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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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18 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1989

Novel local symmetries and chiral-symmetry-broken phases in S = 1/2 triangular-lattice Heisenberg model

Using a nonmean-field approach the triangular-lattice S = 1/2 Heisenberg antiferromagnet with nearest- and next-nearest-neighbor couplings is shown undergo an Ising-type phase transition into a chiral-symmetry-broken phase (Kalmeyer-Laughlin-like state) at small T. Removal of next-nearest-neighbor coupling introduces a local Z2 symmetry, thereby suppressing any finite-T chiral order.

Baskaran, G.↗
NASA NTRS1989

Phase diagram of the frustrated spin-1/2 Heisenberg antiferromagnet in two dimensions

A Lanczos technique is used to study the frustrated spin-1/2 Heisenberg model on square lattices of 16 and 20 sites. Frustration is introduced by an interaction along the diagonals of the plaquettes with coupling J2 greater than or equal to 0. For large J2, the ground state breaks (spontaneously) the lattice rotational symmetry. For intermediate values of J2, the squares of order parameters associated with spin-Peierls and 'twisted'states have a peak, while a similar quantity for a chiral state shows no interesting structure.

Dagotto, Elbio↗
NASA NTRS1989

Ground-state energies of the nonlinear sigma model and the Heisenberg spin chains

A theorem on the O(3) nonlinear sigma model with the topological theta term is proved, which states that the ground-state energy at theta = pi is always higher than the ground-state energy at theta = 0, for the same value of the coupling constant g. Provided that the nonlinear sigma model gives the correct description for the Heisenberg spin chains in the large-s limit, this theorem makes a definite prediction relating the ground-state energies of the half-integer and the integer spin chains. The ground-state energies obtained from the exact Bethe ansatz solution for the spin-1/2 chain and the numerical diagonalization on the spin-1, spin-3/2, and spin-2 chains support this prediction.

Zhang, Shoucheng↗
NASA NTRS1993

Interacting scales and energy transfer in isotropic turbulence

The dependence of the energy transfer process on the disparity of the interacting scales is investigated in the inertial and far-dissipation ranges of isotropic turbulence. The strategy for generating the simulated flow fields and the choice of a disparity parameter to characterize the scaling of the interactions is discussed. The inertial range is found to be dominated by relatively local interactions, in agreement with the Kolmogorov assumption. The far-dissipation is found to be dominated by relatively non-local interactions, supporting the classical notion that the far-dissipation range is slaved to the Kolmogorov scales. The measured energy transfer is compared with the classical models of Heisenberg, Obukhov, and the more detailed analysis of Tennekes and Lumley. The energy transfer statistics measured in the numerically simulated flows are found to be nearly self-similar for wave numbers in the inertial range. Using the self-similar form measured within the limited scale range of the simulation, an 'ideal' energy transfer function and the corresponding energy flux rate for an inertial range of infinite extent are constructed. From this flux rate, the Kolmogorov constant is calculated to be 1.5, in excellent agreement with experiments.

Zhou, YE↗
NASA NTRS1987

A low dimensional dynamical system for the wall layer

Low dimensional dynamical systems which model a fully developed turbulent wall layer were derived.The model is based on the optimally fast convergent proper orthogonal decomposition, or Karhunen-Loeve expansion. This decomposition provides a set of eigenfunctions which are derived from the autocorrelation tensor at zero time lag. Via Galerkin projection, low dimensional sets of ordinary differential equations in time, for the coefficients of the expansion, were derived from the Navier-Stokes equations. The energy loss to the unresolved modes was modeled by an eddy viscosity representation, analogous to Heisenberg's spectral model. A set of eigenfunctions and eigenvalues were obtained from direct numerical simulation of a plane channel at a Reynolds number of 6600, based on the mean centerline velocity and the channel width flow and compared with previous work done by Herzog. Using the new eigenvalues and eigenfunctions, a new ten dimensional set of ordinary differential equations were derived using five non-zero cross-stream Fourier modes with a periodic length of 377 wall units. The dynamical system was integrated for a range of the eddy viscosity prameter alpha. This work is encouraging.

