The evolution of self-gravitating systems, and long-range interacting systems more generally, from initial configurations far from dynamical equilibrium is often described as a simple two-phase process: a first phase of violent relaxation bringing it to a quasistationary state in a few dynamical times, followed by a slow adiabatic evolution driven by collisional processes. In this context the complex spatial structure evident, for example, in spiral galaxies is understood either in terms of instabilities of quasistationary states or as a result of dissipative nongravitational interactions. We illustrate here, using numerical simulations, that purely self-gravitating systems evolving from quite simple initial configurations can in fact give rise easily to structures of this kind, of which the lifetime can be large compared to the dynamical characteristic time but short compared to the collisional relaxation timescale. More specifically, for a broad range of nonspherical and nonuniform rotating initial conditions, gravitational relaxation gives rise quite generically to long-lived nonstationary structures of a rich variety, characterized by spiral-like arms, bars, and even ringlike structures in special cases. These structures are a feature of the intrinsically out-of-equilibrium nature of the system's collapse, associated with a part of the system's mass while the bulk is well virialized. They are characterized by predominantly radial motions in their outermost parts, but also incorporate an extended flattened region which rotates coherently about a well-virialized core of triaxial shape with an approximately isotropic velocity dispersion. We characterize the kinematical and dynamical properties of these complex velocity fields and we briefly discuss the possible relevance of these simple toy models to the observed structure of real galaxies, emphasizing the difference between dissipative and dissipationless disk formation.

It is well known that resonance phenomena can destroy adiabatic invariance and cause chaos and mixing. In the present Rapid Communication, we show that a nonlinear wave-particle resonant interaction may do the opposite—generate large-scale coherent structures in phase space. The combined action of the drift due to nonlinear scattering on resonance and trapping (capture) into resonance creates a convection cell-like structure, where the areas of particle acceleration and deceleration are macroscopically separated. At the same time, nonlinear scattering also creates a diffusion that cause mixing on and between the energy levels.

We use a three-component replicator system with healthy cells, sensitive cells, and resistant cells, with a prisoner's dilemma payoff matrix from evolutionary game theory, to model and control the nonlinear dynamical system governing the ecological mechanism of competitive release by which tumors develop chemotherapeutic resistance. The control method we describe is based on nonlinear trajectory design and energy transfer methods first introduced in the orbital mechanics literature for Hamiltonian systems. For continuous therapy, the basin boundaries of attraction associated with the chemo-sensitive population and the chemo-resistant population for increasing values of chemo-concentrations have an intertwined spiral structure with extreme sensitivity to changes in chemo-concentration level as well as sensitivity with respect to resistant mutations. For time-dependent therapies, we introduce an orbit transfer method to construct continuous families of periodic (closed) orbits by switching the chemo-dose at carefully chosen times and appropriate levels to design schedules that are superior to both maximum tolerated dose (MTD) schedules and low-dose metronomic (LDM) schedules, both of which ultimately lead to fixation of sensitive cells or resistant cells. By keeping the three subpopulations of cells in competition with each other indefinitely, we avoid fixation of the cancer cell population and regrowth of a resistant tumor. The method can be viewed as a way to dynamically shape the average population fitness landscape of a tumor to steer the chemotherapeutic response curve. We show that the method is remarkably insensitive to initial conditions and small changes in chemo-dosages, an important criterion for turning the method into an actionable strategy.

We study simple stochastic scenarios, based on birth-and-death Markovian processes, that describe populations with the Allee effect, to account for the role of demographic stochasticity. In the mean-field deterministic limit we recover well-known deterministic evolution equations widely employed in population ecology. The mean time to extinction is in general obtained by the Wentzel-Kramers-Brillouin (WKB) approximation for populations with the strong and weak Allee effects. An exact solution for the mean time to extinction can be found via a recursive equation for special cases of the stochastic dynamics. We study the conditions for the validity of the WKB solution and analyze the boundary between the weak and strong Allee effect by comparing exact solutions with numerical simulations.

