Statistically Preserved Structures and Anomalous Scaling in Turbulent Active Scalar Advection

The anomalous scaling of correlation functions in the turbulent statistics of active scalars (like temperature in turbulent convection) is understood in terms of an auxiliary passive scalar which is advected by the same turbulent velocity field. While the odd-order correlation functions of the active and passive fields differ, we propose that the even-order correlation functions are the same to leading order (up to a trivial multiplicative factor). The leading correlation functions are statistically preserved structures of the passive scalar decaying problem, and therefore universality of the scaling exponents of the even-order correlations of the active scalar is demonstrated.Comment: 4 pages, 5 figures, submitted to Phys. Rev. Let

Active and Passive Fields in Turbulent Transport: the Role of Statistically Preserved Structures

We have recently proposed that the statistics of active fields (which affect the velocity field itself) in well-developed turbulence are also dominated by the Statistically Preserved Structures of auxiliary passive fields which are advected by the same velocity field. The Statistically Preserved Structures are eigenmodes of eigenvalue 1 of an appropriate propagator of the decaying (unforced) passive field, or equivalently, the zero modes of a related operator. In this paper we investigate further this surprising finding via two examples, one akin to turbulent convection in which the temperature is the active scalar, and the other akin to magneto-hydrodynamics in which the magnetic field is the active vector. In the first example, all the even correlation functions of the active and passive fields exhibit identical scaling behavior. The second example appears at first sight to be a counter-example: the statistical objects of the active and passive fields have entirely different scaling exponents. We demonstrate nevertheless that the Statistically Preserved Structures of the passive vector dominate again the statistics of the active field, except that due to a dynamical conservation law the amplitude of the leading zero mode cancels exactly. The active vector is then dominated by the sub-leading zero mode of the passive vector. Our work thus suggests that the statistical properties of active fields in turbulence can be understood with the same generality as those of passive fields.Comment: 13 pages, 13 figures, submitted to Phys. Rev.

Local spin density in two-dimensional electron gas with hexagonal boundary

The intrinsic spin-Hall effect in hexagon-shaped samples is investigated. To take into account the spin-orbit couplings and to fit the hexagon edges, we derive the triangular version of the tight-binding model for the linear Rashba [Sov. Phys. Solid State 2, 1109 (1960)] and Dresselhaus [Phys. Rev. 100, 580 (1955)] [001] Hamiltonians, which allow direct application of the Landauer-Keldysh non-equilibrium Green function formalism to calculating the local spin density within the hexagonal sample. Focusing on the out-of-plane component of spin, we obtain the geometry-dependent spin-Hall accumulation patterns, which are sensitive to not only the sample size, the spin-orbit coupling strength, the bias strength, but also the lead configurations. Contrary to the rectangular samples, the accumulation pattern can be very different in our hexagonal samples. Our present work provides a fundamental description of the geometry effect on the intrinsic spin-Hall effect, taking the hexagon as the specific case. Moreover, broken spin-Hall symmetry due to the coexistence of the Rashba and Dresselhaus couplings is also discussed. Upon exchanging the two coupling strengths, the accumulation pattern is reversed, confirming the earlier predicted sign change in spin-Hall conductivity.Comment: 7 pages, 4 figure

Probability Density Function of Longitudinal Velocity Increment in Homogeneous Turbulence

Two conditional averages for the longitudinal velocity increment u_r of the simulated turbulence are calculated: h(u_r) is the average of the increment of the longitudinal Laplacian velocity field with u_r fixed, while g(u_r) is the corresponding one of the square of the difference of the gradient of the velocity field. Based on the physical argument, we suggest the formulae for h and g, which are quite satisfactorily fitted to the 512^3 DNS data. The predicted PDF is characterized as (1) the Gaussian distribution for the small amplitudes, (2) the exponential distribution for the large ones, and (3) a prefactor before the exponential function for the intermediate ones.Comment: 4 pages, 4 figures, using RevTeX3.

Spin and charge transport in U-shaped one-dimensional channels with spin-orbit couplings

A general form of the Hamiltonian for electrons confined to a curved one-dimensional (1D) channel with spin-orbit coupling (SOC) linear in momentum is rederived and is applied to a U-shaped channel. Discretizing the derived continuous 1D Hamiltonian to a tight-binding version, the Landauer-Keldysh formalism (LKF) for nonequilibrium transport can be applied. Spin transport through the U-channel based on the LKF is compared with previous quantum mechanical approaches. The role of a curvature-induced geometric potential which was previously neglected in the literature of the ring issue is also revisited. Transport regimes between nonadiabatic, corresponding to weak SOC or sharp turn, and adiabatic, corresponding to strong SOC or smooth turn, is discussed. Based on the LKF, interesting charge and spin transport properties are further revealed. For the charge transport, the interplay between the Rashba and the linear Dresselhaus (001) SOCs leads to an additional modulation to the local charge density in the half-ring part of the U-channel, which is shown to originate from the angle-dependent spin-orbit potential. For the spin transport, theoretically predicted eigenstates of the Rashba rings, Dresselhaus rings, and the persistent spin-helix state are numerically tested by the present quantum transport calculation.Comment: 16 pages, 7 figure

