We study collections of self-propelled rods (SPR) moving in two dimensions for packing fractions less than or equal to 0.3. We find that in the thermodynamical limit the SPR undergo a phase transition between a disordered gas and a novel phase-separated system state. Interestingly, (global) orientational order patterns—contrary to what has been suggested—vanish in this limit. In the found novel state, the SPR self-organize into a highly dynamical, high-density, compact region—which we call aggregate—which is surrounded by a disordered gas. Active stresses build inside aggregates as a result of the combined effect of local orientational order and active forces. This leads to the most distinctive feature of these aggregates: constant ejection of polar clusters of SPR. This novel phase-separated state represents a novel state of matter characterized by large fluctuations in volume and shape, related to mass ejection, and exhibits positional as well as orientational local order. SPR systems display new physics unseen in other active matter systems.

We investigate segregation phenomena of particles driven in opposite directions with Brownian dynamics simulations. The particles interact via a repulsive potential and are confined in three-dimensional hard-walled pipes with quadratic cross sections. In a systematic finite-size study, the pipe length is varied. Ordering on finite length scales can be observed, but global segregation seems to vanish for infinite channel length, as it was recently found for lane formation in two dimensions. As an additional effect of the finite hard-walled boundary conditions, interface vibrations and longitudinal demixing are found.

According to classical grain growth laws, grain growth is driven by the minimization of surface energy and will continue until a single grain prevails. These laws do not take into account the lattice anisotropy and the details of the microscopic rearrangement of mass between grains. Here we consider coarsening of body-centered-cubic polycrystalline materials in three dimensions using the phase field crystal model. We observe, as a function of the quenching depth, a crossover between a state where grain rotation halts and the growth stagnates and a state where grains coarsen rapidly by coalescence through rotation and alignment of the lattices of neighboring grains. We show that the grain rotation per volume change of a grain follows a power law with an exponent of $-1.25$. The scaling exponent is consistent with theoretical considerations based on the conservation of dislocations.

The three-compartmental demographic model by Korotaeyv-Malkov-Khaltourina, connecting population size, economic surplus, and education level, is considered from the point of view of dynamical systems theory. It is shown that there exist two integrals of motion, which enables the system to be reduced to one nonlinear ordinary differential equation. The study of its structure provides analytical criteria for the dominance ranges of the dynamics of Malthus and Kremer. Additionally, the particular ranges of parameters enable the derived general ordinary differential equations to be reduced to the models of Gompertz and Thoularis-Wallace.

The Luria-Delbrück experiment is a cornerstone of evolutionary theory, demonstrating the randomness of mutations before selection. The distribution of the number of mutants in this experiment has been the subject of intense investigation during the past 70 years. Despite this considerable effort, most of the results have been obtained under the assumption of constant growth rate, which is far from the experimental condition. We derive here the properties of this distribution for arbitrary growth function for both the deterministic and stochastic growth of the mutants. The derivation we propose uses the number of wild-type bacteria as the independent variable instead of time. The derivation is surprisingly simple and versatile, allowing many generalizations to be taken easily into account.

We consider paths in weighted and directed temporal networks, introducing tools to compute sets of paths of high probability. We quantify the relative importance of the most probable path between two nodes with respect to the whole set of paths and to a subset of highly probable paths that incorporate most of the connection probability. These concepts are used to provide alternative definitions of betweenness centrality. We apply our formalism to a transport network describing surface flow in the Mediterranean sea. Despite the full transport dynamics is described by a very large number of paths we find that, for realistic time scales, only a very small subset of high probability paths (or even a single most probable one) is enough to characterize global connectivity properties of the network.

Inspired by the fact that people have diverse propensities to punish wrongdoers, we study a spatial public goods game with defectors and different types of punishing cooperators. During the game, cooperators punish defectors with class-specific probabilities and subsequently share the associated costs of sanctioning. We show that in the presence of different punishing cooperators the highest level of public cooperation is always attainable through a selection mechanism. Interestingly, the selection does not necessarily favor the evolution of punishers who would be able to prevail on their own against the defectors, nor does it always hinder the evolution of punishers who would be unable to prevail on their own. Instead, the evolutionary success of punishing strategies depends sensitively on their invasion velocities, which in turn reveals fascinating examples of both competition and cooperation among them. Furthermore, we show that under favorable conditions, when punishment is not strictly necessary for the maintenance of public cooperation, the less aggressive, mild form of sanctioning is the sole victor of the selection process. Our work reveals that natural strategy selection cannot only promote, but sometimes also hinders competition among prosocial strategies.

