Slow Spatial Variations Research Articles

A Fully Consistent Hybrid Les/Rans Conditional Transported Pdf Method for Non-premixed Reacting Flows

ABSTRACT A novel hybrid modeling approach that combines a finite-volume large eddy simulation (LES) with a Reynold-Averaged Navier-Stokes (RANS) conditional probability density function (PDF) method for turbulent non-premixed reacting flows is presented. The hybrid method incorporates the turbulent flow modeling of the LES with the chemistry–turbulence interaction modeling of the Lagrangian RANS-PDF. Specifically, the conditional composition RANS-PDF method is applied as the turbulence-chemistry closure for the LES. For a statistically steady-state case, the evolution of stochastic particles in a RANS framework reduces the computational effort, compared to the classical LES filtered density function (FDF), by performing the expensive chemical ODE integration at a lower spatial resolution. This approach is justified by the slow spatial variations of the reacting variables conditioned on the mixture fraction. Here, a consistent two-way coupling between the LES flow-field and the conditional composition RANS-PDF is formulated. The accuracy and the consistency of the method are established studying the Sandia flame series with detailed chemistry. Good predictions of the mean flow-fields and mean and conditional reactive scalars have been obtained, compared with the experimental data, with an overall decrease of the computational effort up to two orders of magnitude.

The contribution of magnetic monopoles to the ponderomotive force

When magnetic monopoles are assumed to exist in plasma dynamics, the propagation of electromagnetic waves is modified as Maxwell equations acquire a symmetrical structure due to the existence of electric and magnetic charge and current densities. This work presents a theoretical exploration on how far we can push the limits of a plasma theory under the presence of magnetic monopoles. In particular, we study the modification of ponderomotive forces in a plasma composed by electric and magnetic charges. We show that the general ponderomotive force on this plasma depends non-trivially on the magnetic monopoles, through the slow temporal and spatial variations of the electromagnetic field amplitudes. The magnetic charges introduce corrections even if the plasma is unmagnetized. Also, it is shown that the magnetic monopoles also experience a ponderomotive force due to the electrons. This force is in the direction of propagation of the electromagnetic waves.

Effect of dimensionality on sliding charge density waves: The quasi-two-dimensionalTbTe3system probed by coherent x-ray diffraction

We report on sliding Charge Density Wave (CDW) in the quasi two-dimensional TbTe$_3$ system probed by coherent x-ray diffraction combined with {\it in-situ} transport measurements. We show that the non-Ohmic conductivity in TbTe$_3$ is made possible thanks to a strong distortion of the CDW. Our diffraction experiment versus current shows first that the CDW remains undeformed below the threshold current I$_S$ and then suddenly rotates and reorders by motion above threshold. Contrary to quasi-one dimensional systems, the CDW in TbTe$_3$ does not display any phase shifts below I$_S$ and tolerates only slow spatial variations of the phase above. This is a first observation of CDW behavior in the bulk in a quasi-two dimensional system allowing collective transport of charges at room temperature.

Fourth Moment Sum Rule for the Charge Correlations of a Two-Component Classical Plasma

We consider an ionic fluid made with two species of mobile particles carrying either a positive or a negative charge. We derive a sum rule for the fourth moment of equilibrium charge correlations. Our method relies on the study of the system response to the potential created by a weak external charge distribution with slow spatial variations. The induced particle densities, and the resulting induced charge density, are then computed within density functional theory, where the free energy is expanded in powers of the density gradients. The comparison with the predictions of linear response theory provides a thermodynamical expression for the fourth moment of charge correlations, which involves the isothermal compressibility as well as suitably defined partial compressibilities. The familiar Stillinger-Lovett condition is also recovered as a by-product of our method, suggesting that the fourth moment sum rule should hold in any conducting phase. This is explicitly checked in the low density regime, within the Abe-Meeron diagrammatical expansions. Beyond its own interest, the fourth-moment sum rule should be useful for both analyzing and understanding recently observed behaviours near the ionic critical point.

Phase diagram and the pseudogap state in a linear chiral homopolymer model.

The phase structure of a single self-interacting homopolymer chain is investigated in terms of a universal theoretical model, designed to describe the chain in the infrared limit of slow spatial variations. The effects of chirality are studied and compared with the influence of a short-range attractive interaction between monomers, at various ambient temperature values. In the high-temperature limit the homopolymer chain is in the self-avoiding random walk phase. At very low temperatures two different phases are possible: When short-range attractive interactions dominate over chirality, the chain collapses into a space-filling conformation. But when the attractive interactions weaken, there is a low-temperature unfolding transition and the chain becomes like a straight rod. Between the high- and low-temperature limits, several intermediate states are observed, including the θ regime and pseudogap state, which is a novel form of phase state in the context of polymer chains. Applications to polymers and proteins, in particular collagen, are suggested.

