As emphasized by the recent pandemic crisis, the design of coherent policies against epidemic propagation is of major importance and required to model both epidemic quantities and individuals behavior because the latter has a strong influence on the former. To address this issue, we consider the spread of infectious diseases through a mean field game version of a SIR compartmental model with social structure, in which individuals are grouped by their age class and interact together in different settings. In our game theoretical approach, individuals can choose to limit their contacts if the epidemic is too virulent, but this effort comes with a social cost. We further compare the Nash equilibrium obtained in this way with the societal optimum that would be obtained if a benevolent central planner could decide on the strategy of each individual, as well as to the more realistic situation where an approximation of this optimum is reached through social policies such as lockdown.

We present a simple strategy for constructing an information ratchet or memory-tape model of Maxwell's demon, from a feedback-controlled model. We illustrate our approach by converting the Annby-Andersson feedback-controlled double quantum dot model [Phys. Rev. B 101, 165404 (2020)] to a memory-tape model. We use the underlying network structure of the original model to design a set of bit interaction rules for the information ratchet. The new model is solved analytically in the limit of long interaction times. For finite-time interactions, semianalytical phase diagrams of operational modes are obtained. Stochastic simulations are used to verify theoretical results.

It is well known that some thermodynamic quantities demonstrate maxima in the vicinity of a critical point. The lines of these maxima in the density-temperature or pressure-temperature planes are called “Widom lines.” The behavior of Widom lines of one-component fluids has already been well studied in a number of papers by different authors. However, up to now the understanding of Widom lines in binary mixtures is still lacking. In this paper we study the boiling curve and the near-critical maxima of mixtures of nitrogen and propane by means of molecular dynamics simulation. We calculate the boiling curves and estimate the critical temperatures in a set of concentrations from pure nitrogen to pure propane. The influence of the composition of the mixture on the Widom lines of the system is evaluated. We find that the mixture of propane and nitrogen behaves as a type I mixture in the van Konynenburg–Scott classification, i.e., when the concentration is changed, the critical point and the corresponding Widom lines continuously shift in the density-temperature plane.

In particle-based computer simulations of polydisperse glassforming systems, the particle diameters $\sigma ={\sigma }_1,\cdots ,{\sigma }_N$ of a system with $N$ particles are chosen with the intention to approximate a desired distribution density $f$ with the corresponding histogram. One method to accomplish this is to draw each diameter randomly and independently from the density $f$. We refer to this stochastic scheme as model $\mathcal{S}$. Alternatively, one can apply a deterministic method, assigning an appropriate set of $N$ values to the diameters. We refer to this method as model $\mathcal{D}$. We show that, for sample-to-sample fluctuations, especially for the glassy dynamics at low temperatures, it matters whether one chooses model $\mathcal{S}$ or model $\mathcal{D}$. Using molecular dynamics computer simulations, we investigate a three-dimensional polydisperse nonadditive soft-sphere system with $f\left(s\right)\sim s^{-3}$. The swap Monte Carlo method is employed to obtain equilibrated samples at very low temperatures. We show that for model $\mathcal{S}$ the sample-to-sample fluctuations due to the quenched disorder imposed by the diameters $\sigma$ can be explained by an effective packing fraction. Dynamic susceptibilities in model $\mathcal{S}$ can be split into two terms: one that is of thermal nature and can be identified with the susceptibility of model $\mathcal{D}$, and another one originating from the disorder in $\sigma$. At low temperatures the latter contribution is the dominating term in the dynamic susceptibility. Our study clarifies the pros and cons of the use of models $\mathcal{S}$ and $\mathcal{D}$ in practice.

Recent experiments have shown that the nematode T. aceti can assemble into collectively undulating groups at the edge of fluid drops. This coordinated state consists of metachronal waves and drives fluid circulation inside the drop. We find that the circulation velocity is about 2 mm/s and nearly half the speed of the metachronal wave. We develop a quasi-two-dimensional hydrodynamics model using the Stokes flow approximation. The periodic motion of the nematodes constitute our moving boundary condition that drives the flow. Our model suggests that large-amplitude excursions of the nematode tails produce the fluid circulation. We discuss the constraints on containers that would enhance fluid motion, which could be used in the future design of on demand flow generating systems.

