Neural synchronization by means of mutual learning provides an avenue to design public key exchange protocols, bringing about what is known as neural cryptography. Two identically structured neural networks learn from each other and reach full synchronization eventually. The full synchronization enables two networks to have the same weight, which can be used as a secret key for many subsequent cryptographic purposes. It is striking to observe that after the first decade of neural cryptography, the tree parity machine (TPM) network with hidden unit $K=3$ appears to be the sole network that is suitable for a neural protocol. No convincingly secure neural protocol is well designed by using other network structures despite considerable research efforts. With the goal of overcoming the limitations of a suitable network structure, in this paper we develop a two-layer tree-connected feed-forward neural network (TTFNN) model for a neural protocol. The TTFNN model captures the notion that two partners are capable of exchanging a vector with multiple bits in each time step. An in-depth study of the dynamic process of TTFNN-based protocols is then undertaken, based upon which a feasible condition is theoretically obtained to seek applicable protocols. Afterward, according to two analytically derived heuristic rules, a complete methodology for designing feasible TTFNN-based protocols is elaborated. A variety of feasible neural protocols are constructed, which exhibit the effectiveness and benefits of the proposed model. With another look from the perspective of application, TTFNN-based instances, which can outperform the conventional TPM-based protocol with respect to synchronization speed, are also experimentally confirmed.

We investigate interacting phase oscillators whose mean field is at a different frequency from the mean or mode of their natural frequencies. The associated asymmetries lead to a macroscopic traveling wave. We show that the mean-ensemble frequency of such systems differs from their entrainment frequency. In some scenarios these frequencies take values that, counterintuitively, lie beyond the limits of the natural frequencies. The results indicate that a clear distinction should be drawn between the two variables describing the macroscopic dynamics of cooperative systems. This has important implications for real systems where a nontrivial distribution of parameters is common.

Recent studies of network science have revealed the sensitive dependence of network collective behaviors on structures; here we employ this feature of topological sensitivity for the purpose of pattern control. By simple models of networked chaotic oscillators, we are able to argue and demonstrate that, by manipulating just a single link in the network, the synchronous patterns of the system can be effectively adjusted or controlled. In particular, by changing the weight or the connection of a shortcut link in the network, we find not only that various stable synchronous patterns can be generated from the system but also that the synchronous patterns can be successfully switched among different forms. The stability of the synchronous patterns is analyzed by the method of eigenvalue analysis, and the feasibility of the control is verified by numerical simulations. Our study provides a step forward to the control of sophisticated collective behaviors in more complex networks, as well as insights to the evolution and function of some realistic complex systems.

We report that electrically driven shape deformation of a drop strongly affects the impacting behavior. The experiment shows that when a nonaxisymmetric drop impacts on hydrophobic substrates, it alternately spreads and recoils along two principal axes, subsequently suppressing its rebound. The rebound suppressions of the drops are investigated as a function of the Weber number, and consequently the critical We causing rebound is considerably higher than that of an axisymmetric drop. We rationalize the impacting behaviors originated from the breakup of axisymmetry using the three-dimensional numerical simulation. The simulations of nonaxisymmetric drops completely predict the axis-switching and reveal the consequent kinetic energy transfer between the horizontal principal axes rather than the vertical axis.

We investigate dynamo action in three-dimensional numerical simulations of turbulent spherical Couette flows. Close to the onset of dynamo action, the magnetic field exhibits an intermittent behavior, characterized by a series of short bursts of the magnetic energy separated by low-energy phases. We show that this behavior corresponds to the so-called on-off intermittency. This behavior is here reported for dynamo action with realistic boundary conditions. We investigate the role of magnetic boundary conditions in this phenomenon.

Fluid flow through isotropic and anisotropic porous medium systems is investigated for a range of Reynolds numbers corresponding to both Darcy and non-Darcy regimes. A non-dimensional formulation is developed for a Forchheimer approximation of the momentum balance, and lattice Boltzmann simulations are used to elucidate the effects of porous medium characteristics on macroscale constitutive relation parameters. The geometric orientation tensor of the solid phase is posited as a morphological measure of leading-order importance for the description of anisotropic flows. Simulation results are presented to confirm this hypothesis, and parameter correlations are developed to predict closure relation coefficients as a function of porous medium porosity, specific interfacial area of the solid phase, and the geometric orientation tensor. The developed correlations provide improved estimates of model coefficients compared to available estimates and extend predictive capabilities to fully determine macroscopic momentum parameters for three-dimensional flows in anisotropic porous media.

We present experimental results for laser pulse compression due to wakefield excitation in the relativistic regime using the spectral phase interferometry for direct electric-field reconstruction technique for complete pulse characterization. The results indicate that the pulse was compressed to a 10-fs duration which was verified by fully relativistic three-dimensional particle-in-cell simulations. Optimized modeling based on a hydrodynamic code was also done, showing the possibility of producing laser pulses of few-cycle duration.