Steady State–Hopf Mode Interactions at the Onset of Electroconvection in the Nematic Liquid Crystal Phase V

We report on a new mode interaction found in electroconvection experiments on the nematic liquid crystal mixture Phase V in planar geometry. The mode interaction (codimension two) point occurs at a critical value of the frequency of the driving AC voltage. For frequencies below this value the primary pattern-forming instability at the onset voltage is an oblique stationary instability involving oblique rolls, and above this value it is an oscillatory instability giving rise to normal traveling rolls (oriented perpendicular to and traveling in the director direction). The transition has been confirmed by measuring the roll angle and the dominant frequency of the time series, as both quantities exhibit a discontinuous jump across zero when the AC frequency is varied near threshold. The globally coupled system of Ginzburg–Landau equations that qualitatively describe this mode interaction is constructed, and the resulting normal form, in which slow spatial variations of the mode amplitudes are ignored, is analyzed. This analysis shows that the Ginzburg–Landau system provides the adequate theoretical description for the experimentally observed phenomenon. The experimentally observed patterns at and higher above the onset allow us to narrow down the range of the parameters in the normal form.

Improved Newton–Raphson digital image correlation method for full-field displacement and strain calculation

The two-dimensional in-plane displacement and strain calculation problem through digital image processing methods has been studied extensively in the past three decades. Out of the various algorithms developed, the Newton-Raphson partial differential correction method performs the best quality wise and is the most widely used in practical applications despite its higher computational cost. The work presented in this paper improves the original algorithm by including adaptive spatial regularization in the minimization process used to obtain the motion data. Results indicate improvements in the strain accuracy for both small and large strains. The improvements become even more significant when employing small displacement and strain window sizes, making the new method highly suitable for situations where the underlying strain data presents both slow and fast spatial variations or contains highly localized discontinuities.

Chemical binding in small molecules by the spin-density-functional formalism

A brief review is given of some results within the spin-density-functional (SDF) formalism. The local-spin-density (LSD) approximation, that is, the approximation which is formally exact in the limit of slow and weak spatial variations, gives results of a useful accuracy for valence electrons in atoms and solids, and the accuracy for molecules may be illustrated by the hydrogen-molecule energy curves in the lowest 1Σ+θ and 3Σ+u states being about 0.3 eV from the exact result. Good results are obtained for H+3, H3 and H-3, too. Applications to He+2 and He2+2 inform about the range of applicability of the approximation. Further, the new numerical method developed for these molecular applications allows an evaluation of the multiple-scattering Xα method, showing shortcomings of both the potential and the multiple-scattering approach used in this method. We argue that the SDF formalism within the LSD approximation is physically superior to the Xα method and provides a simple and useful method for applications within a broad range, such as calculations on molecules and chemisorption systems.

Background velocity estimation with cross correlations of incoherent waves in the parabolic scaling

In this paper the incoherent waves reflected by a random medium in the parabolic regime are considered. The case in which the medium has anisotropic three-dimensional rapid random fluctuations and one-dimensional slow variations is analyzed. First, it is shown how the second-order statistics of the reflected wave is determined by the slow spatial variations of the background velocity, the scattering coefficient and the absorption coefficient of the medium via a system of transport equations. Next, it is shown how observations of the time-dependent intensity, spatial radius and spectral radius of the reflected wave can be used to invert this system in order to reconstruct the parameters of the medium. Finally, it is shown that the analytic framework set forth can also be used to analyze the time dynamics of weak localization.

Retrieval of microphysical and optical properties in aerosol plumes with hyperspectral imagery: L-APOM method

This paper presents the retrieval method L-APOM which aims at characterizing the microphysical and optical properties of aerosol plumes from hyperspectral images with high spatial resolution. The inversion process is divided into three steps: estimation of the ground reflectance below the plume, characterization of the standard atmosphere (gases and background aerosols) and estimation of the plume aerosols properties. As using spectral information only is not sufficient to insure uniqueness of solutions, original constraints are added by assuming slow spatial variations of particles properties within the plume. The whole inversion process is validated on a large set of simulated images and reveals to remain accurate even in the worst cases of noise: relative estimation errors of aerosol properties remain between 10% and 20% in most cases. L-APOM is applied on a real AVIRIS hyperspectral image of a biomass burning plume for which in situ measurements are available. Retrieved properties appear globally consistent with measurements.

