scholarly journals A theorem for a fluid Stokes flow

1994 ◽  
Vol 35 (3) ◽  
pp. 335-347 ◽  
Author(s):  
D. Palaniappan ◽  
S. D. Nigam ◽  
T. Amaranath
Keyword(s):  
Viscous Fluid ◽  
Linear Combination ◽  
Stokes Flow ◽  
Fluid Sphere ◽  
Sphere Theorem ◽  
Present Theorem ◽  
Special Cases ◽  
Sphere Theorems

AbstractA sphere theorem for non-axisymmetric Stokes flow of a viscous fluid of viscosity μe past a fluid sphere of viscosity μi is stated and proved. The existing sphere theorems in Stokes flow follow as special cases from the present theorem. It is observed that the expression for drag on the fluid sphere is a linear combination of rigid and shear-free drags.

scholarly journals Analytical Expressions of Hydro-Seismic Forces on Dams

2018 ◽  
Author(s):  
Abdelmadjid Tadjadit ◽  
Boualem Tiliouine
Keyword(s):  
Viscous Fluid ◽  
Linear Combination ◽  
Upstream Face ◽  
Compressible Viscous Fluid ◽  
Natural Modes ◽  
Boundary Method ◽  
Complete Sets ◽  
Seismic Forces ◽  
Analytical Expressions

Analytical expressions for the determination of hydro-seismic forces acting on a rigid dam with irregular upstream face geometry in presence of a compressible viscous fluid are derived through a linear combination of the natural modes of water in the reservoir based on a boundary method making use of complete sets of complex T-functions.Analytical expressions for the determination of hydro-seismic forces acting on a rigid dam with irregular upstream face geometry in presence of a compressible viscous fluid are derived through a linear combination of the natural modes of water in the reservoir based on a boundary method making use of complete sets of complex T-functions. The formulas obtained for distributions of both shear forces and overturning moments are simple, computationally effective and useful for the preliminary design of dams. They show clearly the separate and combined effects of compressibility and viscosity of water. They also have the advantage of being able to cover a wide range of excitation frequencies even beyond the cut-off frequencies of the natural modes of the reservoir. Key results obtained using the proposed analytical expressions of the hydrodynamic forces are validated using numerical and experimental solutions published for some particular cases available in the specialized literature.

On the busy period distribution of the M/G/2 queueing system

1989 ◽  
Vol 26 (04) ◽  
pp. 858-865 ◽  
Author(s):  
Douglas P. Wiens
Keyword(s):  
Linear Combination ◽  
Busy Period ◽  
Queueing System ◽  
Rate Parameter ◽  
Period Distribution ◽  
Special Cases ◽  
Service Times ◽  
Arbitrary Linear Combination

Equations are derived for the distribution of the busy period of the GI/G/2 queue. The equations are analyzed for the M/G/2 queue, assuming that the service times have a density which is an arbitrary linear combination, with respect to both the number of stages and the rate parameter, of Erlang densities. The coefficients may be negative. Special cases and examples are studied.

scholarly journals Moffatt-type flows in a trihedral cone

2013 ◽  
Vol 725 ◽  
pp. 446-461 ◽  
Author(s):  
Julian F. Scott
Keyword(s):  
Linear Combination ◽  
Particle Motion ◽  
Particle Trajectory ◽  
Three Dimensional ◽  
Parameter Family ◽  
The Other ◽  
Transient Phase ◽  
Primary Flow ◽  
Special Cases ◽  
Two Parameter

AbstractThe three-dimensional analogue of Moffatt eddies is derived for a corner formed by the intersection of three orthogonal planes. The complex exponents of the first few modes are determined and the flows resulting from the primary modes (those which decay least rapidly as the apex is approached and, hence, should dominate the near-apex flow) examined in detail. There are two independent primary modes, one symmetric, the other antisymmetric, with respect to reflection in one of the symmetry planes of the cone. Any linear combination of these modes yields a possible primary flow. Thus, there is not one, but a two-parameter family of such flows. The particle-trajectory equations are integrated numerically to determine the streamlines of primary flows. Three special cases in which the flow is antisymmetric under reflection lead to closed streamlines. However, for all other cases, the streamlines are not closed and quasi-periodic limiting trajectories are approached when the trajectory equations are integrated either forwards or backwards in time. A generic streamline follows the backward-time trajectory in from infinity, undergoes a transient phase in which particle motion is no longer quasi-periodic, before being thrown back out to infinity along the forward-time trajectory.

On Some Classes of Idempotent Operators

1997 ◽  
Vol 05 (04) ◽  
pp. 401-410 ◽  
Author(s):  
G. Mayor ◽  
J. Torrens
Keyword(s):  
Linear Combination ◽  
Representation Theorem ◽  
Special Kind ◽  
Classical Representation ◽  
Aggregation Functions ◽  
Idempotent Operators ◽  
Special Cases ◽  
Convex Linear Combination

In this paper we deal with the idempotency equation H(x,x)=x for all x∈[0,1]. In particular we solve it for two special cases. First when H is a convex linear combination of a strict t-norm and its (1-j)-dual and second, when H is a convex linear combination of a special kind of aggregation functions F=<(f,N)> and its N-dual, being these aggregation functions, called L-representable aggregation functions, a kind of functions verifying a similar representation theorem to the classical representation theorem for non strict Archimedean t-norms.

