In data-based reconstruction of complex networks, dynamical information can be measured and exploited to generate a functional network, but is it a true representation of the actual (structural) network? That is, when do the functional and structural networks match and is a perfect matching possible? To address these questions, we use coupled nonlinear oscillator networks and investigate the transition in the synchronization dynamics to identify the conditions under which the functional and structural networks are best matched. We find that, as the coupling strength is increased in the weak-coupling regime, the consistency between the two networks first increases and then decreases, reaching maximum in an optimal coupling regime. Moreover, by changing the network structure, we find that both the optimal regime and the maximum consistency will be affected. In particular, the consistency for heterogeneous networks is generally weaker than that for homogeneous networks. Based on the stability of the functional network, we propose further an efficient method to identify the optimal coupling regime in realistic situations where the detailed information about the network structure, such as the network size and the number of edges, is not available. Two real-world examples are given: corticocortical network of cat brain and the Nepal power grid. Our results provide new insights not only into the fundamental interplay between network structure and dynamics but also into the development of methodologies to reconstruct complex networks from data.

Intermittency of Lagrangian velocity and acceleration is a key to understanding transport in complex systems ranging from fluid turbulence to flow in porous media. High-resolution optical particle tracking in a three-dimensional (3D) porous medium provides detailed 3D information on Lagrangian velocities and accelerations. We find sharp transitions close to pore throats, and low flow variability in the pore bodies, which gives rise to stretched exponential Lagrangian velocity and acceleration distributions characterized by a sharp peak at low velocity, superlinear evolution of particle dispersion, and double-peak behavior in the propagators. The velocity distribution is quantified in terms of pore geometry and flow connectivity, which forms the basis for a continuous-time random-walk model that sheds light on the observed Lagrangian flow and transport behaviors.

We investigated the appearance of Chern-Simons terms in electrodynamics at the surface or interface of materials. The requirement of locality, gauge invariance, and renormalizability in this model is imposed. Scattering and reflection of electromagnetic waves in three different homogeneous layers of media is determined. Snell's law is preserved. However, the transmission and reflection coefficient depend on the strength of the Chern-Simons interaction (connected with Hall conductance), and parallel and perpendicular components are mixed.

Methods for forecasting time series are a critical aspect of the understanding and control of complex networks. When the model of the network is unknown, nonparametric methods for prediction have been developed, based on concepts of attractor reconstruction pioneered by Takens and others. In this Rapid Communication we consider how to make use of a subset of the system equations, if they are known, to improve the predictive capability of forecasting methods. A counterintuitive implication of the results is that knowledge of the evolution equation of even one variable, if known, can improve forecasting of all variables. The method is illustrated on data from the Lorenz attractor and from a small network with chaotic dynamics.

We obtain explicit susceptibilities for the countable infinity of phase transition temperatures of Müller-Hartmann-Zitartz on a Cayley tree. The susceptibilities are a product of the zeroth spin with the sum of an appropriate set of averages of spins on the outermost layer of the tree. A clear physical understanding for these strange phase transitions emerges naturally. In the thermodynamic limit, the susceptibilities tend to zero above the transition and to infinity below it.

A modified Ginzburg-Landau model with a screened nonlocal interaction in the quartic term is treated via Wilson's renormalization-group scheme at one-loop order to explore the critical behavior of the paramagnetic-to-ferromagnetic phase transition in perovskite manganites. We find the Fisher exponent $\eta$ to be $O\left(\epsilon \right)$ and the correlation exponent to be $\nu =\frac{1}{2}+O\left(\epsilon \right)$ through epsilon expansion in the parameter $\epsilon =d_c-d$, where $d$ is the space dimension, $d_c=4+2\sigma$ is the upper critical dimension, and $\sigma$ is a parameter coming from the nonlocal interaction in the model Hamiltonian. The ensuing critical exponents in three dimensions for different values of $\sigma$ compare well with various existing experimental estimates for perovskite manganites with various doping levels. This suggests that the nonlocal model Hamiltonian contains a wide variety of such universality classes.

