We investigate pattern formation in the very early stages of solutal convective instabilities in a suspension of highly thermophilic nanoparticles heated from above. The processing of shadowgraph images allows us to recover the spatial power spectrum of the excitations at the onset. Remarkably, the power spectra obtained at large solutal Rayleigh numbers $2.56\times {10}^6\le {\text{Ra}}_s\le 4.53\times {10}^8$ scale onto a single curve without adjustable parameters. The critical wave number exhibits power-law scaling with exponent 1/4 as a function of ${\text{Ra}}_s$, in excellent agreement with recent theoretical predictions.

The optical conductivity of a dense femtosecond laser-heated aluminum plasma heated to 0.1–1.5 eV was measured using frequency-domain interferometry with chirped pulses, permitting simultaneous observation of optical probe reflectivity and probe pulse phase shift. Coupled with published models of bound-electron contributions to the conductivity, these two independent experimental data yielded a direct measurement of both real and imaginary components of the plasma conductivity.

In this paper, we use a partition of the links of a network in order to uncover its community structure. This approach allows for communities to overlap at nodes so that nodes may be in more than one community. We do this by making a node partition of the line graph of the original network. In this way we show that any algorithm that produces a partition of nodes can be used to produce a partition of links. We discuss the role of the degree heterogeneity and propose a weighted version of the line graph in order to account for this.

The dynamical instability of rough hard-disk fluids in two dimensions is characterized through the Lyapunov spectrum and the Kolmogorov-Sinai entropy $h_{KS}$ for a wide range of densities and moments of inertia $I$. For small $I$ the spectrum separates into translation-dominated and rotation-dominated parts. With increasing $I$ the rotation-dominated part is gradually filled in at the expense of translation until such a separation becomes meaningless. At any density, the rate of phase-space mixing, given by $h_{KS}$, becomes less and less effective the more the rotation affects the dynamics. However, the degree of dynamical chaos, measured by the maximum Lyapunov exponent, is only enhanced by the rotational degrees of freedom for high-density gases but is diminished for lower densities. Surprisingly, no traces of Lyapunov modes were found in the spectrum for larger moments of inertia. The spatial localization of the perturbation vector associated with the maximum exponent however persists for any $I$.

We propose a noise reduction algorithm based on adaptive neighborhood selection that is able to obtain high levels of noise reduction for chaotic vector time series corrupted by observational noises with a noise-to-signal ratio of up to 300%.

We study the decaying Burgers dynamics in $d$ dimensions for random Gaussian initial conditions. We focus on power-law initial energy spectra, such that the system shows a self-similar evolution. This is the case of interest for the “adhesion model” in cosmology and a standard framework for “decaying Burgers turbulence.” We briefly describe how the system can be studied through perturbative expansions at early time or large scale (quasilinear regime). Next, we develop a saddle-point method, based on spherical instantons, that allows to obtain the asymptotic probability distributions $\mathcal{P}\left({\eta }_r\right)$ and $\mathcal{P}\left({\Theta }_r\right)$, of the density and velocity increment over spherical cells, reached in the quasilinear regime. Finally, we show how this approach can be extended to take into account the formation of shocks and we derive the rare-event tails of these probability distributions, at any finite time and scale. This also gives the high-mass tail of the mass function of pointlike singularities (shocks in the one dimensional case).

We study discrete surface breathers in two-dimensional lattices of inductively coupled split-ring resonators with capacitive nonlinearity. We consider both conservative (Hamiltonian) and analyze the properties of the modes localized in space and periodic in time (discrete breathers) located in the corners and on the edges of the lattice. We find that surface breathers in the Hamiltonian systems have lower energy than their bulk counterparts and they are generally more stable.

Mechanical equilibrium at zero temperature does not necessarily imply thermodynamic equilibrium at finite temperature for a particle confined by a static but nonconservative force field. Instead, the diffusing particle can enter into a steady state characterized by toroidal circulation in the probability flux, which we call a Brownian vortex. The circulatory bias in the particle’s thermally driven trajectory is not simply a deterministic response to the solenoidal component of the force but rather reflects interplay between advection and diffusion in which thermal fluctuations extract work from the nonconservative force field. As an example of this previously unrecognized class of stochastic heat engines, we consider a colloidal sphere diffusing in a conventional optical tweezer. We demonstrate both theoretically and experimentally that nonconservative optical forces bias the particle’s fluctuations into toroidal vortexes whose circulation can reverse direction with temperature or laser power.

