Three-dimensional solidification of a pure material with isotropic properties of the solid phase is studied in cylindrical capillaries of various cross sections (circular, hexagonal, and square). As the undercooling is increased, we find, depending on the width of the capillary, a number of different growth modes and dynamical behaviors, including stationary symmetric single fingers, stationary asymmetric fingers, and oscillating double and quadruple fingers. Chaotic states are also observed, some of them in unexpected parameter regions. Our simulations suggest that the bifurcation from symmetric to asymmetric fingers is supercritical. We discuss the nature of the oscillatory states, one of which is chirality breaking, and the origin of the unexpected chaotic finger. Bifurcation diagrams are given comparing three different ratios of capillary length to channel width in the hexagonal channel as well as the three different geometries.

Using two-dimensional Langevin dynamics simulations, we investigate the dynamics of polymer translocation into a fluidic channel with diameter $R$ through a nanopore under a driving force $F$. Due to the crowding effect induced by the partially translocated monomers, the translocation dynamics is significantly altered in comparison to an unconfined environment, namely, we observe a nonuniversal dependence of the translocation time $\tau$ on the chain length $N$. $\tau$ initially decreases rapidly and then saturates with increasing $R$, and a dependence of the scaling exponent $\alpha$ of $\tau$ with $N$ on the channel width $R$ is observed. The otherwise inverse linear scaling of $\tau$ with $F$ breaks down and we observe a minimum of $\alpha$ as a function of $F$. These behaviors are interpreted in terms of the waiting time of an individual segment passing through the pore during translocation.

We theoretically consider specific adhesion of a fluctuating membrane to a hard substrate via the formation of bonds between receptors attached to the substrate and ligands in the membrane. By integrating out the degrees of freedom of the membrane shape, we show that in the biologically relevant limit specific adhesion is well described by a lattice gas model, where lattice sites correspond to bond sites. We derive an explicit expression for the effective bond interactions induced by the thermal undulations of the membrane. Furthermore, we compare kinetic Monte Carlo simulations for our lattice gas model with full dynamic simulations that take into account both the shape fluctuations of the membrane and reactions between receptors and ligands at bond sites. We demonstrate that an appropriate mapping of the height dependent binding and unbinding rates in the full scheme to rates in the lattice gas model leads to good agreement.

Brain functioning such as cognitive performance depends on the functional interactions between brain areas, namely, the functional brain networks. The functional brain networks of a group of patients with brain tumors are measured before and after tumor resection. In this work, we perform a weighted network analysis to understand the effect of neurosurgery on the characteristics of functional brain networks. Statistically significant changes in network features have been discovered in the beta (13–30 Hz) band after neurosurgery: the link weight correlation around nodes and within triangles increases which implies improvement in local efficiency of information transfer and robustness; the clustering of high link weights in a subgraph becomes stronger, which enhances the global transport capability; and the decrease in the synchronization or virus spreading threshold, revealed by the increase in the largest eigenvalue of the adjacency matrix, which suggests again the improvement of information dissemination.

We derive an approximate expression for mutual information in a broad class of discrete-time stationary channels with continuous input, under the constraint of vanishing input amplitude or power. The approximation describes the input by its covariance matrix, while the channel properties are described by the Fisher information matrix. This separation of input and channel properties allows us to analyze the optimality conditions in a convenient way. We show that input correlations in memoryless channels do not affect channel capacity since their effect decreases fast with vanishing input amplitude or power. On the other hand, for channels with memory, properly matching the input covariances to the dependence structure of the noise may lead to almost noiseless information transfer, even for intermediate values of the noise correlations. Since many model systems described in mathematical neuroscience and biophysics operate in the high-noise regime and weak-signal conditions, we believe, that the described results are of potential interest also to researchers in these areas.

Although it is unambiguously agreed that structure plays a fundamental role in shaping the collective dynamics of complex systems, how structure determines dynamics exactly still remains unclear. We investigate a general computational transformation by which we can map the network topology directly to the dynamical patterns emergent on it—independent of the nature of the dynamical processes. Remarkably, we find that many seemingly different dynamical processes on networks, such as coupled oscillators, ensemble neuron firing, epidemic spreading and diffusion can all be understood and unified through this same procedure. Utilizing the inherent multiscale nature of this structure-dynamics transformation, we further define a multiscale complexity measure, which can quantify the functional diversity a general network can support at different organization levels using only its structure. We find that a wide variety of topological features observed in real networks, such as modularity, hierarchy, degree heterogeneity and mixing all result in higher complexity. This result suggests that the demand for functional diversity is driving the structural evolution of physical networks.

