Strong Coupling of a Cavity QED Architecture for a Current-biased Flux Qubit

We propose a scheme for a cavity quantum electrodynamics (QED) architecture for a current-biased superconducting flux qubit with three Josephson junctions. The qubit operation is performed by using a bias current coming from the current mode of the circuit resonator. If the phase differences of junctions are to be coupled with the bias current, the Josephson junctions should be arranged in an asymmetric way in the qubit loop. Our QED scheme provides a strong coupling between the flux qubit and the transmission line resonator of the circuit.Comment: 5 pages, 3 figure

Equilibrium Sequences and Gravitational Instability of Rotating Isothermal Rings

Nuclear rings at centers of barred galaxies exhibit strong star formation activities. They are thought to undergo gravitational instability when sufficiently massive. We approximate them as rigidly-rotating isothermal objects and investigate their gravitational instability. Using a self-consistent field method, we first construct their equilibrium sequences specified by two parameters: alpha corresponding to the thermal energy relative to gravitational potential energy, and R_B measuring the ellipticity or ring thickness. Unlike in the incompressible case, not all values of R_B yield an isothermal equilibrium, and the range of R_B for such equilibria shrinks with decreasing alpha. The density distributions in the meridional plane are steeper for smaller alpha, and well approximated by those of infinite cylinders for slender rings. We also calculate the dispersion relations of nonaxisymmetric modes in rigidly-rotating slender rings with angular frequency Omega_0 and central density rho_max. Rings with smaller alpha are found more unstable with a larger unstable range of the azimuthal mode number. The instability is completely suppressed by rotation when Omega_0 exceeds the critical value. The critical angular frequency is found to be almost constant at ~ 0.7 sqrt(G*rho_c) for alpha > 0.01 and increases rapidly for smaller alpha. We apply our results to a sample of observed star-forming rings and confirm that rings without a noticeable azimuthal age gradient of young star clusters are indeed gravitationally unstable.Comment: 17 figures and 2 tables; Accepted for publication in the Ap

Construction of periodic adapted orthonormal frames on closed space curves

The construction of continuous adapted orthonormal frames along C1 closed–loop spatial curves is addressed. Such frames are important in the design of periodic spatial rigid–body motions along smooth closed paths. The construction is illustrated through the simplest non–trivial context — namely, C1 closed loops defined by a single Pythagorean–hodograph (PH) quintic space curve of a prescribed total arc length. It is shown that such curves comprise a two–parameter family, dependent on two angular variables, and they degenerate to planar curves when these parameters differ by an integer multiple of π. The desired frame is constructed through a rotation applied to the normal–plane vectors of the Euler–Rodrigues frame, so as to interpolate a given initial/final frame orientation. A general solution for periodic adapted frames of minimal twist on C1 closed–loop PH curves is possible, although this incurs transcendental terms. However, the C1 closed–loop PH quintics admit particularly simple rational periodic adapted frames