scholarly journals Style-content separation by anisotropic part scales

2010 ◽  
Vol 29 (6) ◽  
pp. 1-10 ◽  
Author(s):  
Kai Xu ◽  
Honghua Li ◽  
Hao Zhang ◽  
Daniel Cohen-Or ◽  
Yueshan Xiong ◽  
...  
Keyword(s):  
Anisotropic Part

Spin–Lattice Relaxation and the Anisotropic Part of the He–H2 Intermolecular Potential

1968 ◽  
Vol 49 (12) ◽  
pp. 5276-5281 ◽  
Author(s):  
John W. Riehl ◽  
James L. Kinsey ◽  
John S. Waugh ◽  
John H. Rugheimer
Keyword(s):  
Lattice Relaxation ◽  
Spin Lattice Relaxation ◽  
Intermolecular Potential ◽  
Spin Lattice ◽  
Anisotropic Part

Calculation of second virial coefficients for nitrogen and carbon monoxide

1980 ◽  
Vol 58 (6) ◽  
pp. 820-827 ◽  
Author(s):  
M. D. Whitmore ◽  
D. A. Goodings
Keyword(s):  
Carbon Monoxide ◽  
Good Accuracy ◽  
Power Series Expansion ◽  
Virial Coefficients ◽  
Coulomb Repulsion ◽  
Intermolecular Potential ◽  
Potential Models ◽  
Second Virial Coefficients ◽  
Gaussian Integration ◽  
Anisotropic Part

The classical second virial coefficients B(T) for nitrogen and carbon monoxide have been calculated exactly as a function of temperature for three different realistic models of the intermolecular potential. The potential models, due to Kohin, Raich and Mills, and Raich and Gillis, differ mainly, but not solely, in the way in which they represent the short-range Coulomb repulsion between molecules. As this interaction depends on the molecules' shapes, it is highly anisotropic. To ensure good accuracy in the results for B(T) the angular and radial integrals were performed by suitable Gaussian integration methods.The contributions to B(T) of various anisotropic terms are considered, and a power series expansion in terms of the anisotropic part of the potential discussed. The calculated results are compared with experiments, and some general conclusions drawn.

Optical Detection of Electron Nuclear Double Resonance on the Residual Donor in GaN

1996 ◽  
Vol 1 ◽  
Author(s):  
F. K. Koschnick ◽  
K. Michael ◽  
J.-M. Spaeth ◽  
B. Beaumont ◽  
Pierre Gibart
Keyword(s):  
Hyperfine Interaction ◽  
Quadrupole Splitting ◽  
Luminescence Band ◽  
Optical Detection ◽  
Double Resonance ◽  
Yellow Luminescence ◽  
Electron Nuclear Double Resonance ◽  
Anisotropic Part ◽  
Optically Detected

Optically detected electron nuclear double resonance (ODENDOR) was measured in the 2.2 eV ‘yellow’ luminescence band associated with the residual donor in n-type undoped GaN. The ODENDOR lines are due to gallium and show a quadrupole splitting which can be described with an axial tensor. The quadrupole parameter was estimated to be q(69Ga) = 1/2 Qzz = 0.22 MHz. A hyperfine interaction for 69Ga of about 0.3 MHz for the isotropic and of about 0.15 MHz for the anisotropic part was estimated from the width of the ODENDOR lines. It is tentatively suggested that a Ga interstitial is the residual donor.

Exchange interactions in antiferromagnetic salts of iridium. I. Paramagnetic resonance experiments

1959 ◽  
Vol 250 (1260) ◽  
pp. 84-96 ◽  
Keyword(s):  
Magnetic Susceptibility ◽  
Theoretical Analysis ◽  
Resonance Spectrum ◽  
Exchange Interactions ◽  
Ammonium Salts ◽  
Nearest Neighbour ◽  
Helium Temperature ◽  
Paramagnetic Resonance ◽  
Anisotropic Part ◽  
Rhombic Symmetry

Paramagnetic resonance methods have been used to investigate Ir-Ir exchange interactions in K 2 IrCl 6 and (NH 4 ) 2 IrCl 6 . Measurements are described of the resonance spectrum from nearest-neighbour pairs of Ir ions in semi-dilute mixed crystals where Pt is substituted for Ir. The results show that the isotropic p art of the Ir-Ir exchange, J / k , is antiferromagnetic and of magnitude 11.5 ± 1°K and 7.5 ± 1°K for the potassium and ammonium salts, respectively. There is also found to be an anisotropic part with rhombic symmetry and with magnitude of order 1 cm -1 . No lines attributable to next-nearest-neighbour pairs were found, and it is suggested that this interaction is small. The results are com pared briefly with the magnetic susceptibility experiments of Cooke et al . (part II) who find that the concentrated salts go antiferromagnetic in the liquid-helium temperature range, and also with the theoretical analysis of the superexchange mechanism given by Judd (part III).

scholarly journals Algorithms for quadratic forms over global function fields of odd characteristic

2021 ◽  
Vol 55 (3) ◽  
pp. 68-72
Author(s):  
Mawunyo Kofi Darkey-Mensah
Keyword(s):  
Quadratic Form ◽  
Quadratic Forms ◽  
Function Fields ◽  
Number Fields ◽  
Global Function ◽  
Global Function Fields ◽  
Anisotropic Part ◽  
Pythagoras Number ◽  
Present Algorithm

This paper presents an adaptation of recently developed algorithms for quadratic forms over number fields in [4] to global function fields of odd characteristics. First, we present algorithm for checking if a given non-degenerate quadratic form is isotropic or hyperbolic. Next we devise a method for computing the dimension of the anisotropic part of a quadratic form. Finally we present algorithms computing two field invariants: the level and the Pythagoras number.

