Zum Energiespektrum der isotropen hydromagnetischen Turbulenz

The physical consequences emerging from a theory stated byKraichnan are considered with regard to isotropic hydromagnetic turbulence. This theory involves the direct-interaction approximation retaining the phase correlation within each triad of Fourier amplitudes. These interactions are suggested to be very important in hydromagnetic turbulence. Hydrodynamic as well as magnetic impulse-response function and time-correlation are unequivocally the same. This result suggests the existence of a universal equilibrium range. Within the inertial range the total energy spectrumE _g (k)=E(k)+E _m (k) obeys the same law as in hydrodynamic turbulenceE(k). The valueE _m (k)≈E(k) corresponds roughly to maximum energy flux through this range. The magnetic energy flux decreases rapidly for eddies with larger wave-numbers within the range of ohmic ? viscous dissipation.     

Anisotropic characteristics of the kraichnan direct cascade in two-dimensional hydrodynamic turbulence

The statistical characteristics of the Kraichnan direct cascade for two-dimensional hydrodynamic turbulence are numerically studied (with spatial resolution 8192 × 8192) in the presence of pumping and viscous-like damping. It is shown that quasi-shocks of vorticity and their Fourier partnerships in the form of jets introduce an essential influence in turbulence leading to strong angular dependencies for correlation functions. The energy distribution as a function of modulus k for each angle in the inertial interval has the Kraichnan behavior, ~k ^–4, and simultaneously a strong dependence on angles. However, angle average provides with a high accuracy the Kraichnan turbulence spectrum E _k = C _Kη^2/3k^–3, where η is the enstrophy flux and the Kraichnan constant C _K ? 1.3, in correspondence with the previous simulations. Familiar situation takes place for third-order velocity structure function S ₃ ^L which, as for the isotropic turbulence, gives the same scaling with respect to the separation length R and η, S ₃ ^L = C ₃ηR ³, but the average over the angles and time differs from its isotropic value.     

Topological noise scalings in superfluid and classical turbulence

We calculate the topological noise characterizing the direction of line vortices in superfluid and classical turbulence by finding the intersection of line vortices with square surfaces of edge length l_s positioned normal to three orthogonal axes. In the case of homogeneous superfluid turbulence in thermal counterflow, we find that the noise scales as l_s along the two directions normal to the counterflow and as l _s ^3/2 along the direction parallel to it. In homogeneous isotropic superfluid turbulence, at T→0 K, the noise scales as l _s ^7/4 . In homogeneous isotropic classical turbulence, the scaling is l _s ² . We offer possible interpretations of the computed scalings, as well as justification for their differences.     

Fractality feature in incompressible three-dimensional magnetohydrodynamic turbulence

Direct Numerical Simulation (DNS) of decaying isotropic 3D magnetohydrodynamic (MHD) turbulence based on the 10243-modes in a periodic box is used to study the statistical properties of turbulence. In this paper, the presence of intermittency in MHD turbulence is investigated through the analysis of the Probability Distribution Function (PDF) for Elsässer fields and total energy fluctuations. We observe that the PDFs of the Elsässer fields fluctuations display a strong non-Gaussian behavior at small scale, which can be ascribed to multifractality feature, while the PDFs of the total energy fluctuations have the same shape over all observed scales and are monofractal. The PDFs have stretched exponential tail and satisfy the function P(|δX|) ～ exp(?A|δX| ^μ ). Numerically, we extract the exponent μ and find that it is constant for monofractal behavior as the length scale varies. To check the notion of self-similarity in the respective fluctuation, we apply the compensated structure functions.     

Calculation of the diffusion coefficient in acoustic turbulence

The first (Born) approximation commonly used to calculate the diffusion coefficient D_T of a passive scalar in acoustic turbulence is shown to be insufficient. Even for a small main parameter—the Mach number, M?1—the next approximation gives a larger contribution to D_T than does the first approximation, but negative in sign. We present a procedure for correctly calculating D_T based on the solution of a nonlinear DIA (direct interaction approximation) equation for the mean Green’s function of the problem. We include an additional term in the general formula for D_T that directly describes the compressibility of acoustic turbulence. This term has not been known previously and has been disregarded even in the Born approximation. A positive value was obtained for D_T=CM³u₀/p₀. The spectrum E(x) was assumed to be smooth at distances Δ x～M²?1.     