The spread of an infectious disease can be promoted by previous infections with other pathogens. This cooperative effect can give rise to violent outbreaks, reflecting the presence of an abrupt epidemic transition. As for other diffusive dynamics, the topology of the interaction pattern of the host population plays a crucial role. It was conjectured that a discontinuous transition arises when there are relatively few short loops and many long loops in the contact network. Here we focus on the role of local clustering in determining the nature of the transition. We consider two mutually cooperative pathogens diffusing in the same population: An individual already infected with one disease has an increased probability of getting infected by the other. We look at how a disease obeying the susceptible-infected-removed dynamics spreads on contact networks with tunable clustering. Using numerical simulations we show that for large cooperativity the epidemic transition is always abrupt, with the discontinuity decreasing as clustering is increased. For large clustering strong finite-size effects are present and the discontinuous nature of the transition is manifest only in large networks. We also investigate the problem of influential spreaders for cooperative infections, revealing that both cooperativity and clustering strongly enhance the dependence of the spreading influence on the degree of the initial seed.

We present a simultaneous study of the phase properties of rational breather waves generated in a water wave tank and in an optical fiber platform, namely, the Peregrine soliton and related second-order solution. Our analysis of experimental wave measurements makes use of standard demodulation and filtering techniques in hydrodynamics and more complex phase retrieval techniques in optics to quantitatively confirm analytical and numerical predictions. We clearly highlight a characteristic phase shift that is a multiple of $\pi$ between the central pulsed part and the continuous background of rational breathers at their maximum compression. Moreover, we reveal a large longitudinal phase shift across the point of maximum compression.

We present a model and protocol that enable the generation of extremely stable computer glasses at minimal computational cost. The protocol consists of an instantaneous quench in an augmented potential energy landscape, with particle radii as additional degrees of freedom. We demonstrate how our glasses' mechanical stability, which is readily tunable in our approach, is reflected in both microscopic and macroscopic observables. Our observations indicate that the stability of our computer glasses is at least comparable to that of computer glasses generated by the celebrated Swap Monte Carlo algorithm. Strikingly, some key properties support even qualitatively enhanced stability in our scheme: the density of quasilocalized excitations displays a gap in our most stable computer glasses, whose magnitude scales with the polydispersity of the particles. We explain this observation, which is consistent with the lack of plasticity we observe at small stress. It also suggests that these glasses are depleted from two-level systems, similarly to experimental vapor-deposited ultrastable glasses.

We have developed an experimental platform to generate radiatively heated solid density samples for warm dense matter studies at the OMEGA laser facility. Cylindrical samples of boron and beryllium are isochorically heated by K- and L-shell emission from x-ray converter foils wrapped around the cylinders' radii. X-ray Thomson scattering (XRTS) measures the temperature and the ionization state of the samples as function of time. Temperatures approach 10 eV, and the ionization states are found to be $Z_{\text{B}}=3$ and $Z_{\text{Be}}=2$. Radiation hydrodynamics simulations were performed to confirm a homogeneous plasma state exists in the center of the sample for the duration of the experiment. Results from the study can be extended to improve understanding of radiative heating processes in the warm dense matter regime.

Industrial as well as natural aggregation of fine particles is believed to be associated with electrostatics. Yet like charges repel, so it is unclear how similarly treated particles aggregate. To resolve this apparent contradiction, we analyze conditions necessary to hold aggregates together with electrostatic forces. We find that aggregates of particles charged with the same sign can be held together due to dielectric polarization, we evaluate the effect of aggregate size, and we briefly summarize consequences for practical aggregation.

Density gradient theory has become an important tool for calculating the surface tension of pure components as well as mixtures. The calculation requires knowledge about the so-called influence parameter. Since in most applications this parameter is obtained by fitting results of the density gradient theory to experimental data for surface tensions, the approach lacks predictive power. We propose a predictive density gradient theory based on nonlocal density functional theory (DFT) using the perturbed chain polar statistical associating fluid theory (PCP-SAFT) as equation of state. The formalism can also be applied to other Helmholtz energy functionals based on weighted densities. The predictive density gradient theory (pDGT) is obtained by applying a gradient expansion to the weighted densities of the PCP-SAFT Helmholtz energy functional to second order and expanding the Helmholtz energy density to first order. The resulting model approximates the DFT and can be cast into the form of a density gradient theory. The resulting influence parameter depends on local densities and on temperature. We assess the predictive power of the proposed pDGT to calculate surface tensions of vapor-liquid interfaces of pure components as well as mixtures. The results show that pDGT reduces the computational complexity compared with nonlocal DFT calculations, while largely preserving its accuracy as well as its predictive capability.

