It is investigated how a spatial quenched disorder modifies the dynamics of coupled map lattices. The disorder is introduced via the presence or absence of coupling terms among lattice sites. Two nonlinear maps have been considered embodying two paradigmatic dynamics. The Miller and Huse map can be associated with an Ising-type dynamics, whereas the logistic coupled maps is a prototype of a nontrivial collective dynamics. Various indicators quantifying the overall behavior, demonstrates that even a small amount of spatial disorder is capable to alter the dynamics found for purely ordered cases.

An analytical investigation is presented for the stretch flow of a viscous Newtonian ferrofluid highly confined between parallel plates. We focus on the development of interfacial instabilities when the upper plate is lifted at a described rate, under the action of an applied magnetic field. We derive the mode-coupling differential equation for the interface perturbation amplitudes and study both linear and nonlinear flow regimes. In contrast to the great majority of works in stretch flow we take into account stresses originated from velocity gradients normal to the ferrofluid interface. The impact of such normal stresses is accounted for through a modified Young-Laplace pressure jump interfacial boundary condition, which also includes the contribution from magnetic normal traction. We study how the stability properties of the interface and the shape of the emerging patterns respond to the combined action of normal stresses and magnetic field, both in the presence and absence of surface tension. We show that the inclusion of normal viscous stresses introduces a pertinent dependence on the initial aspect ratio, indicating that the number of fingers formed would be overestimated if such stresses are not taken into account. At early linear stages it is found that such stresses regularize the system, acting as an effective interfacial tension. At weakly nonlinear stages we verified that normal stresses reduce finger competition, which can be completely suppressed with the assistance of an azimuthal magnetic field. We have also found that the magnetic normal traction introduces a purely nonlinear contribution to the problem, revealing the key role played by the magnetic susceptibility in the control of finger competition.

The coupling of the resonances of spherical particles embedded near the surface of a metal and the surface plasmon is investigated by calculations using a multiple scattering formalism. The system we considered is a periodic array of glass spheres buried just beneath the surface of an Ag substrate. The calculated absorption spectra show features that can be traced to the resonance frequency of the microsphere cavity or the surface mode of the metal. In general, the absorption peaks for both the cavity and the surface mode are relatively weak when their resonance frequencies are far from each other. However, if the system is designed such that the cavitylike mode and the surface mode have almost the same frequency, the coupling of the resonances will lead to enhanced frequency-selective absorption. Such systems can be employed to modify or control thermal emission.

A method is presented for generating surrogates that are constrained realizations of a time series but which preserve the local mean and variance of the original signal. The method is based on the popular iterated amplitude adjusted Fourier transform method but makes use of a wavelet transform to constrain behavior in the time domain. Using this method it is possible to test for local changes in the nonlinear properties of the signal. We present an example for a change in Hurst exponent in a time series produced by fractional Brownian motion.

The properties of a wide variety of growing models, generically called $X$-RD, involving the deposition of particles according to competitive processes, such that a particle is attached to the aggregate with probability $p$ following the mechanisms of a generic model $X$ that provides the correlations and at random [random deposition (RD)] with probability $(1-p)$, are studied by means of numerical simulations and analytic developments. The study comprises the following $X$ models: Ballistic deposition, random deposition with surface relaxation, Das Sarma–Tamboronea, Kim-Kosterlitz, Lai–Das Sarma, Wolf-Villain, large curvature, and three additional models that are variants of the ballistic deposition model. It is shown that after a growing regime, the interface width becomes saturated at a crossover time $\left(t_{x2}\right)$ that, by fixing the sample size, scales with $p$ according to $t_{x2}\left(p\right)\propto p^{-y}$ $(p>0)$, where $y$ is an exponent. Also, the interface width at saturation $\left(W_{\mathrm{sat}}\right)$ scales as $W_{\mathrm{sat}}\left(p\right)\propto p^{-\delta }$ $(p>0)$, where $\delta$ is another exponent. It is proved that, in any dimension, the exponents $\delta$ and $y$ obey the following relationship: $\delta =y{\beta }_{\mathrm{RD}}$, where ${\beta }_{\mathrm{RD}}=1∕2$ is the growing exponent for RD. Furthermore, both exponents exhibit universality in the $p\to 0$ limit. By mapping the behavior of the average height difference of two neighboring sites in discrete models of type $X$-RD and two kinds of random walks, we have determined the exact value of the exponent $\delta$. When the height difference between two neighbouring sites corresponds to a random walk that after walking $⟨n⟩$ steps returns to a distance from its initial position that is proportional to the maximum distance reached (random walk of type A), one has $\delta =1∕2$. On the other hand, when the height difference between two neighboring sites corresponds to a random walk that after $⟨n⟩$ steps moves $⟨l⟩$ steps towards the initial position (random walk of type B), one has $\delta =1$. Finally, by linking four well-established universality classes (namely Edwards-Wilkinson, Kardar-Parisi-Zhang, linear [molecular beam epitaxy (MBE)] and nonlinear MBE) with the properties of type A and B of random walks, eight different stochastic equations for all the competitive models studied are derived.

