This paper presents analytical and numerical results on the energetics of nonharmonic, undamped, single-well, stochastic oscillators driven by additive Gaussian white noises. The absence of damping and the action of noise are responsible for the lack of stationary states in such systems. We explore the properties of average kinetic, potential, and total energies along with the generalized equipartition relations. It is demonstrated that in frictionless dynamics, nonequilibrium stationary states can be produced by stochastic resetting. For an appropriate resetting protocol, the average energies become bounded. If the resetting protocol is not characterized by a finite variance of renewal intervals, stochastic resetting can only slow down the growth of the average energies but it does not bound them. Under special conditions regarding the frequency of resets, the ratios of the average energies follow the generalized equipartition relations.

We show the equivalence between the Hamiltonian and non-Hamiltonian forms of a fourth-order nonlinear Schrödinger equation for a particular example of the physical system described by the nonlinear Klein-Gordon equation with cubic nonlinearity.

If deterministic dynamics is dominant in the data, then methods based on predictions in reconstructed state spaces can serve to detect causal relationships between and within the systems. Here we introduce two algorithms for such causal analysis. They are designed to detect causality from two time series but are potentially also applicable in a multivariate context. The first method is based on cross-predictions, and the second one on the so-called mixed predictions. In terms of performance, the cross-prediction method is considerably faster and less prone to false negatives. The predictability improvement method is slower, but in addition to causal detection, in a multivariate scenario, it also reveals which specific observables can help the most if we want to improve prediction. The study also highlights cases where our methods and state-space approaches generally seem to lose reliability. We propose a new perspective on these situations, namely that the variables under investigation have weak observability due to the complex nonlinear information flow in the system. Thus, in such cases, the failure of causality detection cannot be attributed to the methods themselves but to the use of data that do not allow reliable reconstruction of the underlying dynamics.

Monte Carlo simulations are used to study adsorption of highly asymmetric diblock copolymers to a polymer-polymer interface, and the results compared to self-consistent field theory (SCFT) predictions. The simulation model used here is a bead-spring model that has been used previously to study equilibrium and kinetic properties of spherical micelles [J. A. Mysona et al., Phys. Rev. E 100, 012602 (2019); Phys. Rev. E 100, 012603 (2019); Phys. Rev. Lett. 123, 038003 (2019)]. Interfacial copolymer concentration $\mathrm{\Gamma }$ and interfacial tension $\gamma$ are measured as functions of bulk copolymer concentration at concentrations up to the critical micelle concentration over a range of values of the Flory-Huggins $\chi$ parameter. The dependence of interfacial pressure $\mathrm{\Pi }$ = ${\gamma }_0-\gamma$ on $\mathrm{\Gamma }$ (where ${\gamma }_0$ is the interfacial tension in the absence of copolymer) is found to be almost independent of $\chi$ and to be accurately predicted by SCFT. The bare interfacial tension ${\gamma }_0$ and total interfacial tension $\gamma \left(\mathrm{\Gamma }\right)$ can also be accurately predicted by SCFT using an estimate of $\chi$ obtained from independent analysis of properties of symmetric diblock copolymer melts. SCFT predictions obtained with this estimate of $\chi$ do not, however, adequately describe the thermodynamics of the coexisting bulk copolymer solution, as a result of contraction of the strongly interacting core block of dissolved copolymers. Accurate predictions of the relationship between bulk and interfacial properties can thus only be obtained for this system by combining SCFT predictions of the interfacial equation of state with a fit to the measured equation of state for the bulk solution.

The viscoelastic behavior of a physically crosslinked gel involves a spectrum of molecular relaxation processes, which at the single-chain level involve the chain undergoing transient hand-to-hand motion through the network. We develop a self-consistent theory for describing transiently associating polymer solutions that captures these complex dynamics. A single polymer chain transiently binds to a viscoelastic background that represents the polymer network formed by surrounding polymer chains. The viscoelastic background is described in the equation of motion as a memory kernel, which is self-consistently determined based on the predicted rheological behavior from the chain itself. The solution to the memory kernel is translated into rheological predictions of the complex modulus over a wide range of frequencies to capture the time-dependent behavior of a physical gel. Using the loss tangent predictions, a phase diagram is shown for the sol-gel transition of polymers with dynamic association affinities. This theory provides a predictive, molecular-level framework for the design of associating gels and supramolecular assemblies with targeted rheological properties.

