The deformation of a viscous particle surrounded by an elastic shell in a general time-dependent linear flow field

1983 ◽  
Vol 126 ◽  
pp. 533-544 ◽  
Author(s):  
P. O. Brunn
Keyword(s):  
Flow Field ◽  
Shell Thickness ◽  
Elastic Shell ◽  
Time Dependent ◽  
Linear Flow ◽  
Special Cases ◽  
Arbitrary Thickness ◽  
Elastic Membranes ◽  
Freely Suspended ◽  
General Time

The dynamics of a viscous particle surrounded by an elastic shell of arbitrary thickness freely suspended in a general linear flow field is investigated. Assuming the unstressed shell to be spherical, an analysis is presented for the case in which the flow-induced deformation leads to small departures from sphericity. The general time-dependent evolution of shape is derived and various special cases (purely elastic sphere, rigid and gaseous interior, elastic membranes) are discussed in detail. It is found that for steady-state flows the equilibrium deformations are absolutely stable and depend only upon the shell thickness, although the rates at which they are attained show the effect of the inside viscosity, too.

THE QUADRATIC TIME-DEPENDENT HAMILTONIAN: EVOLUTION OPERATOR, SQUEEZING REGIONS IN PHASE SPACE AND TRAJECTORIES

1994 ◽  
Vol 08 (11n12) ◽  
pp. 1563-1576 ◽  
Author(s):  
S.S. MIZRAHI ◽  
M.H.Y. MOUSSA ◽  
B. BASEIA
Keyword(s):  
Phase Space ◽  
Unitary Transformation ◽  
Uniform Magnetic Field ◽  
Evolution Operator ◽  
Single Mode ◽  
Time Dependent ◽  
Special Cases ◽  
Complete Set ◽  
Hamiltonian Evolution ◽  
General Time

We consider the most general Time-Dependent (TD) quadratic Hamiltonian written in terms of the bosonic operators a and a+, which may represent either a charged particle subjected to a harmonic motion, immersed in a TD uniform magnetic field, or a single mode photon field going through a squeezing medium. We solve the TD Schrödinger equation by a method that uses, sequentially, a TD unitary transformation and the diagonalization of a TD invariant, and we verify that the exact solution is a complete set of TD states. We also obtain the evolution operator which is essential to express operators in the Heisenberg picture. The variances of the quadratures are calculated and a phase space of parameters introduced, in which we identify squeezing regions. The results for some special cases are presented and as an illustrative example the parametric oscillator is revisited and the trajectories in phase space drawn.

scholarly journals Time-dependent lift and drag on a rigid body in a viscous steady linear flow

2019 ◽  
Vol 864 ◽  
pp. 554-595 ◽  
Author(s):  
Fabien Candelier ◽  
Bernhard Mehlig ◽  
Jacques Magnaudet
Keyword(s):  
Reynolds Number ◽  
Flow Field ◽  
Rigid Body ◽  
Slip Velocity ◽  
Fluid Velocity ◽  
The Body ◽  
Time Dependent ◽  
Leading Order ◽  
Linear Flow ◽  
Force Components

We compute the leading-order inertial corrections to the instantaneous force acting on a rigid body moving with a time-dependent slip velocity in a linear flow field, assuming that the square root of the Reynolds number based on the fluid-velocity gradient is much larger than the Reynolds number based on the slip velocity between the body and the fluid. As a first step towards applications to dilute sheared suspensions and turbulent particle-laden flows, we seek a formulation allowing this force to be determined for an arbitrarily shaped body moving in a general linear flow. We express the equations governing the flow disturbance in a non-orthogonal coordinate system moving with the undisturbed flow and solve the problem using matched asymptotic expansions. The use of the co-moving coordinates enables the leading-order inertial corrections to the force to be obtained at any time in an arbitrary linear flow field. We then specialize this approach to compute the time-dependent force components for a sphere moving in three canonical flows: solid-body rotation, planar elongation, and uniform shear. We discuss the behaviour and physical origin of the different force components in the short-time and quasi-steady limits. Last, we illustrate the influence of time-dependent and quasi-steady inertial effects by examining the sedimentation of prolate and oblate spheroids in a pure shear flow.