In this work we study pedestrian-pedestrian interactions from observational experimental data in diluted pedestrian crowds. While in motion, pedestrians continuously adapt their walking paths trying to preserve mutual comfort distances and to avoid collisions. Leveraging on a high-quality, high-statistics data set, composed of several few millions real-life trajectories acquired from state-of-the-art observational experiments (about 6 months of high-resolution pedestrian tracks acquired in a train station), we develop a quantitative model capable of addressing interactions in the case of binary collision avoidance. We model interactions in terms of both long-range (sight based) and short-range (hard-contact avoidance) forces, which we superimpose on our Langevin model for noninteracting pedestrian motion [Corbetta et al., Phys. Rev. E 95, 032316 (2017)] (here further tested and extended). The model that we propose here features a Langevin dynamics with fast random velocity fluctuations that are superimposed on the slow dynamics of a hidden model variable: the intended walking path. In the case of interactions, social forces may act both on the intended path and on the actual walked path. The model is capable of reproducing quantitatively relevant statistics of the collision avoidance motion, such as the statistics of the side displacement and of the passing speed. Rare occurrences of actual bumping events are also recovered. Furthermore, comparing with large data sets of real-life tracks involves an additional computational challenge so far neglected: identifying automatically, within a database containing very heterogeneous conditions, only the relevant events corresponding to binary avoidance interactions. In order to tackle this challenge, we propose a general approach based on a graph representation of pedestrian trajectories, which allows us to effectively operate complexity reduction for efficient data classification and selection.

In this paper, we present a pedestrian single-file movement experiment that directly captures the characteristics of the interacting pedestrians’ continuous stepping behaviors. We find that the relationship between step length (duration) and spatial headway exhibits piecewise linear behavior: It first increases linearly as the headway increases and then remains constant when the headway exceeds 1.20 m (0.71 m). Three different regimes are observed and defined on the basis of their relationships. The continuous small-step phenomena are found in a strongly constrained regime. We reveal that the relationship between the step duration and the step velocity is nonmonotonous and that the longest duration is seen at a velocity of 1.35 m/s, whereas the relationship between the step length and the step velocity is monotonous and can be well represented by a quartic function. Furthermore, we show that the dependency of the ratio between head displacement and foot displacement in a step on the headway is a piecewise linear relationship. We were interested to find that the ratio is less (greater) than 0.5 when the headway is less (greater) than 1 m. This finding reveals the backward- (forward-) deviating phenomena of the body and can be used to indirectly interpret the differences in some of the results of this paper and previous studies. Finally, we show that step synchronization (asynchronization) is most likely to occur at a headway of 0.76 m (0.51 m). These interesting findings greatly deepen our understanding of basic human stepping behavior.

A solvable model is proposed and analyzed to reveal the mechanism underlying the diffusion enhancement recently reported for a model of molecular motors and predicted to be observed in the biological rotary motor ${\mathrm{F}}_1$-ATPase. It turns out that the diffusion enhancement for the present model can approximately be described by a random walk in which the waiting time for a step to occur is exponentially distributed and it takes nonzero time to proceed forward by the step. It is shown that the diffusion coefficient of such a random walk can significantly be increased when the average waiting time is comparable to the average stepping time.

The embryos of the green alga Volvox carteri are spherical sheets of cells that turn themselves inside out at the close of their development through a program of cell shape changes. This process of inversion is a model for morphogenetic cell sheet deformations; it starts with four lips opening up at the anterior pole of the cell sheet, flipping over, and peeling back to invert the embryo. Experimental studies have revealed that inversion is arrested if some of these cell shape changes are inhibited, but the mechanical basis for these observations has remained unclear. Here, we analyze the mechanics of this inversion by deriving an averaged elastic theory for these lips and we interpret the experimental observations in terms of the mechanics and evolution of inversion.

