Identifying causal relations from observational data sets has posed great challenges in data-driven causality inference studies. One of the successful approaches to detect direct coupling in the information theory framework is transfer entropy. However, the core of entropy-based tools lies on the probability estimation of the underlying variables. Here we propose a data-driven approach for causality inference that incorporates recurrence plot features into the framework of information theory. We define it as the recurrence measure of conditional dependence (RMCD), and we present some applications. The RMCD quantifies the causal dependence between two processes based on joint recurrence patterns between the past of the possible driver and present of the potentially driven, excepting the contribution of the contemporaneous past of the driven variable. Finally, it can unveil the time scale of the influence of the sea-surface temperature of the Pacific Ocean on the precipitation in the Amazonia during recent major droughts.

We have studied a two-dimensional piecewise linear map to examine how the hierarchical structure of stable regions affects the slow dynamics in Hamiltonian systems. In the phase space there are infinitely many stable regions, each of which is polygonal-shaped, and the rest is occupied by chaotic orbits. By using symbolic representation of stable regions, a procedure to compute the edges of the polygons is presented. The stable regions are hierarchically distributed in phase space and the edges of the stable regions show the marginal instability. The cumulative distribution of the recurrence time obeys a power law as $\sim t^{-2}$, the same as the one for the system with phase space, which is composed of a single stable region and chaotic components. By studying the symbol sequence of recurrence trajectories, we show that the hierarchical structure of stable regions has no significant effect on the power-law exponent and that only the marginal instability on the boundary of stable regions is responsible for determining the exponent. We also discuss the relevance of the hierarchical structure to those in more generic chaotic systems.

Influencing various aspects of human activity, migration is associated also with language formation. To examine the mutual interaction of these processes, we study a Naming Game with migrating agents. The dynamics of the model leads to formation of low-mobility clusters, which turns out to break the symmetry of the model: although the Naming Game remains symmetric, low-mobility languages are favored. High-mobility languages are gradually eliminated from the system, and the dynamics of language formation considerably slows down. Our model is too simple to explain in detail language competition of migrating human communities, but it certainly shows that languages of settlers are favored over nomadic ones.

We study the problem of stabilized coexistence in a three-species public goods game in which each species simultaneously contributes to one public good while freeloading off another public good (“cheating”). The proportional population growth is governed by an appropriately modified replicator equation, depending on the returns from the public goods and the cost. We show that the replicator dynamic has at most one interior unstable fixed point and that the population becomes dominated by a single species. We then show that by applying an externally imposed penalty, or “tax” on success can stabilize the interior fixed point, allowing for the symbiotic coexistence of all species. We show that the interior fixed point is the point of globally minimal total population growth in both the taxed and untaxed cases. We then formulate an optimal taxation problem and show that it admits a quasilinearization, resulting in novel necessary conditions for the optimal control. In particular, the optimal control problem governing the tax rate must solve a certain second-order ordinary differential equation.

Given that the assumption of perfect rationality is rarely met in the real world, we explore a graded notion of rationality in socioecological systems of networked actors. We parametrize an actors' rationality via their place in a social network and quantify system rationality via the average Jensen-Shannon divergence between the games Nash and logit quantal response equilibria. Previous work has argued that scale-free topologies maximize a system's overall rationality in this setup. Here we show that while, for certain games, it is true that increasing degree heterogeneity of complex networks enhances rationality, rationality-optimal configurations are not scale-free. For the Prisoner's Dilemma and Stag Hunt games, we provide analytic arguments complemented by numerical optimization experiments to demonstrate that core-periphery networks composed of a few dominant hub nodes surrounded by a periphery of very low degree nodes give strikingly smaller overall deviations from rationality than scale-free networks. Similarly, for the Battle of the Sexes and the Matching Pennies games, we find that the optimal network structure is also a core-periphery graph but with a smaller difference in the average degrees of the core and the periphery. These results provide insight on the interplay between the topological structure of socioecological systems and their collective cognitive behavior, with potential applications to understanding wealth inequality and the structural features of the network of global corporate control.

