37,052 research outputs found
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
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
The Grad-Shafranov Reconstruction of Toroidal Magnetic Flux Ropes: Method Development and Benchmark Studies
We develop an approach of Grad-Shafranov (GS) reconstruction for toroidal
structures in space plasmas, based on in-situ spacecraft measurements. The
underlying theory is the GS equation that describes two-dimensional
magnetohydrostatic equilibrium as widely applied in fusion plasmas. The
geometry is such that the arbitrary cross section of the torus has rotational
symmetry about the rotation axis , with a major radius . The magnetic
field configuration is thus determined by a scalar flux function and a
functional that is a single-variable function of . The algorithm is
implemented through a two-step approach: i) a trial-and-error process by
minimizing the residue of the functional to determine an optimal
axis orientation, and ii) for the chosen , a minimization process
resulting in the range of . Benchmark studies of known analytic solutions
to the toroidal GS equation with noise additions are presented to illustrate
the two-step procedures and to demonstrate the performance of the numerical GS
solver, separately. For the cases presented, the errors in and are
9 and 22\%, respectively, and the relative percent error in the
numerical GS solutions is less than 10\%. We also make public the computer
codes for these implementations and benchmark studies.Comment: submitted to Sol. Phys. late Dec 2016; under review; code will be
made public once review is ove
Throughput Maximization and Fairness Assurance in Data and Energy Integrated Communication Networks
A typical data and energy integrated network (DEIN) conceives a conventional base station (BS), which is capable of simultaneously transmitting the data and energy to user equipments (UEs) during the downlink (DL) transmissions by invoking the time-division-multiple-access (TDMA) protocol in the medium access control (MAC) layer. Several UEs operating in this DEIN are capable of harvesting the energy from the DL transmissions by adopting the power splitting (PS) technique and they are also capable of exploiting the harvested energy for powering their uplink (UL) data transmissions by invoking the TDMA protocol in the MAC layer. Both of the UL sum-throughput and the UL fair-throughput of the DEIN is maximised by deciding the duration of each time-slot during the DL/UL transmissions and by determining the optimal PS factor for each UE. Both of these optimization problems are finally solved by the classic method of Lagrange multipliers in close-form. An interesting observation shows that supporting low-throughput data services during the DL transmissions does not degrade the wireless energy transfer and hence does not reduce the throughput of the UL transmissions
Indirect exchange of magnetic impurities in zigzag graphene ribbon
We use quantum Monte Carlo method to study the indirect coupling between two
magnetic impurities on the zigzag edge of graphene ribbon, with respect to the
chemical potential . We find that the spin-spin correlation between two
adatoms located on the nearest sites in the zigzag edge are drastically
suppressed around the zero-energy. As we switch the system away from
half-filling, the antiferromagnetic correlation is first enhanced and then
decreased. If the two adatoms are adsorbed on the sites belonging to the same
sublattice, we find similar behavior of spin-spin correlation except for a
crossover from ferromagnetic to antiferromagentic correlation in the vicinity
of zero-energy. We also calculated the weight of different components of
d-electron wave function and local magnet moment for various values of
parameters, and all the results are consistent with those of spin-spin
correlation between two magnetic impurities.Comment: 3 pages, 4 figures, conference proceedin
Ternary Hom-Nambu-Lie algebras induced by Hom-Lie algebras
The purpose of this paper is to investigate ternary multiplications
constructed from a binary multiplication, linear twisting maps and a trace
function. We provide a construction of ternary Hom-Nambu and Hom-Nambu-Lie
algebras starting from a binary multiplication of a Hom-Lie algebra and a trace
function satisfying certain compatibility conditions involving twisting maps.
We show that mutual position of kernels of twisting maps and the trace play
important role in this context, and provide examples of Hom-Nambu-Lie algebras
obtained using this construction
Parametric Instability of Supersonic Shear Layers Induced by Periodic Mach Waves
It is suggested that parametric instability can be induced in a confined supersonic shear layer by the use of a periodic Mach wave system generated by a wavy wall. The existence of such an instability solution is demonstrated computationally by solving the Floquet system of equations. The solution is constructed by means of a Fourier-Chebyshev expansion. Numerical convergence is assured by using a very large number of Fourier and Chebyshev basis functions. The computed growth rate of the induced flow instability is found to vary linearly with the amplitude of the mach waves when the amplitude is not excessively large. This ensures that the instability is, indeed, tied to the presence of the Mach waves. It is proposed that enhanced mixing of supersonic shear layers may be achieved by the use of such a periodic Mach wave system through the inducement of parametric instabilities in the flow. © 1991 American Institute of Physics
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