We study the classical dynamics of two bodies, a massive line segment or slash (/) and a massive point or dot (.), interacting gravitationally. For this slash-dot (/.) body problem, we derive algebraic expressions for the force and torque on the slash, which greatly facilitate analysis. The diverse dynamics include a stable synchronous orbit, generic chaotic orbits, sequences of unstable periodic orbits, spin-stabilized orbits, and spin-orbit coupling that can unbind the slash and dot. The extension of the slash provides an extra degree of freedom that enables the interplay between rotation and revolution. In this way, the slash-dot body problem exhibits some of the richness of the three body problem with only two bodies and serves as a valuable prototype for more realistic systems. Applications include the dynamics of asteroid-moonlet pairs and asteroid rotation and escape rates.

We present a statistical analysis of defect-mediated turbulence in a kinetic model of catalytic CO oxidation on Pt(110). A probabilistic description based on the gain and loss rates of defects is derived. For low values of the CO partial pressure the statistics of topological defects agree with earlier results for the complex Ginzburg-Landau equation. For high values of the CO partial pressure, we observe an additional autocatalytic reproduction of defects that results in a linear dependence of the defect creation rate on the number of defects in the system. The role of correlations between defects of opposite topological charge was found to be weaker than in the experimental system.

The flow behaviors of polymer melt composed of short chains with ten beads between parallel plates are simulated by using a hybrid method of molecular dynamics and computational fluid dynamics. Three problems are solved: creep motion under a constant shear stress and its recovery motion after removing the stress, pressure-driven flows, and the flows in rapidly oscillating plates. In the creep/recovery problem, the delayed elastic deformation in the creep motion and evident elastic behavior in the recovery motion are demonstrated. The velocity profiles of the melt in pressure-driven flows are quite different from those of Newtonian fluid due to shear thinning. Velocity gradients of the melt become steeper near the plates and flatter at the middle between the plates as the pressure gradient increases and the temperature decreases. In the rapidly oscillating plates, the viscous boundary layer of the melt is much thinner than that of Newtonian fluid due to the shear thinning of the melt. Three different rheological regimes, i.e., the viscous fluid, viscoelastic liquid, and viscoelastic solid regimes, form over the oscillating plate according to the local Deborah numbers. The melt behaves as a viscous fluid in a region for $\omega {\tau }^R\lesssim 1$, and the crossover between the liquidlike and solidlike regime takes place around $\omega {\tau }^{\alpha }\simeq 1$ (where $\omega$ is the angular frequency of the plate and ${\tau }^R$ and ${\tau }^{\alpha }$ are Rouse and $\alpha$ relaxation time, respectively).

Following a recent Letter by Bret et al. [Phys. Rev. Lett. 100, 205008 (2008)], we present a detailed report of the entire unstable $\mathbf{k}$ spectrum of a relativistic collisionless beam-plasma system within a fully kinetic framework. In contrast to a number of previously published studies, our linear analysis makes use of smooth momentum distribution functions of the Maxwell-Jüttner form. The three competing classes of instabilities, namely, two-stream, filamentation, and oblique modes, are dealt with in a unified manner, no approximation being made regarding the beam-plasma densities, temperatures, and drift energies. We investigate the hierarchy between the competing modes, paying particular attention to the relatively poorly known quasielectrostatic oblique modes in the regime where they govern the system. The properties of the fastest growing oblique modes are examined in terms of the system parameters and compared to those of the dominant two-stream and filamentation modes.

The low-frequency portion of the x-ray Thomson scattering spectrum is determined by electrons that follow the slow ion motion. This ion motion is characterized by the ion-ion dynamic structure factor, which contains a wealth of information about the ions, including structure and collective modes. The frequency-integrated (diffraction) contribution is considered first. An effective dressed-particle description of warm dense matter is derived from the quantum Ornstein-Zernike equations, and this is used to identify a Yukawa model for warm dense matter. The efficacy of this approach is validated by comparing a predicted structure with data from the extreme case of a liquid metal; good agreement is found. A Thomas-Fermi model is then introduced to allow the separation of bound and free states at finite temperatures, and issues with the definition of the ionization state in warm dense matter are discussed. For applications, analytic structure factors are given on either side of the Kirkwood line. Finally, several models are constructed for describing the slow dynamics of warm dense matter. Two classes of models are introduced that both satisfy the basic sum rules. One class of models is the “plasmon-pole”-like class, which yields the dispersion of ion-acoustic waves. Damping is then included via generalized hydrodynamics models that incorporate viscous contributions.

