Structural, dynamical, and thermal properties of germanium dioxide are investigated with classical molecular dynamics simulations from the amorphous to the liquid state. Pair correlation functions and coordination numbers are computed under pressure change and show the progressive conversion of the tetrahedral network into an octahedral network, in agreement with experiments. The thermodynamical behavior of the liquid is investigated by means of an equation of state that allows a precise estimation of the compressibility. At low temperature, the diffusion constant $D$ shows an Arrhenius law that progressively deviates when the temperature is increased. The overall comparison with simulated silica permits finally to outline not only the differences in the physical behavior of these two similar systems but also to stress the limitation of the employed germania potential.

Small scale particle motion is the cause of dynamic roughening and plays a role during film growth. To study surface waves on the molecular level, a continuum approach is used that links atomic and macroscopic dynamics though a Fokker-Planck equation for the distribution of particle trajectories. The dynamic equation for the density interfacial profile includes inertia terms indispensable for high frequency fluctuations. For wave vectors below the critical value, an initial periodic deformation of the surface on the order of the density correlation length simply decays with time. Above the critical wave vector, collective periodic motion is induced in the interface. A picture of short lived, localized high frequency wavelets emerges with contributions from acoustic, capillary, and elastic surface modes.

Conditions for surface nucleation and growth of a film are determined in a diffuse interface model. A method is given, derived from a Fokker-Planck equation for the nonequilibrium particle distribution, which links atomic and mesoscopic events in a rheological description similar to the classical continuum theory of fluid flow. Film nucleation and growth are modeled by the spatially inhomogeneous continuous evolution of the instantaneous density profile which measures the average number of particles or molecules at given time and position. It is shown how an alteration in the distribution of particles in the vicinity of the boundary between parent and product phases induces transient film growth and damped vibrations at the surface. The method is general but as an illustration, the condensation of a simple classical fluid on cooling is considered in detail.

We model the spontaneous elastic shear deformations of smectic elastomers as they make the thermal transition between the $A$ and $C$ phases. Tilt of the director is accompanied by shear. Unlike nematic elastomers where spontaneous elongation is associated with changes in the magnitude of order, spontaneous distortion in smectics is instead shear and is associated with rotation of the director of the underlying nematic order. The effect of the multistage cross-linking associated with creating monodomain elastomers is taken into account. The angle of molecular tilt and the angle associated with spontaneous shear deformation are not simply related.

The functionality of proteins is governed by their structure in the native state. Protein structures are made up of emergent building blocks of helices and almost planar sheets. A simple coarse-grained geometrical model of a flexible tube barely subject to compaction provides a unified framework for understanding the common character of globular proteins. We argue that a recent critique of the tube idea is not well founded.

We develop an analytical approach for the delayed feedback control of the Lorenz system close to a subcritical Hopf bifurcation. The periodic orbits arising at this bifurcation have no torsion and cannot be stabilized by a conventional delayed feedback control technique. We utilize a modification based on an unstable delayed feedback controller. The analytical approach employs the center manifold theory and the near identity transformation. We derive the characteristic equation for the Floquet exponents of the controlled orbit in an analytical form and obtain simple expressions for the threshold of stability as well as for an optimal value of the control gain. The analytical results are supported by numerical analysis of the original system of nonlinear differential-difference equations.

We report nonlinear solutions for a system of conservation laws describing the dynamics of the large-scale coherent structure of bubbles and spikes in the Rayleigh-Taylor instability (RTI) for fluids with a finite density ratio. Three-dimensional flows are considered with general type of symmetry in the plane normal to the direction of gravity. The nonlocal properties of the interface evolution are accounted for on the basis of group theory. It is shown that isotropic coherent structures are stable. For anisotropic structures, secondary instabilities develop with the growth rate determined by the density ratio. For stable structures, the curvature and velocity of the nonlinear bubble have nontrivial dependencies on the density ratio, yet their mutual dependence on one another has an invariant form independent of the density ratio. The process of bubble merge is not considered. Based on the obtained results we argue that the large-scale coherent dynamics in RTI has a multiscale character and is governed by two length scales: the period of the coherent structure and the bubble (spike) position.

Topological chaos relies on the periodic motion of obstacles in a two-dimensional flow in order to form nontrivial braids. This motion generates exponential stretching of material lines, and hence efficient mixing. Boyland, Aref, and Stremler [J. Fluid Mech. 403, 277 (2000)] have studied a specific periodic motion of rods that exhibits topological chaos in a viscous fluid. We show that it is possible to extend their work to cases where the motion of the stirring rods is topologically trivial by considering the dynamics of special periodic points that we call “ghost rods”, because they play a similar role to stirring rods. The ghost rods framework provides a new technique for quantifying chaos and gives insight into the mechanisms that produce chaos and mixing. Numerical simulations for Stokes flow support our results.

The interaction of regular nonlinear structures (such as subcycle solitons, electron vortices, and wake Langmuir waves) with a strong wake wave in a collisionless plasma can be exploited in order to produce ultrashort electromagnetic pulses. The electromagnetic field of the nonlinear structure is partially reflected by the electron density modulations of the incident wake wave and a single-cycle high-intensity electromagnetic pulse is formed. Due to the Doppler effect the length of this pulse is much shorter than that of the nonlinear structure. This process is illustrated with two-dimensional particle-in-cell simulations. The considered laser-plasma interaction regimes can be achieved in present day experiments and can be used for plasma diagnostics.

