The Topology of Foliations Formed by the Generic K-Orbits of a Subclass of the Indecomposable MD5-Groups

The present paper is a continuation of [13], [14] of the authors. Specifically, the paper considers the MD5-foliations associated to connected and simply connected MD5-groups such that their Lie algebras have 4-dimensional commutative derived ideal. In the paper, we give the topological classification of all considered MD5-foliations. A description of these foliations by certain fibrations or suitable actions of $\mathbb{R}^{2}$ and the Connes' C*-algebras of the foliations which come from fibrations are also given in the paper.Comment: 20 pages, no figur

Elementary proofs of Berndt's reciprocity laws

Using analytic functional equations, Berndt derived three reciprocity laws connecting five arithmetical sums analogous to Dedekind sums. This paper gives elementary proofs of all three reciprocity laws and obtains them all from a common source, a polynomial reciprocity formula of L. Carlitz

Partial decode-forward for quantum relay channels

A relay channel is one in which a Source and Destination use an intermediate Relay station in order to improve communication rates. We propose the study of relay channels with classical inputs and quantum outputs and prove that a "partial decode and forward" strategy is achievable. We divide the channel uses into many blocks and build codes in a randomized, block-Markov manner within each block. The Relay performs a standard Holevo-Schumacher-Westmoreland quantum measurement on each block in order to decode part of the Source's message and then forwards this partial message in the next block. The Destination performs a novel "sliding-window" quantum measurement on two adjacent blocks in order to decode the Source's message. This strategy achieves non-trivial rates for classical communication over a quantum relay channel.Comment: 7 pages, submission to the 2012 International Symposium on Information Theory (ISIT 2012), Boston, MA, US

Cyclic tridiagonal pairs, higher order Onsager algebras and orthogonal polynomials

The concept of cyclic tridiagonal pairs is introduced, and explicit examples are given. For a fairly general class of cyclic tridiagonal pairs with cyclicity N, we associate a pair of `divided polynomials'. The properties of this pair generalize the ones of tridiagonal pairs of Racah type. The algebra generated by the pair of divided polynomials is identified as a higher-order generalization of the Onsager algebra. It can be viewed as a subalgebra of the q-Onsager algebra for a proper specialization at q the primitive 2Nth root of unity. Orthogonal polynomials beyond the Leonard duality are revisited in light of this framework. In particular, certain second-order Dunkl shift operators provide a realization of the divided polynomials at N=2 or q=i.Comment: 32 pages; v2: Appendices improved and extended, e.g. a proof of irreducibility is added; v3: version for Linear Algebra and its Applications, one assumption added in Appendix about eq. (A.2

Local stiffener and skin pocket buckling prediction by special PASCO modeling technique: Correlation to test data

Waffle panels are often used on fuselage structures such as that of the Space Shuttle. The waffle panel design is an efficient design for carrying biaxial, in-plane, and shear loads. The WAFFLE program was designed for application on waffle panels. The Panel Analysis and Sizing Code (PASCO) program was designed for analyzing and sizing uniaxially stiffened panels. The application of the PASCO program in conjunction with the WAFFLE program is discussed to account for both the fillet radius and the presence of stiffness in both directions. The results of the tests are used to verify that these adjustments are valid and necessary if accurate analysis of the waffle panel is to be achieved

Coupled THM analysis of long-term anisotropic convergence in the full-scale micro tunnel excavated in the Callovo-Oxfordian argillite

The main purpose of this paper is to analyse the convergence measurements of the ALC1604 in situ heating test carried out in the Callovo-Oxfordian claystone formation (COx) in the Meuse/Haute-Marne underground research laboratory (MHM URL). The concept of the test consists of horizontal micro-tunnel, equipped with a steel casing. The micro-tunnel is excavated in the direction of the horizontal principal major stress (sH). In situ observations showed anisotropic convergence with the maximum and minimum values in the horizontal and vertical directions, respectively. Coupled THM numerical analyses have been carried out to provide a structured framework for interpretation, and to enhance understanding of THM behaviour of Callovo-Oxfordian claystone. However, a special mechanical constitutive law is adopted for the description of the time-dependent anisotropic behaviour of the COx. The simulation of the test using this enhanced model provides a satisfactory reproduction of the THM long-term anisotropic convergence results. It also provides a better understanding of the observed test response.Postprint (published version

Editorial

We use a linear FROG technique based on electro-optic modulation to fully characterise for the first time pulses from a 1.06 µm FP laser diode and design a grating to provide optimum pulse compression

Thermo-hydro-mechanical simulation of a full-scale steel-lined micro-tunnel excavated in the callovooxfordian claystone

The paper presents an interpretation of the full-scale ALC1604 in situ heating test carried out in Callovo-Oxfordian claystone (COx) in the Meuse/Haute-Marne underground research laboratory (MHM URL). The MHM URL is a site-specific facility planned to study radioactive waste disposal in the COx. The thermo-hydro-mechanical (THM) behaviour of the host rock is significant for the design of the underground radioactive waste disposal facility and for its long-term safety. When subjected to thermal loading, the Callovo-Oxfordian claystone of low permeability (~10-20-10-21 m2) exhibits a strong pore pressure response that significantly affects the hydraulic and mechanical behaviour of the material. The observations gathered in the in situ test have provided an opportunity to examine the integrated thermo-hydromechanical (THM) response of this sedimentary clay. Coupled THM numerical analyses have been carried out to provide a structured framework for interpretation, and to enhance understanding of THM behaviour of COx. Numerical analyses have been based on a coupled theoretical formulation that incorporates a constitutive law specially developed for this type of material. The law includes a number of features that are relevant for a satisfactory description of the hydromechanical behaviour. By performing the numerical analysis, it has been possible to incorporate anisotropy of material parameters and of in situ stresses. The performance and analysis of the in situ tests have significantly enhanced the understanding of a complex THM problem and have proved the capability of the numerical formulation to provide adequate predictive capacity

Optomechanical Transduction and Characterization of a Silica Microsphere Pendulum via Evanescent Light

Dissipative optomechanics has some advantages in cooling compared to the conventional dispersion dominated systems. Here, we study the optical response of a cantilever-like, silica, microsphere pendulum, evanescently coupled to a fiber taper. In a whispering gallery mode resonator the cavity mode and motion of the pendulum result in both dispersive and dissipative optomechanical interactions. This unique mechanism leads to an experimentally observable, asymmetric response function of the transduction spectrum which can be explained using coupled-mode theory. The optomechanical transduction, and its relationship to the external coupling gap, are investigated and we show that the experimental behavior is in good agreement with the theoretical predictions. A deep understanding of this mechanism is necessary to explore trapping and cooling in dissipative optomechanical systems.Comment: 5 page