Nucleation of ${}^4$He crystals from the metastable superfluid in high porosity silica aerogel was investigated by an optical measurement. Critical overpressures at which the first ${}^4$He crystal appeared during pressurization were measured 50 times at each temperature. Contrary to the intuitive pore-size-limited nucleation suggested in previous studies in small pores, the critical overpressure did show a characteristic temperature dependence, indicating that the critical size of nucleation is also temperature dependent. It is confirmed that quantum nucleation at low temperatures and thermal nucleation at high temperatures occur as in the case of bulk crystal. Nucleation in this high porosity material shows characters of nucleation in both bulk and pores.

Period variability, quantified by the standard deviation (SD) of the cycle-to-cycle period, is investigated for noisy phase oscillators. We define the checkpoint phase as the beginning or end point of one oscillation cycle and derive an expression for the SD as a function of this phase. We find that the SD is dependent on the checkpoint phase only when oscillators are coupled. The applicability of our theory is verified using a realistic model. Our work clarifies the relationship between period variability and synchronization from which valuable information regarding coupling can be inferred.

We study the periodically driven Brownian motion of a massive particle in one dimension subject to dry (Coulombic) friction. Analytical results are obtained by noticing that the particle velocity obeys the same Langevin equation as the spatial coordinate of an overdamped particle bound to a wedge potential, also in one dimension. The response to an external sinusoidal drive is calculated in linear response theory approximation. The analytical results thus obtained closely compare with the outcome of extensive numerical simulations. Finally we show how this model of Brownian motion can be utilized to characterize the diffusion of ultrarelativistic Brownian particles in the plane, a mechanism recently proposed to model diffusive transport of charge carriers in a graphene sheet.

The social network is a main tunnel of rumor spreading. Previous studies concentrated on a static rumor spreading. The content of the rumor is invariable during the whole spreading process. Indeed, the rumor evolves constantly in its spreading process, which grows shorter, more concise, more easily grasped, and told. In an early psychological experiment, researchers found about $70\%$ of details in a rumor were lost in the first six mouth-to-mouth transmissions. Based on these observations, we investigate rumor spreading on social networks, where the content of the rumor is modified by the individuals with a certain probability. In the scenario, they have two choices, to forward or to modify. As a forwarder, an individual disseminates the rumor directly to their neighbors. As a modifier, conversely, an individual revises the rumor before spreading it out. When the rumor spreads on the social networks, for instance, scale-free networks and small-world networks, the majority of individuals actually are infected by the multirevised version of the rumor, if the modifiers dominate the networks. The individuals with more social connections have a higher probability to receive the original rumor. Our observation indicates that the original rumor may lose its influence in the spreading process. Similarly, a true information may turn out to be a rumor as well. Our result suggests the rumor evolution should not be a negligible question, which may provide a better understanding of the generation and destruction of a rumor.

We consider off-equilibrium dynamics at the critical temperature in a class of glassy systems. The off-equilibrium correlation and response functions obey a precise scaling form in the aging regime. The structure of the equilibrium replicated Gibbs free energy fixes the corresponding off-equilibrium scaling functions implicitly through two functional equations. The details of the model enter these equations only through the ratio $w_2/w_1$ of the cubic coefficients (proper vertexes) of the replicated Gibbs free energy. Therefore the off-equilibrium dynamical exponents are controlled by the very same parameter exponent $\lambda =w_2/w_1$ that determines equilibrium dynamics. We find approximate solutions to the equations and validate the theory by means of analytical computations and numerical simulations.

We consider periodically driven dynamical systems with energetic and entropic barriers in the presence of deterministic noise. Due to the relaxational delay, the response of the system lags behind the applied field and exhibits dynamical hysteresis manifested in the nonvanishing area of the response-function–field loop. It is demonstrated that the hysteresis loop area satisfies a scaling law with exponents that depend on the nature of the barrier.

We study the freezing kinetics of colloidal polycrystals made of micelles of Pluronic F108, a thermosensitive copolymer, to which a small amount of silica nanoparticles of a size comparable to that of the micelles are added. We use rheology and calorimetry to measure $T_c$, the crystallization temperature, and find that $T_c$ increases with the heating rate $\dot{T}$ used to crystallize the sample. To rationalize our results, we first use viscosity measurements to establish a linear mapping between temperature $T$ and the effective volume fraction, $\phi$, of the micelles, treated as hard spheres. Next, we reproduce the experimental $\dot{T}$ dependence of the crystallization temperature with numerical calculations based on standard models for the nucleation and growth of hard-sphere crystals, classical nucleation theory and the Johnson-Mehl-Avrami-Kolmogorov theory. The models have been adapted to account for the peculiarities of our experiments: the presence of nanoparticles that are expelled in the grain boundaries and the steady increase of $T$ and, hence, $\phi$ during the experiment. We moreover show that the polycrystal grain size obtained from the calculations is in good agreement with light microscopy data. Finally, we find that the $\phi$ dependence of the nucleation rate for the micellar polycrystal is in remarkable quantitative agreement with that found in previous experiments on colloidal hard spheres. These results suggests that deep analogies exist between hard-sphere colloidal crystals and Pluronics micellar crystals, in spite of the difference in particle softness. More generally, our results demonstrate that crystallization processes can be quantitatively probed using standard rheometry.