The system of two scalar order parameters on a complex scale-free network is analyzed in the spirit of Landau theory. To add a microscopic background to the phenomenological approach, we also study a particular spin Hamiltonian that leads to coupled scalar order behavior using the mean-field approximation. Our results show that the system is characterized by either of two types of ordering: either one of the two order parameters is zero or both are nonzero but have the same value. While the critical exponents do not differ from those of a model with a single order parameter on a scale-free network, there are notable differences for the amplitude ratios and the susceptibilities. Another peculiarity of the model is that the transverse susceptibility is divergent at all $T<T_c$, when $O\left(n\right)$ symmetry is present. This behavior is related to the appearance of Goldstone modes.

Certain techniques characterizing diffusive processes, such as single-particle tracking or molecular dynamics simulation, provide time averages rather than ensemble averages. Whereas the ensemble-averaged mean-squared displacement (MSD) of an unbounded continuous time random walk (CTRW) with a broad distribution of waiting times exhibits subdiffusion, the time-averaged MSD, $\overline{{\delta }^2}$, does not. We demonstrate that, in contrast to the unbounded CTRW, in which $\overline{{\delta }^2}$ is linear in the lag time $\Delta$, the time-averaged MSD of the CTRW of a walker confined to a finite volume is sublinear in $\Delta$, i.e., for long lag times $\overline{{\delta }^2}\sim {\Delta }^{1-\alpha }$. The present results permit the application of CTRW to interpret time-averaged experimental quantities.

Spiky particles are constructed by superposing spheres and oblate ellipsoids. The resulting star particles (but nonconvex) are randomly packed by a sequential algorithm. The geometry, the conductivity, and the permeability of the resulting packings are systematically studied. Overall correlations are proposed to approximate these properties when the geometry of the particle is known.

Using our standard pore-level model, we have extended our earlier study of the crossover from fractal viscous fingering to compact /linear flow at a characteristic crossover time, $\tau$, in three dimensions to systems with as many as a ${10}^6$ pore bodies. These larger systems enable us to investigate the flows in the fully compact/well-past-crossover regime. The center of mass of the injected fluid exhibits basically the same behavior as found earlier but with an improved characteristic time. However, our earlier study of much smaller systems was unable to study the interfacial width in the important well-past-crossover regime, $t⪢\tau$. Now, we can study both the time evolution and roughness of the interfacial width. The interfacial width exhibits the same fractal-to-compact crossover as the center of mass, with the same characteristic time. In the fully compact regime, $t⪢\tau$, the interfacial width grows approximately linearly with time so that the standard growth exponent is approximately unity, $\beta =1.0\pm 0.1$. We find that neither is the interface self-affine nor is the roughness of the interface in the compact regime consistent with an effective long-range surface tension as assumed by various theories. In fact, similar to Lévy flights, the height variations across the interface appear to be random with occasional large height variations.

Fanelli and McKane [Phys. Rev. E 78, 051406 (2008)] recently described the growth of vesicles due to the accretion of lipid molecules onto their surface in terms of linear irreversible thermodynamics. They calculated the critical radius at which the shape of a spherical vesicle becomes unstable. Their treatment is different from those previously put forward and, in the following, we explain why we regard their thermodynamic description to be deficient.

We respond to the Comment of Božič and Svetina [Phys. Rev. E 80, 013401 (2009)] by first questioning the consistency of their approach. We then argue, on the basis of numerical estimates of relevant experimental quantities, that the vesicles may be assumed to be turgid as they grow in size, thus justifying our earlier methodology. Finally, we comment on the remaining issues where our approaches differ.

While most studies of deterministic network growth have been of one- or two-case models, here a more diverse and comprehensive method of deterministic network evolution is presented. The range of observed behavior is classified and the underlying causes of the various types of growth are investigated. The potential for prediction of the different types of network growth is also examined. It is discovered that a wide variety of behavior can be produced by a simple evolutionary setup and that the networks resulting from this method of evolution warrant further study.

The complete knowledge of Laplacian eigenvalues and eigenvectors of complex networks plays an outstanding role in understanding various dynamical processes running on them; however, determining analytically Laplacian eigenvalues and eigenvectors is a theoretical challenge. In this paper, we study the Laplacian spectra and their corresponding eigenvectors of a class of deterministically growing treelike networks. The two interesting quantities are determined through the recurrence relations derived from the structure of the networks. Beginning from the rigorous relations one can obtain the complete eigenvalues and eigenvectors for the networks of arbitrary size. The analytical method opens the way to analytically compute the eigenvalues and eigenvectors of some other deterministic networks, making it possible to accurately calculate their spectral characteristics.

