A set of quantum states, dynamically related to the classical periodic orbits of a chaotic map, is used as a basis in which the description of the eigenstates of its quantum version is greatly simplified. This set can be improved with the inclusion of short time propagation along the stable and unstable manifolds of the periodic orbits resulting in a construction similar to the scar functions of Vergini [J. Phys. A 33, 4709 (2000)]. The average participation ratio is used to quantify the quality of the basis.

We report on simulations of two-dimensional turbulence in the inverse energy cascade regime. Focusing on the statistics of Lagrangian tracer particles, scaling behavior of the probability density functions of velocity fluctuations is investigated. The results are compared to the three-dimensional case. In particular an analysis in terms of compensated cumulants reveals the transition from a strong non-Gaussian behavior with large tails to Gaussianity. The reported computation of correlation functions for the acceleration components sheds light on the underlying dynamics of the tracer particles.

A preliminary essential procedure in time series analysis is the separation of the deterministic component from the random one. If the signal is the result of superposing a noise over a deterministic trend, then the first one must estimate and remove the trend from the signal to obtain an estimation of the stationary random component. The errors accompanying the estimated trend are conveyed as well to the estimated noise, taking the form of detrending errors. Therefore the statistical errors of the estimators of the noise parameters obtained after detrending are larger than the statistical errors characteristic to the noise considered separately. In this paper we study the detrending errors by means of a Monte Carlo method based on automatic numerical algorithms for nonmonotonic trends generation and for construction of estimated polynomial trends alike to those obtained by subjective methods. For a first order autoregressive noise we show that in average the detrending errors of the noise parameters evaluated by means of the autocovariance and autocorrelation function are almost uncorrelated to the statistical errors intrinsic to the noise and they have comparable magnitude. For a real time series with significant trend we discuss a recursive method for computing the errors of the estimated parameters after detrending and we show that the detrending error is larger than the half of the total error.

The strong interactions between particles will make the energy within the granular materials propagate through the network of contacts and be partly dissipated. Establishing a model that can clearly classify the dissipation and dispersion effects is crucial for the understanding of the global behaviors in the granular materials. For particles with rate-independent material, the dissipation effects come from the local plastic deformation and can be constrained at the energy level by using energetic restitution coefficients. On the other hand, the dispersion effects should depend on the intrinsic nature of the interaction law between two particles. In terms of a bistiffness compliant contact model that obeys the energetical constraint defined by the energetic coefficients, our recent work related to the issue of multiple impacts indicates that the propagation of energy during collisions can be represented by a distributing law. In particular, this law shows that the dispersion effects are dominated by the relative contact stiffness and the relative potential energy stored at the contact points. In this paper, we will apply our theory to the investigation of the wave behavior in granular chain systems. The comparisons between our numerical results and the experimental ones by Falcon et al., [Eur. Phys. J. B 5, 111 (1998)] for a column of beads colliding against a wall show very good agreement and confirm some conclusions proposed by Falcon et al. Other numerical results associated with the case of several particles impacting a chain, and the collisions between two so-called solitary waves in a Hertzian type chain are also presented.

In pure water a hydrothermally treated zeolite Y is hydrophilic, while with the addition of an electrolyte it can no longer be soaked up spontaneously. The effective degree of hydrophobicity increases with the ion concentration, which is reflected by the increase in infiltration pressure. The pressure-induced infiltration behavior is not only determined by the cations, but also highly dependent on the anion species. This phenomenon can be attributed to the confinement effect of nanopore walls.

Microbead rheology maps the fluctuations of beads immersed in soft matter to viscoelastic properties of the surrounding medium. In this paper, we present modeling extensions of the seminal results of Mason and Weitz [Phys. Rev. Lett. 74, 1250 (1995)] for a single bead and of Crocker et al. [Phys. Rev. Lett. 85, 888 (2000)] and Levine and Lubensky [Phys. Rev. Lett. 85, 1774 (2000)] for two beads. We formulate the linear response analysis for two beads so that the model equations retain the local diffusive properties of each bead (through the memory kernel of the shell or depletion zone surrounding each bead) and the nonlocal dynamic moduli of the medium separating the beads (through the memory kernel that transmits fluctuations of one bead to the other). We then derive a $3\times 3$ invertible system of equations relating: an isolated bead’s autocorrelations, the autocorrelations and cross-correlations of two coupled beads; and the shell radius surrounding each bead, the memory kernels of the shell, and of the medium between the two beads.