The temperature dependence of the dynamics of water inside microporous activated carbon fibers (ACF) is investigated by means of incoherent elastic and quasielastic neutron-scattering techniques. The aim is to evaluate the effect of increasing pore size on the water dynamics in these primarily hydrophobic slit-shaped channels. Using two different micropore sizes ($\sim 12$ and 18 Å, denoted, respectively, ACF-10 and ACF-20), a clear suppression of the mobility of the water molecules is observed as the pore gap or temperature decreases. This suppression is accompanied by a systematic dependence of the average translational diffusion coefficient $D_r$ and relaxation time $\langle {\tau }_0\rangle$ of the restricted water on pore size and temperature. The observed $D_r$ values are tested against a proposed scaling law, in which the translational diffusion coefficient $D_r$ of water within a porous matrix was found to depend solely on two single parameters, a temperature-independent translational diffusion coefficient $D_c$ associated with the water bound to the pore walls and the ratio $\theta$ of this strictly confined water to the total water inside the pore, yielding unique characteristic parameters for water transport in these carbon channels across the investigated temperature range.

We study the effect of viscoelastic dynamics on the frictional properties of a (mean-field) spring-block system pulled on a rough surface by an external drive. When the drive moves at constant velocity $V$, two dynamical regimes are observed: at fast driving, above a critical threshold $V^c$, the system slides at the drive velocity and displays a friction force with velocity weakening. Below $V^c$ the steady sliding becomes unstable and a stick-slip regime sets in. In the slide-hold-slide driving protocol, a peak of the friction force appears after the hold time and its amplitude increases with the hold duration. These observations are consistent with the frictional force encoded phenomenologically in the rate-and-state equations. Our model gives a microscopical basis for such macroscopic description.

In this work, we study the synchronization in a generalized Kuramoto model with frequency-weighted coupling. In particular, we focus on the situations in which the frequency distributions of oscillators are asymmetric. For typical unimodal frequency distributions, such as Lorentzian, Gaussian, triangle, and even special Rayleigh, we find that the synchronization transition in the model generally converts from the first order to the second order as the central frequency shifts toward positive direction. We characterize two interesting coherent states in the system: In the former, two phase-locking clusters are formed, rotating with the same frequency. They correspond to those oscillators with relatively high frequencies while the oscillators with relatively small frequencies are not entrained. In the latter, two phase-locking clusters rotate with different frequencies, leading to the oscillation of the order parameter. We further conduct theoretical analysis to reveal the relation between the asymmetric frequency distribution and the conversion of synchronization type, and justify the coherent states observed in the system.

We investigate the level density for several ensembles of positive random matrices of a Wishart-like structure, $W=X{X}^{†}$, where $X$ stands for a non-Hermitian random matrix. In particular, making use of the Cauchy transform, we study the free multiplicative powers of the Marchenko-Pastur (MP) distribution, ${\mathrm{MP}}^{⊠s}$, which for an integer $s$ yield Fuss-Catalan distributions corresponding to a product of $s$-independent square random matrices, $X=X_1\cdots X_s$. New formulas for the level densities are derived for $s=3$ and $s=1/3$. Moreover, the level density corresponding to the generalized Bures distribution, given by the free convolution of arcsine and MP distributions, is obtained. We also explain the reason of such a curious convolution. The technique proposed here allows for the derivation of the level densities for several other cases.

We discuss the details of ambipolar relaxation of the electric field in liquid asymmetric electrolytes to its stationary value. It is demonstrated that the account for finite boundary conditions modifies the existing concepts of this diffusion process. In particular, we succeeded to suggest a qualitatively correct explanation of the observed distribution of the electric fields over the bulk of the cuvette and its nonmonotonic behavior in measurements on the finite-size cuvette. We analyze the conditions of such an anomaly at the intermediate stages of the relaxation process.

We have measured the dynamic structure factor of liquid para-hydrogen mixed with normal deuterium $(T=20 \mathrm{K}$) at two different concentration levels using incoherent inelastic neutron scattering. This choice has been made since the presence of ${\mathrm{D}}_2$ modifies the self-dynamics of ${\mathrm{H}}_2$ in a highly nontrivial way, acting both on its pseudophononic and its diffusive parts in a tunable way. After an accurate data reduction, recorded neutron spectra were studied through the modified Young and Koppel model and the ${\mathrm{H}}_2$ center-of-mass self-dynamics structure factor was finally extracted for the two mixtures. Some physical quantities (i.e., self-diffusion coefficient and mean kinetic energy) were determined and compared with accurate quantum calculations, which, in addition, also provided estimates of the velocity autocorrelation function for the ${\mathrm{H}}_2$ centers of mass. These estimates, in conjunction with the Gaussian approximation, were used to simulate the ${\mathrm{H}}_2$ center-of-mass self-dynamics structure factor in the same range as the experimental one. The agreement between measured and calculated spectra was globally good, but some discrepancies proved the unquestionable breakdown of the Gaussian approximation in these semiquantum systems at a level comparable to that already observed in pure liquid para-hydrogen.