Hybrid two-dimensional navigator correction: A new technique to suppress respiratory-induced physiological noise in multi-shot echo-planar functional MRI

A troublesome source of physiological noise in functional magnetic resonance imaging (fMRI) is due to the spatio-temporal modulation of the magnetic field in the brain caused by normal subject respiration. fMRI data acquired using echo-planar imaging are very sensitive to these respiratory-induced frequency offsets, which cause significant geometric distortions in images. Because these effects increase with main magnetic field, they can nullify the gains in statistical power expected by the use of higher magnetic fields. As a study of existing navigator correction techniques for echo-planar fMRI has shown that further improvements can be made in the suppression of respiratory-induced physiological noise, a new hybrid two-dimensional (2D) navigator is proposed. Using a priori knowledge of the slow spatial variations of these induced frequency offsets, 2D field maps are constructed for each shot using spatial frequencies between ±0.5 cm−1 in k-space. For multi-shot fMRI experiments, we estimate that the improvement of hybrid 2D navigator correction over the best performance of one-dimensional navigator echo correction translates into a 15% increase in the volume of activation, 6% and 10% increases in the maximum and average t-statistics, respectively, for regions with high t-statistics, and 71% and 56% increases in the maximum and average t-statistics, respectively, in regions with low t-statistics due to contamination by residual physiological noise.

A 2-D comparison of ionospheric convection derived from SuperDARN and DMSP measurements

Ion drift vectors measured by the DMSP satellites are compared with plasma convection vectors obtained by the SuperDARN HF radars through the standard Map Potential algorithm of Ruohoniemi and Baker [Ruohoniemi, M., Baker, K.B. Large-scale imaging of high-latitude convection with super dual auroral radar network HF radar observations. J. Geophys. Res. 103, 20797–20811, 1998]. Despite significant data spread, the agreement can be qualified as reasonable for a data set comprising of 149 satellite passes over the Northern Hemisphere at high latitudes. The slope of the best-fit line relating SuperDARN and DMSP velocity magnitudes is of the order of 0.3 with a tendency for the SuperDARN velocities to be smaller. The agreement between the azimuths of the ion drift and convection is better with the slope of the best-fit line being close to 1. It is shown that consistency between the radar and satellite measurements is much better if the SuperDARN line-of-sight velocities are compared with the DMSP cross-track ion drifts for events showing slow spatial and temporal variations of the convection. If areas of strong convection changes are included into comparison, the degree of agreement deteriorates drastically. This result implies that differences in the spatial and temporal resolutions of DMSP and SuperDARN measurements are crucial factors contributing to the observed discrepancies. In addition, some differences are introduced when the SuperDARN line-of-sight velocities are filtered and reprocessed into vectors with the application of a background convection model.

Zonal flow dynamics and anomalous transport

Nonlinear equations for the slow space-time evolution of the radial drift wave-ion-temperature gradient (DW-ITG) envelope and zonal flow (ZF) amplitude have been derived within a coherent four-wave drift wave-zonal flow model. In the local limit this model demonstrates spontaneous generation of zonal flow and nonlinear drift wave-zonal flow dynamics in toroidal plasmas. The model allows slow temporal and spatial variations of the DW-ITG radial envelope, incorporating the effects of equilibrium variations, i.e., turbulence spreading and size dependence of the saturated wave intensities and transport coefficients. The competition between linear drive/damping and drift wave spreading due to linear and nonlinear group velocities and nonlinear energy transfer between DW and ZF determines the saturation levels of the fluctuating fields. The turbulence intensity level exhibits a transition from Bohm scaling at small system size (Lp∕ρi) to gyro-Bohm for large system size. This system exhibits chaotic behavior and intermittency, depending on system size and proximity to marginal stability.

An approximate effective index model for efficient analysis and control of beam propagation effects in photonic Crystals

Propagation of optical beams through a photonic crystal (PC) is analyzed and modeled. It is shown that the propagation effects for beams with slow spatial variations can be effectively modeled by diffraction behavior obtained directly from band structure. In particular, we present here an approximate model based on defining an effective index for the PC that can be used to analyze the propagation of optical beams inside the PC using the well-known analytic formulas for wave propagation in bulk media. The model presented here allows for considerable reduction in computation time and complexity. It also allows us to obtain more intuitive and design-oriented information about beam propagation effects inside PCs. We apply this model to several practical cases and show that its results agree very well with direct (time-consuming) numerical simulations.

