The equivalence problem and rigidity for hypersurfaces embedded into hyperquadrics

We consider the class of Levi nondegenerate hypersurfaces $M$ in \bC^{n+1} that admit a local (CR transversal) embedding, near a point $p\in M$, into a standard nondegenerate hyperquadric in $\Bbb C^{N+1}$ with codimension $k:=N-n$ small compared to the CR dimension $n$ of $M$. We show that, for hypersurfaces in this class, there is a normal form (which is closely related to the embedding) such that any local equivalence between two hypersurfaces in normal form must be an automorphism of the associated tangent hyperquadric. We also show that if the signature of $M$ and that of the standard hyperquadric in \bC^{N+1} are the same, then the embedding is rigid in the sense that any other embedding must be the original embedding composed with an automorphism of the quadric

Modeling of gyrosynchrotron radio emission pulsations produced by MHD loop oscillations in solar flares

A quantitative study of the observable radio signatures of the sausage, kink, and torsional MHD oscillation modes in flaring coronal loops is performed. Considering first non-zero order effect of these various MHD oscillation modes on the radio source parameters such as magnetic field, line of sight, plasma density and temperature, electron distribution function, and the source dimensions, we compute time dependent radio emission (spectra and light curves). The radio light curves (of both flux density and degree of polarization) at all considered radio frequencies are than quantified in both time domain (via computation of the full modulation amplitude as a function of frequency) and in Fourier domain (oscillation spectra, phases, and partial modulation amplitude) to form the signatures specific to a particular oscillation mode and/or source parameter regime. We found that the parameter regime and the involved MHD mode can indeed be distinguished using the quantitative measures derived in the modeling. We apply the developed approach to analyze radio burst recorded by Owens Valley Solar Array and report possible detection of the sausage mode oscillation in one (partly occulted) flare and kink or torsional oscillations in another flare.Comment: ApJ, accepte

Holomorphic extension of smooth CR-mappings between real-analytic and real-algebraic CR-manifolds

We establish results on holomorphic extension of CR-mappings of class $C^\infty$ between a real-analytic CR-submanifold of \C^N and a real-algebraic CR-submanifold of \C^{N'}

High intermodulation gain in a micromechanical Duffing resonator

In this work we use a micromechanical resonator to experimentally study small signal amplification near the onset of Duffing bistability. The device consists of a PdAu beam serving as a micromechanical resonator excited by an adjacent gate electrode. A large pump signal drives the resonator near the onset of bistability, enabling amplification of small signals in a narrow bandwidth. To first order, the amplification is inversely proportional to the frequency difference between the pump and signal. We estimate the gain to be about 15dB for our device

The Power Flow Angle of Acoustic Waves in Thin Piezoelectric Plates

The curves of slowness and power flow angle (PFA) of quasi-antisymmetric (A0) and quasi-symmetric (S0) Lamb waves as well as quasi-shear-horizontal (SH0) acoustic waves in thin plates of lithium niobate and potassium niobate of X-,Y-, and Z-cuts for various propagation directions and the influence of electrical shorting of one plate surface on these curves and PFA have been theoretically investigated. It has been found that the group velocity of such waves does not coincide with the phase velocity for the most directions of propagation. It has been also shown that S0 and SH0 wave are characterized by record high values of PFA and its change due to electrical shorting of the plate surface in comparison with surface and bulk acoustic waves in the same material. The most interesting results have been verified by experiment. As a whole, the results obtained may be useful for development of various devices for signal processing, for example, electrically controlled acoustic switchers

Proximity Effect in Normal Metal - High Tc Superconductor Contacts

We study the proximity effect in good contacts between normal metals and high Tc (d-wave) superconductors. We present theoretical results for the spatially dependent order parameter and local density of states, including effects of impurity scattering in the two sides, s-wave pairing interaction in the normal metal side (attractive or repulsive), as well as subdominant s-wave paring in the superconductor side. For the [100] orientation, a real combination d+s of the order parameters is always found. The spectral signatures of the proximity effect in the normal metal includes a suppression of the low-energy density of states and a finite energy peak structure. These features are mainly due to the impurity self-energies, which dominate over the effects of induced pair potentials. For the [110] orientation, for moderate transparencies, induction of a d+is order parameter on the superconductor side, leads to a proximity induced is order parameter also in the normal metal. The spectral signatures of this type of proximity effect are potentially useful for probing time-reversal symmetry breaking at a [110] interface.Comment: 10 pages, 10 figure