Aubry, N.↗
NASA NTRS1985

Is the Kolmogoroff model applicable to large-scale turbulence?

In view of the present discussion, the Heisenberg-Kolmogoroff (HK) model of turbulence that is often used for turbulent phenomena on all scales is actually valid for a turbulent spectrum wavelength band typically much smaller than the size of the system, and cannot describe phenomena at large scales in astrophysical systems. The results of mixing length theory cannot be accommodated within the HK model's framework without the adoption of an unreasonable coupling constant. It is also noted that the use of the observed velocity-size relationship in molecular clouds with turbulent velocity values of about l to the 1/2-power, within the HK model, gives rise to a growth rate that does not correspond to any known physical processes suspected of operating in molecular clouds.

Canuto, V. M.↗
NASA NTRS1986

Propagation of electromagnetic waves in a turbulent medium

Theoretical modeling of the wealth of experimental data on propagation of electromagnetic radiation through turbulent media has centered on the use of the Heisenberg-Kolmogorov (HK) model, which is, however, valid only for medium to small sized eddies. Ad hoc modifications of the HK model to encompass the large-scale region of the eddy spectrum have been widely used, but a sound physical basis has been lacking. A model for large-scale turbulence that was recently proposed is applied to the above problem. The spectral density of the temperature field is derived and used to calculate the structure function of the index of refraction N. The result is compared with available data, yielding a reasonably good fit. The variance of N is also in accord with the data. The model is also applied to propagation effects. The phase structure function, covariance of the log amplitude, and variance of the log intensity are calculated. The calculated phase structure function is in excellent agreement with available data.

Canuto, V. M.↗
NASA NTRS1999

Investigation of Next-Generation Earth Radiation Budget Radiometry

The current effort addresses two issues important to the research conducted by the Thermal Radiation Group at Virginia Tech. The first research topic involves the development of a method which can properly model the diffraction of radiation as it enters an instrument aperture. The second topic involves the study of a potential next-generation space-borne radiometric instrument concept. Presented are multiple modeling efforts to describe the diffraction of monochromatic radiant energy passing through an aperture for use in the Monte-Carlo ray-trace environment. Described in detail is a deterministic model based upon Heisenberg's uncertainty principle and the particle theory of light. This method is applicable to either Fraunhofer or Fresnel diffraction situations, but is incapable of predicting the secondary fringes in a diffraction pattern. Also presented is a second diffraction model, based on the Huygens-Fresnel principle with a correcting obliquity factor. This model is useful for predicting Fraunhofer diffraction, and can predict the secondary fringes because it keeps track of phase. NASA is planning for the next-generation of instruments to follow CERES (Clouds and the Earth's Radiant Energy System), an instrument which measures components of the Earth's radiant energy budget in three spectral bands. A potential next-generation concept involves modification of the current CERES instrument to measure in a larger number of wavelength bands. This increased spectral partitioning would be achieved by the addition of filters and detectors to the current CERES geometry. The capacity of the CERES telescope to serve for this purpose is addressed in this thesis.

Coffey, Katherine L.↗
NASA NTRS2001

Semi-Classical Models for Virtual Antiparticle Pairs

Virtual particle-antiparticle pairs of massive elementary particle& are predicted in Quantum Field Theory (QFT) to appear from the vacuum and annihilate each other again within their Heisenberg lifetimes h/4mc(exp 2). In this work, semiclassical models of this process - for the cases of massive leptons, quarks, and the massive weak bosons W and Z - are constructed. It is shown that the dynamical lifetime of the particle- antiparticle system in each case equals the Heisenberg lifetime to good approximation, and obeys appropriate quantization conditions on the field fluctuation action. In other words, the dynamical lifetime of the semiclassical model agrees with QED and QCD to good approximation. But the formula for the dynamical lifetime in each model includes the force strength coupling constant (e in the lepton case, alpha(sup s) (q(exp 2)) in the quark cases), while the Heisenberg lifetime formula does not. Observing the agreement of the Heisenberg and dynamical lifetimes, we may derive the QED and QCD coupling constants in terms of h, c, and numerical factors only.

