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 $N-1$ curved hypersurface embedded in $N$ 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 $Z$, with a major radius $r_0$. The magnetic field configuration is thus determined by a scalar flux function $\Psi$ and a functional $F$ that is a single-variable function of $\Psi$. The algorithm is implemented through a two-step approach: i) a trial-and-error process by minimizing the residue of the functional $F(\Psi)$ to determine an optimal $Z$ axis orientation, and ii) for the chosen $Z$, a $\chi^2$ minimization process resulting in the range of $r_0$. 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 $Z$ and $r_0$ are 9$^\circ$ 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 $\mu$. 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

H2A.Z facilitates access of active and repressive complexes to chromatin in embryonic stem cell self-renewal and differentiation.

SummaryChromatin modifications have been implicated in the self-renewal and differentiation of embryonic stem cells (ESCs). However, the function of histone variant H2A.Z in ESCs remains unclear. We show that H2A.Z is highly enriched at promoters and enhancers and is required for both efficient self-renewal and differentiation of murine ESCs. H2A.Z deposition leads to an abnormal nucleosome structure, decreased nucleosome occupancy, and increased chromatin accessibility. In self-renewing ESCs, knockdown of H2A.Z compromises OCT4 binding to its target genes and leads to decreased binding of MLL complexes to active genes and of PRC2 complex to repressed genes. During differentiation of ESCs, inhibition of H2A.Z also compromises RA-induced RARα binding, activation of differentiation markers, and the repression of pluripotency genes. We propose that H2A.Z mediates such contrasting activities by acting as a general facilitator that generates access for a variety of complexes, both activating and repressive