R fluids

Serbian Astronomical Journal ◽

10.2298/saj0876023c ◽

2008 ◽

pp. 23-35 ◽

Cited By ~ 1

Author(s):

R. Caimmi

Keyword(s):

Kinetic Energy ◽

Velocity Component ◽

Axial Velocity ◽

Tangential Velocity ◽

Random Motion ◽

Moment Of Inertia ◽

Random Velocity ◽

Principal Axes ◽

The Moment ◽

Figure Rotation

A theory of collisionless fluids is developed in a unified picture, where nonrotating (?f1 = ?f2 = ?f3 = 0) figures with some given random velocity component distributions, and rotating (?f1 = ?f2 = ?f3 ) figures with a different random velocity component distributions, make adjoint configurations to the same system. R fluids are defined as ideal, self-gravitating fluids satisfying the virial theorem assumptions, in presence of systematic rotation around each of the principal axes of inertia. To this aim, mean and rms angular velocities and mean and rms tangential velocity components are expressed, by weighting on the moment of inertia and the mass, respectively. The figure rotation is defined as the mean angular velocity, weighted on the moment of inertia, with respect to a selected axis. The generalized tensor virial equations (Caimmi and Marmo 2005) are formulated for R fluids and further attention is devoted to axisymmetric configurations where, for selected coordinate axes, a variation in figure rotation has to be counterbalanced by a variation in anisotropy excess and vice versa. A microscopical analysis of systematic and random motions is performed under a few general hypotheses, by reversing the sign of tangential or axial velocity components of an assigned fraction of particles, leaving the distribution function and other parameters unchanged (Meza 2002). The application of the reversion process to tangential velocity components is found to imply the conversion of random motion rotation kinetic energy into systematic motion rotation kinetic energy. The application of the reversion process to axial velocity components is found to imply the conversion of random motion translation kinetic energy into systematic motion translation kinetic energy, and the loss related to a change of reference frame is expressed in terms of systematic motion (imaginary) rotation kinetic energy. A number of special situations are investigated in greater detail. It is found that an R fluid always admits an adjoint configuration where figure rotation occurs around only one principal axis of inertia (R3 fluid), which implies that all the results related to R3 fluids (Caimmi 2007) may be ex- tended to R fluids. Finally, a procedure is sketched for deriving the spin parameter distribution (including imaginary rotation) from a sample of observed or simulated large-scale collisionless fluids i.e. galaxies and galaxy clusters.

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Finding Principal Axes of Complex Plane Rigid Body with Rending-Image of MATLAB

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.490-495.2156 ◽

2012 ◽

Vol 490-495 ◽

pp. 2156-2159

Author(s):

Wu Gang Li

Keyword(s):

Rigid Body ◽

Complex Plane ◽

Principal Axis ◽

Flat Surface ◽

Moment Of Inertia ◽

Principal Axes ◽

The Moment

In order to find the principal axes of inertia and calculate their moment of inertia to any plane homogeneous rigid body for calculating easily the moment of inertia to any axis of this rigid body, the principal axes could be found and their moment of inertia could be calculated automatically by using the reading-image of MATLAB to read the image messages about the flat surface of the rigid body and by the procedures which ware made according to the logic relation about the principal axis and the moment of inertia of the rigid body. Applying this method in a homogeneous cube, a result was acquired, error of which is small compared with the theoretical value. So this method is reliable, convenient and practical

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Magnetic Field Amplification and Polar Jet Formation in Protostars

Symposium - International Astronomical Union ◽

10.1017/s0074180900096017 ◽

1987 ◽

Vol 115 ◽

pp. 384-384

Author(s):

S. Hinata

Keyword(s):

Magnetic Field ◽

Angular Momentum ◽

Kinetic Energy ◽

Accretion Disk ◽

Outer Edge ◽

Moment Of Inertia ◽

Simple Relationship ◽

Field Amplification ◽

Background Magnetic Field ◽

The Moment

There is a simple relationship among moment of inertia I, rotational kinetic energy K, and momentum L given by (David Layzer, private communication), 2IK ≧ L. During the Hayashi phase a rotating protostar will amplify the trapped magnetic field by a dynamo-like process. Since the rotation is expected to be fast, many unstable modes will be excited and will grow exponentially in time until some nonlinear processes saturate the amplitude. However, it may happen that the reduction in rotational kinetic energy becomes so large that without increasing the moment of inertia the inequality given above may not be satisfied. The only way to increase the moment of inertia is to move the mass outward. This can be done by transferring the angular momentum outward through the magnetic field. So we will have a fast rotating mass shell at the outer edge of the star. Further transfer of angular momentum will push the shell against the accretion disk; the moving masses of the disk will divert the mass flow along the background magnetic field which extends perpendicular to the accretion disk. This results in the hollow cone jets from both poles because the outward motion is primarily on the equatorial plane.

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SUM RULE FOR MULTISCALE REPRESENTATIONS OF KINEMATICALLY DESCRIBED SYSTEMS

Advances in Complex Systems ◽

10.1142/s0219525902000638 ◽

2002 ◽

Vol 05 (04) ◽

pp. 409-431 ◽

Cited By ~ 5

Author(s):

YANEER BAR-YAM

Keyword(s):

Kinetic Energy ◽

Degrees Of Freedom ◽

Collective Motion ◽

Space Time ◽

Moment Of Inertia ◽

Sum Rule ◽

Effective Moment ◽

External Frame ◽

The Moment ◽

Effective Moment Of Inertia

We derive a sum rule that constrains the scale based decomposition of the trajectories of finite systems of particles. The sum rule reflects a tradeoff between the finer and larger scale collective degrees of freedom. For short duration trajectories, where acceleration is irrelevant, the sum rule can be related to the moment of inertia and the kinetic energy (times a characteristic time squared). Thus, two nonequilibrium systems that have the same kinetic energy and moment of inertia can, when compared to each other, have different scales of behavior, but if one of them has larger scales of behavior than the other, it must compensate by also having smaller scales of behavior. In the context of coherence or correlation, the larger scale of behavior corresponds to the collective motion, while the smaller scales of behavior correspond to the relative motion of correlated particles. For longer duration trajectories, the sum rule includes the full effective moment of inertia of the system in space-time with respect to an external frame of reference, providing the possibility of relating the class of systems that can exist in the same space-time domain.

