8,956 research outputs found
The centripetal force law and the equation of motion for a particle on a curved hypersurface
It is pointed out that the current form of extrinsic equation of motion for a
particle constrained to remain on a hypersurface is in fact a half-finished
version for it is established without regard to the fact that the particle can
never depart from the geodesics on the surface. Once the fact be taken into
consideration, the equation takes that same form as that for centripetal force
law, provided that the symbols are re-interpreted so that the law is applicable
for higher dimensions. The controversial issue of constructing operator forms
of these equations is addressed, and our studies show the quantization of
constrained system based on the extrinsic equation of motion is favorable.Comment: 5 pages, major revisio
Heisenberg equation for a nonrelativistic particle on a hypersurface: from the centripetal force to a curvature induced force
In classical mechanics, a nonrelativistic particle constrained on an
curved hypersurface embedded in flat space experiences the centripetal
force only. In quantum mechanics, the situation is totally different for the
presence of the geometric potential. We demonstrate that the motion of the
quantum particle is "driven" by not only the the centripetal force, but also a
curvature induced force proportional to the Laplacian of the mean curvature,
which is fundamental in the interface physics, causing curvature driven
interface evolution.Comment: 4 page
On the nonlinear stability of a high-speed, axisymmetric boundary layer
The stability of a high-speed, axisymmetric boundary layer is investigated using secondary instability theory and direct numerical simulation. Parametric studies based on the temporal secondary instability theory identify subharmonic secondary instability as a likely path to transition on a cylinder at Mach 4.5. The theoretical predictions are validated by direct numerical simulation at temporally-evolving primary and secondary disturbances in an axisymmetric boundary-layer flow. At small amplitudes of the secondary disturbance, predicted growth rates agree to several significant digits with values obtained from the spectrally-accurate solution of the compressible Navier-Stokes equations. Qualitative agreement persists to large amplitudes of the secondary disturbance. Moderate transverse curvature is shown to significantly affect the growth rate of axisymmetric second mode disturbances, the likely candidates of primary instability. The influence of curvature on secondary instability is largely indirect but most probably significant, through modulation of the primary disturbance amplitude. Subharmonic secondary instability is shown to be predominantly inviscid in nature, and to account for spikes in the Reynolds stress components at or near the critical layer
Luminosity goals for a 100-TeV pp collider
We consider diverse examples of science goals that provide a framework to
assess luminosity goals for a future 100-TeV proton-proton collider.Comment: 11 pages, 9 figures. Discussion white paper, arising from the
programme on "The future of high energy physics", January 5-30, 2015, Jockey
Club Institute for Advanced Study of the Hong Kong University of Science and
Technology
The transition prediction toolkit: LST, SIT, PSE, DNS, and LES
The e(sup N) method for predicting transition onset is an amplitude ratio criterion that is on the verge of full maturation for three-dimensional, compressible, real gas flows. Many of the components for a more sophisticated, absolute amplitude criterion are now emerging: receptivity theory, secondary instability theory, parabolized stability equations approaches, direct numerical simulation and large-eddy simulation. This paper will provide a description of each of these new theoretical tools and provide indications of their current status
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