We present a quantitative measure of physical complexity, based on the amount of information required to build a given physical structure through self-assembly. Our procedure can be adapted to any given geometry, and thus, to any given type of physical structure that can be divided into building blocks. We illustrate our approach using self-assembling polyominoes, and demonstrate the breadth of its potential applications by quantifying the physical complexity of molecules and protein complexes. This measure is particularly well suited for the detection of symmetry and modularity in the underlying structure, and allows for a quantitative definition of structural modularity. Furthermore we use our approach to show that symmetric and modular structures are favored in biological self-assembly, for example in protein complexes. Lastly, we also introduce the notions of joint, mutual and conditional complexity, which provide a useful quantitative measure of the difference between physical structures.

A great number of physical processes are described within the context of Hamiltonian scattering. Previous studies have rather been focused on trajectories starting outside invariant structures, since the ones starting inside are expected to stay trapped there forever. This is true though only for the deterministic case. We show however that, under finitely small random fluctuations of the field, trajectories starting inside Kolmogorov-Arnold-Moser (KAM) islands escape within finite time. The nonhyperbolic dynamics gains then hyperbolic characteristics due to the effect of the random perturbed field. As a consequence, trajectories which are started inside KAM curves escape with hyperboliclike time decay distribution, and the fractal dimension of a set of particles that remain in the scattering region approaches that for hyperbolic systems. We show a universal quadratic power law relating the exponential decay to the amplitude of noise. We present a random walk model to relate this distribution to the amplitude of noise, and investigate these phenomena with a numerical study applying random maps.

The electromagnetic two-body problem has neutral differential delay equations of motion that, for generic boundary data, can have solutions with discontinuous derivatives. If one wants to use these neutral differential delay equations with arbitrary boundary data, solutions with discontinuous derivatives must be expected and allowed. Surprisingly, Wheeler-Feynman electrodynamics has a boundary value variational method for which minimizer trajectories with discontinuous derivatives are also expected, as we show here. The variational method defines continuous trajectories with piecewise defined velocities and accelerations, and electromagnetic fields defined by the Euler-Lagrange equations on trajectory points. Here we use the piecewise defined minimizers with the Liénard-Wierchert formulas to define generalized electromagnetic fields almost everywhere (but on sets of points of zero measure where the advanced/retarded velocities and/or accelerations are discontinuous). Along with this generalization we formulate the generalized absorber hypothesis that the far fields vanish asymptotically almost everywhere and show that localized orbits with far fields vanishing almost everywhere must have discontinuous velocities on sewing chains of breaking points. We give the general solution for localized orbits with vanishing far fields by solving a (linear) neutral differential delay equation for these far fields. We discuss the physics of orbits with discontinuous derivatives stressing the differences to the variational methods of classical mechanics and the existence of a spinorial four-current associated with the generalized variational electrodynamics.

We relate the second-order structure function of a time series with the power spectrum of the original variable, taking an assumption of statistical stationarity. With this approach, we find that the structure function is strongly influenced by the large scales. The large-scale contribution and the contribution range are, respectively, 79% and 1.4 decades for a Kolmogorov $-5/3$ power spectrum. We show numerically that a single scale influence range, over smaller scales is about 2 decades. We argue that the structure function is not a good method to extract the scaling exponents when the data possess large energetic scales. An alternative methodology, the arbitrary order Hilbert spectral analysis which may constrain this influence within 0.3 decade, is proposed to characterize the scaling property directly in an amplitude-frequency space. An analysis of passive scalar (temperature) turbulence time series is presented to show the influence of large-scale structures in real turbulence and the efficiency of the Hilbert-based methodology. The corresponding scaling exponents ${\zeta }_{\theta }\left(q\right)$ provided by the Hilbert-based approach indicate that the passive scalar turbulence field may be less intermittent than what was previously believed.

We examine the dynamics of a two-dimensional drop on an inclined substrate vibrating vertically. The drop is assumed to be driven by its contact lines, while its shape is determined by a quasistatic balance of surface tension, gravity, and vibration-induced inertial force. It is shown that, if the dependence of the inertial force on time involves narrow/deep “troughs” and wide/low “plateaus,” the drop can climb uphill. For thin drops, this conclusion is obtained analytically, whereas the general case is treated numerically. It is demonstrated that the nonlinear effects (associated with the large thickness of the drop) dramatically strengthen the drop’s uphill motion.

Radiative opacity and emissivity of tin plasmas at average ionization degree of about 10 was investigated in detail by using a fully relativistic detailed level accounting approach, in which main physical effects on the opacity were carefully taken into account. Among these physical effects, configuration interaction, in particular core-valence electron correlations, plays an important role on the determination of accurate atomic data required in the calculation of opacity. It results in a strong narrowing of lines from all transition arrays and strong absorption is located in a narrow wavelength region of 12.5–14 nm for Sn plasmas. Using a complete accurate atomic data, we investigated the opacity of Sn plasmas at a variety of physical condition. Among the respective ions of ${\text{Xe}}^{6+}{\text{-Xe}}^{15+}$, ${\text{Xe}}^{10+}$ has the largest absorption cross section at 13.5 nm, while the favorable physical condition for maximal absorption at 13.5 nm do not mean that ${\text{Xe}}^{10+}$ has the largest fraction. Comparison with other theoretical results showed that a complete set of consistent accurate atomic data, which lacks very much, is essential to predict accurate opacity. Our atomic model is useful and can be applied to interpret opacity experiments. Further benchmark experiments are urgently needed to clarify the physical effects on the opacity of Sn plasmas.