A key ingredient in social contagion dynamics is reinforcement, as adopting a certain social behavior requires verification of its credibility and legitimacy. Memory of nonredundant information plays an important role in reinforcement, which so far has eluded theoretical analysis. We first propose a general social contagion model with reinforcement derived from nonredundant information memory. Then, we develop a unified edge-based compartmental theory to analyze this model, and a remarkable agreement with numerics is obtained on some specific models. We use a spreading threshold model as a specific example to understand the memory effect, in which each individual adopts a social behavior only when the cumulative pieces of information that the individual received from his or her neighbors exceeds an adoption threshold. Through analysis and numerical simulations, we find that the memory characteristic markedly affects the dynamics as quantified by the final adoption size. Strikingly, we uncover a transition phenomenon in which the dependence of the final adoption size on some key parameters, such as the transmission probability, can change from being discontinuous to being continuous. The transition can be triggered by proper parameters and structural perturbations to the system, such as decreasing individuals' adoption threshold, increasing initial seed size, or enhancing the network heterogeneity.

Previous studies of quantum chaotic scattering established a connection between classical dynamics and quantum transport properties: Integrable or mixed classical dynamics can lead to sharp conductance fluctuations but chaos is capable of smoothing out the conductance variations. Relativistic quantum transport through single-layer graphene systems, for which the quasiparticles are massless Dirac fermions, exhibits, due to scarring, this classical-quantum correspondence, but sharp conductance fluctuations persist to a certain extent even when the classical system is fully chaotic. There is an open issue regarding the effect of finite mass on relativistic quantum transport. To address this issue, we study quantum transport in chaotic bilayer graphene quantum dots for which the quasiparticles have a finite mass. An interesting phenomenon is that, when traveling along the classical ballistic orbit, the quasiparticle tends to hop back and forth between the two layers, exhibiting a Zitterbewegung-like effect. We find signatures of abrupt conductance variations, indicating that the mass has little effect on relativistic quantum transport. In solid-state electronic devices based on Dirac materials, sharp conductance fluctuations are thus expected, regardless of whether the quasiparticle is massless or massive and whether there is chaos in the classical limit.

Viscous fingering formation in flat Hele-Shaw cells is a classical and widely studied fluid mechanical problem. We examine the development of viscous fluid fingering on a two-dimensional surface of constant negative Gaussian curvature, the hyperbolic plane $H^2$. A perturbative mode-coupling formalism is applied to study the influence of the negative surface curvature on the two most important pattern formation mechanisms of the system: fingertip splitting and finger competition. We also report on a time-dependent control strategy placed on the injection rate, which is able to minimize viscous fingering growth on $H^2$.

Thermocapillary (Marangoni) convection in a thin film on a plate oscillating with a frequency ranging from ultralow to high is considered. By adjusting the vibration amplitude, the impact of the vibration is kept non-negligible. Using the long-wave approximation framework, the amplitude equations are derived for each frequency interval, and linear and weakly nonlinear stability analyses are performed, supplemented by computations where necessary. In the case of a high vibration frequency, the surface tension effectively increases due to vibration, but the film still ruptures. When the frequency is ultralow, the vibration provides gravity modulation, and the surface deformation emerges subcritically, grows fast, and then decays, all during less than half of the vibration period. In the intermediate regime, the vibration either results in a short-wavelength instability or it does not affect the Marangoni convection.

We use one- and two-dimensional particle-in-cell simulations to demonstrate that the propagation of an ultraintense laser $(I={10}^{19}\text{W}/{\mathrm{cm}}^2)$ in critical density plasma can be interfered with by a high density plasma wall region generated at the propagation front. When the electron flow speed of the wall region exceeds a certain relativistic threshold, the region behaves as an overdense plasma due to a decrease of the effective critical density. The region forms then very small overdense plasma islands. The islands impede the propagation intermittently and slow down the propagation speed significantly.

A modified phase-field-crystal (PFC) model is proposed to describe solid-liquid phase transitions by reconstructing the correlation function. The effects of fitting parameters of our modified PFC model on the bcc-liquid phase diagram, numerical stability, and solid-liquid interface properties during planar interface growth are examined carefully. The results indicate that the increase of the correlation function peak width at $k=k_m$ will enhance the stability of the ordered phase, while the increase of peak height at $k=0$ will narrow the two-phase coexistence region. The third-order term in the free-energy function and the short wave-length of the correlation function have significant influences on the numerical stability of the PFC model. During planar interface growth, the increase of peak width at $k=k_m$ will decrease the interface width and the velocity coefficient $C$, but increase the anisotropy of $C$ and the interface free energy. Finally, the feasibility of the modified phase-field-crystal model is demonstrated with a numerical example of three-dimensional dendritic growth of a body-centered-cubic structure.

