The back-reaction of a radiated wave on the emitting source is a general problem. In the most general case, back-reaction on moving wave sources depends on their whole history. Here we study a model system in which a pointlike source is piloted by its own memory-endowed wave field. Such a situation is implemented experimentally using a self-propelled droplet bouncing on a vertically vibrated liquid bath and driven by the waves it generates along its trajectory. The droplet and its associated wave field form an entity having an intrinsic dual particle-wave character. The wave field encodes in its interference structure the past trajectory of the droplet. In the present article we show that this object can self-organize into a spinning state in which the droplet possesses an orbiting motion without any external interaction. The rotation is driven by the wave-mediated attractive interaction of the droplet with its own past. The resulting “memory force” is investigated and characterized experimentally, numerically, and theoretically. Orbiting with a radius of curvature close to half a wavelength is shown to be a memory-induced dynamical attractor for the droplet's motion.

Various real-world networks interact with and depend on each other. The design of the interconnection between interacting networks is one of the main challenges to achieve a robust interdependent network. Due to cost considerations, network providers are inclined to interconnect nodes that are geographically close. Accordingly, we propose two topologies, the random geographic graph and the relative neighborhood graph, for the design of interconnection in interdependent networks that incorporates the geographic location of nodes. Differing from the one-to-one interconnection studied in the literature, one node in one network can depend on an arbitrary number of nodes in the other network. We derive the average number of interdependent links for the two topologies, which enables their comparison. For the two topologies, we evaluate the impact of the interconnection structure on the robustness of interdependent networks against cascading failures. The two topologies are assessed on the real-world coupled Italian Internet and the electric transmission network. Finally, we propose the derivative of the largest mutually connected component with respect to the fraction of failed nodes as a robustness metric. This robustness metric quantifies the damage of the network introduced by a small fraction of initial failures well before the critical fraction of failures at which the whole network collapses.

Real-world multilayer networks feature nontrivial dependencies among links of different layers. Here we argue that if links are directed, then dependencies are twofold. Besides the ordinary tendency of links of different layers to align as the result of “multiplexity,” there is also a tendency to antialign as a result of what we call “multireciprocity,” i.e., the fact that links in one layer can be reciprocated by opposite links in a different layer. Multireciprocity generalizes the scalar definition of single-layer reciprocity to that of a square matrix involving all pairs of layers. We introduce multiplexity and multireciprocity matrices for both binary and weighted multiplexes and validate their statistical significance against maximum-entropy null models that filter out the effects of node heterogeneity. We then perform a detailed empirical analysis of the world trade multiplex (WTM), representing the import-export relationships between world countries in different commodities. We show that the WTM exhibits strong multiplexity and multireciprocity, an effect which is, however, largely encoded into the degree or strength sequences of individual layers. The residual effects are still significant and allow us to classify pairs of commodities according to their tendency to be traded together in the same direction and/or in opposite ones. We also find that the multireciprocity of the WTM is significantly lower than the usual reciprocity measured on the aggregate network. Moreover, layers with low (high) internal reciprocity are embedded within sets of layers with comparably low (high) mutual multireciprocity. This suggests that, in the WTM, reciprocity is inherent to groups of related commodities rather than to individual commodities. We discuss the implications for international trade research focusing on product taxonomies, the product space, and fitness and complexity metrics.

The electric-field-assisted directed assembly of spherical colloidal particles near an electrode has been studied for nearly three decades. Recently, focus has shifted to the electric-field-assisted assembly and propulsion of nonspherical (i.e., anisotropic) particles. This paper describes calculations and results for a doublet of asymmetric ζ potential and size responding to a dc electric field. The doublet experienced a net vertical force that depended on both the asymmetry in ζ potential and lobe size. In addition, the doublet experienced a net lateral force perpendicular to the applied electric field. The lateral force depended on the difference in ζ potential of the two lobes, the lobe size asymmetry, and also the angle of inclination of the doublet. The net force was used to predict an apparent lateral velocity, which was found to be perpendicular to the applied electric field. In addition, the particle experienced rotation from a net torque that depended on the lobe size asymmetry and also the angle of inclination of the doublet. The magnitude of the predicted velocity was of the same order of magnitude as has been observed for particles responding to ac electric fields in experiments. These results demonstrate that lobe ζ potential, lobe size, and orientation of a colloidal doublet can be tuned to achieve propulsion.