We study the effect of a rapid quench to zero temperature in a model with competing interactions, evolving through conserved spin dynamics. In a certain regime of model parameters, we find that the model belongs to the broader class of kinetically constrained models, however, the dynamics is different from that of a glass. The system shows stretched exponential relaxation with the unusual feature that the relaxation time diverges as a power of the system size. Explicitly, we find that the spatial correlation function decays as $exp(-2r/\sqrt{L})$ as a function of spatial separation $r$ in a system with $L$ sites in the steady state, while the temporal autocorrelation function follows $exp[-{(t/{\tau }_L)}^{1/2}]$, where $t$ is the time and ${\tau }_L$ proportional to $L$. In the coarsening regime, after time $t_w$, there are two growing length scales, namely $\mathcal{L}\left(t_w\right)\sim t_w^{1/2}$ and $\mathcal{R}\left(t_w\right)\sim t_w^{1/4}$; the spatial correlation function decays as $exp[-r/\mathcal{R}\left(t_w\right)]$. Interestingly, the stretched exponential form of the autocorrelation function of a single typical sample in the steady state differs markedly from that averaged over an ensemble of initial conditions resulting from different quenches; the latter shows a slow power-law decay at large times.

We investigate properties of the particle distribution near the tip of one-dimensional branching random walks at large times $t$, focusing on unusual realizations in which the rightmost lead particle is very far ahead of its expected position, but still within a distance smaller than the diffusion radius $\sim \sqrt{t}$. Our approach consists in a study of the generating function $G_{\mathrm{\Delta }x}\left(\lambda \right)={\sum }_n{\lambda }^n{p}_n\left(\mathrm{\Delta }x\right)$ for the probabilities $p_n\left(\mathrm{\Delta }x\right)$ of observing $n$ particles in an interval of given size $\mathrm{\Delta }x$ from the lead particle to its left, fixing the position of the latter. This generating function can be expressed with the help of functions solving the Fisher-Kolmogorov-Petrovsky-Piscounov (FKPP) equation with suitable initial conditions. In the infinite-time and large-$\mathrm{\Delta }x$ limits, we find that the mean number of particles in the interval grows exponentially with $\mathrm{\Delta }x$, and that the generating function obeys a nontrivial scaling law, depending on $\mathrm{\Delta }x$ and $\lambda$ through the combined variable ${[\mathrm{\Delta }x-f\left(\lambda \right)]}^3/\mathrm{\Delta }{x}^2$, where $f\left(\lambda \right)\equiv -ln(1-\lambda )-ln[-ln(1-\lambda \left)\right]$. From this property, one may conjecture that the growth of the typical particle number with the size of the interval is slower than exponential, but, surprisingly enough, only by a subleading factor at large $\mathrm{\Delta }x$. The scaling we argue is consistent with results from a numerical integration of the FKPP equation.

Classical quasi-integrable systems are known to have Lyapunov times much shorter than their ergodicity time—the clearest example being the Solar System—but the situation for their quantum counterparts is less well understood. As a first example, we examine the quantum Lyapunov exponent, defined by the evolution of the four-point out-of-time-order correlator (OTOC), of integrable systems which are weakly perturbed by an external noise, a setting that has proven to be illuminating in the classical case. In analogy to the tangent space in classical systems, we derive a linear superoperator equation which dictates the OTOC dynamics. (1) We find that in the semiclassical limit the quantum Lyapunov exponent is given by the classical one: it scales as ${\epsilon }^{1/3}$, with $\epsilon$ being the variance of the random drive, leading to short Lyapunov times compared to the diffusion time (which is $\sim {\epsilon }^{-1}$). (2) We also find that in the highly quantal regime the Lyapunov instability is suppressed by quantum fluctuations, and (3) for sufficiently small perturbations the ${\epsilon }^{1/3}$ dependence is also suppressed—another purely quantum effect which we explain. These essential features of the problem are already present in a rotor that is kicked weakly but randomly. Concerning quantum limits on chaos, we find that quasi-integrable systems are relatively good scramblers in the sense that the ratio between the Lyapunov exponent and $kT/\hslash$ may stay finite at a low temperature $T$.

We consider the statistical inference problem of recovering an unknown perfect matching, hidden in a weighted random graph, by exploiting the information arising from the use of two different distributions for the weights on the edges inside and outside the planted matching. A recent work has demonstrated the existence of a phase transition, in the large size limit, between a full and a partial-recovery phase for a specific form of the weights distribution on fully connected graphs. We generalize and extend this result in two directions: we obtain a criterion for the location of the phase transition for generic weights distributions and possibly sparse graphs, exploiting a technical connection with branching random walk processes, as well as a quantitatively more precise description of the critical regime around the phase transition.