We discuss several techniques for the evaluation of the generalized Lyapunov exponents which characterize the growth of products of random matrices in the large-deviation regime. A Monte Carlo algorithm that performs importance sampling using a simple random resampling step is proposed as a general-purpose numerical method which is both efficient and easy to implement. Alternative techniques complementing this method are presented. These include the computation of the generalized Lyapunov exponents by solving numerically an eigenvalue problem, and some asymptotic results corresponding to high-order moments of the matrix products. Taken together, the techniques discussed in this paper provide a suite of methods which should prove useful for the evaluation of the generalized Lyapunov exponents in a broad range of applications. Their usefulness is demonstrated on particular products of random matrices arising in the study of scalar mixing by complex fluid flows.

Phyllotaxis refers to the arrangement of primordia (the first stage in the development of a structure such as a leaf) on plants and phyllotactic planforms refer to the shapes of the primordia in a phyllotactic arrangement. This paper focuses on invariances in phyllotactic planforms as the van Iterson parameter $\Gamma$—a measurement of the ratio of the size of the annular generative region at the plant tip where the patterns form to primordium area—varies. We demonstrate discrete invariance in phyllotactic planforms, by which we mean a similarity in the planform under a scaling $\Gamma \to \Gamma {\varphi }^n$, where $\varphi$ is the golden number and $n$ is an integer. Continuous invariance in planforms is then motivated by examples in which the shapes of primordia are homogeneous as $n$ varies over the real numbers. We also show how continuous invariance results from classical number-theoretical theorems on the approximation of irrational numbers (such as $\varphi$) by rational numbers. We define these notions first for the underlying phyllotactic lattice and then for primordium shapes and amplitude equations resulting from partial differential equation (PDE) models.

Genes and human languages are discrete combinatorial systems (DCSs), in which the basic building blocks are finite sets of elementary units: nucleotides or codons in a DNA sequence, and letters or words in a language. Different combinations of these finite units give rise to potentially infinite numbers of genes or sentences. This type of DCSs can be represented as an alphabetic bipartite network (ABN) where there are two kinds of nodes, one type represents the elementary units while the other type represents their combinations. Here, we extend and generalize recent analytical findings for ABNs derived in [Peruani et al., Europhys. Lett. 79, 28001 (2007)] and empirically investigate two real world systems in terms of ABNs, the codon gene and the phoneme-language network. The one-mode projections onto the elementary basic units are also studied theoretically as well as in real world ABNs. We propose the use of ABNs as a means for inferring the mechanisms underlying the growth of real world DCSs.

In a frequency range where a microwave resonator simulates a chaotic quantum billiard, we have measured moduli and phases of reflection and transmission amplitudes in the regimes of both isolated and of weakly overlapping resonances and for resonators with and without time-reversal invariance. Statistical measures for $S$-matrix fluctuations were determined from the data and compared with extant and/or newly derived theoretical results obtained from the random-matrix approach to quantum chaotic scattering. The latter contained a small number of fit parameters. The large data sets taken made it possible to test the theoretical expressions with unprecedented accuracy. The theory is confirmed by both a goodness-of-fit-test and the agreement of predicted values for those statistical measures that were not used for the fits, with the data.

By means of full exact diagonalization, we study level statistics and the structure of the eigenvectors of one-dimensional gapless bosonic and fermionic systems across the transition from integrability to quantum chaos. These systems are integrable in the presence of only nearest-neighbor terms, whereas the addition of next-nearest-neighbor hopping and interaction may lead to the onset of chaos. We show that the strength of the next-nearest-neighbor terms required to observe clear signatures of nonintegrability is inversely proportional to the system size. Interestingly, the transition to chaos is also seen to depend on particle statistics, with bosons responding first to the integrability breaking terms. In addition, we discuss the use of delocalization measures as main indicators for the crossover from integrability to chaos and the consequent viability of quantum thermalization in isolated systems.

