible. Examples of reversible and irreversible linear SDEs are studied to illustrate our results.

We investigate block diagonal and hierarchical nested stochastic multivariate Gaussian models by studying their sample cross-correlation matrix on high dimensions. By performing numerical simulations, we compare a filtered sample cross-correlation with the population cross-correlation matrices by using several rotationally invariant estimators (RIEs) and hierarchical clustering estimators (HCEs) under several loss functions. We show that at large but finite sample size, sample cross-correlations filtered by RIE estimators are often outperformed by HCE estimators for several of the loss functions. We also show that for block models and for hierarchically nested block models, the best determination of the filtered sample cross-correlation is achieved by introducing two-step estimators combining state-of-the-art nonlinear shrinkage models with hierarchical clustering estimators.

Why are living systems complex? Why does the biosphere contain living beings with complexity features beyond those of the simplest replicators? What kind of evolutionary pressures result in more complex life forms? These are key questions that pervade the problem of how complexity arises in evolution. One particular way of tackling this is grounded in an algorithmic description of life: living organisms can be seen as systems that extract and process information from their surroundings to reduce uncertainty. Here we take this computational approach using a simple bit string model of coevolving agents and their parasites. While agents try to predict their worlds, parasites do the same with their hosts. The result of this process is that, to escape their parasites, the host agents expand their computational complexity despite the cost of maintaining it. This, in turn, is followed by increasingly complex parasitic counterparts. Such arms races display several qualitative phases, from monotonous to punctuated evolution or even ecological collapse. Our minimal model illustrates the relevance of parasites in providing an active mechanism for expanding living complexity beyond simple replicators, suggesting that parasitic agents are likely to be a major evolutionary driver for biological complexity.

Machine learning algorithms offer a tool to boost mobility and flexibility of a synthetic microswimmer, hence may help us design truly smart microrobots. In this work, we design a two-gait microrobot swimming in circular or helical trajectory. It utilizes the coupling between flagellum elasticity and resistive force to change the characteristics of swimming trajectory. Leveraging a deep reinforcement learning (DRL) approach, we show that the microrobot can self-learn chemotactic motion autonomously (without heuristics) using only several current and historical chemoattractant concentration and curvature information. The learned strategy is more efficient than a human-devised shortsighted strategy and can be further greatly improved in a stochastic environment. Furthermore, in the helical trajectory case, if additional heuristic information of direction is supplemented to evaluate the strategy during the learning process, then a highly efficient strategy can be discovered by the DRL. The microrobot can quickly align the helix vector to the gradient direction using just several smart sequential gait switchings. The success for the efficient strategies depends on how much historical information is provided and also the steering angle step size of the microrobot. Our results provide useful guidance for the design and smart maneuver of synthetic spermlike microswimmers.

Very soft grain assemblies have unique shape-changing capabilities that allow them to be compressed far beyond the rigid jammed state by filling void spaces more effectively. However, accurately following the formation of these systems by monitoring the creation of new contacts, monitoring the changes in grain shape, and measuring grain-scale stresses is challenging. We developed an experimental method that overcomes these challenges and connects their microscale behavior to their macroscopic response. By tracking the local strain energy during compression, we reveal a transition from granular-like to continuous-like material. Mean contact geometry is shown to vary linearly with the packing fraction, which is supported by a mean field approximation. We also validate a theoretical framework which describes the compaction from a local view. Our experimental framework provides insights into the granular micromechanisms and opens perspectives for rheological analysis of highly deformable grain assemblies in various fields ranging from biology to engineering.

With the advancement in the understanding of plasma discontinuous structures and the progress of related research, numerical methods for simulating plasmas based on continuous medium approach have encountered significant challenges. In this paper, a numerical model is presented to simulate the motion trajectory of an atmospheric pressure plasma jet under an external nonuniform electric field. The method proposes to treat the plasma jet as equivalent particles with permittivity and conductivity, based on its dielectric properties and motion characteristics. The numerical model demonstrates short calculation times and excellent agreement between simulation results and experimental observations, validating its high efficiency and effectiveness. This work contributes to a deeper understanding of the collective effect of the plasma jet and provides an effective and efficient method for predicting the motion trajectory of the plasma jet, along with guidelines for controlling plasma using external nonuniform electric fields.

To achieve the highest possible laser intensities with the least laser energy, shorter-wavelengths lasers are advantaged if they can be focused to spots of a few laser wavelengths and durations of several laser periods. However, the top laser pulse energies available nowadays are megajoules at near-optical wavelengths and millijoules at shorter wavelengths. Thus, to produce the highest laser intensities, what is required is an efficient spectral transfer of the huge near-optical energies to shorter wavelengths. It is proposed here that the desired spectral transfer could occur via resonant photon interactions associated with nonlinearity of mildly relativistic motions of plasma electrons in intense laser fields, specifically via the six-photon resonant scattering of collinear laser pulses in plasma. The six-photon interaction can, in fact, be the dominant resonant photon interaction to achieve collinear frequency up-conversion.

We present simulation results of ultracold Sr plasma expansion in a quadrupole magnetic field by means of molecular dynamics. An analysis of plasma evolution influenced by a magnetic field is given. Plasma confinement time behavior under variation of magnetic field strength is estimated. Similarity of the time dependence of the concentration and distribution of ion velocities against the parameters of the plasma and magnetic field is established. Simulation results are in agreement with the experimental ones.

Model averaging is a useful and robust method for dealing with model uncertainty in statistical analysis. Often, it is useful to consider data subset selection at the same time, in which model selection criteria are used to compare models across different subsets of the data. Two different criteria have been proposed in the literature for how the data subsets should be weighted. We compare the two criteria closely in a unified treatment based on the Kullback-Leibler divergence and conclude that one of them is subtly flawed and will tend to yield larger uncertainties due to loss of information. Analytical and numerical examples are provided.