Tests of nonlocal kinetic energy functionals
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The accuracies of various nonlocal kinetic energy functionals are evaluated by considering the kinetic energies of rare gas atoms and the kinetic energy contributions to the interaction energy (ΔEk) for pairs of rare gas atoms. The most accurate kinetic energy functionals are those that combine the density gradient factors of accurate exchange energy functionals with the Thomas–Fermi (TF) kinetic energy functional; these functionals, including a new one proposed in this paper, give total atomic kinetic energies to within 1%, as well as accurate values of ΔEk. Other gradient-corrected functionals give good results for total kinetic energies, but give poor results for ΔEk.Keywords:
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We probe, using a model system, elastic and kinetic energies for sheared granular materials. For large enough P/Ey (pressure/Young's modulus) and P/ρv2 (P/kinetic energy density) elastic dominates kinetic energy, and energy fluctuations become primarily elastic in nature. This regime has likely been reached in recent experiments. We consider a generalization of the granular temperature, Tg, with both kinetic and elastic terms and that changes smoothly from one regime to the other. This Tg is roughly consistent with a temperature adapted from equilibrium statistical mechanics.
Elastic energy
Mean kinetic temperature
Kinetic Theory
Statistical Mechanics
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Mean kinetic temperature
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Rotational energy
Mean kinetic temperature
Typhoon
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The average kinetic energy is widely used to characterize temperature in molecular dynamics (MD) simulation. In this letter, the applicability of three types of average kinetic energy as measures of temperature is investigated, i.e., the total kinetic energy, kinetic energy without the centroid translation part, and thermal disturbance kinetic energy. Our MD simulations indicate that definitions of temperature based on the kinetic energy including rigid translational or rotational motion may yield unrealistic results. In contrast, the thermal disturbance kinetic energy has wider applicability to temperature computation in non-equilibrium molecular dynamics simulation. If small samples need to be used for local temperature, then a calibration approach is proposed to eliminate the sample-size dependence of the average disturbance kinetic energy.
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Rotational energy
Typhoon
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Tsai and MacDonald (1973, 1978) published a critical analysis of the authors' molecular dynamic simulation of shockwave propagation. Most of their criticism was directed to the authors' definition of temperature and kinetic energy. It is shown that their analysis is incorrect and that the authors' calculation of kinetic energy is correct and the definition of temperature is reasonable. Most of the misunderstanding arose from the other not understanding that all the authors' calculations were performed in a stationary frame of reference. It is further shown that, when there is a variation in the planar velocity, the Tsai-MacDonald local kinetic temperature is neither equal to the local kinetic energy (expressed as temperature) nor does it have the characteristics of temperature.
Mean kinetic temperature
Kinetic Theory
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The kinetic theory of rarefied gases is used to show that there is a difference between the kinetic temperature and the thermodynamic one. The former represents the mean kinetic energy of the molecules while the latter is the one measured by a contact thermometer. The argument is based upon a recent paper [1] by Müller and Ruggeri.
Kinetic Theory
Thermodynamic temperature
Thermometer
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A new terminal area energy management method is proposed for the suborbital vehicle which adopts many parameters;energy and azimuth for it are controlled separately,kinetic energy and potential energy decrease matched.The energy control method based on energy profile gets angle of attack by position of the energy/range what takes the kinetic energy and potential energy as restriction,and takes the range as optimization.Then it gives three attitude angles.The simulation tests for the TAEM show that this method mentioned above gets good guidance result.
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Before entering the subject of magnetohydrodynamic dissipation we comment briefly on the question of the supply of kinetic energy to the interstellar gas. This topic has been considered in the 1953 Symposium by Schlüter and myself, and also by Oort. As had been pointed out already by Spitzer in Paris, 1949, the visible HII regions, owing to their excess pressure as compared with the HI regions and the dilute HII regions, must be assumed to expand with a velocity of the order of 10 or 20 km/sec. By this expansion part of the radiation energy of the star is converted into kinetic energy. It was estimated (p. 153 of the proceedings) that a typical HII region around a BO star feeds 10 35 ergs/sec to the instellar gas, and that the number of these regions is such, that each region has to provide kinetic energy on the average to 10 36 −10 37 g of interstellar material. Thus a value of 10 −2 −10 −1 erg g −1 sec −1 was found (which corresponds to 10 −26 −10 −25 erg cm −3 sec −1 , assuming 10 −24 g/cm 3 for the mean density of the interstellar material in the disk).
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