Active fluids containing self-propelled particles are relevant for applications such as self-mixing, micropumping, and targeted drug delivery. With a confined boundary, active fluids can generate bulk flow inside the system, which has the potential to create self-propelled active matter. In this study, we propose that an active droplet is driven by a collective motion of enclosed microswimmers. We show that the droplet migrates via the flow field generated by the enclosed microswimmers; moreover, the locomotion direction depends on the swimming mode of these internal particles. The locomotion mechanism of the droplet can be well explained by interfacial velocity, and the locomotion velocity shows good agreement with the Lighthill-Blake theory. These findings are essential to understand the interplay between the motion of self-propelled particles and the bulk motion response of active matter.

We consider stochastic dynamics of self-propelled particles with nonlocal normalized alignment interactions subject to phase lag. The role of the lag is to indirectly generate chirality into particle motion. To understand large-scale behavior, we derive a continuum description of an active Brownian particle flow with macroscopic scaling in the form of a partial differential equation for a one-particle probability density function. Due to indirect chirality, we find a spatially homogeneous nonstationary analytic solution for this class of equations. Our development of kinetic and hydrodynamic theories towards such a solution reveals the existence of a wide variety of spatially nonhomogeneous patterns reminiscent of traveling bands, clouds, and vortical structures of linear active matter. Our model may thereby serve as the basis for understanding the nature of chiral active media and designing multiagent swarms with designated behavior.

As the places where most of the fuel of the cell, namely, ATP, is synthesized, mitochondria are crucial organelles in eukaryotic cells. The shape of the invaginations of the mitochondria inner membrane, known as a crista, has been identified as a signature of the energetic state of the organelle. However, the interplay between the rate of ATP synthesis and the crista shape remains unclear. In this work, we investigate the crista membrane deformations using a pH-dependent Helfrich model, maintained out of equilibrium by a diffusive flux of protons. This model gives rise to shape changes of a cylindrical invagination, in particular to the formation of necks between wider zones under variable, and especially oscillating, proton flux.

Equilibrium free-energy-landscape parameters governing biomolecular folding can be determined from nonequilibrium force-induced unfolding by measuring the rates $k$ for transitioning back and forth between states as a function of force F. However, bias in the observed forward and reverse rates is introduced by limited effective temporal resolution, which includes the mechanical response time of the force probe and any smoothing used to improve the signal-to-noise ratio. Here we use simulations to characterize this bias, which is most prevalent when the ratio of forward and reverse rates is far from unity. We find deviations in $k$(F) at high rates, due to unobserved transitions from short- to long-lived states, and at low rates, due to the corresponding unobserved transitions from long- to short-lived states. These missing events introduce erroneous curvature in log($k$) vs F that leads to incorrect landscape parameter determination. To correct the measured $k$(F), we derive a pair of model-independent analytical formulas. The first correction accounts for unobserved transitions from short- to long-lived states, but does surprisingly little to correct the erroneous energy-landscape parameters. Only by subsequently applying the second formula, which corrects the corresponding reverse process, do we recover the expected $k$(F) and energy-landscape quantities. Going forward, these corrections should be applied to transition-rate data whenever the highest measured rate is not at least an order of magnitude slower than the effective temporal resolution.

We present simulation results on the properties of packings of frictionless spherocylindrical particles. Starting from a random distribution of particles in space, a packing is produced by minimizing the potential energy of interparticle contacts until a force-equilibrated state is reached. For different particle aspect ratios $\alpha =10\cdots 40$, we calculate contacts $z$, pressure as well as bulk and shear modulus. Most important is the fraction $f_0\left(\alpha \right)$ of spherocylinders with contacts at both ends, as it governs the jamming threshold $z_c\left(\alpha \right)=8+2f_0\left(\alpha \right)$. These results highlight the important role of the axial “sliding” degree of freedom of a spherocylinder, which is a zero-energy mode but only if no end contacts are present.

A pore-network model is an upscaled representation of the pore space and fluid displacement, which is used to simulate two-phase flow through porous media. We use the results of pore-scale imaging experiments to calibrate and validate our simulations, and specifically to find the pore-scale distribution of wettability. We employ energy balance to estimate an average, thermodynamic, contact angle in the model, which is used as the initial estimate of contact angle. We then adjust the contact angle of each pore to match the observed fluid configurations in the experiment as a nonlinear inverse problem. The proposed algorithm is implemented on two sets of steady state micro-computed-tomography experiments for water-wet and mixed-wet Bentheimer sandstone. As a result of the optimization, the pore-by-pore error between the model and experiment is decreased to less than that observed between repeat experiments on the same rock sample. After calibration and matching, the model predictions for capillary pressure and relative permeability are in good agreement with the experiments. The proposed algorithm leads to a distribution of contact angle around the thermodynamic contact angle. We show that the contact angle is spatially correlated over around 4 pore lengths, while larger pores tend to be more oil-wet. Using randomly assigned distributions of contact angle in the model results in poor predictions of relative permeability and capillary pressure, particularly for the mixed-wet case.