BOUNDARY INTEGRAL EQUATIONS FOR A THREE-DIMENSIONAL STOKES–BRINKMAN CELL MODEL

2008 ◽  
Vol 18 (12) ◽  
pp. 2055-2085 ◽  
Author(s):  
MIRELA KOHR ◽  
G. P. RAJA SEKHAR ◽  
WOLFGANG L. WENDLAND
Keyword(s):  
Stokes Flow ◽  
Existence And Uniqueness ◽  
Stokes Equations ◽  
Boundary Integral Equations ◽  
Cell Model ◽  
Uniqueness Result ◽  
Boundary Integral ◽  
Porous Particle ◽  
Brinkman Equation ◽  
Special Cases

The purpose of this paper is to prove the existence and uniqueness of the solution in Sobolev or Hölder spaces for a cell model problem which describes the Stokes flow of a viscous incompressible fluid in a bounded region past a porous particle. The flow within the porous particle is described by the Brinkman equation. In order to obtain the desired existence and uniqueness result, we use an indirect boundary integral formulation and potential theory for both Brinkman and Stokes equations. Some special cases, which refer to the cell model for a porous particle with large permeability, or to the exterior Stokes flow past a porous particle, are also presented.

VANISHING AND TOPOLOGICAL SPHERE THEOREMS FOR SUBMANIFOLDS IN A HYPERBOLIC SPACE

2008 ◽  
Vol 19 (07) ◽  
pp. 811-822 ◽  
Author(s):  
HAIPING FU ◽  
HONGWEI XU
Keyword(s):  
Hyperbolic Space ◽  
Measure Theory ◽  
Geometric Measure Theory ◽  
Vanishing Theorem ◽  
Sphere Theorem ◽  
Homology Groups ◽  
Geometric Measure ◽  
Complete Submanifolds ◽  
Negative Constant ◽  
Sphere Theorems

We extend the vanishing and sphere theorems due to Lawson, Simons, Xin, Shiohama and Xu. By using the techniques of calculus of variations in the geometric measure theory, we prove the vanishing theorem for homology groups of submanifolds in the hyperbolic space Hn(c) with negative constant curvature c. Moreover, we obtain a topological sphere theorem for certain complete submanifolds in Hn(c).

Slow steady rotation of axially symmetric bodies in a viscous fluid

1961 ◽  
Vol 10 (1) ◽  
pp. 17-24 ◽  
Author(s):  
R. P. Kanwal
Keyword(s):  
Angular Velocity ◽  
Flow Field ◽  
Viscous Fluid ◽  
Stokes Flow ◽  
Flow Problem ◽  
Analytic Solutions ◽  
The Body ◽  
Axially Symmetric ◽  
Steady Rotation ◽  
Axis Of Symmetry

The Stokes flow problem is considered here for the case in which an axially symmetric body is uniformly rotating about its axis of symmetry. Analytic solutions are presented for the heretofore unsolved cases of a spindle, a torus, a lens, and various special configurations of a lens. Formulas are derived for the angular velocity of the flow field and for the couple experienced by the body in each case.

Stokes Flow Around Slowly Rotating Concentric Pervious Spheres

2013 ◽  
Vol 60 (2) ◽  
pp. 165-219 ◽  
Author(s):  
Deepak Kumar Srivastava ◽  
Raja Ram Yadav ◽  
Supriya Yadav
Keyword(s):  
Angular Velocity ◽  
Stokes Flow ◽  
Outer Sphere ◽  
Present Situation ◽  
Subject Classification ◽  
Dissipated Energy ◽  
Azimuthal Component ◽  
Special Cases ◽  
Inner Sphere ◽  
Angular Velocities

In this paper, the problem of concentric pervious spheres carrying a fluid sink at their centre and rotating slowly with different uniform angular velocities 1, 2 about a diameter has been studied. The analysis reveals that only azimuthal component of velocity exists and the torque, rate of dissipated energy is found analytically in the present situation. The expression of torque on inner sphere rotating slowly with uniform angular velocity 1, while outer sphere also rotates slowly with uniform angular velocity Ω2, is evaluated. The special cases like, (i) inner sphere is fixed (i.e. Ω1 = 0), while outer sphere rotates with uniform angular velocity Ω2, (ii) outer sphere is fixed (i.e. Ω2 = 0), while inner sphere rotates with uniform angular velocity Ω1, (iii.) inner sphere rotates with uniform angular velocity 1, while outer rotates at infinity with angular velocity 2; have been deduced. The corresponding variation of torque with respect to sink parameter has been shown via figures. AMS subject classification - 76 D07

Flow due to a point source of momentum in a viscous fluid contained in a sphere

1967 ◽  
Vol 63 (1) ◽  
pp. 249-256
Author(s):  
K. B. Ranger
Keyword(s):  
Reynolds Number ◽  
Viscous Fluid ◽  
Stokes Flow ◽  
Fluid Motion ◽  
Perturbation Expansion ◽  
General Term ◽  
Axially Symmetric ◽  
Order Of Magnitude ◽  
Self Consistency ◽  
Viscous Fluid Motion

AbstractIt is argued that the zero Reynolds limit of the steady incompressible axially symmetric viscous fluid motion interior to a sphere due to a Landau source at the centre is a Stokes flow. The first three terms of the perturbation expansion are determined and the order of magnitude of the general term not derivable from the Landau source is established. Comparison of the convection terms with the diffusion terms for each order of the Reynolds number demonstrates self consistency at each stage of the expansion.

Sign in / Sign up

Export Citation Format

Share Document