Human migration is often studied using gravity models. These models, however, have known limitations, including analytic inconsistencies and a dependence on empirical data to calibrate multiple parameters for the region of interest. Overcoming these limitations, the radiation model has been proposed as an alternative, universal approach to predicting different forms of human mobility, but has not been adopted for studying migration. Here we show, using data on within-country migration from the USA and Mexico, that the radiation model systematically underpredicts long-range moves, while the traditional gravity model performs well for large distances. The universal opportunity model, an extension of the radiation model, shows an improved fit of long-range moves compared to the original radiation model, but at the cost of introducing two additional parameters. We propose a more parsimonious extension of the radiation model that introduces a single parameter. We demonstrate that it fits the data over the full distance spectrum and also—unlike the universal opportunity model—preserves the analytical property of the original radiation model of being equivalent to a gravity model in the limit of a uniform population distribution.

Deep neural networks can be trained in reciprocal space by acting on the eigenvalues and eigenvectors of suitable transfer operators in direct space. Adjusting the eigenvalues while freezing the eigenvectors yields a substantial compression of the parameter space. This latter scales by definition with the number of computing neurons. The classification scores as measured by the displayed accuracy are, however, inferior to those attained when the learning is carried in direct space for an identical architecture and by employing the full set of trainable parameters (with a quadratic dependence on the size of neighbor layers). In this paper, we propose a variant of the spectral learning method as in Giambagli et al. [Nat. Commun. 12, 1330 (2021)], which leverages on two sets of eigenvalues for each mapping between adjacent layers. The eigenvalues act as veritable knobs which can be freely tuned so as to (1) enhance, or alternatively silence, the contribution of the input nodes and (2) modulate the excitability of the receiving nodes with a mechanism which we interpret as the artificial analog of the homeostatic plasticity. The number of trainable parameters is still a linear function of the network size, but the performance of the trained device gets much closer to those obtained via conventional algorithms, these latter requiring, however, a considerably heavier computational cost. The residual gap between conventional and spectral trainings can be eventually filled by employing a suitable decomposition for the nontrivial block of the eigenvectors matrix. Each spectral parameter reflects back on the whole set of internode weights, an attribute which we effectively exploit to yield sparse networks with stunning classification abilities as compared to their homologs trained with conventional means.

Living polymers composed of noncovalently bonded building blocks with weak backbone flexibility may self-assemble into thermoresponsive lyotropic liquid crystals. We demonstrate that the reversible polymer assembly and phase behavior can be controlled by the addition of (nonadsorbing) rigid colloidal disks which act as an entropic reorienting “template” onto the supramolecular polymers. Using a particle-based second-virial theory that correlates the various entropies associated with the polymers and disks, we demonstrate that small fractions of discotic additives promote the formation of a polymer nematic phase. At larger disk concentrations, however, the phase is disrupted by collective disk alignment in favor of a discotic nematic fluid in which the polymers are dispersed antinematically. We show that the antinematic arrangement of the polymers generates a nonexponential molecular-weight distribution and stimulates the formation of oligomeric species. At sufficient concentrations the disks facilitate a liquid-liquid phase separation which can be brought into simultaneously coexistence with the two fractionated nematic phases, providing evidence for a four-fluid coexistence in reversible shape-dissimilar hard-core mixtures without cohesive interparticle forces. We stipulate the conditions under which such a phenomenon could be found in experiment.

The orientational memory of particles can serve as an effective measure of diffusivity, spreading, and search efficiency in complex stochastic processes. We develop a theoretical framework to describe the decay of directional correlations in a generic class of stochastic active processes consisting of distinct states of motion characterized by their persistence and switching probabilities between the states. For exponentially distributed sojourn times, the orientation autocorrelation is analytically derived and the characteristic times of its crossovers are obtained in terms of the persistence of each state and the switching probabilities. We show how nonexponential sojourn-time distributions of interest, such as Gaussian and power-law distributions, can result from history-dependent transitions between the states. The relaxation behavior of the correlation function in such non-Markovian processes is governed by the history dependence of the switching probabilities and cannot be solely determined by the mean sojourn times of the states.

