As a defined model of outer membranes of gram negative bacteria, we investigated the interaction of monolayers of lipopolysacchrides from Salmonella enterica rough strains R90 (LPS Ra) with natural and synthetic peptides. The fine structures perpendicular to the membrane plane and the ion distribution near the interface were determined by specular x-ray reflectivity (XRR) and grazing-incidence x-ray fluorescence (GIXF) in the presence and absence of divalent cations. The unique combination of XRR and GIXF allows for the quantitative identification of different modes of interactions in a high spatial resolution, which cannot be assessed by other experimental methods. Natural fish protamine disrupts the stratified membrane structures in the absence of Ca${}^{2+}$ ions, while staying away from the membrane surface in the presence of Ca${}^{2+}$ ions. In contrast, synthetic antisepsis peptide Pep 19-2.5 weakly adsorbs to the membrane and stays near the uncharged sugar units even in the absence of Ca${}^{2+}$. In the presence of Ca${}^{2+}$, Pep 19-2.5 can reach the negatively charged inner core without destroying the barrier capability against ions.

Fractional reaction-diffusion equations are derived by exploiting the geometrical similarities between a comb structure and a spiny dendrite. In the framework of the obtained equations, two scenarios of reaction transport in spiny dendrites are explored, where both a linear reaction in spines and nonlinear Fisher-Kolmogorov-Petrovskii-Piskunov reactions along dendrites are considered. In the framework of fractional subdiffusive comb model, we develop a Hamilton-Jacobi approach to estimate the overall velocity of the reaction front propagation. One of the main effects observed is the failure of the front propagation for both scenarios due to either the reaction inside the spines or the interaction of the reaction with the spines. In the first case the spines are the source of reactions, while in the latter case, the spines are a source of a damping mechanism.

We study the structural robustness of scale-free networks against overload failures induced by loads exceeding the node capacity, based on analytical and numerical approaches to the percolation problem in which a fixed number of nodes are removed according to the overload probability. Modeling fluctuating loads by random walkers in a network, we find that the degree dependence of the overload probability drastically changes with respect to the total load. We also elucidate that there exist two types of structural robustness of networks against overload failures. One is measured by the critical total load $W_{\text{c}}$ and the other is by the critical node removal fraction $f_{\text{c}}$. Enhancing the scale-free property, networks become fragile in both senses of $W_{\text{c}}$ and $f_{\text{c}}$. By contrast, increasing the node tolerance, scale-free networks become robust in the sense of the critical total load, while they come to be fragile in the sense of the critical node removal fraction. Furthermore, we show that these trends are not affected by degree-degree correlations, although assortative mixing makes networks robust in both senses of $W_{\text{c}}$ and $f_{\text{c}}$.

We consider the sectoral composition of a country's gross domestic product (GDP), i.e., the partitioning into agrarian, industrial, and service sectors. Exploring a simple system of differential equations, we characterize the transfer of GDP shares between the sectors in the course of economic development. The model fits for the majority of countries providing four country-specific parameters. Relating the agrarian with the industrial sector, a data collapse over all countries and all years supports the applicability of our approach. Depending on the parameter ranges, country development exhibits different transfer properties. Most countries follow three of eight characteristic paths. The types are not random but show distinct geographic and development patterns.

We study a class of network growth models with attachment rules governed by intrinsic node fitness. Both the individual node degree distribution and the degree correlation properties of the network are obtained as functions of the network growth rules. We also find analytical solutions to the inverse, design, problems of matching the growth rules to the required (e.g., power-law) node degree distribution and more generally to the required degree correlation function. We find that the design problems do not always have solutions. Among the specific conditions on the existence of solutions to the design problems is the requirement that the node degree distribution has to be broader than a certain threshold and the fact that factorizability of the correlation functions requires singular distributions of the node fitnesses. More generally, the restrictions on the input distributions and correlations that ensure solvability of the design problems are expressed in terms of the analytical properties of their generating functions.

We investigate the dynamics of correlations present between pairs of industry indices of U.S. stocks traded in U.S. markets by studying correlation-based networks and spectral properties of the correlation matrix. The study is performed by using 49 industry index time series computed by K. French and E. Fama during the time period from July 1969 to December 2011, which spans more than 40 years. We show that the correlation between industry indices presents both a fast and a slow dynamics. The slow dynamics has a time scale longer than 5 years, showing that a different degree of diversification of the investment is possible in different periods of time. Moreover, we also detect a fast dynamics associated with exogenous or endogenous events. The fast time scale we use is a monthly time scale and the evaluation time period is a 3-month time period. By investigating the correlation dynamics monthly, we are able to detect two examples of fast variations in the first and second eigenvalue of the correlation matrix. The first occurs during the dot-com bubble (from March 1999 to April 2001) and the second occurs during the period of highest impact of the subprime crisis (from August 2008 to August 2009).

