Comptonization of the free-free radiation in an isothermal medium of constant density

Astrophysics ◽  
1989 ◽  
Vol 29 (2) ◽  
pp. 634-644 ◽  
Author(s):  
L. G. Titarchuk
Keyword(s):  
Constant Density ◽  
Isothermal Medium

Pressure variation in a fluid at rest (hydrostatics)

2018 ◽  
Author(s):  
Marcel Escudier
Keyword(s):  
Equation Of State ◽  
Static Pressure ◽  
Applied Pressure ◽  
Pressure Variation ◽  
Constant Density ◽  
Fluid Temperature ◽  
Earth’S Atmosphere ◽  
Hydrostatic Equation ◽  
Depth Increase ◽  
Pressure Changes

The three fundamental principles for the variation of static pressure p throughout a body of fluid at rest are (a) the pressure at a point is the same in all directions (Pascal’s law), (b) the pressure is the same at all points on the same horizontal level, and (c) the pressure increases with depth z according to the hydrostatic equation. dp/dz= ρ‎g For a fluid with constant density ρ‎, the increase in pressure over a depth increase h is ρ‎gh, a result which can be used to analyse the response of simple barometers and manometers to applied pressure changes and differences. In situations where very large changes in pressure occur an equation of state may be required to relate pressure and density together with an assumption about the fluid temperature. The hydrostatic equation is still valid but more difficult to integrate, as illustrated by consideration of the earth’s atmosphere.

scholarly journals Recursive algorithms for the computation of the potential harmonic coefficients of a constant density polyhedron

2009 ◽  
Vol 83 (10) ◽  
pp. 925-942 ◽  
Author(s):  
Dimitrios Tsoulis ◽  
Olivier Jamet ◽  
Jérôme Verdun ◽  
Nicolas Gonindard
Keyword(s):  
Constant Density ◽  
Recursive Algorithms ◽  
Potential Harmonic

Laminar natural convection about an isothermally heated sphere at small Grashof number

1968 ◽  
Vol 34 (1) ◽  
pp. 163-176 ◽  
Author(s):  
Francis E. Fendell
Keyword(s):  
Natural Convection ◽  
Three Dimensional ◽  
Perturbation Expansion ◽  
Outer Sphere ◽  
Convective Transport ◽  
Convection Flow ◽  
Constant Density ◽  
Boussinesq Model ◽  
Grashof Number ◽  
Recirculating Flow

The flow induced by gravity about a very small heated isothermal sphere introduced into a fluid in hydrostatic equilibrium is studied. The natural-convection flow is taken to be steady and laminar. The conditions under which the Boussinesq model is a good approximation to the full conservation laws are described. For a concentric finite cold outer sphere with radius, in ratio to the heated sphere radius, roughly less than the Grashof number to the minus one-half power, a recirculating flow occurs; fluid rises near the inner sphere and falls near the outer sphere. For a small heated sphere in an unbounded medium an ordinary perturbation expansion essentially in the Grashof number leads to unbounded velocities far from the sphere; this singularity is the natural-convection analogue of the Whitehead paradox arising in three-dimensional low-Reynolds-number forced-convection flows. Inner-and-outer matched asymptotic expansions reveal the importance of convective transport away from the sphere, although diffusive transport is dominant near the sphere. Approximate solution is given to the nonlinear outer equations, first by seeking a similarity solution (in paraboloidal co-ordinates) for a point heat source valid far from the point source, and then by linearization in the manner of Oseen. The Oseen solution is matched to the inner diffusive solution. Both outer solutions describe a paraboloidal wake above the sphere within which the enthalpy decays slowly relative to the rapid decay outside the wake. The updraft above the sphere is reduced from unbounded growth with distance from the sphere to constant magnitude by restoration of the convective accelerations. Finally, the role of vertical stratification of the ambient density in eventually stagnating updrafts predicted on the basis of a constant-density atmosphere is discussed.

A static generalization of the Einstein universe

1958 ◽  
Vol 245 (1241) ◽  
pp. 202-212
Keyword(s):  
General Problem ◽  
Constant Density ◽  
De Sitter ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Einstein Universe

Solutions of the Einstein field equations are found for the problem of a sphere of constant density surrounded by matter of different constant density. The solutions are discussed and particular attention paid to the topology of the surrounding matter. The Schwarzschild, de Sitter, and Einstein solutions emerge as particular cases of the general problem.

Effect of radiative heat loss on steady hypersonic flow past a blunt body

1967 ◽  
Vol 29 (3) ◽  
pp. 485-494 ◽  
Author(s):  
M. I. G. Bloor
Keyword(s):  
Numerical Solution ◽  
Heat Loss ◽  
Blunt Body ◽  
Radiative Heat ◽  
Constant Density ◽  
Axially Symmetric ◽  
Radiative Heat Loss ◽  
Stagnation Region ◽  
Expansion Procedure ◽  
Axis Of Symmetry

Using the grey gas approximation, the effect of radiative heat loss on axially symmetric flows is studied. Using an expansion procedure about the axis of symmetry, a numerical solution for the stagnation region is found taking the shock to be spherical. The results of this calculation are compared with the results of Lighthill's non-radiative constant density solution.