Investigations of the phase diagram of biaxial liquid-crystal systems through analyses of general Hamiltonian models within the simplifications of mean-field theory (MFT), as well as by computer simulations based on microscopic models, are directed toward an appreciation of the role of the underlying molecular-level interactions to facilitate its spontaneous condensation into a nematic phase with biaxial symmetry. Continuing experimental challenges in realizing such a system unambiguously, despite encouraging predictions from MFT, for example, are requiring more versatile simulational methodologies capable of providing insights into possible hindering barriers within the system, typically gleaned through its free-energy dependences on relevant observables as the system is driven through the transitions. The recent paper from this group [Kamala Latha et al., Phys. Rev. E 89, 050501(R) (2014)], summarizing the outcome of detailed Monte Carlo simulations carried out employing an entropic sampling technique, suggested a qualitative modification of the MFT phase diagram as the Hamiltonian is asymptotically driven toward the so-called partly repulsive regions. It was argued that the degree of (cross) coupling between the uniaxial and biaxial tensor components of neighboring molecules plays a crucial role in facilitating a ready condensation of the biaxial phase, suggesting that this could be a plausible factor in explaining the experimental difficulties. In this paper, we elaborate this point further, providing additional evidence from curious variations of free-energy profiles with respect to the relevant orientational order parameters, at different temperatures bracketing the phase transitions.

Star polymers provide model architectures to understand the dynamic and rheological effects of chain confinement for a range of complex topological structures like branched polymers, colloids, and micelles. It is important to describe the structure of such macromolecular topologies using small-angle neutron and x-ray scattering to facilitate understanding of their structure-property relationships. Modeling of scattering from linear, Gaussian polymers, such as in the melt, has applied the random phase approximation using the Debye polymer scattering function. The Flory-Huggins interaction parameter can be obtained using neutron scattering by this method. Gaussian scaling no longer applies for more complicated chain topologies or when chains are in good solvents. For symmetric star polymers, chain scaling can differ from $\nu =0.5(d_f=2)$ due to excluded volume, steric interaction between arms, and enhanced density due to branching. Further, correlation between arms in a symmetric star leads to an interference term in the scattering function first described by Benoit for Gaussian chains. In this work, a scattering function is derived which accounts for interarm correlations in symmetric star polymers as well as the polymer-solvent interaction parameter for chains of arbitrary scaling dimension using a hybrid Unified scattering function. The approach is demonstrated for linear, four-arm and eight-arm polyisoprene stars in deuterated $p$-xylene.

Recordings in the human medial temporal lobe have found many neurons that respond to pictures (and related stimuli) of just one particular person of those presented. It has been proposed that these are concept cells, responding to just a single concept. However, a direct experimental test of the concept cell idea appears impossible, because it would need the measurement of the response of each cell to enormous numbers of other stimuli. Here we propose a new statistical method for analysis of the data that gives a more powerful way to analyze how close data are to the concept-cell idea. Central to the model is the neuronal sparsity, defined as the total fraction of stimuli that elicit an above-threshold response in the neuron. The model exploits the large number of sampled neurons to give sensitivity to situations where the average response sparsity is much less than one response for the number of presented stimuli. We show that a conventional model where a single sparsity is postulated for all neurons gives an extremely poor fit to the data. In contrast, a model with two dramatically different populations gives an excellent fit to data from the hippocampus and entorhinal cortex. In the hippocampus, one population has 7% of the cells with a 2.6% sparsity. But a much larger fraction (93%) respond to only 0.1% of the stimuli. This can result in an extreme bias in the responsiveness of reported neurons compared with a typical neuron. Finally, we show how to allow for the fact that some identified units correspond to multiple neurons and find that our conclusions at the neural level are quantitatively changed but strengthened, with an even stronger difference between the two populations.

We present a general method for analyzing mixed-mode oscillations (MMOs) in parametrically and externally excited systems with two low excitation frequencies (PEESTLEFs) for the case of arbitrary $m\text{:}n$ relation between the slow frequencies of excitations. The validity of the approach has been demonstrated using the equations of Duffing and van der Pol, separately. Our study shows that, by introducing a slow variable and finding the relation between the slow variable and the slow excitations, PEESTLEFs can be transformed into a fast-slow form with a single slow variable and therefore MMOs observed in PEESTLEFs can be understood by the classical machinery of fast subsystem analysis of the transformed fast-slow system.