Latent community discovery that combines links and contents of a text-associated network has drawn more attention with the advance of social media. Most of the previous studies aim at detecting densely connected communities and are not able to identify general structures, e.g., bipartite structure. Several variants based on the stochastic block model are more flexible for exploring general structures by introducing link probabilities between communities. However, these variants cannot identify the degree distributions of real networks due to a lack of modeling of the differences among nodes, and they are not suitable for discovering communities in text-associated networks because they ignore the contents of nodes. In this paper, we propose a popularity-productivity stochastic block (PPSB) model by introducing two random variables, popularity and productivity, to model the differences among nodes in receiving links and producing links, respectively. This model has the flexibility of existing stochastic block models in discovering general community structures and inherits the richness of previous models that also exploit popularity and productivity in modeling the real scale-free networks with power law degree distributions. To incorporate the contents in text-associated networks, we propose a combined model which combines the PPSB model with a discriminative model that models the community memberships of nodes by their contents. We then develop expectation-maximization (EM) algorithms to infer the parameters in the two models. Experiments on synthetic and real networks have demonstrated that the proposed models can yield better performances than previous models, especially on networks with general structures.

In the absence of confinement, localization of waves takes place due to randomness or nonlinearity and relies on their phase coherence. We quantitatively probe the sensitivity of localized wave packets to random phase fluctuations and confirm the necessity of phase coherence for localization. Decoherence resulting from a dynamical random environment leads to diffusive spreading and destroys linear and nonlinear localization. We find that maximal spreading is achieved for optimal phase fluctuation characteristics, which is a consequence of the competition between diffusion due to decoherence and ballistic transport within the mean free path distance.

Nonlinear networks with time-delayed couplings may show strong and weak chaos, depending on the scaling of their Lyapunov exponent with the delay time. We study strong and weak chaos for semiconductor lasers, either with time-delayed self-feedback or for small networks. We examine the dependence on the pump current and consider the question of whether strong and weak chaos can be identified from the shape of the intensity trace, the autocorrelations, and the external cavity modes. The concept of the sub-Lyapunov exponent ${\lambda }_0$ is generalized to the case of two time-scale-separated delays in the system. We give experimental evidence of strong and weak chaos in a network of lasers, which supports the sequence of weak to strong to weak chaos upon monotonically increasing the coupling strength. Finally, we discuss strong and weak chaos for networks with several distinct sub-Lyapunov exponents and comment on the dependence of the sub-Lyapunov exponent on the number of a laser's inputs in a network.

We present an algorithm for a time-delayed feedback control design to stabilize periodic orbits with an odd number of positive Floquet exponents in autonomous systems. Due to the so-called odd-number theorem such orbits have been considered as uncontrollable by time-delayed feedback methods. However, this theorem has been refuted by a counterexample and recently a corrected version of the theorem has been proved. In our algorithm, the control matrix is designed using a relationship between Floquet multipliers of the systems controlled by time-delayed and proportional feedback. The efficacy of the algorithm is demonstrated with the Lorenz and Chua systems.

We study vortex dynamics in a trapped Bose-Einstein condensate with tunable two- and three-body interactions. The dynamics is governed by two-dimensional cubic-quintic Gross-Pitaevskii equation. A time-dependent variational method has been used to obtain critical rotational frequency and surface mode frequency analytically and are compared with numerical simulation results. An imaginary time propagation method and Crank-Nicolson scheme for discretization have been used for numerical simulation. The numerically calculated average value of the angular momentum per particle shows very clearly its dynamical relation with the time development of the vortex formation. The rotational frequency dependence of the variation of average value of the angular momentum per particle with time shows that vortices form much faster in time for higher rotational frequency. Similarly, the vortex forms much faster in time with an increase of the strength of the repulsive three-body interaction. The simulation of the vortex lattice formation in the condensate shows that the presence of the three-body interactions does not alter the vortex lattice pattern but it helps in the shape deformations of the condensate thereby leading to vortex lattice formation. Likewise, the three-body interactions enable the vortex lattice formation in Bose-Einstein condensates even with attractive two-body interactions and in purely quintic BEC.

Predicting dynamo self-generation in liquid metal experiments has been an ongoing question for many years. In contrast to simple dynamical systems for which reliable techniques have been developed, the ability to predict the dynamo capacity of a flow and the estimate of the corresponding critical value of the magnetic Reynolds number (the control parameter of the instability) has been elusive, partly due to the high level of turbulent fluctuations of flows in such experiments (with kinetic Reynolds numbers in excess of ${10}^6$). We address these issues here, using the von Kármán sodium experiment and studying its response to an externally applied magnetic field. We first show that a dynamo threshold can be estimated from analysis related to critical slowing down and susceptibility divergence, in configurations for which dynamo action is indeed observed. These approaches are then applied to flow configurations that have failed to self-generate magnetic fields within operational limits, and we quantify the dynamo capacity of these configurations.

