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

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

Performance analysis of contention based bandwidth request mechanisms in WiMAX networks

This article is posted here with the permission of IEEE. The official version can be obtained from the DOI below - Copyright @ 2010 IEEEWiMAX networks have received wide attention as they support high data rate access and amazing ubiquitous connectivity with great quality-of-service (QoS) capabilities. In order to support QoS, bandwidth request (BW-REQ) mechanisms are suggested in the WiMAX standard for resource reservation, in which subscriber stations send BW-REQs to a base station which can grant or reject the requests according to the available radio resources. In this paper we propose a new analytical model for the performance analysis of various contention based bandwidth request mechanisms, including grouping and no-grouping schemes, as suggested in the WiMAX standard. Our analytical model covers both unsaturated and saturated traffic load conditions in both error-free and error-prone wireless channels. The accuracy of this model is verified by various simulation results. Our results show that the grouping mechanism outperforms the no-grouping mechanism when the system load is high, but it is not preferable when the system load is light. The channel noise degrades the performance of both throughput and delay.This work was supported by the U.K. Engineering and Physical Sciences Research Council (EPSRC) under Grant EP/G070350/1 and by the Brunel University’s BRIEF Award

The linear complexity of whiteman's generalized cyclotomic sequences of period p {m+1}q n+1

In this paper, we mainly get three results. First, let p, q be distinct primes with \gcd ((p-1)p,(q-1)q)=\gcd (p-1,q-1)=e ; we give a method to compute the linear complexity of Whiteman's generalized cyclotomic sequences of period p^{m+1}q n+1. Second, if e=4, we compute the exact linear complexity of Whiteman's generalized cyclotomic sequences. Third, if p \equiv q \equiv 5∼({\rm mod}∼8), \gcd (p-1, q-1)=4, and we fix a common primitive root g of both p and q, then 2\in H-{0}=(g), which is a subgroup of the multiplicative group Z-{pq} \ast, if and only if Whiteman's generalized cyclotomic numbers of order 4 depend on the decomposition pq=a^{2}+4b 2 with 4\vert b. © 1963-2012 IEEE.published_or_final_versio

Calorimetric Evidence of Strong-Coupling Multiband Superconductivity in Fe(Te0.57Se0.43) Single Crystal

We have investigated the specific heat of optimally-doped iron chalcogenide superconductor Fe(Te0.57Se0.43) with a high-quality single crystal sample. The electronic specific heat Ce of this sample has been successfully separated from the phonon contribution using the specific heat of a non-superconducting sample (Fe0.90Cu0.10)(Te0.57Se0.43) as a reference. The normal state Sommerfeld coefficient gamma_n of the superconducting sample is found to be ~ 26.6 mJ/mol K^2, indicating intermediate electronic correlation. The temperature dependence of Ce in the superconducting state can be best fitted using a double-gap model with 2Delta_s(0)/kBTc = 3.92 and 2Delta_l(0)/kBTc = 5.84. The large gap magnitudes derived from fitting, as well as the large specific heat jump of Delta_Ce(Tc)/gamma_n*Tc ~ 2.11, indicate strong-coupling superconductivity. Furthermore, the magnetic field dependence of specific heat shows strong evidence for multiband superconductivity

Power Set of Some Quasinilpotent Weighted shifts on lpl^p

For a quasinilpotent operator $T$ on a Banach space $X$, Douglas and Yang defined $k_x=\limsup\limits_{z\rightarrow 0}\frac{\ln\|(z-T)^{-1}x\|}{\ln\|(z-T)^{-1}\|}$ for each nonzero vector $x\in X$, and call $\Lambda(T)=\{k_x: x\ne 0\}$ the power set of $T$. $\Lambda(T)$ have a close link with $T$'s lattice of hyperinvariant subspaces. This paper computes the power set of quasinilpotent weighted shifts on $l^p$ for $1\leq p< \infty$. We obtain the following results: (1) If $T$ is an injective quasinilpotent forward unilateral weighted shift on $l^p(\mathbb{N})$, then $\Lambda(T)=\{1\}$ when $k_{e_0}=1$, where $\{e_n\}_{n=0}^{\infty}$ be the canonical basis for $l^p(\mathbb{N})$; (2) There is a class of backward unilateral weighted shifts on $l^p(\mathbb{N})$ whose power set is $[0,1]$; (3) There exists a bilateral weighted shift on $l^p(\mathbb{Z})$ with power set $[\frac{1}{2},1]$ for $1<p<\infty$.Comment: 22 page