A fundamental task in developmental biology is to identify the mechanisms which drive morphogenesis. Traditionally pattern formation have been modeled mainly using Turing-type mechanisms, where complex patterns arise by symmetry breaking. However, there is a growing experimental evidence that the influence of signals derived from surrounding tissues can contribute to the patterning processes. In this paper, we show that the interplay between the shape of surrounding tissues and a hierarchically organized gene regulatory network can be able to induce stable complex patterns. The rise of these patterns depends strongly on the shape of the surrounding tissues.

We propose a mechanism by which changes of the mechanical tension of a composite lipid membrane are buffered by the invagination of membrane domains. We show that domain invagination, driven by differences in chemical composition, is a first-order transition controlled by membrane tension. The invaginated domains play the role of a membrane reservoir, exchanging area with the main membrane, and impose an equilibrium tension entirely controlled by their mechanical properties. The dynamical response of the reservoir reflects the tension-dependent kinetics of the domain shape transition, so that the tension of such a composite membrane is inherently transient and dynamical. The implications of this phenomenon for the mechanical properties of the membranes of living cells, where invaginated membrane domains are known to exist, are discussed.

An elastic rod model of a protein-bound DNA loop is adapted for application in multi-scale simulations of protein-DNA complexes. The classical Kirchhoff system of equations which describes the equilibrium structure of the elastic loop is modified to account for the intrinsic twist and curvature, anisotropic bending properties, and electrostatic charge of DNA. The effects of bending anisotropy and electrostatics are studied for the DNA loop clamped by the lac repressor protein. For two possible lengths of the loop, several topologically different conformations are predicted and extensively analyzed over the broad range of model parameters describing DNA bending and electrostatic properties. The scope and applications of the model in already accomplished and in future multi-scale studies of protein-DNA complexes are discussed.

We study the coupled-map lattice model with both local and global couplings. We find necessary conditions for observing synchronous chaos and investigate the transition to synchronization as a dynamic phase transition. We discover that this transition, if continuous, shows scaling and universal behavior with the dynamic exponent $z=2$. We also define and illustrate an interesting quantity similar to persistence at critical point.

A method to determine cutoff frequencies for linear acoustic waves propagating in nonisothermal media is introduced. The developed method is based on wave variable transformations that lead to Klein-Gordon equations, and the oscillation theorem is applied to obtain the turning point frequencies. Physical arguments are used to justify the choice of the largest turning point frequency as the cutoff frequency. The method is used to derive the cutoff frequencies in nonisothermal media modeled by exponential and power law temperature gradients, for which the cutoffs cannot be obtained based on known analytical solutions. An interesting result is that the acoustic cutoff frequencies calculated by the method are local quantities that vary in the media, and that their specific values at a given height determine the frequency that acoustic waves must have in order to be propagating at this height. To extend this physical interpretation of the acoustic cutoff frequency to nonisothermal media of arbitrary temperature gradients, a generalized version of the method applicable to these media is also presented.

We report a systematic finite-difference time-domain study on the dielectric properties of two-dimensional lossless heterostructures with inclusion of deterministic fractal geometry (Koch’s snowflake, Sierpinski’s square and triangle) constrained to sit in a circumscribed circle, for a wide range of surface fractions. In all the configurations investigated, we observed (i) a strong deviation of the surface fraction dependence of the effective permittivity based on Maxwell Garnett analysis, and (ii) a permittivity change with reduced perimeter according to a similarity transformation, at least for the first three iterations of the fractal pattern. We show that the results of our numerical analysis disagree with expectations from the duality (phase interchange) relation, and explain this as being due to the intrinsic complexity of the morphology which requires a multipolar approach to correctly describe the microstructure features of these heterostructures.

A method for analyzing the x-ray scattering of a stack of phospholipid membranes at the solid-liquid interface in excess water is presented. It is argued that bilayers near the substrate fluctuate less significantly than the ones away from it and, therefore, make a larger contribution to the specular reflection at the low index Bragg peaks. But the diffuse scattering due to thermal fluctuations corrupts the Bragg peaks at high angles so that the specular contribution is not clearly observable. In the midst the specular reflection and the diffuse scattering cannot be separated easily and must be analyzed simultaneously. The height-difference correlation function derived from a modified Caillé theory enables one to simulate the longitudinal and the transverse scans in the same theoretical framework to yield more reliable structural parameters. The theoretical apparatus is successfully applied to the experimental data on DOPC membranes.

It is shown that homogeneous Rayleigh-Bénard flow, i.e., Rayleigh-Bénard turbulence with periodic boundary conditions in all directions and a volume forcing of the temperature field by a mean gradient, has a family of exact, exponentially growing, separable solutions of the full nonlinear system of equations. These solutions are clearly manifest in numerical simulations above a computable critical value of the Rayleigh number. In our numerical simulations they are subject to secondary numerical noise and resolution dependent instabilities that limit their growth to produce statistically steady turbulent transport.