A detailed analysis of the structure and dynamics of the crystal-melt interface region in silicon, modeled with the Stillinger-Weber potential, is performed via molecular dynamics simulations. The focus is on the faceted (111) crystal-melt interface, but properties of the rough (100) interface are also determined. We find an intrinsic 10-90 interface width of $0.681\pm 0.001\mathrm{nm}$ for the coarse-grained density profile at the (111) interface and a $0.570\pm 0.005\mathrm{nm}$ width at the (100) interface. Coarse-grained profiles of a suitably defined local order parameter are found to show a smaller width anisotropy between (111) and (100) interfaces while the order profiles exhibit a $0.20–0.25\mathrm{nm}$ shift in position toward the crystal phase relative to the corresponding density profiles. The structural analysis of the layer of melt adjacent to the (111) facet of the crystal finds ordered clusters with average lifetimes of $16\mathrm{ps}$, as determined from autocorrelations of time-dependent layer structure factors, and cluster radii of gyration from $0.2\mathrm{nm}$ for the smallest cells to as large as $1.5\mathrm{nm}$.

Cells swell in response a hypoosmotic challenge. By converting osmotic pressure to hydrostatic pressure at the cell membrane via van’t Hoff’s law, and converting that to tension via Laplace’s law one predicts that the cell membrane should stretch and become stiff. We tested this prediction using the atomic force microscopy. During osmotic swelling cells did not become stiff and generally became softer. This result contradicts the assumption of the cell membrane as the constraining element in osmotic stress but is consistent with the cytoskeleton acting as a cross-linked gel. Models of the cells’ response to osmotic stress must include energy terms for three-dimensional stresses.

We study the statistics of the interoccurrence times between events above some threshold $Q$ in two kinds of multifractal data sets (multiplicative random cascades and multifractal random walks) with vanishing linear correlations. We show that in both data sets the relevant quantities (probability density functions and the autocorrelation function of the interoccurrence times, as well as the conditional return period) are governed by power laws with exponents that depend explicitly on the considered threshold. By studying a large number of representative financial records (market indices, stock prices, exchange rates, and commodities), we show explicitly that the interoccurrence times between large daily returns follow the same behavior, in a nearly quantitative manner. We conclude that this kind of behavior is a general consequence of the nonlinear memory inherent in the multifractal data sets.

We use a semiclassical expansion as an alternative derivation of the well-known, rigorous result obtained by Hepp and Lieb for the classical limit of the spin-boson model. We also explicitly derive correction terms to the classical limit previously obtained in the context of Heisenberg equations of motion. We analyze the size and shape of the $N$ (number of atoms) vs $t$ (time) domain whithin which the corrections so obtained are useful.

Forced turbulence combined with the effect of rotation and shear flow is studied. In a previous paper [N. Leprovost and E. J. Kim, Phys. Rev. E 78, 016301 (2008)], we considered the case where the shear and the rotation are perpendicular. Here, we consider the complementary case of parallel rotation and shear, elucidating how rotation and flow shear influence the generation of shear flow (e.g., the direction of energy cascade), turbulence level, transport of particles, and momentum. We show that turbulence amplitude and transport are always quenched due to strong shear ($\xi =\nu k_y^2∕\mathcal{A}⪡1$, where $\mathcal{A}$ is the shearing rate, $\nu$ is the molecular viscosity, and $k_y$ is a characteristic wave number of small-scale turbulence), with stronger reduction in the direction of the shear than those in the perpendicular directions. In contrast with the case where rotation and shear are perpendicular, we found that rotation affects turbulence amplitude only for very rapid rotation $(\Omega ⪢\mathcal{A})$ where it reduces slightly the anisotropy due to shear flow. Also, concerning the transport properties of turbulence, we find that rotation affects only the transport of particle and only for rapid rotation, leading to an almost isotropic transport (whereas, in the case of perpendicular rotation and shear, rotation favors isotropic transport even for slow rotation). Furthermore, the interaction between the shear and the rotation is shown to give rise to nondiffusive flux of angular momentum ($\Lambda$ effect), even in the absence of external sources of anisotropy, which can provide a mechanism for the creation of shearing structures in astrophysical and geophysical systems.

An alternative drag coefficient $C_d^a$ $[=\overline{F}∕\left(\frac{1}{2}\rho U_{\infty }^2{U}_{\infty }{T}_s\right)]$, is proposed for an isolated bluff-body wake, where $\overline{F}$ is the drag force on the body per unit length, $U_{\infty }$ is the free-stream velocity, $\rho$ is the density of fluid, and $T_s$ is the vortex shedding period. Theoretical analysis presently conducted indicates that, while the conventional drag coefficient $C_d$ $[=\overline{F}∕\left(\frac{1}{2}\rho U_{\infty }^{2}d\right)]$ may be interpreted as the intensity of the mean kinetic energy deficit distributed over the characteristic length of cylinder height $d$, $C_d^a$ is the intensity of the mean kinetic energy deficit distributed over the characteristic length of the Karman vortex wavelength $U_{\infty }{T}_s$. Therefore, $C_d^a$ may be considered to be a drag coefficient with the characteristic length given by $U_{\infty }{T}_s$, instead of $d$. As long as a bluff body is isolated, without energy exchange between the cylinder and its support, this drag coefficient is invariant, as confirmed by our experimental data as well as those in the literature, with respect to the bluff-body geometry, angle of attack, and Reynolds number, with a caveat of limited cases examined presently.