The final shape of a virus is dictated by the self-assembly pathway of its constituents. Using standard thin-shell elasticity, we highlight the prominent role of the viral shell's spontaneous curvature in determining the assembly pathway. In particular, we demonstrate that the mechanical stress inherent to the growth of a curved surface can be relaxed in two different ways in the early steps of assembly, depending on the value of the spontaneous curvature of the surface. This important result explains why most viral shells have either a compact shape with icosahedral symmetry or an elongated shape lacking this symmetry.

Embedding rigid inclusions into elastic matrix materials is a procedure of high practical relevance, for instance, for the fabrication of elastic composite materials. We theoretically analyze the following situation. Rigid spherical inclusions are enclosed by a homogeneous elastic medium under stick boundary conditions. Forces and torques are directly imposed from outside onto the inclusions or are externally induced between them. The inclusions respond to these forces and torques by translations and rotations against the surrounding elastic matrix. This leads to elastic matrix deformations, and in turn results in mutual long-ranged matrix-mediated interactions between the inclusions. Adapting a well-known approach from low-Reynolds-number hydrodynamics, we explicitly calculate the displacements and rotations of the inclusions from the externally imposed or induced forces and torques. Analytical expressions are presented as a function of the inclusion configuration in terms of displaceability and rotateability matrices. The role of the elastic environment is implicitly included in these relations. That is, the resulting expressions allow a calculation of the induced displacements and rotations directly from the inclusion configuration, without having to explicitly determine the deformations of the elastic environment. In contrast to the hydrodynamic case, compressibility of the surrounding medium is readily taken into account. We present the complete derivation based on the underlying equations of linear elasticity theory. In the future, the method will, for example, be helpful to characterize the behavior of externally tunable elastic composite materials, to accelerate numerical approaches, as well as to improve the quantitative interpretation of microrheological results.

A long elastic cylinder, with radius $a$ and shear-modulus $\mu$, becomes unstable given sufficient surface tension $\gamma$. We show this instability can be simply understood by considering the energy, $E\left(\lambda \right)$, of such a cylinder subject to a homogenous longitudinal stretch $\lambda$. Although $E\left(\lambda \right)$ has a unique minimum, if surface tension is sufficient $[\mathrm{\Gamma }\equiv \gamma /\left(a\mu \right)>\sqrt{32}]$ it loses convexity in a finite region. We use a Maxwell construction to show that, if stretched into this region, the cylinder will phase-separate into two segments with different stretches ${\lambda }_1$ and ${\lambda }_2$. Our model thus explains why the instability has infinite wavelength and allows us to calculate the instability's subcritical hysteresis loop (as a function of imposed stretch), showing that instability proceeds with constant amplitude and at constant (positive) tension as the cylinder is stretched between ${\lambda }_1$ and ${\lambda }_2$. We use full nonlinear finite-element calculations to verify these predictions and to characterize the interface between the two phases. Near $\mathrm{\Gamma }=\sqrt{32}$ the length of such an interface diverges, introducing a new length scale and allowing us to construct a one-dimensional effective theory. This treatment yields an analytic expression for the interface itself, revealing that its characteristic length grows as $l_{\text{wall}}\sim a/\sqrt{\mathrm{\Gamma }-\sqrt{32}}$.

We present a systematic derivation of relativistic lattice kinetic equations for finite-mass particles, reaching close to the zero-mass ultrarelativistic regime treated in the previous literature. Starting from an expansion of the Maxwell-Jüttner distribution on orthogonal polynomials, we perform a Gauss-type quadrature procedure and discretize the relativistic Boltzmann equation on space-filling Cartesian lattices. The model is validated through numerical comparison with standard tests and solvers in relativistic fluid dynamics such as Boltzmann approach multiparton scattering and previous relativistic lattice Boltzmann models. This work provides a significant step towards the formulation of a unified relativistic lattice kinetic scheme, covering both massive and near-massless particles regimes.