Hybrid-aligned nematic (HAN) liquid crystal (LC) devices have both fundamental and technological importance for their applications in LC adaptive lenses, low voltage LC displays, smart windows, and many more. We report the fabrication and characterization of a nanostructure-based HAN device employing vertically aligned carbon nanotube (VA-CNT) arrays as the homeotropic alignment agent on one side and two-dimensional (2D) hexagonal boron nitride ($h$-BN) as the planar alignment agent on the other side of the LC cell. The LC achieves the HAN configuration in the cell, i.e., homeotropic alignment at the VA-CNT side due to the $\pi \text{−}\pi$ stacking interaction between the LC and CNTs, and planar alignment at the $h$-BN side due to the $\pi \text{−}\pi$ stacking interaction between the LC and $h$-BN. When an applied electric field is ramped up across this VA-CNT/$h$-BN HAN cell, the LC (positive anisotropic) obtains a homeotropic state, requiring no threshold voltage to start the reorientation process; this effect is similar to that of a traditional polyimide (PI)-based HAN device. This VA-CNT/$h$-BN HAN cell successfully demonstrates the optical, electro-optical operations and the electric field-induced dynamic response. This study reveals that two inorganic nanostructured surfaces, VA-CNT arrays and 2D $h$-BN, can efficiently replace the organic PI alignment agents when needed and retain the HAN device's necessary electro-optical performances. These results substantially expand the fundamental understanding and the scope of utilizing various nanostructured surfaces for LC alignment mechanisms.

The orientational configurations of thermotropic nematic liquid crystal in cylindrical capillaries with nondegenerated planar surface anchoring are investigated. The boundary conditions were determined by a photoaligning coating on the inner wall of the capillary treated with a linearly polarized UV light while rotating the capillary around its long axis, thus providing the easy alignment axis perpendicular to the polarization direction of illuminating light. By changing the angle between the incident light polarization and the capillary axis, this procedure allows us to realize axially symmetric twisted structure with any angle of twist, ranging from a trivial axial alignment with zero twist (when the UV polarization is perpendicular to the capillary axis) to the ${180}^{\circ }$-twisted configuration (when the UV polarization is along the capillary). These two extreme configurations together with an intermediate configuration induced by UV light polarized at an angle of ${45}^{\circ }$ to the capillary axis were produced and their director profiles were studied using polarizing microscopy techniques. UV light intensity and polarization distribution over inner capillary surface covered with photoaligning layer were analyzed using optical ray tracing calculations. An analytical model of the observed configurations of the liquid crystal director field is proposed, which takes into account the finite anchoring on the capillary surface. By comparing the theoretically calculated and experimentally estimated director profiles, the liquid crystal anchoring energy on the photoaligned capillary surface was estimated.

We develop a mathematical model to quantitatively describe the imbibition dynamics of an elastic non-Newtonian fluid in a conical (nonuniform cross section) microfluidic assay. We consider the simplified Phan-Thien-Tanner viscoelastic model to represent the rheology of the elastic non-Newtonian fluid. Our model accounts for the geometrical features of the fluidic assay, the key parameters affecting the rheological behavior of the fluid, and predicts the imbibition dynamics effectively. By demonstrating the temporal advancement of the filling length in the conical capillary graphically, obtained for pertinent parametric values belonging to their physically permissible range, we report an underlying balance between capillary and viscous forces during imbibition resulting in three distinct regimes of filling. Nonuniformity in the capillary cross section gives rise to an alteration in the viscous force being applied at the contact line (manifested through the alteration in shear rate) during the imbibition process, which upon maintaining a balance with the dominant capillary force results in three different regimes of filling. We believe that the present analysis has a twofold significance. First, this work will enhance the understanding of underlying imbibition dynamics of viscoelastic fluids (most of the biofluids exhibit viscoelastic rheology) in nonuniform fluidic pathways. Second, the developed model is of significant practical relevance for the optimum design of microfluidic assays, primarily used for sample diagnostics in biochemical and biomedical applications.