The mixing of materials due to the Richtmyer-Meshkov instability and the ensuing turbulent behavior is of intense interest in a variety of physical systems including inertial confinement fusion, combustion, and the final stages of stellar evolution. Extensive numerical and laboratory studies of shock-driven mixing have demonstrated the rich behavior associated with the onset of turbulence due to the shocks. Here we report on progress in understanding shock-driven mixing at interfaces between fluids of differing densities through three-dimensional (3D) numerical simulations using the rage code in the implicit large eddy simulation context. We consider a shock-tube configuration with a band of high density gas (${\mathrm{SF}}_6$) embedded in low density gas (air). Shocks with a Mach number of 1.26 are passed through ${\mathrm{SF}}_6$ bands, resulting in transition to turbulence driven by the Richtmyer-Meshkov instability. The system is followed as a rarefaction wave and a reflected secondary shock from the back wall pass through the ${\mathrm{SF}}_6$ band. We apply a variety of initial perturbations to the interfaces between the two fluids in which the physical standard deviation, wave number range, and the spectral slope of the perturbations are held constant, but the number of modes initially present is varied. By thus decreasing the density of initial spectral modes of the interface, we find that we can achieve as much as 25% less total mixing at late times. This has potential direct implications for the treatment of initial conditions applied to material interfaces in both 3D and reduced dimensionality simulation models.

Jamming is a geometric phase transition occurring in dense particle systems in the absence of temperature. We use computer simulations to analyze the effect of thermal fluctuations on several signatures of the transition. We show that scaling laws for bulk and shear moduli only become relevant when thermal fluctuations are extremely small, and propose their relative ratio as a quantitative signature of jamming criticality. Despite the nonequilibrium nature of the transition, we find that thermally induced fluctuations and mechanical responses obey equilibrium fluctuation-dissipation relations near jamming, provided the appropriate fluctuating component of the particle displacements is analyzed. This shows that mechanical moduli can be directly measured from particle positions in mechanically unperturbed packings, and suggests that the definition of a “nonequilibrium index” is unnecessary for amorphous materials. We find that fluctuations of particle displacements are spatially correlated, and define a transverse and a longitudinal correlation length scale which both diverge as the jamming transition is approached. We analyze the frozen component of density fluctuations and find that it displays signatures of nearly hyperuniform behavior at large length scales. This demonstrates that hyperuniformity in jammed packings is unrelated to a vanishing compressibility and explains why it appears remarkably robust against temperature and density variations. Differently from jamming criticality, obstacles preventing the observation of hyperuniformity in colloidal systems do not originate from thermal fluctuations.

Numerical methods are proposed for an advanced Poisson-Nernst-Planck-Fermi (PNPF) model for studying ion transport through biological ion channels. PNPF contains many more correlations than most models and simulations of channels, because it includes water and calculates dielectric properties consistently as outputs. This model accounts for the steric effect of ions and water molecules with different sizes and interstitial voids, the correlation effect of crowded ions with different valences, and the screening effect of polarized water molecules in an inhomogeneous aqueous electrolyte. The steric energy is shown to be comparable to the electrical energy under physiological conditions, demonstrating the crucial role of the excluded volume of particles and the voids in the natural function of channel proteins. Water is shown to play a critical role in both correlation and steric effects in the model. We extend the classical Scharfetter-Gummel (SG) method for semiconductor devices to include the steric potential for ion channels, which is a fundamental physical property not present in semiconductors. Together with a simplified matched interface and boundary (SMIB) method for treating molecular surfaces and singular charges of channel proteins, the extended SG method is shown to exhibit important features in flow simulations such as optimal convergence, efficient nonlinear iterations, and physical conservation. The generalized SG stability condition shows why the standard discretization (without SG exponential fitting) of NP equations may fail and that divalent ${\mathrm{Ca}}^{2+}$ may cause more unstable discrete ${\mathrm{Ca}}^{2+}$ fluxes than that of monovalent ${\mathrm{Na}}^{+}$. Two different methods—called the SMIB and multiscale methods—are proposed for two different types of channels, namely, the gramicidin A channel and an L-type calcium channel, depending on whether water is allowed to pass through the channel. Numerical methods are first validated with constructed models whose exact solutions are known. The experimental data of both channels are then used to verify and explain novel features of PNPF as compared with previous PNP models. The PNPF currents are in accord with the experimental I-V (V for applied voltages) data of the gramicidin A channel and I-C (C for bath concentrations) data of the calcium channel with ${10}^{-8}$-fold bath concentrations that pose severe challenges in theoretical simulations.