A series of direct-drive implosions performed on OMEGA were used to isolate the effect of an adiabat on the in-flight shell thickness. The maximum in-flight shell thickness was measured to decrease from $75\pm 2$ to $60\pm 2\mu \mathrm{m}$ when the adiabat of the shell was reduced from 6 to 4.5, but when decreasing the adiabat further (1.8), the shell thickness increased to $75\pm 2\mu \mathrm{m}$ due to the growth of the Rayleigh-Taylor instability. Hydrodynamic simulations suggest that a laser imprint is the dominant seed for these nonuniformities.

We study the dynamical response to small distortions of a lattice about its uniform state, drifting through a dissipative medium due to an external force, and show, analytically and numerically, that the fluctuations, both transverse and longitudinal to the direction of the drift, exhibit spatiotemporal scaling belonging to the Kardar-Parisi-Zhang universality class. Further, we predict that a colloidal crystal drifting in a constant electric field is linearly stable against distortions and the distortions propagate as underdamped waves.

We address the issue of the dynamics of wealth accumulation and economic crisis triggered by extreme inequality, attempting to stick to most possibly intrinsic assumptions. Our general framework is that of pure or modified multiplicative processes, basically geometric Brownian motions. In contrast with the usual approach of injecting into such stochastic agent models either specific, idiosyncratic internal nonlinear interaction patterns or macroscopic disruptive features, we propose a dynamic inequality model where the attainment of a sizable fraction of the total wealth by very few agents induces a crisis regime with strong intermittency, the explicit coupling between the richest and the rest being a mere normalization mechanism, hence with minimal extrinsic assumptions. The model thus harnesses the recognized lack of ergodicity of geometric Brownian motions. It also provides a statistical intuition to the consequences of Thomas Piketty's recent “$r>g$” (return rate $>$ growth rate) paradigmatic analysis of very-long-term wealth trends. We suggest that the “water-divide” of wealth flow may define effective classes, making an objective entry point to calibrate the model. Consistently, we check that a tax mechanism associated to a few percent relative bias on elementary daily transactions is able to slow or stop the build-up of large wealth. When extreme fluctuations are tamed down to a stationary regime with sizable but steadier inequalities, it should still offer opportunities to study the dynamics of crisis and the inner effective classes induced through external or internal factors.

Many biological populations, such as bacterial colonies, have developed through evolution a protection mechanism, called bet hedging, to increase their probability of survival under stressful environmental fluctuation. In this context, the concept of preadaptation refers to a common type of bet-hedging protection strategy in which a relatively small number of individuals in a population stochastically switch their phenotypes to a dormant metabolic state in which they increase their probability of survival against potential environmental shocks. Hence, if an environmental shock took place at some point in time, preadapted organisms would be better adapted to survive and proliferate once the shock is over. In many biological populations, the mechanisms of preadaptation and proliferation present delays whose influence in the fitness of the population are not well understood. In this paper, we propose a rigorous mathematical framework to analyze the role of delays in both preadaptation and proliferation mechanisms in the survival of biological populations, with an emphasis on bacterial colonies. Our theoretical framework allows us to analytically quantify the average growth rate of a bet-hedging bacterial colony with stochastically delayed reactions with arbitrary precision. We verify the accuracy of the proposed method by numerical simulations and conclude that the growth rate of a bet-hedging population shows a nontrivial dependency on their preadaptation and proliferation delays. Contrary to the current belief, our results show that faster reactions do not, in general, increase the overall fitness of a biological population.

Diffusion in nature is usually considered as a smooth redistribution process. However, it appears that the diffusion of chiral molecules and the propagation of chirality may proceed in quite different ways. Indeed, in the present work, unexpected quantization of the spatial concentration of chiral molecules is discovered in self-aligned molecular liquids. It is shown that the interpenetration of two liquids is forming discrete diffusion barrier walls resulting in steplike concentration distribution of chiral molecules in space. The concentration gradient is at least an order of magnitude stronger from both sides of the barrier wall compared to the gradient between those walls. It is also shown that this microscopic diffusion process may be controlled by macroscopic boundary conditions imposed on the host molecular system. Both of those phenomena are related to the collective long-range orientational “elastic” interactions of molecules of the host. The observed phenomena may radically change our understanding of diffusion of chiral molecules, among others, in biological tissue, which contains many examples of self-aligned molecular liquids. This, in turn, has the potential to revolutionize drug design and delivery techniques.