Proton Magnetic Resonance Study of Mercury Dimethyl in a Nematic Liquid Crystal

1969 ◽  
Vol 24 (7) ◽  
pp. 1074-1077 ◽  
Author(s):  
Gerhard Englert
Keyword(s):  
Liquid Crystal ◽  
Nematic Liquid Crystal ◽  
Proton Magnetic Resonance ◽  
Symmetry Axis ◽  
Methyl Groups ◽  
Magnetic Resonance Study ◽  
Dipole Interactions ◽  
Anisotropic Part ◽  
Proton Magnetic Resonance Study ◽  
The Magnetic Field

Abstract The P.M.R.-spectrum of mercury dimethyl partially oriented in a nematic liquid crystal has been studied. From the ratio of the direct magnetic dipole-dipole interactions of the protons the ratio ξ0/ρ is calculated. ξ0 being the distance of the two parallel planes containing the methyl protons, and ρ being the distance of the methyl protons from the molecular symmetry axis. From this ratio the splitting due to the direct coupling of the protons with 199Hg of spin 1/2, present in about 17% natural abundance, is calculated and compared with the experimentally observed one. Exact agreement is obtained under the assumption that the methyl groups are rapidly rotating and that the direct and indirect 199Hg-H-couplings have like signs. Since the preferred orientation of the long axis of mercury dimethyl is probably parallel to the direction of the magnetic field, the absolute sign of J199Hg, H is found to be negative. Correspondingly it is shown that the sign of JCH3, CH3 is positive. No evidence is found for a possible contribution of the anisotropic part of the indirect couplings.

ROTATIONAL WINGS OF RAMAN BANDS AND FREE ROTATION IN LIQUID OXYGEN, NITROGEN, AND METHANE

1952 ◽  
Vol 30 (2) ◽  
pp. 81-98 ◽  
Author(s):  
M. F. Crawford ◽  
H. L. Welsh ◽  
J. H. Harrold
Keyword(s):  
Raman Spectrum ◽  
Transition Probability ◽  
Energy Levels ◽  
Anisotropic Scattering ◽  
Rotational Energy ◽  
Rate Of Change ◽  
Liquid Oxygen ◽  
Discrete Structure ◽  
Anisotropic Part ◽  
Liquid Methane

Rotation-vibrational Raman bands have been observed in liquid oxygen, nitrogen, and methane, and in solid methane. In every case the Q branches associated with isotropic Raman scattering are sharp lines; but the Q branches and rotational wings associated with anisotropic scattering form broad continuous bands, with extent and intensity distribution consistent with free molecular rotation. The lack of discrete structure in the broad bands is attributed to a removal of the m degeneracy of the rotational energy levels in the intermolecular force fields. Removal of the m degeneracy broadens those transitions for which the transition probability depends on the anisotropic part of the rate of change of the polarizability, but not those for which J and m are unchanged and for which the transition probability depends only on the isotropic part. The Raman spectrum of liquid oxygen yields no evidence for O4 aggregates. The Raman spectrum of liquid methane displays all fundamental vibrations of the molecule and two overtones, with Raman shifts (in cm.−1): 1300, band (ν4); 1535, band (ν2); 2570, line, and 2600, band (2ν4); 2906, line (ν1); 3020, band (ν3); 3053, line (2ν2).

On the magnetic anisotropy and susceptibility of Fe(NH 4 SO 4 ) 2 , 6H 2 O

1961 ◽  
Vol 261 (1305) ◽  
pp. 207-214 ◽  
Keyword(s):  
Thermal Expansion ◽  
Magnetic Anisotropy ◽  
Crystal Lattice ◽  
Crystal Field ◽  
Coupling Coefficient ◽  
Orbit Coupling ◽  
Spin Orbit Coupling ◽  
Spin Orbit ◽  
Anisotropic Part ◽  
Free Ion

The theory of magnetic anisotropy and susceptibility of Fe 2+ in Tutton salts has been worked out on the basis of Abragam & Pryce’s method. It is found that the anisotropic part of the crystal field changes with temperature owing to the thermal expansion of the crystal lattice. The spin-orbit coupling coefficient has to be decreased by ~ 20 % from its free ion value of - 103 cm -1 which indicates some amount of overlap between the 3 d -Fe 2+ and 8 - and p -O 2- charge clouds. The agreement of the theoretical values with the experiment is good within the limitations of the approximations involved.

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