Smectic-$A$ monolayers self-assembled in aqueous solutions of chiral $\mathit{fd}$ viruses and a polymer depletant have been shown to exhibit a variety of structures, including large, flat disks and twisted ribbons. The virus particles twist near the edge of the structure in a direction determined by the chirality of the viruses. When $\mathit{fd}$ viruses and their mutants of opposite chirality are mixed together in nearly equal amounts, unusual structures referred to as “crenellated” disks can appear. These disks are achiral overall but the twist at the edge alternates between left- and right-handedness. To minimize the mismatch where the two regions of opposing twist meet, the crenellated structure exhibits cusps rising out of the plane of the monolayer. We use a phenomenological elastic theory previously applied to flat disks and twisted ribbons to analyze an analytic model proposed to describe the crenellated structure. When compared with flat, circular disks, we find that the model crenellated disks are stable or at least metastable in a wide region of the phase diagram spanned by the Gaussian curvature modulus and the edge energy modulus, with a large energy barrier separating the two structures. The director pattern and geometric parameters of the crenellated disks are found to be in qualitative agreement with experimental observations.

In the current work, we investigate the evolutionary dynamics of a spatially structured population model defined on a continuous lattice. In the model, individuals disperse at a constant rate $v$ and competition is local and delimited by the competition radius $R$. Due to dispersal, the neighborhood size (number of individuals competing for reproduction) fluctuates over time. Here we address how these new variables affect the adaptive process. While the fixation probabilities of beneficial mutations are roughly the same as in a panmitic population for small fitness effects $s$, a dependence on $v$ and $R$ becomes more evident for large $s$. These quantities also strongly influence fixation times, but their dependencies on $s$ are well approximated by $s^{-1/2}$, which means that the speed of the genetic wave front is proportional to $\sqrt{s}$. Most important is the observation that the model exhibits a dual behavior displaying a power-law growth for the fixation rate and speed of adaptation with the beneficial mutation rate, as observed in other spatially structured population models, while simultaneously showing a nonsaturating behavior for the speed of adaptation with the population size $N$, as in homogeneous populations.

Collective properties of many rodlike circle swimmers are explored by computer simulations in two spatial dimensions. In the model considered, the center of mass of a single swimmer moves on a circle with radius $R$. Therefore, the model provides an interpolation between an interacting self-propelled-rod model for linear swimmers ($R\to \infty$) and that of interacting passive rotors ($R=0$). We map out the state diagram for various swimmer densities and radii $R$. For increasing density, the dilute state is followed by vortices consisting of single particles (singlet-vortex state), where neighboring particles are perpendicularly oriented, and vortices of swimmer pairs (doublet-vortex state). The vortices exhibit strong structural ordering on an array. At higher densities, a slowed rotor fluid with a significant degree of mutual rotation hindrance occurs. The single-particle vortex structure becomes unstable above a threshold in the circling radius $R$, while pair vortices are stable only for intermediate radii $R$. A simple theory is proposed to predict the topology of the state diagram. Our results are verifiable for bacterial and artificial rodlike circle swimmers.

We introduce a simple model of earthquakes, inspired by the spring-block models, but describing contacts at a mesoscale. A single contact point synthesizes many rock contacts so that these “macrocontacts” can have an internal dynamics, described by a stochastic process, that leads to an evolution of their breaking thresholds. This aging process leads to the Gutenberg-Richter law, which relates the probability of occurrence of earthquakes to their magnitude. An analytical approach is used to determine the range of magnitudes in which this law applies.

Reaction-diffusion processes, used to model various spatially distributed dynamics such as epidemics, have been studied mostly on regular lattices or complex networks with simplex links that are identical and invariant in transferring different kinds of particles. However, in many self-organized systems, different particles may have their own private channels to keep their purities. Such division of links often significantly influences the underlying reaction-diffusion dynamics and thus needs to be carefully investigated. This article studies a special reaction-diffusion process, named susceptible-infected-susceptible (SIS) dynamics, given by the reaction steps $\beta \to \alpha$ and $\alpha +\beta \to 2\beta$, on duplex networks where links are classified into two groups: $\alpha$ and $\beta$ links used to transfer $\alpha$ and $\beta$ particles, which, along with the corresponding nodes, consist of an $\alpha$ subnetwork and a $\beta$ subnetwork, respectively. It is found that the critical point of particle density to sustain reaction activity is independent of the network topology if there is no correlation between the degree sequences of the two subnetworks, and this critical value is suppressed or extended if the two degree sequences are positively or negatively correlated, respectively. Based on the obtained results, it is predicted that epidemic spreading may be promoted on positive correlated traffic networks but may be suppressed on networks with modules composed of different types of diffusion links.