A multi-layer model for nonlinear internal wave propagation in shallow water

2012 ◽  
Vol 695 ◽  
pp. 341-365 ◽  
Author(s):  
Philip L.-F. Liu ◽  
Xiaoming Wang
Keyword(s):  
Wave Propagation ◽  
Internal Wave ◽  
Shallow Water ◽  
Internal Waves ◽  
Bottom Topography ◽  
Laboratory Data ◽  
Constant Density ◽  
Layer Model ◽  
Fluid System ◽  
Nonlinear Internal Wave

AbstractIn this paper, a multi-layer model is developed for the purpose of studying nonlinear internal wave propagation in shallow water. The methodology employed in constructing the multi-layer model is similar to that used in deriving Boussinesq-type equations for surface gravity waves. It can also be viewed as an extension of the two-layer model developed by Choi & Camassa. The multi-layer model approximates the continuous density stratification by an $N$-layer fluid system in which a constant density is assumed in each layer. This allows the model to investigate higher-mode internal waves. Furthermore, the model is capable of simulating large-amplitude internal waves up to the breaking point. However, the model is limited by the assumption that the total water depth is shallow in comparison with the wavelength of interest. Furthermore, the vertical vorticity must vanish, while the horizontal vorticity components are weak. Numerical examples for strongly nonlinear waves are compared with laboratory data and other numerical studies in a two-layer fluid system. Good agreement is observed. The generation and propagation of mode-1 and mode-2 internal waves and their interactions with bottom topography are also investigated.

SOME COMMENTS ON THE DYNAMICS OF EXTENDED OBJECTS

1998 ◽  
Vol 13 (17) ◽  
pp. 2979-2990 ◽  
Author(s):  
U. KHANAL
Keyword(s):  
Wave Equation ◽  
Energy Density ◽  
Pure Shear ◽  
Equation Of Motion ◽  
Conducting Medium ◽  
Constant Density ◽  
Metric Tensor ◽  
World Volume ◽  
The World ◽  
Hilbert Action

A variational method is used to investigate the dynamics of extended objects. The stationary world volume requires the internal coordinates to propagate as free waves. Stationarity of the action which is the integral of a variable energy density over the world volume leads to the wave equation in a medium, with conductivity given by the gradient of the logarithm of reciprocal energy density, constant density corresponding to free space. The Einstein–Hilbert action for the world curvature gives an equation of motion which, in world space with the Einstein tensor proportional to the metric tensor, reduces to the free wave equation. A similar method applied to the action consisting of the surface area enclosing an incompressible world volume undergoing pure shear again yields the wave equation in a conducting medium. Simultaneous stationarity of the volume can be imposed with a stationary area only in the case of pure shear; stationary Einstein–Hilbert action can also be included and lead to an equation of motion which has a similar interpretation of the wave in the conducting medium. Some Green functions applicable to the medium with constant conductivity are also presented.

A Study of Two-Dimensional Supersonic Air Ejector Systems

1973 ◽  
Vol 187 (1) ◽  
pp. 733-743
Author(s):  
R. S. Benson ◽  
V. A. Eustace
Keyword(s):  
Flow Field ◽  
Secondary Flow ◽  
Ambient Pressure ◽  
Performance Characteristics ◽  
Constant Density ◽  
Two Dimensional ◽  
Theoretical Predictions ◽  
Flow Field Characteristics ◽  
Air Ejector

The performance and flow field characteristics for two-dimensional ejector systems are determined theoretically for the condition when operation is independent of ambient pressure. The method considers the detailed inviscid interaction between the primary and secondary streams within the mixing tube and an estimate is made of the secondary flow entrained by the two-stream viscous mixing region. The validity of the theory is tested by comparing the performance characteristics of an experimental ejector facility with theoretical predictions and by comparing the theoretical flow field, in terms of constant density contours, with infinite fringe interferograms.

scholarly journals TESLA GPUs versus MPI with OpenMP for the Forward Modeling of Gravity and Gravity Gradient of Large Prisms Ensemble

2013 ◽  
Vol 2013 ◽  
pp. 1-15 ◽  
Author(s):  
Carlos Couder-Castañeda ◽  
Carlos Ortiz-Alemán ◽  
Mauricio Gabriel Orozco-del-Castillo ◽  
Mauricio Nava-Flores
Keyword(s):  
Parallel Computing ◽  
Graphics Processing Units ◽  
Forward Modeling ◽  
Gravity Gradient ◽  
Constant Density ◽  
Gravitational Fields ◽  
Design And Implementation ◽  
Cuda Technology ◽  
Performance Results ◽  
Graphics Processing

An implementation with the CUDA technology in a single and in several graphics processing units (GPUs) is presented for the calculation of the forward modeling of gravitational fields from a tridimensional volumetric ensemble composed by unitary prisms of constant density. We compared the performance results obtained with the GPUs against a previous version coded in OpenMP with MPI, and we analyzed the results on both platforms. Today, the use of GPUs represents a breakthrough in parallel computing, which has led to the development of several applications with various applications. Nevertheless, in some applications the decomposition of the tasks is not trivial, as can be appreciated in this paper. Unlike a trivial decomposition of the domain, we proposed to decompose the problem by sets of prisms and use different memory spaces per processing CUDA core, avoiding the performance decay as a result of the constant calls to kernels functions which would be needed in a parallelization by observations points. The design and implementation created are the main contributions of this work, because the parallelization scheme implemented is not trivial. The performance results obtained are comparable to those of a small processing cluster.

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