Aussagen der Theorie von Kraichnan für die isotrope hydromagnetische Turbulenz

The theory ofKraichnan is applied to quasi-stationary isotropic hydromagnetic turbulence. The average infinitesimal-impulse-response functionsg(k, τ), g _m (k, τ) and the time-correlationsr(k, τ), r _m (k, τ) are evaluated by the non-local direct-interaction approximation within the inertial range. For the range of ohmic but no viscous dissipation it is found that the magnetic energy spectrumE _m (k) obeys aE(k)k ^?2-law in accordance with results ofGolitsyn andMoffatt.     

Relaxation of a 2D MHD flow across a magnetic field (2D hydrodynamic flow) in a bounded region

The problem on magnetohydrodynamic (MHD) flow of a solitary vortex across a magnetic field in a volume confined by rigid walls is solved numerically for large Reynolds numbers (including magnetic Reynolds numbers) and small Alfven-Mach numbers M _A . In this case, the MHD problem is reduced to that of two-dimensional hydrodynamic turbulence. It is shown that sound is not generated by a turbulent medium for small values of M _A ; consequently, this kinetic energy dissipation channel is closed in this case. Calculations show that, in contrast to 3D turbulence, kinetic energy dissipation for 2D turbulence occurs, as expected, over time periods on the order of L²/v(L is the characteristic size of the system and v is the kinematic viscosity). In our calculations with numerical viscosity v～vΔx (Δx is the unit cell size), this corresponds to time values on the order of ～(L/Δx)(L/v). In the kinetic energy spectra for a turbulent flow in a bounded region in the inertial interval (lying between the energy-carrying and viscosity regions), the values of E(k) decrease with increasing wave numbers k at a higher rate than in proportion to k^?3. The volume distribution of vorticity becomes narrower with time (the characteristic values of curlv decrease) and is blurred; for large time periods, the distribution approximately retains its shape as well as asymmetry with respect to positive and negative values, which is associated with the asymmetry of the initial conditions.     

Reduction in transmitter power requirement for earth-to-satellite and satellite-to-earth free space optical links with spatial diversity

In the scenario of first laser communication relay satellite being launched into geostationary earth orbit, we evaluate the reduction in transmitter power requirement for earth-to-satellite and satellite-to-earth free space optical links in presence of turbulence and various weather conditions using spatial diversity technique. In channel modeling, Beer Lambert Law incorporates the weather effects. The log-normal probability density function (pdf) models weak turbulence and gamma–gamma pdf moderate to strong turbulence. Using the combined channel state pdf, bit error rate (BER) expressions are derived for on-off keying (OOK), M-ary pulse position modulation (M-PPM) and M-ary differential PPM (M-DPPM) schemes. From the BER plots, we evaluate the minimum average received power required to achieve a desired BER for all three schemes for different channel conditions. Subsequently, minimum transmitter power requirement is evaluated for both uplink and downlink using the range equation. It is observed that presence of moderate, light and thin fog cause additional power requirement. Also, among the three schemes, M-PPM scheme requires the least transmitter power, followed by M-DPPM and OOK schemes. Further, it is seen that the transmitter diversity or multiple input single output technique reduces the uplink minimum transmitter power requirement, whereas for downlink aperture averaging and receiver diversity or single input multiple output techniques can achieve the same. The power requirement for uplink is 8–10 dB more as compared to downlink in presence of turbulence and various weather conditions.     

Isotropization of two-dimensional hydrodynamic turbulence in the direct cascade

We present results of numerical simulation of the direct cascade in two-dimensional hydrodynamic turbulence (with spatial resolution up to ). If at the earlier stage (at the time of order of the inverse pumping growth rate τ-Γ_max ^?1), the turbulence develops according to the same scenario as in the case of a freely decaying turbulence [1, 2]: quasi-singular distribution of di-vorticity are formed, which in k-space correspond to jets, leading to a strong turbulence anisotropy, then for times of the order of 10τ turbulence becomes almost isotropic. In particular, at these times any significant anisotropy in the angular fluctuations for the energy spectrum (for a fixed k) is not visible, while the probability distribution function of vorticity for large arguments has the exponential tail with the exponent linearly dependent on vorticity, in the agreement with the theoretical prediction [3].     

