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

Magneto-controlled nonlinear optical materials

We exploit theoretically a magneto-controlled nonlinear optical material which contains ferromagnetic nanoparticles with a non-magnetic metallic nonlinear shell in a host fluid. Such an optical material can have anisotropic linear and nonlinear optical properties and a giant enhancement of nonlinearity, as well as an attractive figure of merit.Comment: 11 pages, 2 figures. To be published in Appl. Phys. Let

Sum-of-squares of polynomials approach to nonlinear stability of fluid flows: an example of application

With the goal of providing the first example of application of a recently proposed method, thus demonstrating its ability to give results in principle, global stability of a version of the rotating Couette flow is examined. The flow depends on the Reynolds number and a parameter characterising the magnitude of the Coriolis force. By converting the original Navier-Stokes equations to a finite-dimensional uncertain dynamical system using a partial Galerkin expansion, high-degree polynomial Lyapunov functionals were found by sum-of-squares-of-polynomials optimization. It is demonstrated that the proposed method allows obtaining the exact global stability limit for this flow in a range of values of the parameter characterising the Coriolis force. Outside this range a lower bound for the global stability limit was obtained, which is still better than the energy stability limit. In the course of the study several results meaningful in the context of the method used were also obtained. Overall, the results obtained demonstrate the applicability of the recently proposed approach to global stability of the fluid flows. To the best of our knowledge, it is the first case in which global stability of a fluid flow has been proved by a generic method for the value of a Reynolds number greater than that which could be achieved with the energy stability approach

Structure and spectroscopy of doped helium clusters using quantum Monte Carlo techniques

We present a comparative study of the rotational characteristics of various molecule-doped 4He clusters using quantum Monte Carlo techniques. The theoretical conclusions obtained from both zero and finite temperature Monte Carlo studies confirm the presence of two different dynamical regimes that correlate with the magnitude of the rotational constant of the molecule, i.e., fast or slow rotors. For a slow rotor, the effective rotational constant for the molecule inside the helium droplet can be determined by a microscopic two-fluid model in which helium densities computed by path integral Monte Carlo are used as input, as well as by direct computation of excited energy levels. For a faster rotor, the conditions for application of the two-fluid model for dynamical analysis are usually not fulfilled and the direct determination of excitation energies is then mandatory. Quantitative studies for three molecules are summarized, showing in each case excellent agreement with experimental results

Investigation of a novel elastic-mechanical wheel transmission under light duty conditions

A novel 'Elastic Engagement and Friction Coupled' (EEFC) mechanical transmission has been proposed recently in which the power is transmitted through elastic tines on the surfaces of the driving and driven wheels. This study introduces new variations of EEFC mechanical wheel transmission ( broadly emulating a gear-pair) with small contact areas for use under light duty conditions. Because a drive of this type inevitably has a strong statistical component, theoretical analysis of the geometrical and mechanical relationships has been attempted by using linear modeling and empirical weightings. Several simple forms of the EEFC wheel transmission are tested under limiting ( slip) conditions for transmission force and transmission coefficients against normal load. Normalized standard deviation of these parameters is used to summarize noise performance. Models and experiments are in reasonable agreement, suggesting that the model parameters reflect important design considerations. EEFC transmissions appear well suited to force regimes of a few tenths of a newton and to have potential for use in, for example, millimetre-scale robots

Dirac cohomology, elliptic representations and endoscopy

The first part (Sections 1-6) of this paper is a survey of some of the recent developments in the theory of Dirac cohomology, especially the relationship of Dirac cohomology with (g,K)-cohomology and nilpotent Lie algebra cohomology; the second part (Sections 7-12) is devoted to understanding the unitary elliptic representations and endoscopic transfer by using the techniques in Dirac cohomology. A few problems and conjectures are proposed for further investigations.Comment: This paper will appear in `Representations of Reductive Groups, in Honor of 60th Birthday of David Vogan', edited by M. Nervins and P. Trapa, published by Springe

Distilling Quantum Entanglement via Mode-Matched Filtering

We propose a new avenue towards distillation of quantum entanglement that is implemented by directly passing the entangled qubits through a mode-matched filter. This approach can be applied to a common class of entanglement impurities appearing in photonic systems where the impurities inherently occupy different spatiotemporal modes than the entangled qubits. As a specific application, we show that our method can be used to significantly purify the telecom-band entanglement generated via the Kerr nonlinearity in single-mode fibers where a substantial amount of Raman-scattering noise is concomitantly produced.Comment: 6 pages, 2 figures, to appear in Phys. Rev.

Diffraction of ultra-cold fermions by quantized light fields: Standing versus traveling waves

We study the diffraction of quantum degenerate fermionic atoms off of quantized light fields in an optical cavity. We compare the case of a linear cavity with standing wave modes to that of a ring cavity with two counter-propagating traveling wave modes. It is found that the dynamics of the atoms strongly depends on the quantization procedure for the cavity field. For standing waves, no correlations develop between the cavity field and the atoms. Consequently, standing wave Fock states yield the same results as a classical standing wave field while coherent states give rise to a collapse and revivals in the scattering of the atoms. In contrast, for traveling waves the scattering results in quantum entanglement of the radiation field and the atoms. This leads to a collapse and revival of the scattering probability even for Fock states. The Pauli Exclusion Principle manifests itself as an additional dephasing of the scattering probability