In the natural world, the properties of interacting oscillatory systems are not constant, but evolve or fluctuating continuously in time. Thus, the basic frequencies of the interacting oscillators are time varying, which makes the system analysis complex. For studying their interactions we propose a complementary approach combining wavelet bispectral analysis and information theory. We show how these methods uncover the interacting properties and reveal the nature, strength, and direction of coupling. Wavelet bispectral analysis is generalized as a technique for detecting instantaneous phase-time dependence for the case of two or more coupled nonlinear oscillators whereas the information theory approach can uncover the directionality of coupling and extract driver-response relationships in complex systems. We generate bivariate time-series numerically to mimic typical situations that occur in real measured data, apply both methods to the same time-series and discuss the results. The approach is applicable quite generally to any system of coupled nonlinear oscillators.

The experiments on two tandem circular cylinders were conducted in a horizontal soap film tunnel for the Reynolds number $\text{Re}=60$, 80, and 100 and the nondimensional center-to-center spacing $\Gamma$ ranging in $1\sim 12$. The flow patterns were recorded by a high-speed camera and the vortex shedding frequency was obtained by a spatiotemporal evolution method. The secondary vortex formation (SVF) mode characterized by the formation of a secondary vortex street in the wake of the downstream cylinder was found at large $\Gamma$. Moreover, some typical modes predicted by previous investigations, including the single bluff-body, shear layer reattachment, and synchronization of vortex shedding modes, were also revisited in our experiments. Further, numerical simulations were carried out using a space-time finite-element method and the results confirmed the existence of the SVF mode. The mechanism of SVF mode was analyzed in terms of the numerical results. The dependence of the Strouhal number Sr on $\Gamma$ was given and the flow characteristics relevant to the critical spacing values and the hysteretic mode transitions were investigated.

Two pressure-driven streams of two miscible liquids can only mix by diffusion in microfluidic channels because of the low Reynolds number. We present an idea to generate mixing by “chaotic advection” in microscale geometries. That is, we consider using induced-charge electro-osmosis to generate a second flow and then modulate between the pressure-driven and induced-charge flows. By using the combined method consisting of the boundary element method, the Lagrangian particle tracking method, and the random-walk method, we analyze mixing efficiency, mixing time, and mixing length, with the effects of modulation frequency and molecular diffusivity, and compare our proposed mixer with other mixers. By this analysis, we find that chaotic mixing can be produced efficiently in a microfluidic channel by switching between pressure-driven and induced-charge flows in a wide range of Péclet number under the specific condition of Strouhal number. By using our proposed mixer, we can expect to realize efficient chaotic mixing with minimum voltage in an ordinary flow channel with a simple structure without an oblique electric field even at large Péclet number.

A recent macroscopic theory of biphasic flow in porous media [R. Hilfer, Phys. Rev. E 73, 016307 (2006)] has proposed to treat microscopically percolating fluid regions differently from microscopically nonpercolating regions. Even in one dimension the theory reduces to an analytically intractable set of ten coupled nonlinear partial differential equations. This paper reports numerical solutions for three different initial and boundary value problems that simulate realistic laboratory experiments. All three simulations concern a closed column containing a homogeneous porous medium filled with two immiscible fluids of different densities. In the first simulation the column is raised from a horizontal to a vertical orientation inducing a buoyancy-driven fluid flow that separates the two fluids. In the second simulation the column is first raised from a horizontal to a vertical orientation and subsequently rotated twice by $180°$ to compare the resulting stationary saturation profiles. In the third simulation the column is first raised from horizontal to vertical orientation and then returned to its original horizontal orientation. In all three simulations imbibition and drainage processes occur simultaneously inside the column. This distinguishes the results reported here from conventional simulations based on existing theories of biphasic flows. Existing theories are unable to predict flow processes where imbibition and drainage occur simultaneously. The approximate numerical results presented here show the same process dependence and hysteresis as one would expect from an experiment.