We analyze a compressible Poiseuille flow of ideal gas in a plane channel. We provide the form of internal energy $U$ for a nonequilibrium stationary state that includes viscous dissipation and pressure work. We demonstrate that $U$ depends strongly on the ratio $\mathrm{\Delta }p/p_0$, where $\mathrm{\Delta }p$ is the pressure difference between inlet and outlet and ${\mathrm{p}}_0$ is the outlet's pressure. In addition, $U$ depends on two other variables: the channel aspect ratio and the parameter equivalent to Reynolds number. The stored internal energy, $\mathrm{\Delta }U=U-U_0$, is small compared to the internal energy $U_0$ of the equilibrium state for a moderate range of values of $\mathrm{\Delta }p/p_0$. However, $\mathrm{\Delta }U$ can become large for big $\mathrm{\Delta }p$ or close to vacuum conditions at the outlet ($p_0\approx 0\mathrm{Pa}$).

The four-roll mill, wherein four identical cylinders undergo rotation of identical magnitude but alternate signs, was originally proposed by G. I. Taylor to create local extensional flows and study their ability to deform small liquid drops. Since an extensional flow has an unstable eigendirection, a drop located at the flow stagnation point will have a tendency to escape. This unstable dynamics can, however, be stabilized using, e.g., a modulation of the rotation rates of the cylinders. Here we use reinforcement learning, a branch of machine learning devoted to the optimal selection of actions based on cumulative rewards, in order to devise a stabilization algorithm for the four-roll mill flow. The flow is modelled as the linear superposition of four two-dimensional rotlets and the drop is treated as a rigid spherical particle smaller than all other length scales in the problem. Unlike previous attempts to devise control, we take a probabilistic approach whereby speed adjustments are drawn from a probability density function whose shape is improved over time via a form of gradient ascent know as actor-critic method. With enough training, our algorithm is able to precisely control the drop and keep it close to the stagnation point for as long as needed. We explore the impact of the physical and learning parameters on the effectiveness of the control and demonstrate the robustness of the algorithm against thermal noise. We finally show that reinforcement learning can provide a control algorithm effective for all initial positions and that can be adapted to limit the magnitude of the flow extension near the position of the drop.

The effect of ionic disorder on the principal Hugoniot is investigated using multiple scattering theory to very high pressure (Gbar). Calculations using molecular dynamics to simulate ionic disorder are compared to those with a fixed crystal lattice, for both carbon and aluminum. For the range of conditions considered here we find that ionic disorder has a relatively minor influence. It is most important at the onset of shell ionization and we find that, at higher pressures, the subtle effect of the ionic environment is overwhelmed by the larger number of ionized electrons with higher thermal energies.

Explicit electromagnetic particle-in-cell (PIC) codes are typically limited by the Courant-Friedrichs-Lewy (CFL) condition, which implies that the timestep multiplied by the speed of light must be smaller than the smallest cell size. In the case of boosted-frame PIC simulations of plasma-based acceleration, this limitation can be a major hindrance, as the cells are often very elongated along the longitudinal direction and the timestep is thus limited by the small, transverse cell size. This entails many small-timestep PIC iterations and can limit the potential speed-up of the boosted-frame technique. Here, by using a CFL-free analytical spectral solver, and by mitigating additional numerical instabilities that arise at large timestep, we show that it is possible to overcome traditional limitations on the timestep and thereby realize the full potential of the boosted-frame technique over a much wider range of parameters.

We have constructed a unified framework for generalizing the finite-time thermodynamic behavior of statistically distinct bosonic and fermionic Stirling cycles with regenerative characteristics. In our formalism, working fluids consisting of particles obeying Fermi-Dirac and Bose-Einstein statistics are treated on equal footing and modeled as a collection of noninteracting harmonic and fermionic oscillators. In terms of the frequency and population of the two oscillators, we have provided an interesting generalization for the definitions of heat and work that are valid for classical as well as nonclassical working fluids. Based on a generic setting under finite-time relaxation dynamics, nice results on low- and high-temperature heat transfer rates are derived. Characterized by equal power, efficiency, entropy production, cycle time, and coefficient of performance, the thermodynamic equivalence between two types of Stirling cycles is established in the low-temperature “quantum” regime.