To set up a mathematical model for the flow of complex magnetic fluids, noninteracting magnetic particles with a small volume or an even point size are typically assumed. Real ferrofluids, however, consist of a suspension of particles with a finite size in an almost ellipsoid shape as well as with particle-particle interactions that tend to form chains of various lengths. To come close to the realistic situation for ferrofluids, we investigate the effect of elongational flow incorporated by the symmetric part of the velocity gradient field tensor, which could be scaled by a so-called transport coefficient ${\lambda }_2$. Based on the hybrid finite-difference and Galerkin scheme, we study the flow of a ferrofluid in the gap between two concentric rotating cylinders subjected to either a transverse or an axial magnetic field with the transport coefficient. Under the influence of a transverse magnetic field with ${\lambda }_2=0$, we show that basic state and centrifugal unstable flows are modified and are inherently three-dimensional helical flows that are either left-winding or right-winding in the sense of the azimuthal mode-2, which is in contrast to the generic cases. That is, classical modulated rotating waves rotate, but these flows do not. We find that under elongational flow (${\lambda }_2\ne 0$), the flow structure from basic state and centrifugal instability flows is modified and their azimuthal vorticity is linearly changed. In addition, we also show that the bifurcation threshold of the supercritical centrifugal unstable flows under a magnetic field depends linearly on the transport coefficient, but it does not affect the general stabilization effect of any magnetic field.

We report quench cooling experiments performed with liquid O${}_2$ under different levels of gravity, simulated with magnetic gravity compensation. A copper disk is quenched from 300 to 90 K. It is found that the cooling time in microgravity is very long in comparison with any other gravity level. This phenomenon is explained by the insulating effect of the gas surrounding the disk. A weak gas pressurization (which results in subcooling of the liquid with respect to the saturation temperature) is shown to drastically improve the heat exchange, thus reducing the cooling time (about 20 times). The effect of subcooling on the heat transfer is analyzed at different gravity levels. It is shown that this type of experiment cannot be used for the analysis of the critical heat flux of the boiling crisis. The film boiling heat transfer and the minimum heat flux of boiling are analyzed as functions of gravity and subcooling.

We present a reduced model for the energy transfer via coupled collective modes in two-temperature plasmas based on quantum statistical theory. The model is compared with exact numerical evaluations of the coupled-mode (CM) energy transfer rate and with alternative reduced approaches over a range of conditions in the warm dense matter (WDM) and inertial confinement fusion (ICF) regimes. Our approach shows excellent agreement with an exact treatment of the CM rate and supports the importance of the coupled-mode effect for the temperature and energy relaxation in WDM and ICF plasmas. We find that electronic damping of collective ion density fluctuations is crucial for correctly describing the mode spectrum and, thus, the energy exchange. The reduced CM approach is studied over a wide parameter space, enabling us to establish its limits of applicability.

For the discrete model suggested by Lorenz in 1996, a one-dimensional long-wave approximation with nonlinear excitation and diffusion is derived. The model is energy conserving but non-Hamiltonian. In a low-order truncation, weak external forcing of the zonal mean flow induces avalanchelike breather solutions which cause reversal of the mean flow by a wave-mean flow interaction. The mechanism is an outburst-recharge process similar to avalanches in a sandpile model.

A stochastic theory is given of an optical vortex occurring in nonlinear Kerr media. This is carried out by starting from the nonlinear Schrödinger type equation which accommodates vortex solution. By using the action functional method, the evolution equation of vortex center is derived. Then the Langevin equation is introduced in the presence of random fluctuations, which leads to the Fokker-Planck equation for the distribution function of the vortex center coordinate by using a functional integral. The Fokker-Planck equation is analyzed for a specific form of pinning potential by taking into account an interplay between the strength of the pinning potential and the random parameters, diffusion and dissipation constants. This procedure is performed by several approximate schemes.

The momentum exchange method has been widely used in lattice Boltzmann simulations for particle-fluid interactions. Although proved accurate for still walls, it will result in inaccurate particle dynamics without corrections. In this work, we reveal the physical cause of this problem and find that the initial momentum of the net mass transfer through boundaries in the moving-boundary treatment is not counted in the conventional momentum exchange method. A corrected momentum exchange method is then proposed by taking into account the initial momentum of the net mass transfer at each time step. The method is easy to implement with negligible extra computation cost. Direct numerical simulations of a single elliptical particle sedimentation are carried out to evaluate the accuracy for our method as well as other lattice Boltzmann-based methods by comparisons with the results of the finite element method. A shear flow test shows that our method is Galilean invariant.

In this article, a method based on the multiphase lattice Boltzmann framework is presented which is applicable to liquid-vapor phase-change phenomena. Both liquid and vapor phases are assumed to be incompressible. For phase changes occurring at the phase interface, the divergence-free condition of the velocity field is no longer satisfied due to the gas volume generated by vaporization or fluid volume generated by condensation. Thus, we extend a previous model by a suitable equation to account for the finite divergence of the velocity field within the interface region. Furthermore, the convective Cahn-Hilliard equation is extended to take into account vaporization effects. In a first step, a D1Q3 LB model is constructed and validated against the analytical solution of a one-dimensional Stefan problem for different density ratios. Finally the model is extended to two dimensions (D2Q9) to simulate droplet evaporation. We demonstrate that the results obtained by this approach are in good agreement with theory.