We investigate the formation and the coarsening dynamics of islands in a strained epitaxial semiconductor film. These islands are commonly observed in thin films undergoing a morphological instability due to the presence of the elastocapillary effect. We first describe both analytically and numerically the formation of an equilibrium island using a two-dimensional continuous model. We have found that these equilibrium island-like solutions have a maximum height $h_0$ and they sit on top of a flat wetting layer with a thickness $h_w$. We then consider two islands, and we report that they undergo a noninterrupted coarsening that follows a two stage dynamics. The first stage may be depicted by a quasistatic dynamics, where the mass transfers are proportional to the chemical potential difference of the islands. It is associated with a time scale $t_c$ that is a function of the distance $d$ between the islands and leads to the shrinkage of the smallest island. Once its height becomes smaller than a minimal equilibrium height $h_0^{*}$, its mass spreads over the entire system. Our results pave the way for a future analysis of coarsening of an assembly of islands.

We investigate a model for fatigue crack growth in which damage accumulation is assumed to follow a power law of the local stress amplitude, a form that can be generically justified on the grounds of the approximately self-similar aspect of microcrack distributions. Our aim is to determine the relation between model ingredients and the Paris exponent governing subcritical crack-growth dynamics at the macroscopic scale, starting from a single small notch propagating along a fixed line. By a series of analytical and numerical calculations, we show that, in the absence of disorder, there is a critical damage-accumulation exponent $\gamma$, namely ${\gamma }_c=2$, separating two distinct regimes of behavior for the Paris exponent $m$. For $\gamma >{\gamma }_c$, the Paris exponent is shown to assume the value $m=\gamma$, a result that proves robust against the separate introduction of various modifying ingredients. Explicitly, we deal here with (i) the requirement of a minimum stress for damage to occur, (ii) the presence of disorder in local damage thresholds, and (iii) the possibility of crack healing. On the other hand, in the regime $\gamma <{\gamma }_c$, the Paris exponent is seen to be sensitive to the different ingredients added to the model, with rapid healing or a high minimum stress for damage leading to $m=2$ for all $\gamma <{\gamma }_c$, in contrast with the linear dependence $m=6-2\gamma$ observed for very long characteristic healing times in the absence of a minimum stress for damage. Upon the introduction of disorder on the local fatigue thresholds, which leads to the possible appearance of multiple cracks along the propagation line, the Paris exponent tends to $m\approx 4$ for $\gamma \lesssim 2$ while retaining the behavior $m=\gamma$ for $\gamma \gtrsim 4$.

In multiphase flow in porous media the consistent pore to Darcy scale description of two-fluid flow processes has been a long-standing challenge. Immiscible displacement processes occur at the scale of individual pores. However, the larger scale behavior is described by phenomenological relationships such as relative permeability, which typically uses only fluid saturation as a state variable. As a consequence pore scale properties such as contact angle cannot be directly related to Darcy scale flow parameters. Advanced imaging and computational technologies are closing the gap between the pore and Darcy scale, supporting the development of new theory. We utilize fast x-ray microtomography to observe pore-scale two-fluid configurations during immiscible flow and initialize lattice Boltzmann simulations that demonstrate that the mobilization of disconnected nonwetting phase clusters can account for a significant fraction of the total flux. We show that fluid topology can undergo substantial changes during flow at constant saturation, which is one of the underlying causes of hysteretic behavior. Traditional assumptions about fluid configurations are therefore an oversimplification. Our results suggest that the role of fluid connectivity cannot be ignored for multiphase flow. On the Darcy scale, fluid topology and phase connectivity are accounted for by interfacial area and Euler characteristic as parameters that are missing from our current models.

The disintegration of a compound thread of fluid can be utilized in a wide variety of applications including the production of compound droplets or capsules. In this paper we investigate the linear instability of a compound inviscid liquid jet falling under gravity in a surrounding gas with respect to nonaxisymmetric waves. We derive an analytical expression for the dispersion relation, which takes into account the non-uniform nature of the jet, and which we then solve numerically. Particular attention is paid to investigating the effects of the liquid-to-gas density ratio on the growth and development of different wave modes as well as the influence of gravity. Our results show that there exists some nonaxisymmetric long wavelength disturbances that are more unstable than their asymmetric equivalents and that the influence of gravity can alter the behavior of these modes.

