Gravitational lensing statistical properties in general FRW cosmologies with dark energy component(s): analytic results

Various astronomical observations have been consistently making a strong case for the existence of a component of dark energy with negative pressure in the universe. It is now necessary to take the dark energy component(s) into account in gravitational lensing statistics and other cosmological tests. By using the comoving distance we derive analytic but simple expressions for the optical depth of multiple image, the expected value of image separation and the probability distribution of image separation caused by an assemble of singular isothermal spheres in general FRW cosmological models with dark energy component(s). We also present the kinematical and dynamical properties of these kinds of cosmological models and calculate the age of the universe and the distance measures, which are often used in classical cosmological tests. In some cases we are able to give formulae that are simpler than those found elsewhere in the literature, which could make the cosmological tests for dark energy component(s) more convenient.Comment: 14 pages, no figure, Latex fil

Testing Cluster Structure of Graphs

We study the problem of recognizing the cluster structure of a graph in the framework of property testing in the bounded degree model. Given a parameter $\varepsilon$, a $d$-bounded degree graph is defined to be $(k, \phi)$-clusterable, if it can be partitioned into no more than $k$ parts, such that the (inner) conductance of the induced subgraph on each part is at least $\phi$ and the (outer) conductance of each part is at most $c_{d,k}\varepsilon^4\phi^2$, where $c_{d,k}$ depends only on $d,k$. Our main result is a sublinear algorithm with the running time $\widetilde{O}(\sqrt{n}\cdot\mathrm{poly}(\phi,k,1/\varepsilon))$ that takes as input a graph with maximum degree bounded by $d$, parameters $k$, $\phi$, $\varepsilon$, and with probability at least $\frac23$, accepts the graph if it is $(k,\phi)$-clusterable and rejects the graph if it is $\varepsilon$-far from $(k, \phi^*)$-clusterable for $\phi^* = c'_{d,k}\frac{\phi^2 \varepsilon^4}{\log n}$, where $c'_{d,k}$ depends only on $d,k$. By the lower bound of $\Omega(\sqrt{n})$ on the number of queries needed for testing graph expansion, which corresponds to $k=1$ in our problem, our algorithm is asymptotically optimal up to polylogarithmic factors.Comment: Full version of STOC 201

Improved rotor-position estimation by signal injection in brushless AC motors, accounting for cross-coupling magnetic saturation

This paper presents an improved signal-injection- based sensorless-control method for permanent-magnet brushless ac (BLAC) motors, accounting for the influence of cross-coupling magnetic saturation between the d- and q-axes. The d- and q-axis incremental self-inductances, the incremental mutual inductance between the d-axis and q-axis, and the cross-coupling factor are determined by finite-element analysis. An experimental method is proposed for measuring the cross-coupling factor which can be used directly in the sensorless-control scheme. Both measurements and predictions show that a significant improvement in the accu- racy of the rotor-position estimation can be achieved under both dynamic and steady-state operation compared with that which is obtained with the conventional signal-injection method

Influence of machine topology and cross-coupling magnetic saturation on rotor position estimation accuracy in extended back-EMF based sensorless PM brushless AC drives

The influence of the machine topology and dq-axis cross-coupling on the rotor position estimation error in an extended back-EMF based sensorless brushless AC drive is investigated by both finite element analysis and experimentally on four brushless AC machines having different rotor topologies, viz. interior circumferentially magnetized, interior radially magnetized, surface-mounted, and inset magnets. The d- and q- axis apparent self- and mutual-inductances, Ld, Lq, Ldq and Lqd, are predicted by finite element analysis for various d- and q-axis currents. The error in the estimated rotor position of the four machines is investigated and compared when (a) the influence of magnetic saturation is neglected, (b) only the influence of the dq-axis current on Lq is considered, but dq-axis cross-coupling magnetic saturation is neglected, and (c) the influence of dq-axis cross-coupling magnetic saturation is taken into account. It is shown that the error is more strongly influenced by the q-axis current/permeance than the dq-axis current/permeance, since the dq-axis current does not distort the symmetrical field distribution about the q-axis, and that dq-axis cross-coupling magnetic saturation can significantly affect the accuracy of the rotor position estimation. However, by introducing an apparent mutual winding inductance in the extended back-EMF based sensorless method, the error in all four machines under consideration is reduced significantly, to a similar level to that which results with surface-mounted magnet machines

Polarization and dispersion properties of elliptical hole golden spiral photonic crystal fiber

An elliptical air-hole golden spiral photonic crystal fiber (EGS-PCF) is analyzed with the full-vectorial finite element method. The air-holes in the EGS-PCF are arranged in a spiral pattern governed by the Golden Ratio, where the design has been inspired by the optimal arrangement of seeds found in nature. The EGS-PCF exhibits extremely high birefringence (∼0.022 at operating wavelength 1550 nm) which is particularly useful for generating a polarization stable supercontinuum (SC). The fiber can also be designed to have a Zero Dispersion Wavelength (ZDW) at a suitable wavelength for only one polarization and large negative dispersion for the other, leading to a single-polarization SC. In addition, the fiber dispersion can be designed to obtain ZDWs at 800 nm and 1064 nm simultaneously, which can facilitate broadband supercontinuum generation (SCG) through multi-wavelength pumping

Next-to-Maximal Helicity Violating Amplitudes in Gauge Theory

Using the novel diagrammatic rules recently proposed by Cachazo, Svrcek, and Witten, I give a compact, manifestly Lorentz-invariant form for tree-level gauge-theory amplitudes with three opposite helicities.Comment: 12 pages, 1 figur

Atomic scale elastic textures coupled to electrons in superconductors

We present an atomic scale theory of lattice distortions using strain related variables and their constraint equations. Our approach connects constrained atomic length scale variations to continuum elasticity and describes elasticity at all length scales. We apply the general approach to a two-dimensional square lattice with a monatomic basis, and find the atomic scale elastic textures around a structural domain wall and a single defect, as exemplary textures. We clarify the microscopic origin of gradient terms, some of which are included phenomenologically in Landau-Ginzburg theory. The obtained elastic textures are used to investigate the effects of elasticity-driven lattice deformation on the nanoscale electronic structure in superconductor by solving the Bogliubov-de Gennes equations with the electronic degrees of freedom coupled to the lattice ones. It is shown that the order parameter is depressed in the regions where the lattice deformation takes place. The calculated local density of states suggests the electronic structure is strongly modulated as a response to the lattice deformation-- the elasticity propagates the electronic response over long distances. In particular, it is possible for the trapping of low-lying quasiparticle states around the defects. These predictions could be directly tested by STM experiments in superconducting materials.Comment: Proceeding paper for "Conference on Dynamic Inhomogeneities in Complex Oxides" (to appear in J. Superconductivity