The “Brownian bees” model describes an ensemble of $N$ independent branching Brownian particles. When a particle branches into two particles, the particle farthest from the origin is eliminated so as to keep the number of particles constant. In the limit of $N\to \infty$, the spatial density of the particles is governed by the solution of a free boundary problem for a reaction-diffusion equation. At long times the particle density approaches a spherically symmetric steady-state solution with a compact support. Here, we study fluctuations of the “swarm of bees” due to the random character of the branching Brownian motion in the limit of large but finite $N$. We consider a one-dimensional setting and focus on two fluctuating quantities: the swarm center of mass $X\left(t\right)$ and the swarm radius $\ell \left(t\right)$. Linearizing a pertinent Langevin equation around the deterministic steady-state solution, we calculate the two-time covariances of $X\left(t\right)$ and $\ell \left(t\right)$. The variance of $X\left(t\right)$ directly follows from the covariance of $X\left(t\right)$, and it scales as $1/N$ as to be expected from the law of large numbers. The variance of $\ell \left(t\right)$ behaves differently: It exhibits an anomalous scaling $(1/N)lnN$. This anomaly appears because all spatial scales, including a narrow region near the edges of the swarm where only a few particles are present, give a significant contribution to the variance. We argue that the variance of $\ell \left(t\right)$ can be obtained from the covariance of $\ell \left(t\right)$ by introducing a cutoff at the microscopic time $1/N$ where the continuum Langevin description breaks down. Our theoretical predictions are in good agreement with Monte Carlo simulations of the microscopic model. Generalizations to higher dimensions are briefly discussed.

A fluid of hard right isosceles triangles was studied using an extension of scaled-particle density-functional theory which includes the exact third virial coefficient. We show that the only orientationally ordered stable liquid-crystal phase predicted by the theory is the uniaxial nematic phase, in agreement with the second-order virial theory. By contrast, Monte Carlo simulations predict exotic liquid-crystal phases exhibiting tetratic and octatic correlations, with orientational distribution functions having four and eight equivalent peaks, respectively. This demonstrates the failure of the standard density-functional theory based on two- and three-body correlations to describe high-symmetry orientational phases in two-dimensional hard right-triangle fluids, and it points to the necessity to reformulate the theory to take into account high-order body correlations and ultimately particle self-assembling and clustering effects. This avenue may represent a great challenge for future research, and we discuss some fundamental ideas to construct a modified version of density-functional theory to account for these clustering effects.

Free energy calculations based on atomistic Hamiltonians provide microscopic insight into the thermodynamic driving forces of biophysical or condensed matter systems. Many approaches use intermediate Hamiltonians interpolating between the two states for which the free energy difference is calculated. The Bennett acceptance ratio (BAR) and variationally derived intermediates (VI) methods are optimal estimator and intermediate states in that the mean-squared error of free energy calculations based on independent sampling is minimized. However, BAR and VI have been derived based on several approximations that do not hold for very few sample points. Analyzing one-dimensional test systems, we show that in such cases BAR and VI are suboptimal and that established uncertainty estimates are inaccurate. Whereas for VI to become optimal, less than seven samples per state suffice in all cases; for BAR the required number increases unboundedly with decreasing configuration space densities overlap of the end states. We show that for BAR, the required number of samples is related to the overlap through an inverse power law. Because this relation seems to hold universally and almost independent of other system properties, these findings can guide the proper choice of estimators for free energy calculations.