Batchelor, David↗
NASA NTRS2001

Semiclassical Models for Virtual Antiparticle Pairs, the Unit of Charge e, and the QCD Coupling alpha(sub s)

New semiclassical models of virtual antiparticle pairs are used to compute the pair lifetimes, and good agreement with the Heisenberg lifetimes from quantum field theory (QFT) is found. The modeling method applies to both the electromagnetic and color forces. Evaluation of the action integral of potential field fluctuation for each interaction potential yields approximately Planck's constant/2 for both electromagnetic and color fluctuations, in agreement with QFT. Thus each model is a quantized semiclassical representation for such virtual antiparticle pairs, to good approximation. When the results of the new models and QFT are combined, formulae for e and alpha(sub s)(q) are derived in terms of only Planck's constant and c.

Batchelor, David↗
NASA NTRS1971

The spectrum of steady state turbulent convection.

Based on Heisenberg's statistical theory of turbulence, a model for steady state turbulent convection is herein proposed, and on the basis of this model, equations for the energy spectrum for steady state turbulent convection are derived. The spectrum is obtained from the solution of a nonlinear integral equation. After the integral equation is brought into a universally valid nondimensional form, it is transformed into a nonlinear first order differential equation to be solved numerically, with the Rayleigh number appearing as the only parameter. The energy spectrum has a substantial deviation from the Kolmogoroff law, as a result of the buoyancy force acting on the rising and falling eddies. The presented theory may be applicable to convection in planetary and stellar atmospheres wherein the radiative heat transport is small.

Winterberg, F.↗
NASA NTRS1987

A model for fully developed turbulence

A model for stationary, fully developed turbulence is presented in which the turbulent spectral energy function is completely determined once the time scale for the energy fed into the eddy interaction is known. The form of the eddy correlation time scale determining the turbulent viscosity is suggested by the basic equation of the model itself, up to a dimensionless constant that is fixed by demanding that the coefficient of the spectrum in the Heisenberg-Kolmogoroff inertial range of wavenunmbers be the experimental value. The model makes quantitative predictions that are compared with data on turbulent convection; the k-epsilon and Smagorinsky relations; the spectral function, transfer term, and dissipation term; the skewness factor; the Kolmogoroff and Batchelor constants; and the inertial-conductive and inertial-convective ranges.

Canuto, V. M.↗
NASA NTRS2001

Virtual Antiparticle Pairs, the Unit of Charge Epsilon and the QCD Coupling Alpha(sub s)

New semi-classical models of virtual antiparticle pairs are used to compute the pair lifetimes, and good agreement with the Heisenberg lifetimes from quantum field theory (QFT) is found. When the results of the new models and QFT are combined, formulae for e and alpha(sub s)(q) are derived in terms of only h and c. The modeling method applies to both the electromagnetic and color forces. Evaluation of the action integral of potential field fluctuation for each interaction potential yields approx. = h/2 for both electromagnetic and color fluctuations, in agreement with QFT. Thus each model is a quantized semiclassical representation for such virtual antiparticle pairs, to good approximation. This work reduces the number of arbitrary parameters of the Standard Model by two from 18 to 16. These are remarkable, unexpected results from a basically classical method.

Batchelor, David↗
NASA NTRS1994

Berry phase in Heisenberg representation

We define the Berry phase for the Heisenberg operators. This definition is motivated by the calculation of the phase shifts by different techniques. These techniques are: the solution of the Heisenberg equations of motion, the solution of the Schrodinger equation in coherent-state representation, and the direct computation of the evolution operator. Our definition of the Berry phase in the Heisenberg representation is consistent with the underlying supersymmetry of the model in the following sense. The structural blocks of the Hamiltonians of supersymmetrical quantum mechanics ('superpairs') are connected by transformations which conserve the similarity in structure of the energy levels of superpairs. These transformations include transformation of phase of the creation-annihilation operators, which are generated by adiabatic cyclic evolution of the parameters of the system.