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A semiclassical, microscopic model for nuclear collective rotation

Canadian Journal of Physics ◽

10.1139/p06-071 ◽

2006 ◽

Vol 84 (10) ◽

pp. 905-923 ◽

Cited By ~ 1

Author(s):

P Gulshani

Keyword(s):

Schrödinger Equation ◽

Time Reversal ◽

Schrodinger Equation ◽

Moment Of Inertia ◽

Time Dependent ◽

Microscopic Model ◽

Expectation Value ◽

Principal Axes ◽

Collective Rotation ◽

The Moment

In this article, a semiclassical, microscopic model (dubbed SMRM) is derived to describe collective rotation in deformed nuclei. The SMRM is derived by transforming the time-dependent, multiparticle Schrodinger equation to a rotating frame whose axes are chosen to coincide with the principal axes of the expectation value of an arbitrary, second-rank, symmetric, tensor (nuclear shape) operator [Formula: see text]. This transformation circumvents the difficulty associated with the introduction of redundant particle coordinates in the Villars' transformation. The SMRM Schrodinger equation, which resembles the cranking model (CM) equation, is a time-dependent, time-reversal-invariant, nonlinear integro-differential equation. In this equation, the angular velocity is determined by the wave function and deformation–rotation shear operators, and this introduces the nonlinearity in the equation. A variational method is proposed and justified to obtain: a stationary solution of the SMRM Schrodinger equation in the Rayleigh–Ritz Hartree–Fock particle–hole formalism, the rotational energy increment, and the associated moment of inertia. When exchange interaction terms are neglected or a separable interaction is used, the SMRM moment of inertia is shown to reduce to that given by the CM provided that a certain relationship exists between the moment of inertia and the expectation value of [Formula: see text]. However, the SMRM and CM wave functions are not the same (SMRM preserves and CM violates time-reversal invariance) implying that the calculated values of other parameters, including the moment of inertia at higher values of the angular momentum, may not be the same in the two models. In any case, the SMRM derives the CM moment of inertia from a microscopic, time-reversal invariant, nonlinear theory.PACS Nos.: 21.60.Ev, 21.60.Fw, 21.60.Jz

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Flow Field and its Flowability in a Stirred Tank with a Plate Propeller

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.781-784.2817 ◽

2013 ◽

Vol 781-784 ◽

pp. 2817-2822

Author(s):

Yong Bin Lai ◽

Ya Li Sun ◽

Yi Jun Zhou ◽

Kun Li ◽

Jun Feng Shu ◽

...

Keyword(s):

Kinetic Energy ◽

Flow Field ◽

Turbulent Kinetic Energy ◽

Axial Velocity ◽

Strong Influence ◽

Tangential Velocity ◽

Stirred Tank ◽

Fluctuation Velocity ◽

Maximum Value ◽

Phase Doppler Particle Analyzer

The flow field produced by a plate propeller in a fully baffled flat bottomed cylindrical stirred tank with the diameter of 300 mm was measured using phase doppler particle analyzer. The radial distributions of the time-averaged, fluctuation velocity and turbulent kinetic energy were analyzed. The effects of off-bottom clearance and baffle on the flow field were investigated. The results showed that the fluctuation velocity and turbulent kinetic energy increased with increasing off-bottom clearance in the impeller region; meanwhile, the maximum values of the time-averaged and fluctuation velocity moved to the center of the stirred tank. The maximum axial velocity decreased with increasing off-bottom clearance in the bulk flow. The turbulent kinetic energy was higher in the impeller region. The maximum value of the turbulent kinetic energy increased with increasing off-bottom clearance and occurred near the end of the impeller. The baffle hindered the tangential velocity and exerted strong influence on the turbulent kinetic energy. The flow field in front of the baffle reflected the distribution of the turbulent kinetic energy in the impeller region.

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Deformability of discs in turbulence

Journal of Fluid Mechanics ◽

10.1017/jfm.2021.1035 ◽

2021 ◽

Vol 933 ◽

Author(s):

Gautier Verhille

Keyword(s):

Kinetic Energy ◽

Turbulent Kinetic Energy ◽

Turbulent Flows ◽

Moment Of Inertia ◽

Inertia Tensor ◽

Experimental Results ◽

Bending Modulus ◽

The Moment ◽

Qualitative Argument

The aim of this study is to investigate experimentally the transition from a rigid regime to a deformed regime for flexible discs freely advected in turbulent flows. For a given disc, the amplitude of the deformation is expected to increase when its bending modulus decreases or when the turbulent kinetic energy increases. To quantify this qualitative argument, experiments are performed where the deformation of flexible discs is measured using three cameras. The amplitude of the deformation has been characterised by the eigenvalues of the moment of inertia tensor. Experimental results exhibit a transition from a rigid regime to a deformed regime that depends on the size, the density and the flexibility of the disc and the turbulent kinetic energy. The modelling of this transition is a generalisation and an extension of the previous models used to characterise the deformation of flexible fibres in turbulent flows.

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