We study localized light bullets and X waves in quadratic media and show how the notion of nonlocality can provide an alternative simple physical picture of both types of multidimensional nonlinear waves. For X waves we show that a local cascading limit in terms of a nonlinear Schrödinger equation does not exist—one needs to use the nonlocal description, because the nonlocal response function does not converge toward a $\delta$ function. Also, we use the nonlocal theory to show that the coupling to the second harmonic is able to generate an X shape in the fundamental field despite having anomalous dispersion, in contrast to the predictions of the cascading limit.

We study families of solitons in a two-dimensional model of the light transmission through a photorefractive medium equipped with a (quasi-)one-dimensional photonic lattice. The soliton families are bounded from below by finite minimum values of the peak and total power. Narrow solitons have a single maximum, while broader ones feature side lobes. Stability of the solitons is checked by direct simulations. The solitons can be set in motion across the lattice (actually, made tilted in the spatial domain), provided that the respective boost parameter does not exceed a critical value. Collisions between moving solitons are studied too. Collisions destroy the solitons, unless their velocities are sufficiently small. In the latter case, the colliding solitons merge into a single stable pulse.

Segregation of large granules in a vibrofluidized granular bed with inhomogeneous granular number density distribution is studied by an event-driven algorithm. Simulation results show that the mean vertical position of large granules decreases with the increase of the density ration of the large granules to the small ones. This conclusion is consistent with the explanation that the net pressure due to the small surrounding particle impacts balances the large granular weight, and indict that the upward movement of the large granules is driven by the buoyancy. The values of temperature, density, and pressure of the systems are also computed by changing the conditions such as heating temperature on the bottom and restitution coefficient of particles. These results indicate that the segregation of large granules also happen in the systems with density inversion or even close-packed cluster of particles floating on a low-density fluid, due to the buoyancy. An equation of state is proposed to explain the buoyancy.

The thin interface layer on colloids in a liquid can be characterized by applying nulling ellipsometry to a scattering experiment. Close to $90°$ scattering angle the ellipsometric quantities $\tan \left(\Psi \right)$ and $\Delta$ of particles smaller than the wavelength behave like at the Brewster angle of reflection ellipsometry. The minimum of $\tan \left(\Psi \right)$ and the slope of $\Delta$ depend on thickness and refractive index of the layer, while the location of the minimum is sensitive to the refractive index of the particle. As an example, the swelling of a thermosensitive layer on colloidal particles has been determined from measurements at two wavelengths.

The hydrophobic free energy and solvent accessibility of amino acids are used to study the relationship between the primary structure and structural classification of large proteins. A measure representation and a Z curve representation of protein sequences are proposed. Fractal analysis of the measure and Z curve representations of proteins and multifractal analysis of their hydrophobic free energy and solvent accessibility sequences indicate that the protein sequences possess correlations and multifractal scaling. The parameters from the fractal and multifractal analyses on these sequences are used to construct some parameter spaces. Each protein is represented by a point in these spaces. A method is proposed to distinguish and cluster proteins from the $\alpha$, $\beta$, $\alpha +\beta$, and $\alpha ∕\beta$ structural classes in these parameter spaces. Fisher’s linear discriminant algorithm is used to give a quantitative assessment of our clustering on the selected proteins. Numerical results indicate that the discriminant accuracies are satisfactory. In particular, they reach 94.12% and 88.89% in separating $\beta$ proteins from $\{\alpha ,\alpha +\beta ,\alpha ∕\beta \}$ proteins in a three-dimensional space.

We present a density-functional theory for describing liquid-crystalline phase transitions in a fluid of semiflexible hard-sphere chain molecules based on the Onsager second-virial approximation for the free energy. Key ingredients of this theory are the generation of semiflexible chain conformations and calculation of the pair excluded volume and excluded area using a single-chain Monte Carlo enumeration method. First, we investigate the isotropic-nematic phase transition. Next, the theory is extended to account for a smectic-A phase by a bifurcation analysis around the nematic solution. The perturbation is calculated using a lowest-order Fourier series representation.

Complex networks are characterized by several topological properties: degree distribution, clustering coefficient, average shortest path length, etc. Using a simple model to generate scale-free networks embedded on geographical space, we analyze the relationship between topological properties of the network and attributes (fitness and location) of the vertices in the network. We find there are two crossovers for varying the scaling exponent of the fitness distribution.

We study the physical implementation of the photon-Carnot engine (PCE) based on the cavity quantum electrodynamics system [M. O. Scully, M. Suhail Zubairy, G. S. Agarwal, and H. Walther, Science 299, 862 (2003)]. Here we analyze two decoherence mechanisms for the more practical systems of PCE, the dissipation of photon field, and the pure dephasing of the input atoms. As a result we find that (i) the PCE can work well to some extent even in the existence of the cavity loss (photon dissipation) and (ii) the short-time atomic dephasing, which can destroy the PCE, is a fatal problem to be overcome.

This paper presents a statistical analysis of the structure of peer-to-peer (P2P) social networks that captures social associations of distributed peers in resource sharing. Peer social networks appear to be mainly composed of pure resource providers that guarantee high resource availability and reliability of P2P systems. The major peers that both provide and request resources are only a small fraction. The connectivity between peers, including undirected, directed (out and in) and weighted connections, is scale-free and the social networks of all peers and major peers are small world networks. The analysis also confirms that peer social networks show in general disassortative correlations, except that active providers are connected between each other and by active requesters. The study presented in this paper gives a better understanding of peer relationships in resource sharing, which may help a better design of future P2P networks and open the path to the study of transport processes on top of real P2P topologies.

We demonstrate that a unidirectional coupling between a pattern forming system and its replića induces complete synchronization of the slave to the master system onto a spatiotemporal chaotic state.