Different scaling properties for the complexity of bidirectional synchronization and unidirectional learning are essential for the security of neural cryptography. Incrementing the synaptic depth of the networks increases the synchronization time only polynomially, but the success of the geometric attack is reduced exponentially and it clearly fails in the limit of infinite synaptic depth. This method is improved by adding a genetic algorithm, which selects the fittest neural networks. The probability of a successful genetic attack is calculated for different model parameters using numerical simulations. The results show that scaling laws observed in the case of other attacks hold for the improved algorithm, too. The number of networks needed for an effective attack grows exponentially with increasing synaptic depth. In addition, finite-size effects caused by Hebbian and anti-Hebbian learning are analyzed. These learning rules converge to the random walk rule if the synaptic depth is small compared to the square root of the system size.

We examine a new second-order integrator recently found by Omelyan et al. The integration error of the new integrator measured in the root mean square of the energy difference, ${⟨\Delta H^2⟩}^{1∕2}$, is about 10 times smaller than that of the standard second-order leapfrog (2LF) integrator. As a result, the step size of the new integrator can be made about three times larger. Taking into account a factor 2 increase in cost, the new integrator is about 50% more efficient than the 2LF integrator. Integrating over positions first, then momenta, is slightly more advantageous than the reverse. Further parameter tuning is possible. We find that the optimal parameter for the new integrator is slightly different from the value obtained by Omelyan et al., and depends on the simulation parameters. This integrator could also be advantageous for the Trotter-Suzuki decomposition in quantum Monte Carlo.

We investigate the effect of nanoscale variations in the surface roughness of individual particles on macroscale granular flow characteristics. Experiments were conducted in circular rotating tumblers with smooth and rough 2 and $3\mathrm{mm}$ steel particles. The smooth beads had a rms surface roughness of approximately 30 to $60\mathrm{nm}$; rough beads had a surface roughness of approximately 240 to $350\mathrm{nm}$. The dynamic angle of repose for rough particles increased by $10°$ to $25°$ over that of smooth particles over a wide range of rotation speeds. Even though surface roughness affects the angle of repose, we were unable to detect any segregation of bidisperse mixtures of rough and smooth particles in the radial direction in two-dimensional (2D) tumblers. Furthermore, no axial banding segregation occurred in 3D tumblers, both cylindrical and spherical. For mixtures of smooth and rough particles, the angle of repose increased monotonically with increasing concentration of rough particles. Particle dynamics simulations verified that the dependence of the angle of repose on the concentration of rough particles can be directly related to the coefficient of friction of the particles. Simulations over a broad range of friction parameters failed to induce segregation solely from differences in the angle of repose. These results indicate that nanoscale surface roughness can affect the flowability and angle of repose of granular matter without driving demixing of the bulk granular material.

Columnar phases made of polycatenar molecules with bent-shaped mesogenic cores are studied. The polar order in this system is associated with the change of the column building blocks from flat disks (${\mathrm{Col}}_h$ phase) into cones (${\mathrm{Col}}_h{P}_A$ phase), which allows for axial polarization of the columns. The nature of the ${\mathrm{Col}}_h$ and ${\mathrm{Col}}_h{P}_A$ phase transition changes from first order for short homologues to continuous for the longest one. This can be attributed to decreasing intercolumnar interactions due to broadening of the columnar scaffold made of partially melted terminal alkyl chains. Decrease of intercolumnar interactions is also responsible for a strong increase of the pretransitional fluctuations in the ${\mathrm{Col}}_h$ phase. The mesophase observed for the longest homologues is reminiscent of the relaxor phase observed for solid crystals.

The Debye-Stokes-Einstein (DSE) model of rotational diffusion predicts that the orientational correlation times ${\tau }_l$ vary as $\left[l\right(l+1){]}^{-1}$, where $l$ is the rank of the orientational time correlation function (given in terms of the Legendre polynomial of rank $l$). One often finds significant deviation from this prediction, in either direction. In supercooled molecular liquids where the ratio ${\tau }_1∕{\tau }_2$ falls considerably below 3 (the Debye limit), one usually invokes a jump diffusion model to explain the approach of the ratio ${\tau }_1∕{\tau }_2$ to unity. Here we show in a computer simulation study of a standard model system for thermotropic liquid crystals that this ratio becomes much less than unity as the isotropic-nematic phase boundary is approached from the isotropic side. Simultaneously, the ratio ${\tau }_2∕\eta$, $\eta$ being the shear viscosity of the liquid, becomes much larger than the hydrodynamic value near the $I\text{−}N$ transition. We also analyze the breakdown of the Debye model of rotational diffusion in ratios of higher order orientational correlation times. We show that the breakdown of the DSE model is due to the growth of orientational pair correlation and provide a mode coupling theory analysis to explain the results.

Networks with a community (or modular) structure underlie many social and biological phenomena. In such a network individuals tend to form sparsely linked local communities, each having dense internal connections. We investigate the dynamics of information propagation on modular networks by using a three-state epidemic model with a unit spreading rate (i.e., the probability for a susceptible individual to be “infected” with the information is one). We find a surprising, resonancelike phenomenon: the information lifetime on the network can be maximized by the number of modules. The result can be useful for optimizing or controlling information spread on social or biological networks.