On the theory of superconductivity in the extended Hubbard model

A microscopic theory of superconductivity in the extended Hubbard model which takes into account the intersite Coulomb repulsion and electron-phonon interaction is developed in the limit of strong correlations. The Dyson equation for normal and pair Green functions expressed in terms of the Hubbard operators is derived. The self-energy is obtained in the noncrossing approximation. In the normal state, antiferromagnetic short-range correlations result in the electronic spectrum with a narrow bandwidth. We calculate superconducting T _c by taking into account the pairing mediated by charge and spin fluctuations and phonons. We found the d-wave pairing with high-T _c mediated by spin fluctuations induced by the strong kinematic interaction for the Hubbard operators. Contributions to the d-wave pairing coming from the intersite Coulomb repulsion and phonons turned out to be small.     

Messung von zwei β-γ-Richtungskorrelationen im Zerfall von J126

In the decay of J¹²⁶ twoβ-γ directional correlations have been measured. The 0.865MeVβ-0.386 MeVγ correlation shows a big anisotropy; the reduced coefficient ?/(p ²/W) has a mean value of 0.0419±0.0005 and is not quite energy independent. The 0.385 MeVβ-0.86 MeVγ correlation is isotropic within about 2%. Therefore the 0.386 MeV 2⁺ state and the 0.86 MeV 2⁺ state in Xe¹²⁶ may not be described by differences in collective properties only.     

Kinetic Theory and Lax Equations for Shock Clustering and Burgers Turbulence

We study shock statistics in the scalar conservation law ? _t u+? _x f(u)=0, x∈?, t>0, with a convex flux f and spatially random initial data. We show that the Markov property (in x) is preserved for a large class of random initial data (Markov processes with downward jumps and derivatives of Lévy processes with downward jumps). The kinetics of shock clustering is then described completely by an evolution equation for the generator of the Markov process u(x,t), x∈?. We present four distinct derivations for this evolution equation, and show that it takes the form of a Lax pair. The Lax equation admits a spectral parameter as in Manakov (Funct. Anal. Appl. 10:328–329, 1976), and has remarkable exact solutions for Burgers equation (f(u)=u ²/2). This suggests the kinetic equations of shock clustering are completely integrable.     

Analytic approximations of Von Krmn plate under arbitrary uniform pressure—equations in integral form

Analytic approximations of the Von Krmn's plate equations in integral form for a circular plate under external uniform pressure to arbitrary magnitude are successfully obtained by means of the homotopy analysis method(HAM), an analytic approximation technique for highly nonlinear problems. Two HAM-based approaches are proposed for either a given external uniform pressure Q or a given central deflection, respectively. Both of them are valid for uniform pressure to arbitrary magnitude by choosing proper values of the so-called convergence-control parameters c_1 and c_2 in the frame of the HAM. Besides, it is found that the HAMbased iteration approaches generally converge much faster than the interpolation iterative method. Furthermore, we prove that the interpolation iterative method is a special case of the first-order HAM iteration approach for a given external uniform pressure Q when c_1 =.θ and c_2 =-1, where θ denotes the interpolation iterative parameter. Therefore, according to the convergence theorem of Zheng and Zhou about the interpolation iterative method, the HAM-based approaches are valid for uniform pressure to arbitrary magnitude at least in the special case c_1 =.θ and c_2 =-1. In addition, we prove that the HAM approach for the Von Krmn's plate equations in differential form is just a special case of the HAM for the Von Krmn's plate equations in integral form mentioned in this paper. All of these illustrate the validity and great potential of the HAM for highly nonlinear problems,and its superiority over perturbation techniques.     

Schrödinger’s Equation with Gauge Coupling Derived from a Continuity Equation

A quantization procedure without Hamiltonian is reported which starts from a statistical ensemble of particles of mass m and an associated continuity equation. The basic variables of this theory are a probability density ρ, and a scalar field S which defines a probability current j=ρ ? S/m. A first equation for ρ and S is given by the continuity equation. We further assume that this system may be described by a linear differential equation for a complex-valued state variable χ. Using these assumptions and the simplest possible Ansatz χ(ρ,S), for the relation between χ and ρ,S, Schrödinger’s equation for a particle of mass m in a mechanical potential V(q,t) is deduced. For simplicity the calculations are performed for a single spatial dimension (variable q). Using a second Ansatz χ(ρ,S,q,t), which allows for an explicit q,t-dependence of χ, one obtains a generalized Schrödinger equation with an unusual external influence described by a time-dependent Planck constant. All other modifications of Schrödinger’ equation obtained within this Ansatz may be eliminated by means of a gauge transformation. Thus, this second Ansatz may be considered as a generalized gauging procedure. Finally, making a third Ansatz, which allows for a non-unique external q,t-dependence of χ, one obtains Schrödinger’s equation with electrodynamic potentials A,φ in the familiar gauge coupling form. This derivation shows a deep connection between non-uniqueness, quantum mechanics and the form of the gauge coupling. A possible source of the non-uniqueness is pointed out.     