We present a numerical study of wavy supercritical cylindrical Couette flow between counter-rotating cylinders in which the wavy pattern propagates either prograde with the inner cylinder or retrograde opposite the rotation of the inner cylinder. The wave propagation reversals from prograde to retrograde and vice versa occur at distinct values of the inner cylinder Reynolds number when the associated frequency of the wavy instability vanishes. The reversal occurs for both twofold and threefold symmetric wavy vortices. Moreover, the wave propagation reversal only occurs for sufficiently strong counter-rotation. The flow pattern reversal appears to be intrinsic in the system as either periodic boundary conditions or fixed end wall boundary conditions for different system sizes always result in the wave propagation reversal. We present a detailed bifurcation sequence and parameter space diagram with respect to retrograde behavior of wavy flows. The retrograde propagation of the instability occurs when the inner Reynolds number is about two times the outer Reynolds number. The mechanism for the retrograde propagation is associated with the inviscidly unstable region near the inner cylinder and the direction of the global average azimuthal velocity. Flow dynamics, spatio-temporal behavior, global mean angular velocity, and torque of the flow with the wavy pattern are explored.

A specific cavitation phenomenon occurs inside the stems of trees. The internal pressure in tree conduits can drop down to significant negative values, which causes the nucleation of bubbles. The bubbles exhibit high-frequency oscillations just after their nucleation. In the present study, this phenomenon is modeled by taking into account acoustic waves produced by bubble oscillations. A dispersion equation is derived, which is then used to calculate the resonance frequency and the attenuation coefficient of the bubble oscillations. Radiation damping is found to be predominant in comparison with viscous damping, except for very small bubbles. A typical number of oscillation cycles before the complete damping of the oscillation is found to be of the order of 10, as observed for cavitation bubbles in biomimetic synthetic trees.

We use a computational technique based on the immersed boundary method to construct a four-roll mill device with which we can generate a broad spectrum of flow types from an extensional flow to a rotational one. We put a vesicle or a bubble in the constructed four-roll mill device to investigate their interaction with the surrounding fluid. The vesicle dynamics are determined by its bending rigidity, inextensibility, and hydrodynamical force, whereas the bubble dynamics is governed by the surface tension and the hydrodynamic interaction. Depending on the type of the flow, these suspended objects go through either a tank-treading motion or a tumbling motion. We validate our numerical method by a convergence study and discuss the transition between tank-treading and tumbling motions for the vesicles and bubbles.

Utilizing synthetically generated random variates and laboratory measurements, we document the inherent limitations of the conventional structure function approach in limited sample size settings. We demonstrate that an alternative approach, based on the principle of maximum likelihood, can provide nearly unbiased structure function estimates with far less uncertainty under such unfavorable conditions. The superiority of this approach over the conventional approach does not diminish even in the case of strongly correlated samples. Two entirely different types of probability distributions, which have been reported in the turbulence literature, are found to be compatible with the proposed approach.

Time-varying community structures exist widely in real-world networks. However, previous studies on the dynamics of spreading seldom took this characteristic into account, especially those on social contagions. To study the effects of time-varying community structures on social contagions, we propose a non-Markovian social contagion model on time-varying community networks based on the activity-driven network model. A mean-field theory is developed to analyze the proposed model. Through theoretical analyses and numerical simulations, two hierarchical features of the behavior adoption processes are found. That is, when community strength is relatively large, the behavior can easily spread in one of the communities, while in the other community the spreading only occurs at higher behavioral information transmission rates. Meanwhile, in spatial-temporal evolution processes, hierarchical orders are observed for the behavior adoption. Moreover, under different information transmission rates, three distinctive patterns are demonstrated in the change of the whole network's final adoption proportion along with the growing community strength. Within a suitable range of transmission rate, an optimal community strength can be found that can maximize the final adoption proportion. Finally, compared with the average activity potential, the promoting or inhibiting of social contagions is much more influenced by the number of edges generated by active nodes.