The redundancy principle provides a framework to study how rare events are made possible with probability 1 in accelerated time, by making many copies of similar random searchers. However, what is a large $n$? To estimate large $n$ with respect to the geometrical properties of a domain and the dynamics, we present here a criterion based on splitting probabilities between a small fraction of the exploration space associated with an activation process and other absorbing regions where trajectories can be terminated. We obtain explicit computations especially when there is a killing region located inside the domain that we compare with stochastic simulations. We also present examples of extreme trajectories with killing in dimension 2. For a large $n$, the optimal trajectories avoid penetrating inside the killing region. Finally, we discuss some applications to cell biology.

A dimer on a periodic potential is a simple system that exhibits a surprisingly rich dynamics. This system is conservative, but it is nonlinear and nonintegrable. In a previous work, we evidenced the autoparametric excitation of the relative motion by the center of mass in two limiting cases (very small or very large initial energy, compared to the external potential depth). We extend these results for arbitrary initial energy. The relevant control parameters are the dimer initial energy and the stiffness of the link between the two particles. In this parameter plane, we build a behavior map which classifies the available dynamical regimes of the dimer. The parameters plane can be separated into domains in which the dimer particles are either trapped in adjacent potential wells, slide along the potential, or exhibit more complex motions in which the particles jumps to farthest well or in which the center-of-mass motion is neither monotonous nor periodic. We discuss the thresholds between these domains.

Urn models are classic stochastic models that have been used to describe a diverse kind of complex systems. Voter and Ehrenfest's models are very well-known urn models. An opinion model that combines these two models is presented in this work and it is used to study a noisy voter model. In particular, at each temporal step, an Ehrenfest's model step is done with probability $\alpha$ or a voter step is done with probability $1-\alpha$. The parameter $\alpha$ plays the role of noise. By performing a spectral analysis, it is possible to obtain explicit expressions for the order parameter, susceptibility, and Binder's fourth-order cumulant. Recursive expressions in terms of the dual Hahn polynomials are given for first passage and return distributions to consensus and the equal coexistence of opinions. In the cases where they follow power-law distributions, their exponents are computed. This model has a pseudocritical noise value that depends on the system size; a discussion about thermodynamic limits is given.

The Ising model is of prime importance in the field of statistical mechanics. Here we show that Ising-type interactions can be realized in periodically driven circuits of stochastic binary resistors with memory. A key feature of our realization is the simultaneous coexistence of ferromagnetic and antiferromagnetic interactions between two neighboring spins—an extraordinary property not available in nature. We demonstrate that the statistics of circuit states may perfectly match the ones found in the Ising model with ferromagnetic or antiferromagnetic interactions, and, importantly, the corresponding Ising model parameters can be extracted from the probabilities of circuit states. Using this finding, the Ising Hamiltonian is reconstructed in several model cases, and it is shown that different types of interaction can be realized in circuits of stochastic memristors.

Scaling methods are fundamental in all branches of physics. In stochastic process, we usually try to describe the long time behavior of a given time correlation function. In this work we investigate a scaling method for anomalous diffusion in systems with memory that produces good results for long and intermediate times. We will initially present a generalization of the diffusion exponent. Then, we present an asymptotic method to obtain an analytical expression for the diffusion coefficient by introducing a time scale factor $\lambda \left(t\right)$. We found an exact expression for the function $\lambda \left(t\right)$, which allows us to describe the diffusive process. For large times, $\lambda \left(t\right)$ becomes a universal parameter determined by the diffusion exponent. In turn, the analytical results are then compared to the numerical results, with a good matching. Then, we'll show the practical effects of scaling. An important first result is that $\lambda \left(t\right)$ quickly converges to a constant. Another very important point was the classification of new forms of diffusion due to the generalized exponent. In previous works, we verified the existence of ergodic ballistic diffusion with diffusion exponent $\alpha =2^{-}$. Here, we verify the existence of the nonergodic ballistic diffusion type with the obtainment of the diffusion coefficient $\alpha =2$. Finally, we show that the scaling works. This method is general and can be applied to various types of stochastic problems.

Several lattice models display a condensation transition in real space when the density of a suitable order parameter exceeds a critical value. We consider one of such models with two conservation laws, in a onedimensional open setup where the system is attached to two external reservoirs. Both reservoirs impose subcritical boundary conditions at the chain ends. When such boundary conditions are equal, the system is in equilibrium below the condensation threshold and no condensate can appear. Instead, when the system is kept out of equilibrium, localization may arise in an internal portion of the lattice. We discuss the origin of this phenomenon, the relevance of the number of conservation laws, and the effect of the pinning of the condensate on the dynamics of the out-of-equilibrium state.