In general we are interested in dynamical systems coupled to complex hysteresis. Therefore as a first step we investigated recently the dynamics of a periodically driven damped harmonic oscillator coupled to independent Ising spins in a random field. Although such a system does not produce hysteresis, we showed how to characterize the dynamics of such a piecewise-smooth system, especially in the case of a large number of spins [Zech, Otto, and Radons, Phys. Rev. E 101, 042217 (2020)]. In this paper we extend our model to spin dimers, thus pairwise interacting spins. We show in which cases two interacting spins can show elementary hysteresis, and we give a connection to the Preisach model, which allows us to consider an infinite number of spin pairs. This thermodynamic limit leads us to a dynamical system with an additional hysteretic force in the form of a generalized play operator. By using methods from general chaos theory, piecewise-smooth system theory, and statistics we investigate the chaotic behavior of the dynamical system for a few spins and also in the case of a larger number of spins by calculating bifurcation diagrams, Lyapunov exponents, fractal dimensions, and self-averaging properties. We find that the fractal dimensions and the magnetization are in general not self-averaging quantities. We show how the dynamical properties of the piecewise-smooth system for a large number of spins differs from the system in its thermodynamic limit.

We numerically study Kuramoto model synchronization consisting of the two groups of conformist-contrarian and excitatory-inhibitory phase oscillators with equal intrinsic frequency. We consider random and small-world (SW) topologies for the connectivity network of the oscillators. In random networks, regardless of the contrarian to conformist connection strength ratio, we found a crossover from the $\pi$-state to the blurred $\pi$-state and then a continuous transition to the incoherent state by increasing the fraction of contrarians. However, for the excitatory-inhibitory model in a random network, we found that for all the values of the fraction of inhibitors, the two groups remain in phase and the transition point of fully synchronized to an incoherent state reduced by strengthening the ratio of inhibitory to excitatory links. In the SW networks we found that the order parameters for both models do not show monotonic behavior in terms of the fraction of contrarians and inhibitors. Up to the optimal fraction of contrarians and inhibitors, the synchronization rises by introducing the number of contrarians and inhibitors and then falls. We discuss that the nonmonotonic behavior in synchronization is due to the weakening of the defects already formed in the pure conformist and excitatory agent model in SW networks. We found that in SW networks, the optimal fraction of contrarians and inhibitors remain unchanged for the rewiring probabilities up to $\sim 0.15$, above which synchronization falls monotonically, like the random network. We also showed that in the conformist-contrarian model, the optimal fraction of contrarians is independent of the strength of contrarian links. However, in the excitatory-inhibitory model, the optimal fraction of inhibitors is approximately proportional to the inverse of inhibition strength.

Sender-receiver games are simple models of information transmission that provide a formalism to study the evolution of honest signaling and deception between a sender and a receiver. In many practical scenarios, lies often affect groups of receivers, which inevitably entangles the payoffs of individuals to the payoffs of other agents in their group, and this makes the formalism of pairwise sender-receiver games inapt for where it might be useful the most. We therefore introduce group interactions among receivers and study how their interconnectedness in higher-order social networks affects the evolution of lying. We observe a number of counterintuitive results that are rooted in the complexity of the underlying evolutionary dynamics, which has thus far remained hidden in the realm of pairwise interactions. We find conditions for honesty to persist even when there is a temptation to lie, and we observe the prevalence of moral strategy profiles even when lies favor the receiver at a cost to the sender. We confirm the robustness of our results by further performing simulations on hypergraphs created from real-world data using the SocioPatterns database. Altogether, our results provide persuasive evidence that moral behavior may evolve on higher-order social networks, at least as long as individuals interact in groups that are small compared to the size of the network.

Confluent cell monolayers and epithelia tissues show remarkable patterns and correlations in structural arrangements and actively driven collective flows. We simulate these properties using multiphase field models. The models are based on cell deformations and cell-cell interactions and we investigate the influence of microscopic details to incorporate active forces on emerging phenomena. We compare four different approaches, one in which the activity is determined by a random orientation, one where the activity is related to the deformation of the cells, and two models with subcellular details to resolve the mechanochemical interactions underlying cell migration. The models are compared with respect to generic features, such as coordination number distribution, cell shape variability, emerging nematic properties, as well as vorticity correlations and flow patterns in large confluent monolayers and confinements. All results are compared with experimental data for a large variety of cell cultures. The appearing qualitative differences of the models show the importance of microscopic details and provide a route towards predictive simulations of patterns and correlations in cell colonies.