The combination of bistability and cooperativity plays a crucial role in several biological and artificial micro- and nanosystems. In particular, the exhaustive understanding of the mechanical response of such systems under the effect of thermal fluctuations is essential to elucidate a rich variety of phenomena. Here a linear chain composed of elastic units, which are bistable (folded or unfolded) and coupled through an Ising-like interaction, is selected as a case study. We assess the macroscopic thermoelastic response of this chain in terms of its microscopic description. For small systems, far from the thermodynamic limit, this response depends on the applied isometric or isotensional boundary conditions, which correspond to the Helmholtz or Gibbs ensembles of the statistical mechanics, respectively. The theoretical analysis is conducted through the spin variables approach, based on a set of discrete quantities able to identify the folded or unfolded state of the chain units. Eventually, this technique yields closed-form expressions for the force-extension curves and the average number of unfolded units, as function of the applied fields. In addition, it allows to unveil a critical behavior of such systems, characterizing the operating regions with negative differential stiffness (spinoidal phase).

The emergence of a predominant phenotype within a cell population is often triggered by the chance accumulation of a sequence of rare genomic DNA mutations within a single cell. For example, tumors may be initiated by a single cell in which multiple mutations cooperate to bypass their natural defense mechanism. The risk of such an event is thus determined by the extremal accumulation of mutations across tissue cells. To address this risk, here we study the statistics of the maximum mutation numbers in a generic, but tested, model of a renewing cell population. By drawing an analogy between the genealogy of a cell population and the theory of branching random walks, we obtain analytical estimates for the probability of exceeding a threshold number of mutations to trigger a proliferative advantage of a cell over its neighbors, and we determine how the statistical distribution of maximum mutation numbers scales with age and cell population size.

The presence of a delay between sensing and reacting to a signal can determine the long-term behavior of autonomous agents whose motion is intrinsically noisy. In a previous work [Mijalkov, McDaniel, Wehr, and Volpe, Phys. Rev. X 6, 011008 (2016)], we have shown that sensorial delay can alter the drift and the position probability distribution of an autonomous agent whose speed depends on the illumination intensity it measures. In this work, we consider an agent whose speed and rotational diffusion both depend on the illumination intensity and are subject to two independent sensorial delays. Using theory, simulations, and experiments with a phototactic robot, we study the dependence of the drift and of the probability distribution of the robot's position on the sensorial delays. In particular, the radial drift may have a positive as well as negative sign, and the position probability density peaks in different regions, depending on the choice of the model's parameters. This not only generalizes previous work but also explores new phenomena resulting from the interaction between the two delay variables.

Universality, where microscopic details become irrelevant, takes place in thermodynamic phase transitions. The universality is captured by a singular scaling function of the thermodynamic variables, where the scaling exponents are determined by symmetries and dimensionality only. Universality can persist even for nonequilibrium phase transitions. It implies that a hydrodynamic approach can capture the singular universal scaling function, even far from equilibrium. In particular, we show these results for phase transitions in the large deviation function of the current in diffusive systems with particle-hole symmetry. For such systems, we find the scaling exponents of the universal function and show they are independent of microscopic details as well as boundary conditions.

We formulate, using the discrete nonlinear Schrödinger equation (DNLS), a general approach to encode and process information based on reservoir computing. Reservoir computing is a promising avenue for realizing neuromorphic computing devices. In such computing systems, training is performed only at the output level by adjusting the output from the reservoir with respect to a target signal. In our formulation, the reservoir can be an arbitrary physical system, driven out of thermal equilibrium by an external driving. The DNLS is a general oscillator model with broad application in physics, and we argue that our approach is completely general and does not depend on the physical realization of the reservoir. The driving, which encodes the object to be recognized, acts as a thermodynamic force, one for each node in the reservoir. Currents associated with these thermodynamic forces in turn encode the output signal from the reservoir. As an example, we consider numerically the problem of supervised learning for pattern recognition, using as a reservoir a network of nonlinear oscillators.

We show that a combined action of noise and delayed feedback on an excitable theta-neuron leads to rather coherent stochastic bursting. An idealized point process, valid if the characteristic timescales in the problem are well separated, is used to describe statistical properties such as the power spectral density and the interspike interval distribution. We show how the main parameters of the point process, the spontaneous excitation rate, and the probability to induce a spike during the delay action can be calculated from the solutions of a stationary and a forced Fokker-Planck equation.