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Scientific and Technical Aerospace Reports Volume 38 July 28, 2000

Scientific and Technical Aerospace Reports Volume 38 July 28, 2000

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<strong>2000</strong>0066597 Geophysical Observatory, Helsinki, Finl<strong>and</strong><br />

On Complex Differential Equations in the Unit Disc<br />

Heittokangas, Janne, Geophysical Observatory, Finl<strong>and</strong>; <strong>2000</strong>; ISSN 1239-6303; 62p; In English; Sponsored in part by Emil Aaltonen<br />

Foundation<br />

Report No.(s): Rept-122; ISBN 951-41-0867-1; Copyright; Avail: Issuing Activity<br />

This paper presents a dissertation on complex differential equations in the unit disc. The topics include: 1) Notations <strong>and</strong> background;<br />

2) Linear first order equations; 3) Linear second order equations; 4) The equation f (sup k) + A (z)f=0; 5) Upper bounds<br />

for the absolute value of f (sup k) (z)/f (sup j)(z) in the unit disc; 6) Linear equations of arbitrary order; 7) Linear non-homogeneous<br />

equations of arbitrary order; <strong>and</strong> 8) Algebraic differential equations.<br />

CASI<br />

Differential Equations; Complex Variables; Meromorphic Functions; Analysis (Mathematics)<br />

70<br />

PHYSICS (GENERAL)<br />

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<strong>2000</strong>0065659 Jet Propulsion Lab., California Inst. of Tech., Pasadena, CA USA<br />

Clock Technology Development in the Laser Cooling <strong>and</strong> Atomic Physics (LCAP) Program<br />

Seidel, Dave, Jet Propulsion Lab., California Inst. of Tech., USA; Thompson, R. J., Jet Propulsion Lab., California Inst. of Tech.,<br />

USA; Klipstein, W. M., Jet Propulsion Lab., California Inst. of Tech., USA; Kohel, J., Jet Propulsion Lab., California Inst. of Tech.,<br />

USA; Maleki, L., Jet Propulsion Lab., California Inst. of Tech., USA; [<strong>2000</strong>]; 15p; In English; No Copyright; Avail: CASI; A03,<br />

Hardcopy; A01, Microfiche<br />

This paper presents the Laser Cooling <strong>and</strong> Atomic Physics (LCAP) program. It focuses on clock technology development.<br />

The topics include: 1) Overview of LCAP Flight Projects; 2) Space Clock 101; 3) Physics with Clocks in microgravity; 4) Space<br />

Clock Challenges; 5) LCAP Timeline; 6) International Space Station (ISS) Science Platforms; 7) ISS Express Rack; 8) Space<br />

Qualification of Components; 9) Laser Configuration; 10) Clock Rate Comparisons: GPS Carrier Phase Frequency Transfer; <strong>and</strong><br />

11) ISS Model Views. This paper is presented in viewgraph form.<br />

CASI<br />

Atomic Physics; Clocks; Laser Cooling; Technology Utilization<br />

71<br />

ACOUSTICS<br />

�������� ����� ����������� ������������� ��� ������������ ��� ����� ��������� ��� �� ����������� ���������� ��� �������� ����� ��� ����<br />

�� ������������ ��� �� �������� ���������� ���������� ��� ������<br />

<strong>2000</strong>0062459 DYNACS Engineering Co., Inc., Clevel<strong>and</strong>, OH USA<br />

Influence of Mean-Density Gradient on Small-Scale Turbulence Noise<br />

Khavaran, Abbas, DYNACS Engineering Co., Inc., USA; June <strong>2000</strong>; 18p; In English; 6th; Aeroacoustics, 12-14 Jun. <strong>2000</strong>,<br />

Lahaina, HI, USA; Sponsored by American Inst. of Aeronautics <strong>and</strong> Astronautics, USA<br />

Contract(s)/Grant(s): NAS3-98008; RTOP 523-90-43<br />

Report No.(s): NASA/CR-<strong>2000</strong>-210226; E-12346; NAS 1.26:210226; AIAA Paper <strong>2000</strong>-2059; Copyright Waived; Avail: CASI;<br />

A03, Hardcopy; A01, Microfiche<br />

A physics-based methodology is described to predict jet-mixing noise due to small-scale turbulence. Both self- <strong>and</strong> shearnoise<br />

source teens of Lilley’s equation are modeled <strong>and</strong> the far-field aerodynamic noise is expressed as an integral over the jet<br />

volume of the source multiplied by an appropriate Green’s function which accounts for source convection <strong>and</strong> mean-flow refraction.<br />

Our primary interest here is to include transverse gradients of the mean density in the source modeling. It is shown that, in<br />

addition to the usual quadrupole type sources which scale to the fourth-power of the acoustic wave number, additional dipole <strong>and</strong><br />

monopole sources are present that scale to lower powers of wave number. Various two-point correlations are modeled <strong>and</strong> an<br />

approximate solution to noise spectra due to multipole sources of various orders is developed. Mean flow <strong>and</strong> turbulence information<br />

is provided through RANS-k(epsilon) solution. Numerical results are presented for a subsonic jet at a range of temperatures<br />

187

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