Electron transport through a nanoscale system is an inherently stochastic quantum mechanical process. Electric current is a time series of electron tunneling events separated by random intervals. Thermal and quantum noise are two sources of this randomness. In this paper we use the quantum master equation to consider the following questions. (i) Given that an electron has tunneled into the electronically unoccupied system from the source electrode at some particular time, how long is it until an electron tunnels out to the drain electrode to leave the system electronically unoccupied, where there are no intermediate tunneling events (the tunneling path)? (ii) Given that an electron tunneled into the unoccupied system from the source electrode at some particular time, how long is it until an electron tunnels out to the drain electrode to leave the system electronically unoccupied, where there are no intermediate tunneling events ($a$ tunneling path)? (iii) What are the distributions of these times? We show that electron correlations suppress the difference between the electron tunneling path and an electron tunneling path.

We study heat flows among three thermal reservoirs via two two-level systems (TLSs). Two reservoirs are coupled to one TLS and the third reservoir to the second TLS. The two TLSs are also coupled to each other, thus bridging the third reservoir with the two other reservoirs. We show that the magnitudes and directions of the reservoirs' heat currents can be controlled by varying the various damping rates of the two TLSs due to coupling with the corresponding reservoirs. First, it is shown that by changing the damping rate due to one reservoir, magnitudes of heat currents of the other two reservoirs can behave in completely different manners, namely, although one may be enhanced, the other may instead be suppressed, and vice versa. Second, the sign of the heat current of one reservoir may change (i.e., crossover from heat absorption to heat release, or vice versa) if a damping rate or the coupling strength between the two TLSs is swept through a critical value, which depends on the temperature settings for the three reservoirs. Due to the asymmetric couplings of the two TLSs to the three reservoirs, the thermal rectification occurs without introducing any additional asymmetry to the systems.

We analyze nonperturbative renormalization group flow equations for the ordered phase of ${\mathbb{Z}}_2$ and $\mathrm{O}\left(N\right)$ invariant scalar models. This is done within the well-known derivative expansion scheme. For its leading order [local potential approximation (LPA)], we show that not every regulator yields a smooth flow with a convex free energy and discuss for which regulators the flow becomes singular. Then we generalize the known exact solutions of smooth flows in the “internal” region of the potential and exploit these solutions to implement an improved numerical algorithm, which is much more stable than previous ones for $N>1$. After that, we study the flow equations at second order of the derivative expansion and analyze how and when the LPA results change. We also discuss the evolution of the field renormalization factors.

We investigate time series by mapping them to the complex networks using a parametric natural visibility graph (PNVG) algorithm that generates graphs depending on arbitrary continuous parameter—the angle of view. We study the behavior of the relative number of clusters in PNVG near the critical value of the angle of view. Artificial and experimental time series of different nature are used for numerical PNVG investigations to find critical exponents above and below the critical point as well as the exponent in the finite size scaling regime. Altogether, they allow us to find the critical exponent of the correlation length for PNVG. The set of calculated critical exponents satisfies the basic Widom relation. The PNVG is found to demonstrate scaling behavior. Our results reveal the similarity between the behavior of the relative number of clusters in PNVG and the order parameter in the second-order phase transitions theory. We show that the PNVG is another example of a system (in addition to magnetic, percolation, superconductivity, etc.) with observed second-order phase transition

Rough energy landscape and noisy environment are two common features in many subjects, such as protein folding. Due to the wide findings of bursting or spiking phenomenon in biology science, small diffusions mixing large jumps are adopted to model the noisy environment that can be properly described by Lévy noise. We combine the Lévy noise with the rough energy landscape, modeled by a potential function superimposed by a fast oscillating function, and study the transport of a particle in a rough triple-well potential excited by Lévy noise, rather than only small perturbations. The probabilities of a particle staying in the middle well are considered under different amplitudes of roughness to find out how roughness affects the steady-state probability density function. Variations in the mean first passage time from the middle well to the right well have been investigated with respect to Lévy parameters and amplitudes of the roughness. In addition, we have examined the influences of roughness on the splitting probabilities of the first escape from the middle well. We uncover that the roughness can enhance significantly the first escape of a particle from the middle well, especially for different skewness parameters, but weak differences are found for stability index and noise intensity on the probabilities a particle staying in the middle well and splitting probability to the right.

We have analyzed the differential flow-induced instability in the presence of diffusive transport in a reaction-diffusion system following activator-inhibitor kinetics. The conspicuous interaction of differential flow and differential diffusivity that leads to pattern selection during transition of the traveling waves from stripes to rotating spots propagating in hexagonal arrays subsequent to wave splitting has been explored on the basis of a few-mode Galerkin scheme.

