On a switching control scheme for nonlinear systems with ill-defined relative degree

This paper discusses the applicability of a switching control scheme for a nonlinear system with ill-defined relative degree. The control scheme switches between exact and approximate input-output linearisation control laws. Unlike a linear system under a switching control scheme, the equilibria of a nonlinear system may change with the switching. It is pointed out that this is not sufficient to cause instability. When the region of the approximate linearisation control law is attractive to the exact zero dynamics, it is possible that the closed-loop system under the switching control scheme is still stable. The results in this paper shows that the switching control scheme proposed in Tomlin and Sastry (Systems Control Lett. 35(3) (1998) 145) is applicable for a wider class of nonlinear systems

An asymmetrical synchrotron model for knots in the 3C 273 jet

To interpret the emission of knots in the 3C 273 jet from radio to X-rays, we propose a synchrotron model in which, owing to the shock compression effect, the injection spectra from a shock into the upstream and downstream emission regions are asymmetric. Our model could well explain the spectral energy distributions of knots in the 3C 273 jet, and predictions regarding the knots spectra could be tested by future observations.Comment: 9 pages, 1 figure, 1 table, new version accepted for publication in Ap

Tunneling Qubit Operation on a Protected Josephson Junction Array

We discuss a protected quantum computation process based on a hexagon Josephson junction array. Qubits are encoded in the punctured array, which is topologically protected. The degeneracy is related to the number of holes. The topological degeneracy is lightly shifted by tuning the flux through specific hexagons. We also show how to perform single qubit operation and basic quantum gate operations in this system.Comment: 8 pages, 4 figures. The published version in Phys. Rev., A81(2010)01232

Towards A Holographic Model of D-Wave Superconductors

The holographic model for S-wave high T_c superconductors developed by Hartnoll, Herzog and Horowitz is generalized to describe D-wave superconductors. The 3+1 dimensional gravitational theory consists a symmetric, traceless second-rank tensor field and a U(1) gauge field in the background of the AdS black hole. Below T_c the tensor field which carries the U(1) charge undergoes the Higgs mechanism and breaks the U(1) symmetry of the boundary theory spontaneously. The phase transition characterized by the D-wave condensate is second order with the mean field critical exponent beta = 1/2. As expected, the AC conductivity is isotropic below T_c and the system becomes superconducting in the DC limit but has no hard gap.Comment: 14 pages, 2 figures, Some typos corrected, Matched with the published versio

Millennial slip rate of the Longitudinal Valley fault from river terraces: Implications for convergence across the active suture of eastern Taiwan

The Longitudinal Valley fault is a key element in the active tectonics of Taiwan. It is the principal structure accommodating convergence across one of the two active sutures of the Taiwan orogeny. To understand more precisely its role in the suturing process, we analyzed fluvial terraces along the Hsiukuluan River, which cuts across the Coastal Range in eastern Taiwan in the fault's hanging wall block. This allowed us to determine both its subsurface geometry and its long-term slip rate. The uplift pattern of the terraces is consistent with a fault-bend fold model. Our analysis yields a listric geometry, with dips decreasing downdip from about 50° to about 30° in the shallowest 2.5 km. The Holocene rate of dip slip of the fault is about 22.7 mm/yr. This rate is less than the 40 mm/yr rate of shortening across the Longitudinal Valley derived from GPS measurements. The discrepancy may reflect an actual difference in millennial and decadal rates of convergence. An alternative explanation is that the discrepancy is accommodated by a combination of slip on the Central Range fault and subsidence of the Longitudinal Valley floor. The shallow, listric geometry of the Longitudinal Valley fault at the Hsiukuluan River valley differs markedly from the deep listric geometry illuminated by earthquake hypocenters near Chihshang, 45 km to the south. We hypothesize that this fundamental along-strike difference in geometry of the fault is a manifestation of the northward maturation of the suturing of the Luzon volcanic arc to the Central Range continental sliver

Extremely Sub-wavelength Planar Magnetic Metamaterials

We present highly sub-wavelength magnetic metamaterials designed for operation at radio frequencies (RFs). A dual layer design consisting of independent planar spiral elements enables experimental demonstration of a unit cell size (a) that is ~ 700 times smaller than the resonant wavelength ({\lambda}0). Simulations indicate that utilization of a conductive via to connect spiral layers permits further optimization and we achieve a unit cell that is {\lambda}0/a ~ 2000. Magnetic metamaterials are characterized by a novel time domain method which permits determination of the complex magnetic response. Numerical simulations are performed to support experimental data and we find excellent agreement. These new designs make metamaterial low frequency experimental investigations practical and suggest their use for study of magneto-inductive waves, levitation, and further enable potential RF applications.Comment: 5 pages, 4 figure

The Last Eight-Billion Years of Intergalactic SiIV Evolution

We identified 24 SiIV absorption systems with z <~ 1 from a blind survey of 49 low-redshift quasars with archival Hubble Space Telescope ultraviolet spectra. We relied solely on the characteristic wavelength separation of the doublet to automatically detect candidates. After visual inspection, we defined a sample of 20 definite (group G = 1) and 4 "highly-likely" (G = 2) doublets with rest equivalent widths W_r for both lines detected at > 3 sigma. The absorber line density of the G = 1 doublets was dN_SiIV/dX = 1.4+0.4/-0.3 for log N(Si+3) > 12.9. The best-fit power law to the G = 1 frequency distribution of column densities f(N(Si+3)) had normalization k = (1.2+0.5/-0.4) x 10^-14 cm2 and slope alpha = -1.6+0.3/-0.3. Using the power-law model of f(N(Si+3)), we measured the Si+3 mass density relative to the critical density: Omega(Si+3) = (3.7+2.8/-1.7) x 10^-8 for 13 < log N(Si+3) < 15. From Monte Carlo sampling of the distributions, we estimated our value to be a factor of 4.8+3.0/-1.9 higher than the 2 . From a simple linear fit to Omega(Si+3) over the age of the Universe, we estimated a slow and steady increase from z = 5.5 --> 0 with dOmega/dt_age = (0.61+/-0.23) x 10^-8 Gyr^-1. We compared our ionic ratios N(Si+3)/N(C+3) to a 2 < z < 4.5 sample and concluded, from survival analysis, that the two populations are similar, with median = 0.16.Comment: 18 pages, 9 figures, 4 tables, added figures and new analysis, results have changed, accepted to Ap

Neutron-proton effective mass splitting in neutron-rich matter at normal density from analyzing nucleon-nucleus scattering data within an isospin dependent optical model

The neutron-proton effective $k$-mass splitting in asymmetric nucleonic matter of isospin asymmetry $\delta$ and normal density is found to be $m^{*}_{n-p}\equiv(m^{*}_{n}-m^{*}_{p})/m=(0.41 \pm0.15)\delta$ from analyzing globally 1088 sets of reaction and angular differential cross sections of proton elastic scattering on 130 targets with beam energies from 0.783 MeV to 200 MeV, and 1161 sets of data of neutron elastic scattering on 104 targets with beam energies from 0.05 MeV to 200 MeV within an isospin dependent non-relativistic optical potential model. It sets a useful reference for testing model predictions on the momentum dependence of the nucleon isovector potential necessary for understanding novel structures and reactions of rare isotopes.Comment: Published version, Physics Letters B743 (2015) 40