This paper numerically investigates the propagation of Laguerre-Gaussian vortex beams launched in nonlocal nonlinear media, such as lead glass. Our results show that the propagation properties depend on the selection of beam parameters $m$ and $p$, which represent the azimuthal and radial mode numbers. When $p=0$, these profiles can be stable solitons for $m\le 2$, or break up and then form a set of single-hump profiles for $m\ge 3$, which are unbounded states with scattered remnants of the energy. However, for $p\ge 1$, the broken beams can evolve into vortex chaoticons, which exhibit both chaotic and solitonlike properties. The chaotic properties are determined by the positive Lyapunov exponents and spatial decoherence, while the solitonlike properties are demonstrated by the invariance of beam width and the interaction of beams in the form of quasielastic collisions. In addition, the power and orbital angular momentum of unbounded beam states both decay in propagation, while those of the chaoticons maintain their values well.

The statistical properties of wave chaotic systems of varying dimensionalities and realizations have been studied extensively. These systems are commonly characterized by the statistics of the eigenmode spacings and the statistics of the eigenfunctions. Here, we propose photonic crystal (PC) defect waveguide graphs as a physical setting for chaotic graph studies. Photonic crystal waveguides possess a dispersion relation for the propagating modes, which is engineerable. Graphs constructed by joining these waveguides possess junctions and bends with distinct scattering properties. We present numerically determined statistical properties of an ensemble of such PC graphs including both eigenfunction amplitude and eigenmode-spacing studies. Our proposed system is compatible with silicon nanophotonic technology and opens chaotic graph studies to a new community of researchers.

The production process of integrated electronic circuitry inherently leads to large heterogeneities on the component level. For electronic clock networks this implies detuned intrinsic frequencies and differences in coupling strength and the characteristic time delays associated with signal transmission, processing, and feedback. Using a phase-model description, we study the effects of such component heterogeneity on the dynamical properties of synchronization in networks of mutually delay-coupled Kuramoto oscillators. We test the theory against experimental results and circuit-level simulations in a prototype system of mutually delay-coupled electronic clocks, so-called phase-locked loops. Interestingly, our results show that heterogeneity in the system can actually enhance the stability of synchronized states. That means that beyond the optimizations that can be achieved by tuning homogeneous coupling strengths, time delays, and loop-filter cut-off frequencies, heterogeneities in these system parameters enable much better optimization of perturbation decay rates, stabilization of synchronous states, and tuning of phase differences between the clocks. Our theory enables the design of custom-fit synchronization layers according to the specific requirements and properties of electronic systems, such as operational frequencies, phase relations, and, e.g., transmission delays. These results are not restricted to electronic systems, because signal transmission, processing, and feedback delays are common to networks of spatially distributed and coupled autonomous oscillators.

Groups of eukaryotic cells can coordinate their crawling motion to follow cues more effectively, stay together, or invade new areas. This collective cell migration depends on cell-cell interactions, which are often studied by colliding pairs of cells together. Can the outcome of these collisions be predicted? Recent experiments on trains of colliding epithelial cells suggest that cells with a smaller contact angle to the surface or larger speeds are more likely to maintain their direction (“win”) upon collision. When should we expect shape or speed to correlate with the outcome of a collision? To investigate this question, we build a model for two-cell collisions within the phase field framework, which allows for cell shape changes. We can reproduce the observation that cells with high speed and small contact angles are more likely to win with two different assumptions for how cells interact: (1) velocity aligning, in which we hypothesize that cells sense their own velocity and align to it over a finite timescale, and (2) front-front contact repolarization, where cells polarize away from cell-cell contact, akin to contact inhibition of locomotion. Surprisingly, though we simulate collisions between cells with widely varying properties, in each case, the probability of a cell winning is completely captured by a single summary variable: its relative speed (in the velocity-aligning model) or its relative contact angle (in the contact repolarization model). Both models are currently consistent with reported experimental results, but they can be distinguished by varying cell contact angle and speed through orthogonal perturbations.