Symmetry energy of the nucleus in the relativistic Thomas–Fermi approach with density-dependent parameters

We introduce an inhomogeneous term, f(t,x), into the right-hand side of the usual Burgers equation and examine the resulting equation for those functions which admit at least one Lie point symmetry. For those functions f(t,x) which depend nontrivially on both t and x, we find that there is just one symmetry. If f is a function of only x, there are three symmetries with the algebra s l(2,R). When f is a function of only t, there are five symmetries with the algebra s l(2,R) ⊕ _s 2A ₁. In all the cases, the Burgers equation is reduced to the equation for a linear oscillator with nonconstant coefficient.     

The Coulomb-oscillator relation on <Emphasis Type="Italic">n</Emphasis>-dimensional spheres and hyperboloids

We establish a relation between Coulomb and oscillator systems on n-dimensional spheres and hyperboloids for n≥2. We show that, as in Euclidean space, the quasiradial equation for the (n+1)-dimensional Coulomb problem coincides with the 2n-dimensional quasiradial oscillator equation on spheres and hyperboloids. Using the solution of the Schrödinger equation for the oscillator system, we construct the energy spectrum and wave functions for the Coulomb problem.     

Properties of weakly collapsing solutions to the nonlinear Schrödinger equation

It is shown that one of the conditions for a weakly collapsing solution with zero energy produces an infinite number of functionals I _N identically vanishing on the regular solutions to the corresponding differential equation. On the parameter plane {A, C₁}, there are at least two singular lines. Along one of these lines (A/C₁=1/6), are located weakly collapsing solutions with zero energy. It is assumed that, along the second line (A/C₁=α_c), another family of weakly collapsing solutions with zero energy is located. In the domain of large values of the parameters C₁, α=A/C₁, there exists a domain of an intermediate asymptotic form, where the amplitude of oscillations of the function U grows in a large domain relative to the ξ coordinate.     

Coulomb corrections to bremsstrahlung in the electric field of a heavy atom at high energies

We consider the differential and partially integrated cross sections for bremsstrahlung from high-energy electrons in an atomic field, with this field taken into account exactly. We use the semiclassical electron Green function and wavefunctions in an external electric field. It is shown that the Coulomb corrections to the differential cross section are very susceptible to screening. Nevertheless, the Coulomb corrections to the cross section summed over the final-electron states are independent of screening in the leading approximation in the small parameter 1/mr _scr (r _scr is the screening radius and m is the electron mass, ? = c = 1). We also consider bremsstrahlung from a finite-size electron beam on a heavy nucleus. The Coulomb corrections to the differential probability are also very susceptible to the beam shape, while the corrections to the probability integrated over momentum transfer are independent of it, apart from the trivial factor, which is the electron-beam density at zero impact parameter. For the Coulomb corrections to the bremsstrahlung spectrum, the next-to-leading terms with respect to the parameters mε (ε is the electron energy) and 1/mr _scr are obtained.     

Interacting Generalized Ghost Dark Energy in Non-isotropic Background

In this work, the generalized Quantum Chromodynamics (QCD) ghost model of dark energy in the framework of Einstein gravity is investigated. At first, the non-interacting generalized ghost dark energy in a Bianchi type I (BI) background is discussed. Then the equation of state parameter, ω _D = p _D /ρ _D , the deceleration parameter, and the evolution equation of the generalized ghost dark energy are obtained. It was found that, in this case, ω _D cannot cross the phantom line (ω _D >?1) and eventually the universe approaches a de-Sitter phase of expansion (ω _D →?1). Then, this investigation was extended to the interacting ghost dark energy in a non-isotropic universe. It was found that the equation of state parameter of the interacting generalized ghost dark energy can cross the phantom line (ω _D <?1) provided the parameters of the model are chosen suitably. It was considered a specific model which permits the standard continuity equation in this theory. Besides Ω_Λ and Ω _m in standard Einstein cosmology, another density parameter, Ω _σ , is expected by the anisotropy. The anisotropy of the universe decreases and the universe transits to an isotropic flat FRW universe accommodating the present acceleration.