Departing from a system of two nonautonomous amplitude equations, demonstrating hyperbolic chaotic dynamics, we construct a one-dimensional medium as an ensemble of such local elements introducing spatial coupling via diffusion. When length of the medium is small, all spatial cells oscillate synchronously, reproducing the local hyperbolic dynamics. This regime is characterized by a single positive Lyapunov exponent. The hyperbolicity survives when the system gets larger in length so that the second Lyapunov exponent passes zero and the oscillations become inhomogeneous in space. However, at a point where the third Lyapunov exponent becomes positive, some bifurcation occur that results in violation of the hyperbolicity due to the emergence of one-dimensional intersections of contracting and expanding tangent subspaces along trajectories on the attractor. Further growth of the length results in the two-dimensional intersections of expanding and contracting subspaces that we classify as a stronger type of the violation. Beyond the point of the hyperbolicity loss, the system demonstrates an extensive spatiotemporal chaos typical for extended chaotic systems: when the length of the system increases the Kaplan-Yorke dimension, the number of positive Lyapunov exponents and the upper estimate for Kolmogorov-Sinai entropy grow linearly, while the Lyapunov spectrum tends to a limiting curve.

We study scaling laws characterizing the interdiffusive zone between two miscible fluids flowing side by side in a Y-shape laminar micromixer using the lattice Boltzmann method. The lattice Boltzmann method solves the coupled three-dimensional (3D) hydrodynamics and mass transfer equations and incorporates intrinsic features of 3D flows related to this problem. We observe the different power-law regimes occurring at the center of the channel and close to the top/bottom wall. The extent of the interdiffusive zone scales as the square root of the axial distance at the center of the channel. At the top/bottom wall, we find an exponent 1/3 at early stages of mixing as observed in the experiments of Ismagilov et al. [Appl. Phys. Lett. 76, 2376 (2000)]. At a larger distance from the entrance, the scaling exponent close to the walls changes to 1/2 [J.-B. Salmon and A. Adjari, J. Appl. Phys. 101, 074902 (2007)]. Here, we focus on the effect of the finite aspect ratio on diffusive broadening. Interestingly, we find the same scaling laws regardless of the channel’s aspect ratio. However, the point at which the exponent 1/3 characterizing the broadening at the top/bottom wall reverts to the normal diffusive behavior downstream strongly depends on the aspect ratio. We propose an interpretation of this observation in terms of the shear rate at the side walls. A criterion for the range of aspect ratios with non-negligible effect on diffusive broadening is also provided.

The forcing term in the lattice Boltzmann equation (LBE) is usually used to mimic Navier-Stokes equations with a body force. To derive axisymmetric model, forcing terms are incorporated into the two-dimensional (2D) LBE to mimic the additional axisymmetric contributions in 2D Navier-Stokes equations in cylindrical coordinates. Many axisymmetric lattice Boltzmann D2Q9 models were obtained through the Chapman-Enskog expansion to recover the 2D Navier-Stokes equations in cylindrical coordinates [I. Halliday et al., Phys. Rev. E 64, 011208 (2001); K. N. Premnath and J. Abraham, Phys. Rev. E 71, 056706 (2005); T. S. Lee, H. Huang, and C. Shu, Int. J. Mod. Phys. C 17, 645 (2006); T. Reis and T. N. Phillips, Phys. Rev. E 75, 056703 (2007); J. G. Zhou, Phys. Rev. E 78, 036701 (2008)]. The theoretical differences between them are discussed in detail. Numerical studies were also carried out by simulating two different flows to make a comparison on these models’ accuracy and $\tau$ sensitivity. It is found all these models are able to obtain accurate results and have the second-order spatial accuracy. However, the model C [J. G. Zhou, Phys. Rev. E 78, 036701 (2008)] is the most stable one in terms of $\tau$ sensitivity. It is also found that if density of fluid is defined in its usual way and not directly relevant to source terms, the lattice Boltzmann model seems more stable.

We assume that the level spectra of quantum systems in the initial phase of transition from integrability to chaos are approximated by superpositions of independent sequences. Each individual sequence is modeled by a random matrix ensemble. We obtain analytical expressions for the level spacing distribution and level number variance for such a system. These expressions are successfully applied to the analysis of the resonance spectrum in a nearly integrable microwave billiard.