Andreev, V. A.↗
NASA NTRS1991

A simple example of modeling hybrid systems using bialgebras: Preliminary version

The authors describe how to construct a hybrid control system using a specific set of data and conditions specified within the paper. Furthermore, they give examples of how to create continuous systems, discrete systems, and simple hybrid systems. Finally, they touch upon Heisenberg and state space representation.

Grossman, R. L.↗
NASA NTRS1990

Electron energy spectrum and magnetic interactions in high-T(sub c) superconductors

The character of magnetic interactions in La-Sr-Cu-O and Y-Ba-Cu-O systems is of primary importance for analysis of high-T(sub c) superconductivity in these compounds. Neutron diffraction experiments showed the antiferromagnetic ground state for nonsuperconducting La2CuO4 and YBa2Cu3O6 with the strongest antiferromagnetic superexchange being in the ab plane. The nonsuperconducting '1-2-3' system has two Neel temperatures T sub N1 and T sub N2. The first one corresponds to the ordering of Cu atoms in the CuO2 planes; T sub N2 reflects the antiferromagnetic ordering of magnetic moments in CuO chains relatively to the moments in the planes T sub N1 and T sub N2 depend strongly on the oxygen content. Researchers describe magnetic interactions in high-T superconductors based on the Linear Muffin-Tin Orbitals (LMTO) band structure calculations. Exchange interaction parameters can be defined from the effective Heisenberg hamiltonian. When the magnetic moments are not too large, as copper magnetic moments in superconducting oxides, J sub ij parameters can be defined through the non-local magnetic susceptibility of spin restricted solution for the crystal. The results of nonlocal magnetic susceptibility calculations and the values of exchange interaction parameters for La CuO and YBa2Cu3O7 systems are given in tabular form. Strong anisotropy of exchange interactions in the ab plane and along the c axis in La2CuO4 is obviously seen. The value of Neel temperature found agrees well with the experimental data available. In the planes of '1-2-3' system there are quite strong antiferromagnetic Cu-O and O-O interaction which appear due to holes in oxygen subbands. These results are in line with the magnetic model of oxygen holes pairing in high-T(sub c) superconductors.

Turshevski, S. A.↗
NASA NTRS1991

Electron energy spectrum and magnetic interactions in high-Tc superconductors

The character of magnetic interactions in La-Sr-Cu-O and Y-Ba-Cu-O systems is of primary importance for analysis of high-T(sub c) superconductivity in these compounds. Neutron diffraction experiments showed the antiferromagnetic ground state for nonsuperconducting La2CuO4 and YBa2Cu3O6 with the strongest antiferromagnetic superexchange being in the ab plane. The nonsuperconducting '1-2-3' system has two Neel temperatures T(sub N1) and T(sub N2). The first one corresponds to the ordering of Cu atoms in the CuO2 planes; T(sub N2) reflects the antiferromagnetic ordering of magnetic moments in CuO chains relatively to the moments in the planes T(sub N1) and T(sub N2) which depend strongly on the oxygen content. Researchers describe magnetic interactions in high-T superconductors based on the Linear Muffin-Tin Orbitals (LMTO) band structure calculations. Exchange interaction parameters can be defined from the effective Heisenberg Hamiltonian. When the magnetic moments are not too large, as copper magnetic moments in superconducting oxides, J(sub ij) parameters can be defined through the non-local magnetic susceptibility of spin restricted solution for the crystal. The results of nonlocal magnetic susceptibility calculations and the values of exchange interaction parameters for La CuO and YBa2Cu3O7 systems are given in tabular form. Strong anisotropy of exchange interactions in the ab plane and along the c axis in La2CuO4 is obviously seen. The value of Neel temperature found agrees well with the experimental data available. In the planes of '1-2-3' system there are quite strong antiferromagnetic Cu-O and O-O interaction which appear due to holes in oxygen subbands. These results are in line with the magnetic model of oxygen holes pairing in high-T(sub c) superconductors.

Turshevski, S. A.↗