Spin Current and Polarization in Impure Two-Dimensional Electron Systems with Spin-Orbit Coupling

We derive the transport equations for two-dimensional electron systems with Rashba spin-orbit interaction and short-range spin-independent disorder. In the limit of slow spatial variations, we obtain coupled diffusion equations for the electron density and spin. Using these equations we calculate electric-field induced spin accumulation and spin current in a finite-size sample for an arbitrary ratio between spin-orbit energy splitting Delta and elastic scattering rate tau(-1). We demonstrate that the spin-Hall conductivity vanishes in an infinite system independent of this ratio.

Karhunen-Loeve local characterization of spatiotemporal chaos in a reaction-diffusion system

By computing the Karhunen-Loeve decomposition (KLD) correlation length xi(KLD) of a reaction-diffusion system in the extensive chaos regime, we show that it is a sensitive measure of spatial dynamical inhomogeneities. It reveals substantial spatial nonuniformity of the dynamics at the boundaries and can also detect slow spatial variations in system parameters. The intensive length xi(KLD) can be easily computed from small local subsystems and is found to have a similar parametric dependence as the two-point correlation length computed over the full system size.

Dynamo waves in semi–infinite and finite domains

In order to model the solar sunspot cycle, Parker introduced the concept of dynamo waves. These waves owe their existence to two processes, the generation of poloidal field from toroidal by the α–effect, and the generation of toroidal field from the poloidal by the Ω–effect. In their simplest realization these waves are plane waves that propagate in latitude. In this paper we show that spatial inhomogeneities, whether due to variations in the driving α–effect, or simply through the imposition of boundaries in latitude to simulate the solar pole and Equator, have an anomalously important effect, and make it necessary to revise the usual notions of weakly nonlinear bifurcation theory. Two distinct cases are considered. In the first, the solution domain is infinite, but the α–effect is antisymmetric about the Equator at x=0. Both dipole and quadrupole states are considered. The linear problem reveals an unusual feature: the frequency spectrum is continuous and the neutral curve Nω , where N is the dynamo number, plays the role of the more usual neutral curve in the spatial domain. However, the critical dynamo number remains equal to that for an unbounded homogeneous layer. In the weakly nonlinear regime the resulting instability takes the form of dynamo waves that are slowly modulated in space, and is described by an evolution equation of Ginzburg—Landau type but with space and time interchanged. The second case, perhaps more appropriate to the Sun, deals with large but finite domains while including possible slow spatial variations of the α–effect. Surprisingly, in this case sustained dynamo action can only occur when the dynamo number exceeds a value somewhat higher than that for an infinite layer. The onset mode is now localized equatorially. At leading order this dynamo number is independent of the domain size and of the boundary conditions imposed at large ∣x∣, i.e. at the poles. This feature of the problem is related to the distinction between convective and absolute instabilities.

High-frequency behavior of layered superconductors with Josephson coupling

Electrodynamic behavior of a layered system with Josephson couplings between layers is considered. It is shown that in the case of slow spatial variations of fields along layers all electrodynamics of the system can be reduced to a set of equations describing evolution of Josephson phases. In a more general case, applicable to high-${\mathit{T}}_{\mathit{c}}$ materials, one cannot reduce description to phases, but needs to consider electromagnetic fields in the system. Such consideration leads to modified, time-dependent London equations, different for longitudinal and transverse fields. Low-lying, nondecaying waves are analyzed for a layered structure. It is shown that the surface impedance is essentially affected by these waves. In systems with large anisotropy excitations of internal waves lead to strong transverse losses appearing at comparatively low frequencies. \textcopyright{} 1996 The American Physical Society.

Semibalance Model—Connection between Geostrophic-Type and Balanced-Type Intermediate Models

Abstract A hybrid intermediate model, called the semibalance model, is derived from a single truncation of the vector vorticity equation with a balanced vorticity approximation that neglects the advection and stretching–tilting of the unbalanced secondary flow vorticity. This approximation applies not only to straight fronts, like the semi-geostrophy (SG), but also to highly curved fronts and vortices in which the balanced leading-order velocity and unbalanced secondary vorticity are nearly parallel with slow spatial variations along the front or vortex flow. The semibalance model is similar to the balance equations based on momentum equations (BEM) except that the leading-order flow is nonlinearly balanced and the secondary circulation is not free of vertical vorticity. As in BEM, the truncated potential vorticity in the semibalance model is more accurate than in SG, and the problem with spurious high-frequency oscillation in BEM is eliminated in the semibalance model. The potential vorticity in the semi...

Diffusion in the quantum kicked rotator with random corrections in the external field

It is argued that the introduction of random corrections in the kicked rotator problem could produce a diffusive regime in momentum space and breaks dynamical localization. The diffusion coefficient is evaluated and becomes linked to correlation in the random potential. Short-range correlation and slow spatial variations at the external deterministic potential, with respect to the correlation length, are assumed.