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Constant Thickness Rotating Disk
2012For the constant thickness disk (h = cost; dh/dr = 0), the solving differential equation (1.28) is specialized in the following form: $$ \frac{{{{d}^2}u}}{{d{{r}^2}}} + \frac{1}{r} \cdot \frac{{du}}{{dr}} - \frac{u}{{{{r}^2}}} - \left( {1 + \nu } \right) \cdot \alpha \cdot \frac{{d{\rm T} }}{{dr}} + \left( {1 - {{\nu }^2}} \right) \cdot \frac ...
Vincenzo Vullo, Francesco Vivio
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Advection-Dominated Thick Accretion Disks
AIP Conference Proceedings, 2008We revisit the vertical structure of black hole accretion disks in spherical coordinates. By comparing the advective cooling with the viscous heating, we show that advection‐dominated disks are geometrically thick, i.e., with the half‐opening angle Δθ>2π/5, rather than slim as supposed previously in the literature.
Gu, Wei-Min +4 more
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Dissipation of thick accretion disks
Astrophysics and Space Science, 1983A thick accretion disk which is isentropic cannot have simple laminar flow because fluid elements follow orbits which intersect the orbits of other fluid elements, leading to turbulence in astrophysical disks which have very large Reynolds numbers.
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Electrostatics of a thick disk
Journal of Applied Physics, 1999An integral equation method is developed and applied to solve approximately the electrostatic problem of a drum-shaped conductor, one whose plane faces have a separation small compared with their diameter and what is called a thick disk. The approximate method is an asymptotic process by which capacitance formulas are obtained corresponding to the ...
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Jets of moderate optical thickness from thick acceretion disks
Astrophysics and Space Science, 1983The intense, super-Eddington, well-collimated radiation field generated by non-Keplerian accretion disks orbiting black holes can accelerate matter to high velocities. By using an energy balance argument which is both simple and physically appealing, we show that ordinary electron-proton plasmas can only reach relativistic gamma-factors up to 1.5.
M. A. Abramowicz, N. A. Sharp
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Extensional, thickness-stretch and symmetric thickness-shear vibrations of piezoceramic disks
IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, 2002A set of two-dimensional (2-D), second-order approximate equations for extensional, thickness-stretch and symmetric thickness-shear vibrations of piezoelectric ceramic plates with electroded faces is extracted from the infinite system of 2-D equations deduced previously.
Rui, Huang +3 more
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Non-Linearly Variable Thickness Disks
2012The topic discussed here goes well beyond those normally addressed in courses on mechanical design. However, it is advisable to provide complete coverage of the mathematical basics of the method for integrating the differential equations that govern the displacement field of rotating disks whose thickness varies according to a two-parameter linear ...
Vincenzo Vullo, Francesco Vivio
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Transient waves in a thick disk
The Journal of the Acoustical Society of America, 1994Transient elastic waves in a free thick disk are analyzed by a modal method. Eigenfunctions are determined by applying the Galerkin technique to trial functions which satisfy the differential equations and shear free conditions on all boundaries. The disk is forced concentrically by a trapezoidal pulse of short duration.
Michael El-Raheb, Paul Wagner
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Thick-walled Cylinders and Disks
2010In this chapter, we shall consider a class of problems in which the stresses and displacements depend only on the radius r in the cylindrical coordinate system (r,θ , z). The problems are therefore axisymmetric (i.e. there is no variation with the angle θ) nor is there any variation with the distance z along the axis.
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The Thickness of Galactic Disks
1984The local dynamical structure of disk galaxies is broadly characterized by a vertical scale height which is nearly independent of radius, the scale height being about 1/10 of the horizontal scale length (Searle and van der Kruit, 1982) and an internal population structure wherein the oldest stars have the largest random velocities (for an analysis of ...
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