Two low-dimensional magnetohydrodynamic models containing three velocity and three magnetic modes are described. One of them (nonhelical model) has zero kinetic and current helicity, while the other model (helical) has nonzero kinetic and current helicity. The velocity modes are forced in both these models. These low-dimensional models exhibit a dynamo transition at a critical forcing amplitude that depends on the Prandtl number. In the nonhelical model, dynamo exists only for magnetic Prandtl number beyond 1, while the helical model exhibits dynamo for all magnetic Prandtl number. Although the model is far from reproducing all the possible features of dynamo mechanisms, its simplicity allows a very detailed study and the observed dynamo transition is shown to bear similarities with recent numerical and experimental results.

We present spectroscopic measurements in which utilized are line-intensity ratios in the near-uv to measure electron energies of several hundred eVs, which usually necessitates the use of emission in the soft x-ray region. The main intensity ratio selected is of the $\mathrm{B}\mathrm{III}$ transition $1s^{2}2s{}^2\mathrm{S}_{1∕2}\text{−}1s^{2}2p{}^2\mathrm{P}_{3∕2}$ $\left(2066\mathrm{\AA }\right)$ and the $\mathrm{B}\mathrm{IV}$ transition $1s2s{}^3\mathrm{S}_1\text{−}1s2p{}^3\mathrm{P}_2$ $\left(2822\mathrm{\AA }\right)$. A detailed atomic-kinetics modeling is made to demonstrate the usefulness of this atomic system for studying transient, ionizing plasmas. Here, it is applied for the characterization of high-electron energies $(\sim 500\mathrm{eV})$ generated due to the rapid penetration of a magnetic field pulse into a low-collisionality plasma. Limitations of the use of the method are discussed.

Many difficult computational problems involve the simultaneous satisfaction of multiple constraints that are individually easy to satisfy. These constraints might be derived from measurements (as in tomography or diffractive imaging), interparticle interactions (as in spin glasses), or a combination of sources (as in protein folding). We present a simple geometric framework to express and solve such problems and apply it to two benchmarks. In the first application (3SAT, a Boolean satisfaction problem), the resulting method exhibits similar performance scaling as a leading context-specific algorithm (WALKSAT). In the second application (sphere packing), the method allowed us to find improved solutions to some old and well-studied optimization problems. Based upon its simplicity and observed efficiency, we argue that this framework provides a competitive alternative to stochastic methods such as simulated annealing.

We study direct energy transfer by multipolar or exchange interactions between diffusive excited donor and diffusive unexcited acceptors. Extending over the case of long-range transfer of an excitation energy a nonperturbative approach by Bray and Blythe [Phys. Rev. Lett. 89, 150601 (2002)], originally developed for contact diffusion-controlled reactions, we determine exactly long-time asymptotics of the donor decay function in one-dimensional systems.

We analyze transport of local magnetization and develop schemes to control transport behavior in finite spin-$1∕2$ Heisenberg chains and spin-$1∕2$ Heisenberg two-leg ladders at zero temperature. By adjusting parameters in the Hamiltonians, these quantum systems may show both integrable and chaotic limits. We provide examples of chaotic systems leading to diffusive and to ballistic transport. In addition, methods of coherent quantum control to induce a transition from diffusive to ballistic transport are proposed.

We investigate a particle in a ratchet potential (the system) coupled to an harmonic bath of $N=1–500$ degrees of freedom (the discrete bath). The dynamics of the energy exchange between the system and the discrete bath is studied in the transition regime from low to high values of $N$. First manifestation of dissipation (energy lost by the system) appears for the bath composed of $10\lesssim N\lesssim 20$ oscillators, as expected. For low values of $N$, beside small dissipation effects, the system experiences the bath-induced particle transfer between different potential wells from the ratchet. We show that this effect decreases the mobility of particles along the ratchet. The hopping probability along the ratchet and the energy decay rates for the system are shown to obey the power law for late times, a behavior typical of discrete baths which for low and intermediate values of $N$ always induce a non-Markovian process. The exponential decay is recovered for high bath frequencies distribution and for high values of $N$, where the Markovian limit is expected. Moreover, by including the external oscillating field with intensity $F$, we show that current reversal occurs in two situations: By increasing $N$ and by switching from low to high frequencies distribution of the bath. The mobility of particles is shown to have a maximum at $F=0.1$, which is $N$ independent (for higher values of $N$).

We review statistical properties of models generated by the application of a (positive and negative order) fractional derivative operator to a standard random walk and show that the resulting stochastic walks display slowly decaying autocorrelation functions. The relation between these correlated walks and the well-known fractionally integrated autoregressive models with conditional heteroskedasticity (FIGARCH), commonly used in econometric studies, is discussed. The application of correlated random walks to simulate empirical financial times series is considered and compared with the predictions from FIGARCH and the simpler FIARCH processes. A comparison with empirical data is performed.