The rheology of noncolloidal suspensions under cyclic shear is studied numerically. The main findings are a strain amplitude (${\gamma }_0$) dependent response in the shear stress and second normal stress difference ($N_2$). Specifically, we find a reduced viscosity, an enhanced intracycle shear thinning, the onset of a finite $N_2$, and its frequency doubling, all near a critical strain amplitude ${\gamma }_c$ that scales with the volume fraction $\varphi$ as ${\gamma }_c\sim {\varphi }^{-2}$. These rheological changes also signify a reversible-irreversible transition (RIT), dividing stroboscopic particle dynamics into a reversible absorbing phase (for ${\gamma }_0<{\gamma }_c$) and a persistently diffusing phase (for ${\gamma }_0>{\gamma }_c$). We explain the results based on two flow-induced mechanisms and elucidate their connection in the context of RIT through the underlying microstructure, which tends toward hyperuniformity near ${\gamma }_0={\gamma }_c$. Overall, we expect this correspondence between rheology and emergent dynamics to hold in a wide range of settings where structural organizations are dominated by volume exclusions.

We propose to use a correlated noise bath to drive an optically trapped Brownian particle that mimics active biological matter. Due to the flexibility and precision of our setup, we are able to control the different parameters that drive the stochastic motion of the particle with unprecedented accuracy, thus reaching strongly correlated regimes that are not easily accessible with real active matter. In particular, by using the correlation time (i.e., the “color”) of the noise as a control parameter, we can trigger transitions between two nonequilibrium steady states with no expended work, but only a calorific cost. Remarkably, the measured heat production is directly proportional to the spectral entropy of the correlated noise, in a fashion that is reminiscent of Landauer's principle. Our procedure can be viewed as a method for harvesting information from the active fluctuations.

The proton-boron-11 (p-B11) fusion reaction is much harder to harness for commercial power than the easiest fusion reaction, namely, the deuterium and tritium (DT) reaction. The p-B11 reaction requires much higher temperatures, and, even at those higher temperatures, the cross section is much smaller. However, as opposed to tritium, the reactants are both abundant and nonradioactive. It is also an aneutronic reaction, thus avoiding radioactivity-inducing neutrons. Economical fusion can only result, however, if the plasma is nearly ignited; in other words if the fusion power is at least nearly equal to the power lost due to radiation and thermal conduction. Because the required temperatures are so high, ignition is thought barely possible for p-B11, with fusion power exceeding the bremsstrahlung power by only around 3%. We show that there is a high upside to changing the natural flow of power in the reactor, putting more power into protons, and less into the electrons. This redirection can be done using waves, which tap the alpha particle power and redirect it into protons through alpha channeling. Using a simple power balance model, we show that such channeling could reduce the required energy confinement time for ignition by a factor of 2.6 when energy is channeled into thermal protons, and a factor of 6.9 when channeled into fast protons near the peak of the reactivity. Thus, alpha channeling could dramatically improve the feasibility of economical p-B11 fusion energy.

We study synchronization in networks of delay-coupled electronic oscillators, so-called phase-locked loops (PLLs). Using a phase-model description, we study the collective dynamics of mutually coupled PLLs and report the phenomenon of heterogeneity-induced synchronization. This phenomenon refers to the observation that heterogeneity in the system's parameters can induce synchronization by stabilizing the states which are unstable without such heterogeneity. In systems where component heterogeneity can be tuned and controlled, we show how the complex collective self-organized dynamics can be guided towards synchronized states with specific operational frequencies and phase relations. This is of importance for the technical applicability of self-organized dynamics. In electrical engineering, for example, where components can be strongly heterogeneous, our theoretical framework can inform the design process for networks of spatially distributed PLLs. The results presented here are also useful in understanding the collective dynamics in ensembles of phase oscillators with time-delayed interactions, inertia, and heterogeneity.

We experimentally investigate the velocity distributions of quasi-two-dimensional granular materials uniformly heated by an electromagnetic vibrator, where the translational velocity and the rotation of a single particle are Gaussian and independent. We observe the non-Gaussian distributions of particle velocity, with the density-independent high-energy tails characterized by an exponent of $\beta =1.50\pm 0.03$ for volume fractions of $0.111\le \varphi \le 0.832$, covering a wide range of structures and dynamics. Surprisingly, our results are not only in excellent agreement with the prediction of the kinetic theories of granular gas but also hold for an extremely high-volume fraction of $\varphi =0.832$ where the granular material forms a crystalline solid and the kinetic theory of granular gas fails fantastically. Our experiment suggests that the density-independent high-energy velocity tails of $\beta =1.50$ are a characteristic of uniformly heated granular matter.