This two-dimensional study is motivated by cardiac electrophysiology, and focuses on rotating spiral waves in reaction-diffusion (RD) models. Here we deal with a spiral's translational drift under a constant externally imposed gradient $\mathbf{G}.$ A long-standing problem may be stated as follows: Given the dimensionless drift velocity $\mathbf{V}/G,$ find its nontrivial direction angle $\mathrm{\Gamma }$ relative to $\mathbf{G}$. A deductive algebraic treatment yields a solution, $cos\mathrm{\Gamma }=-V/G.$ Three features are worth noting: the combination of algebraic and RD contexts; a somewhat extensive derivation contrasting with a compact result; and the generality due to the absence of reaction details in the formula. Agreement with a computational database is good to fair, if spirals of very low density are excluded.

The discrete time mathematical models of evolution (the discrete time Eigen model, the Moran model, and the Wright-Fisher model) have many applications in complex biological systems. The discrete time Eigen model rather realistically describes the serial passage experiments in biology. Nevertheless, the dynamics of the discrete time Eigen model is solved in this paper. The 90% of results in population genetics are connected with the diffusion approximation of the Wright-Fisher and Moran models. We considered the discrete time Eigen model of asexual virus evolution and the Wright-Fisher model from population genetics. We look at the logarithm of probabilities and apply the Hamilton-Jacobi equation for the models. We define exact dynamics for the population distribution for the discrete time Eigen model. For the Wright-Fisher model, we express the exact steady state solution and fixation probability via the solution of some nonlocal equation then give the series expansion of the solution via degrees of selection and mutation rates. The diffusion theories result in the zeroth order approximation in our approach. The numeric confirms that our method works in the case of strong selection, whereas the diffusion method fails there. Although the diffusion method is exact for the mean first arrival time, it provides incorrect approximation for the dynamics of the tail of distribution.

A distinguishing feature of amoeboid motion is that the migrating cell undergoes large deformations, caused by the emergence and retraction of actin-rich protrusions, called pseudopods. Here, we propose a cell motility model that represents pseudopod dynamics, as well as its interaction with membrane signaling molecules. The model accounts for internal and external forces, such as protrusion, contraction, adhesion, surface tension, or those arising from cell-obstacle contacts. By coupling the membrane and cytosol interactions we are able to reproduce a realistic picture of amoeboid motion. The model results are in quantitative agreement with experiments and show how cells may take advantage of the geometry of their microenvironment to migrate more efficiently.

We investigate analytically a microfluidic device consisting of a tube with a nonuniform but spatially periodic diameter, where a fluid driven back and forth by a pump carries colloidal particles. Although the net flow of the fluid is zero, the particles move preferentially in one direction due to the ratchet mechanism, which occurs due to the simultaneous effect of inertial hydrodynamics and Brownian motion. We show that the average current is strongly sensitive to particle size, thus facilitating colloidal particle sorting.

Biomembranes, which are mainly composed of neutral and charged lipids, exhibit a large variety of functional structures and dynamics. Here, we report a coarse-grained molecular dynamics (MD) simulation of the phase separation and morphological dynamics in charged lipid bilayer vesicles. The screened long-range electrostatic repulsion among charged head groups delays or inhibits the lateral phase separation in charged vesicles compared with neutral vesicles, suggesting the transition of the phase-separation mechanism from spinodal decomposition to nucleation or homogeneous dispersion. Moreover, the electrostatic repulsion causes morphological changes, such as pore formation, and further transformations into disk, string, and bicelle structures, which are spatiotemporally coupled to the lateral segregation of charged lipids. Based on our coarse-grained MD simulation, we propose a plausible mechanism of pore formation at the molecular level. The pore formation in a charged-lipid-rich domain is initiated by the prior disturbance of the local molecular orientation in the domain.

The growth of the characteristic length scales both for diffusion and viscosity is investigated by molecular dynamics utilizing the finite-size effect in a binary Lennard-Jones mixture. For those quantities relevant to the diffusion process (e.g., the hydrodynamic value and the spatial correlation function), a strong system-size dependence is found. In contrast, it is weak or absent for the shear relaxation process. Correlation lengths are estimated from the decay of the spatial correlation functions. We find the length scale for viscosity decouples from the one of diffusivity, featured by a saturated length even in high supercooling. This temperature-independent behavior of the length scale is reminiscent of the unapparent structure change upon supercooling, implying the manifestation of configuration entropy. Whereas for the diffusion process, it is manifested by relaxation dynamics and dynamic heterogeneity. The Stokes-Einstein relation is found to break down at the temperature where the decoupling of these lengths happens.