GENERALIZED HANNAY ANGLE FOR THE MOST GENERAL TIME-DEPENDENT HARMONIC OSCILLATOR

1993 ◽  
Vol 07 (28) ◽  
pp. 4827-4840 ◽  
Author(s):  
DONALD H. KOBE ◽  
JIONGMING ZHU
Keyword(s):  
Harmonic Oscillator ◽  
Berry Phase ◽  
Time Dependent ◽  
Canonical Momentum ◽  
Gauge Invariant ◽  
Classical Counterpart ◽  
Mass Spring ◽  
Adiabatic Case ◽  
General Time ◽  
Total Angle

The most general time-dependent Hamiltonian for a harmonic oscillator is both linear and quadratic in the coordinate and the canonical momentum. It describes in general a harmonic oscillator with mass, spring “constant,” and friction (or antifriction) “constant,” all of which are time dependent, that is acted on by a time-dependent force. A generalized Hannay angle, which is gauge invariant, is defined by making a distinction between the Hamiltonian and the energy. The generalized Hannay angle is the classical counterpart of the generalized Berry phase in quantum theory. When friction is present the generalized Hannay angle is nonzero. If the Hamiltonian is (incorrectly) chosen to be the energy, the generalized Hannay angle is different. Nevertheless, in the adiabatic case the same total angle is obtained.

scholarly journals Diffusion of dust particles emitted from a fixed source

2015 ◽  
Vol 4 (4) ◽  
pp. 454
Author(s):  
Khaled Al-mashrafi
Keyword(s):  
Source Function ◽  
Strong Dependence ◽  
Vertical Direction ◽  
Dust Particles ◽  
Special Values ◽  
Diffusion Parameters ◽  
Special Cases ◽  
Small Times ◽  
The Mathematical Model ◽  
General Time

<p>In this paper, we investigate the mathematical model for the diffusion of dust particles emitted from a fixed source. Mathematically, the time-dependent diffusion equation in the presence of a point source whose strength is dependent on time is solved. The solution in closed form for a source of general time dependence is obtained. A number of special cases, in which the source function of time is explicitly given and special values of the diffusion parameters are taken are examined in detail. The numerical calculations show the strong dependence of the concentration of dust on the speed of the wind, the source, and its position in the vertical direction. It is also found that the diffusion parameters play an important role in the spread of the dust particles in the atmosphere. When diffusion is present only in the vertical direction, it is found that for small times the dust spreads with a front that travels with the speed of the wind.</p>

scholarly journals Three-Dimensional Wake Decay Inside of a Compressor Cascade and its Influence on the Downstream Unsteady Flow Field: Part I — Wake Decay Characteristics in the Flow Passage

1990 ◽  
Author(s):  
C. Poensgen ◽  
H. E. Gallus
Keyword(s):  
Flow Field ◽  
Turbulent Flows ◽  
Velocity Vector ◽  
Three Dimensional ◽  
Time Dependent ◽  
Major Influence ◽  
Hot Wire ◽  
Compressor Cascade ◽  
Flow Passage ◽  
Turbulent Flow Field

A measuring technique based on multisensor hot-wire anemometry has been developed to determine the unsteady three-dimensional velocity vector and the structure of turbulent flows. It then has been applied to the passage and the exit flow of an annular compressor cascade, which is periodically disturbed by the wakes of a cylinder rotor, located about 50 percent of blade chord upstream. In part I of this paper the decay of the rotor wakes will be described first without stator and secondly through a stator passage. The time-dependent turbulent flow field downstream of this stator is discussed in Part II. The rotor wakes have a major influence on the development of three-dimensional separated regions inside the compressor cascade, and this interaction will be addressed in both parts of this paper.

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