The linearized potential of a moving test charge in a one-component fully degenerate fermion plasma is studied using the Lindhard dielectric function. The motion is found to greatly enhance the Friedel oscillations behind the charge, especially for velocities larger than half of the Fermi velocity, in which case the asymptotic behavior of their amplitude changes from $1/r^3$ to $1/r^{2.5}$. In the absence of the quantum recoil (tunneling) the potential reduces to a form similar to that in a classical Maxwellian plasma, with a difference being that the plasma oscillations behind the charge at velocities larger than the Fermi velocity are not Landau damped.

We investigate feedback-controlled coherent dynamics in a two-dimensional array of excitable elements. We demonstrate that one can freely enhance or reduce the spatiotemporal coherence of noise-induced oscillation, such as coherence resonance and phase synchronization, by controlling both the delay time and the feedback gain. Furthermore, we find that noise-induced oscillations are entrained by the feedback force in a certain range of the delay time. Experimental observations are approximately reproduced in a numerical simulation with a forced Oregonator model.

Quasielastic neutron scattering was used to study the dynamics of three-dimensional confined water in a hydrophobic mesoporous material designated as CMK-1 in the temperature range from 250 to 170 K. We observe a crossover phenomenon at temperature $T_L$. We find that $T_L$ of water confined in CMK-1 occurs in between previous observations of one-dimensional confined water in materials with different hydrophilicities. This provides the first evidence that besides the obvious surface effect brought about by the hydrophobic confinements, $T_L$ is also dependent on the dimensionality of the geometry of the confinement.

Return distributions of the coherent noise model are studied for the system-size-independent case. It is shown that, in this case, these distributions are in the shape of $q$ Gaussians, which are the standard distributions obtained in nonextensive statistical mechanics. Moreover, an exact relation connecting the exponent $\tau$ of avalanche size distribution and the $q$ value of appropriate $q$ Gaussian has been obtained as $q=\left(\tau +2\right)/\tau$. Making use of this relation one can easily determine $q$ parameter values of the appropriate $q$ Gaussians a priori from one of the well-known exponents of the system. Since the coherent noise model has the advantage of producing different $\tau$ values by varying a model parameter $\sigma$, clear numerical evidences on the validity of the proposed relation have been achieved for various cases. Finally, the effect of the system size has also been analyzed and an analytical expression has been proposed, which is corroborated by the numerical results.

The Weierstrass random walk is a paradigmatic Markov chain giving rise to a Lévy-type superdiffusive behavior. It is well known that special relativity prevents the arbitrarily high velocities necessary to establish a superdiffusive behavior in any process occurring in Minkowski spacetime, implying, in particular, that any relativistic Markov chain describing spacetime phenomena must be essentially Gaussian. Here, we introduce a simple relativistic extension of the Weierstrass random walk and show that there must exist a transition time $t_c$ delimiting two qualitative distinct dynamical regimes: the (nonrelativistic) superdiffusive Lévy flights, for $t<t_c$, and the usual (relativistic) Gaussian diffusion, for $t>t_c$. Implications of this crossover between different diffusion regimes are discussed for some explicit examples. The study of such an explicit and simple Markov chain can shed some light on several results obtained in much more involved contexts.

We study the $q$-state Potts-glass neural network with the pseudoinverse (PI) rule. Its performance is investigated and compared with that of the counterpart network with the Hebbian rule instead. We find that there exists a critical point of $q$, i.e., $q_{cr}=14$, below which the storage capacity and the retrieval quality can be greatly improved by introducing the PI rule. We show that the dynamics of the neural networks constructed with the two learning rules respectively are quite different; but however, regardless of the learning rules, in the $q$-state Potts-glass neural networks with $q\ge 3$ there is a common novel dynamical phase in which the spurious memories are completely suppressed. This property has never been noticed in the symmetric feedback neural networks. Free from the spurious memories implies that the multistate Potts-glass neural networks would not be trapped in the metastable states, which is a favorable property for their applications.

Dynamic stabilization of incompressible and immiscible Newtonian fluids is studied by means of an approximate analytical model that considers the vertical vibration of the interface between the fluids. The force driving the vibration is modeled by periodic sequences of Dirac deltas. The model shows the roles played by surface tension and viscosity in determining the stability boundaries and the relevant similarity parameters are found. The results are compared with previous theoretical and experimental studies that used a sinusoidal vibration and they are found to present the same qualitative features provided a symmetric sequence of Dirac deltas is considered. Instead, important differences are observed when an asymmetric driving is used.