We study the first-passage time, the distribution of the maximum, and the absorption probability of fractional Brownian motion of Hurst parameter $H$ with both a linear and a nonlinear drift. The latter appears naturally when applying nonlinear variable transformations. Via a perturbative expansion in $\varepsilon =H-1/2$, we give the first-order corrections to the classical result for Brownian motion analytically. Using a recently introduced adaptive-bisection algorithm, which is much more efficient than the standard Davies-Harte algorithm, we test our predictions for the first-passage time on grids of effective sizes up to $N_{\mathrm{eff}}=2^{28}\approx 2.7\times {10}^8$ points. The agreement between theory and simulations is excellent, and by far exceeds in precision what can be obtained by scaling alone.

We develop a mathematical framework to study the economic impact of infectious diseases by integrating epidemiological dynamics with a kinetic model of wealth exchange. The multiagent description leads to the study of the evolution over time of a system of kinetic equations for the wealth densities of susceptible, infectious, and recovered individuals, whose proportions are driven by a classical compartmental model in epidemiology. Explicit calculations show that the spread of the disease seriously affects the distribution of wealth, which, unlike the situation in the absence of epidemics, can converge toward a stationary state with a bimodal form. Furthermore, simulations confirm the ability of the model to describe different phenomenon characteristics of economic trends in situations compromised by the rapid spread of an epidemic, such as the unequal impact on the various wealth classes and the risk of a shrinking middle class.

Structures on the front surface of thin foil targets for laser-driven ion acceleration have been proposed to increase the ion source maximum energy and conversion efficiency. While structures have been shown to significantly boost the proton acceleration from pulses of moderate-energy fluence, their performance on tightly focused and high-energy lasers remains unclear. Here, we report the results of laser-driven three-dimensional (3D)-printed microtube targets, focusing on their efficacy for ion acceleration. Using the high-contrast ($\sim {10}^{12}$) PHELIX laser ($150\mathrm{J}$, ${10}^{21}\mathrm{W}/{\mathrm{cm}}^2$), we studied the acceleration of ions from $1\text{−}\mu \mathrm{m}$-thick foils covered with micropillars or microtubes, which we compared with flat foils. The front-surface structures significantly increased the conversion efficiency from laser to light ions, with up to a factor of 5 higher proton number with respect to a flat target, albeit without an increase of the cutoff energy. An optimum diameter was found for the microtube targets. Our findings are supported by a systematic particle-in-cell modeling investigation of ion acceleration using 2D simulations with various structure dimensions. Simulations reproduce the experimental data with good agreement, including the observation of the optimum tube diameter, and reveal that the laser is shuttered by the plasma filling the tubes, explaining why the ion cutoff energy was not increased in this regime.

Current epidemiological models can in principle model the temporal evolution of a pandemic. However, any such model will rely on parameters that are unknown, which in practice are estimated using stochastic and poorly measured quantities. As a result, an early prediction of the long-term evolution of a pandemic will quickly lose relevance, while a late model will be too late to be useful for disaster management. Unless a model is designed to be adaptive, it is bound either to lose relevance over time, or lose trust and thus not have a second chance for retraining. We propose a strategy for estimating the number of infections and the number of deaths, that does away with time-series modeling, and instead makes use of a “phase portrait approach.” We demonstrate that, with this approach, there is a universality to the evolution of the disease across countries, that can then be used to make reliable predictions. These same models can also be used to plan the requirements for critical resources during the pandemic. The approach is designed for simplicity of interpretation, and adaptivity over time. Using our model, we predict the number of infections and deaths in Italy and New York State, based on an adaptive algorithm which uses early available data, and show that our predictions closely match the actual outcomes. We also carry out a similar exercise for India, where in addition to projecting the number of infections and deaths, we also project the expected range of critical resource requirements for hospitalizations in a location.

In chemical reaction networks, bistability can only occur far from equilibrium. It is associated with a first-order phase transition where the control parameter is the thermodynamic force. At the bistable point, the entropy production is known to be discontinuous with respect to the thermodynamic force. We show that the fluctuations of the entropy production have an exponential volume-dependence when the system is bistable. At the phase transition, the exponential prefactor is the height of the effective potential barrier between the two fixed-points. Our results obtained for Schlögl's model can be extended to any chemical network.