Strong Universality in Forced and Decaying Turbulence

The weak version of universality in turbulence refers to the independence of the scaling exponents of the $n$th order strcuture functions from the statistics of the forcing. The strong version includes universality of the coefficients of the structure functions in the isotropic sector, once normalized by the mean energy flux. We demonstrate that shell models of turbulence exhibit strong universality for both forced and decaying turbulence. The exponents {\em and} the normalized coefficients are time independent in decaying turbulence, forcing independent in forced turbulence, and equal for decaying and forced turbulence. We conjecture that this is also the case for Navier-Stokes turbulence.Comment: RevTex 4, 10 pages, 5 Figures (included), 1 Table; PRE, submitte

Hemolysis and methemoglobinemia due to hepatitis E virus infection in patient with G6PD deficiency

published_or_final_versionSpringer Open Choice, 21 Feb 201

Spin-charge conversion in multiterminal Aharonov-Casher ring coupled to precessing ferromagnets: A charge conserving Floquet-nonequilibrium Green function approach

We derive a non-perturbative solution to the Floquet-nonequilibrium Green function (Floquet-NEGF) describing open quantum systems periodically driven by an external field of arbitrary strength of frequency. By adopting the reduced-zone scheme, we obtain expressions rendering conserved charge currents for any given maximum number of photons, distinguishable from other existed Floquet-NEGF-based expressions where, less feasible, infinite number of photons needed to be taken into account to ensure the conservation. To justify our derived formalism and to investigate spin-charge conversions by spin-orbit coupling (SOC), we consider the spin-driven setups as reciprocal to the electric-driven setups in S. Souma et. al., Phys. Rev. B 70, 195346 (2004) and Phys. Rev. Lett. 94, 106602 (2005). In our setups, pure spin currents are driven by the magnetization dynamics of a precessing ferromagnetic (FM) island and then are pumped into the adjacent two- or four-terminal mesoscopic Aharonov-Casher (AC) ring of Rashba SOC where spin-charge conversions take place. Our spin-driven results show reciprocal features that excellently agree with the findings in the electric-driven setups mentioned above. We propose two types of symmetry operations, under which the AC ring Hamiltonian is invariant, to argue the relations of the pumped/converted currents in the leads within the same or between different pumping configurations. The symmetry arguments are independent of the ring width and the number of open channels in the leads, terminals, and precessing FM islands, In particular, net pure in-plane spin currents and pure spin currents can be generated in the leads for certain setups of two terminals and two precessing FM islands with the current magnitude and polarization direction tunable by the pumping configuration, gate voltage covering the two-terminal AC ring in between the FM islands.Comment: Submitted to Physical Review

Current-induced spin polarization in spin-orbit-coupled two-dimensional electron systems

Current-induced spin polarization (CISP) is rederived in ballistic spin-orbit-coupled electron systems, based on equilibrium statistical mechanics. A simple and useful picture is correspondingly proposed to help understand the CISP and predict the polarization direction. Nonequilibrium Landauer-Keldysh formalism is applied to demonstrate the validity of the statistical picture, taking the linear Rashba-Dresselhaus [001] two-dimensional system as a specific example. Spin densities induced by the CISP in semiconductor heterostructures and in metallic surface states are compared, showing that the CISP increases with the spin splitting strength and hence suggesting that the CISP should be more observable on metal and semimetal surfaces due to the discovered strong Rashba splitting. An application of the CISP designed to generate a spin-Hall pattern in the inplane, instead of the out-of-plane, component is also proposed.Comment: 7 pages, 6 figures, 1 table, Phys. Rev. B, in pres

Full potential LAPW calculation of electron momentum density and related properties of Li

Electron momentum density and Compton profiles in Lithium along $$,$$, and $$ directions are calculated using Full-Potential Linear Augmented Plane Wave basis within generalized gradient approximation. The profiles have been corrected for correlations with Lam-Platzman formulation using self-consistent charge density. The first and second derivatives of Compton profiles are studied to investigate the Fermi surface breaks. Decent agreement is observed between recent experimental and our calculated values. Our values for the derivatives are found to be in better agreement with experiments than earlier theoretical results. Two-photon momentum density and one- and two-dimensional angular correlation of positron annihilation radiation are also calculated within the same formalism and including the electron-positron enhancement factor.Comment: 11 pages, 7 figures TO appear in Physical Review