Kinetic energy transformation

Freeman, A. J., and Lowdin, P.-O., On a quantum mechanical kinetic energy transformation."... 

Secular loss of heat of earth through radiation into space Portion of earth s kinetic energy transformed into heat as a result A E 1.1055 J/century... 

Portion of earth s kinetic energy transformed into heat as a result ... 

A structure of the opposed jet interaction zone must provide the maximal efficiency of particle kinetic energy transformation to get a fine product. 

We can see that if particles of similar masses and similar velocities move to meet each other, their velocity after absolutely inelastic collision is zero, and, consequently, the whole kinetic energy transforms into internal energy. 

The potential energy part is diagonal in the coordinate representation, and we drop the hat indicating an operator henceforth. The kinetic energy part may be evaluated by transfonning to the momentum representation and carrying out a Fourier transform. The result is... 

Impact and Erosion. Impact involves the rapid appHcation of a substantial load to a relatively small area. Most of the kinetic energy from the impacting object is transformed into strain energy for crack propagation. Impact can produce immediate failure if there is complete penetration of the impacted body or if the impact induces a macrostress in the piece, causing it to deflect and then crack catastrophically. Failure can also occur if erosion reduces the cross section and load-bearing capacity of the component, causes a loss of dimensional tolerance, or causes the loss of a protective coating. Detailed information on impact and erosion is available (49). 

Fragments. As will be explained in Section 6.4, between 20% and 50% of available explosion energy may be transformed into kinetic energy of fragments and liquid or solid contents. 

A unitary transformation is then introduced whieh diagonalizes the FG matrix, yielding eigenvalues s, and eigenvectors q,. The kinetic energy operator is still diagonal in these eoordinates. 

Temperature swings following frontal passages are common in North America and Eurasia, but are rare in the tropics, where differences in cloudiness and precipitation arise from seasonal variability in thermal forcing. Poleward from the tropical regions, extratropical cyclones transform latitudinal temperature gradients into kinetic energy. 

The kinetic energy stored in the flywheel rotor is proportional to the mass of the rotor and the square of its linear velocity. Transformed into a cylindrical system, the stored kinetic energy, KE, is... 

Often the actions of the radial parts of the kinetic energy (see Section IIIA) on a wave packet are accomplished with fast Fourier transforms (FFTs) in the case of evenly spaced grid representations [24] or with other types of discrete variable representations (DVRs) [26, 27]. Since four-atom and larger reaction dynamics problems are computationally challenging and can sometimes benefit from implementation within parallel computing environments, it is also worthwhile to consider simpler finite difference (FD) approaches [25, 28, 29], which are more amenable to parallelization. The FD approach we describe here is a relatively simple one developed by us [25]. We were motivated by earlier work by Mazziotti [28] and we note that later work by the same author provides alternative FD methods and a different, more general perspective [29]. 

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