We discuss the use of multivariate Granger causality in presence of redundant variables: the application of the standard analysis, in this case, leads to under estimation of causalities. Using the un-normalized version of the causality index, we quantitatively develop the notions of redundancy and synergy in the frame of causality and propose two approaches to group redundant variables: (i) for a given target, the remaining variables are grouped so as to maximize the total causality and (ii) the whole set of variables is partitioned to maximize the sum of the causalities between subsets. We show the application to a real neurological experiment, aiming to a deeper understanding of the physiological basis of abnormal neuronal oscillations in the migraine brain. The outcome by our approach reveals the change in the informational pattern due to repetitive transcranial magnetic stimulations.

We provide an expression quantitatively describing the specific heat of the Ising model on the simple-cubic lattice in the critical region. This expression is based on finite-size scaling of numerical results obtained by means of a Monte Carlo method. It agrees satisfactorily with series expansions and with a set of experimental results. Our results include a determination of the universal amplitude ratio of the specific-heat divergences at both sides of the critical point.

We propose a unified physical framework for transport in variably saturated porous media. This approach allows fluid flow and solute migration to be treated as ensemble averages of fluid and solute particles, respectively. We consider the cases of homogeneous and heterogeneous porous materials. Within a fractal mobile-immobile continuous time random-walk framework, the heterogeneity will be characterized by algebraically decaying particle retention times. We derive the corresponding (nonlinear) continuum-limit partial differential equations and we compare their solutions to Monte Carlo simulation results. The proposed methodology is fairly general and can be used to track fluid and solutes particles trajectories for a variety of initial and boundary conditions.

The nematic-to-smectic-$A$ (NA) transition in 8CB (4-octyl-$4^{\prime }$-cyanobiphenyl) is especially interesting because experimentally, it has been observed to be second order, but theoretically, it has been predicted that it must have a latent heat. The effect on the NA transition due to confinement in an adsorbed film has hitherto not been investigated. Previous study of adsorbed 8CB films on silicon for coverages less than 100 nm showed the existence of a broad coexistence region, identified by the formation of thick and thin islands on the surface that extends between the bulk NA and the isotropic-to-nematic transition temperatures. In this paper, optical and ellipsometric measurements of 8CB films as a function of temperature are used to identify the location of the NA transition in the film in relation to the coexistence region. The NA transition temperature in the film is found to occur at $32.2\pm 0.4°\text{C}$ independent of film thickness for films between 62 to 270 nm thick, based on the decrease in the film anisotropy. This decrease in the anisotropy is found to be surprisingly abrupt. For thicknesses below 62 nm, the NA transition line is joined to the thin-thick coexistence region found previously.

To rationalize the disentangling action of type II topoisomerases, an improved wormlike DNA model was used to delineate the degree of unknotting and decatenating achievable by selective segment passage at specific juxtaposition geometries and to determine how these activities were affected by DNA circle size and solution ionic strength. We found that segment passage at hooked geometries can reduce knot populations as dramatically as seen in experiments. Selective segment passage also provided theoretical underpinning for an intriguing empirical scaling relation between unknotting and decatenating potentials.

Using analytical calculations and computer simulations, we consider both the lateral diffusion of a membrane protein and the fluctuation spectrum of the membrane in which the protein is embedded. The membrane protein interacts with the membrane shape through its spontaneous curvature and bending rigidity. The lateral motion of the protein may be viewed as diffusion in an effective potential, hence, the effective mobility is always reduced compared to the case of free diffusion. Using a rigorous path-integral approach, we derive an analytical expression for the effective diffusion coefficient for small ratios of temperature and bending rigidity, which is the biologically relevant limit. Simulations show very good quantitative agreement with our analytical result. The analysis of the correlation functions contributing to the diffusion coefficient shows that the correlations between the stochastic force of the protein and the response in the membrane shape are responsible for the reduction. Our quantitative analysis of the membrane height correlation spectrum shows an influence of the protein-membrane interaction causing a distinctly altered wave-vector dependence compared to a free membrane. Furthermore, the time correlations exhibit the two relevant time scales of the system: that of membrane fluctuations and that of lateral protein diffusion with the latter typically much longer than the former. We argue that the analysis of the long-time decay of membrane height correlations can thus provide a new means to determine the effective diffusion coefficient of proteins in the membrane.