We use our quantum Gibbs ensemble Monte Carlo algorithm to perform computer experiments for the two-phase coexistence of a hydrogen-helium mixture. Our results are in quantitative agreement with the experimental results of Sneed, Streett, Sonntag, and Van Wylen. The difference between our results and the experimental ones is in all cases less than 15% relative to the experiment, reducing to less than 5% in the low helium concentration phase. At the gravitational inversion between the vapor and the liquid phase, at low temperatures and high pressures, the quantum effects become relevant. At extremely low temperature and pressure, the first component to show superfluidity is the helium in the vapor phase.

A discrete-time random process is described, which can generate bursty sequences of events. A Bernoulli process, where the probability of an event occurring at time $t$ is given by a fixed probability $x$, is modified to include a memory effect where the event probability is increased proportionally to the number of events that occurred within a given amount of time preceding $t$. For small values of $x$ the interevent time distribution follows a power law with exponent $-2-x$. We consider a dynamic network where each node forms, and breaks connections according to this process. The value of $x$ for each node depends on the fitness distribution, $\rho \left(x\right)$, from which it is drawn; we find exact solutions for the expectation of the degree distribution for a variety of possible fitness distributions, and for both cases where the memory effect either is, or is not present. This work can potentially lead to methods to uncover hidden fitness distributions from fast changing, temporal network data, such as online social communications and fMRI scans.

The dynamics of an annular layer of low-viscosity liquid inside a rapidly rotating horizontal cylinder is experimentally studied. Under gravity, the liquid performs forced azimuthal oscillations in the cavity frame. We examined the stability of the two-dimensional azimuthal flow and discovered two novel types of axisymmetric liquid flows. First, a large-scale axially symmetric flow is excited near the end walls. The inertial modes generated in the corner regions are proven to be responsible for such a flow. Second, a small-scale flow in the form of the Taylor-Gortler vortices appears due to the centrifugal instability of the oscillatory liquid flow. The spatial period of the vortices is in qualitative agreement with the data obtained in the experimental and numerical studies of cellular flow in librating containers.

We study the influence of turbulence on upward motion of phytoplankton. Interaction with the flow is described by the Pedley-Kessler model considering spherical microorganisms. We find a range of parameters when the upward drift is only weakly perturbed or when turbulence completely randomizes the drift direction. When the perturbation is small, the drift is either determined by the local vorticity or is Gaussian. We find a range of parameters where the phytoplankton interaction with the flow can be described consistently as diffusion of orientation in effective potential. By solving the corresponding Fokker-Planck equation we find exponential steady-state distribution of phytoplankton's propulsion orientation. We further identify the range of parameters where phytoplankton's drift velocity with respect to the flow is determined uniquely by its position. In this case, one can describe phytoplankton's motion by a smooth flow and phytoplankton concentrates on fractal. We find fractal dimensions and demonstrate that phytoplankton forms vertical stripes in space with a nonisotropic pair-correlation function of concentration increased in the vertical direction. The probability density function of the distance between two particles obeys power law with the negative exponent given by the ratio of integrals of the turbulent energy spectrum. We find the regime of strong clustering where the exponent is of order one so that turbulence increases the rate of collisions by a large factor. The predictions hold for Navier-Stokes turbulence and stand for testing.

Dual-frequency modes of the dust acoustic surface waves propagating at the interface between a nonmagnetized multicomponent Lorentzian dusty plasma and a vacuum are investigated, including nonthermal and positron effects. The dispersion relation is kinetically derived by employing the specular reflection boundary condition and the dielectric permittivity for dusty plasma containing positrons. We found that there exist two modes of the dust acoustic surface wave; high- and low-frequency modes. We observe that both H and L modes are enhanced by the increase of the pair annihilation rate. However, the effects of positron density are twofold depending on the ratio of annihilated positrons. The effects of nonthermal plasmas are also investigated on the H and L modes of dust acoustic surface waves. We found that the nonthermal plasmas reduce the frequencies of both H and L modes.

We study the effect of freeze-thaw cycling on the packing fraction of equal spheres immersed in water. The water located between the grains experiences a dilatation during freezing and a contraction during melting. After several cycles, the packing fraction converges to a particular value ${\eta }_{\infty }=0.595$ independently of its initial value ${\eta }_0$. This behavior is well reproduced by numerical simulations. Moreover, the numerical results allow one to analyze the packing structural configuration. With a Voronoï partition analysis, we show that the piles are fully random during the whole process and are characterized by two parameters: the average Voronoï volume ${\mu }_v$ (related to the packing fraction $\eta$) and the standard deviation ${\sigma }_v$ of Voronoï volumes. The freeze-thaw driving modify the volume standard deviation ${\sigma }_v$ to converge to a particular disordered state with a packing fraction corresponding to the random loose packing fraction ${\eta }_{\text{BRLP}}$ obtained by Bernal during his pioneering experimental work. Therefore, freeze-thaw cycling is found to be a soft and spatially homogeneous driving method for disordered granular materials.