We present a compact discontinuous Galerkin (CDG) method for an elliptic model problem. The problem is first cast as a system of first order equations by introducing the gradient of the primal unknown, or flux, as an additional variable. A standard discontinuous Galerkin (DG) method is then applied to the resulting system of equations. The numerical inter-element fluxes are such that the equati...

We prove that for q ∈ C not a nontrivial root of unity any symmetric invariant 2cocycle for a completion of Uqg is the coboundary of a central element. Equivalently, a Drinfeld twist relating the coproducts on completions of Uqg and Ug is unique up to coboundary of a central element. As an application we show that the spectral triple we defined in an earlier paper for the q-deformation of a com...

In this paper, a compact slow-light microfiber coil resonator (MCR) is fabricated and the slow-light properties of it are analyzed and tested. Based on coupled-wave theory, a theoretical model for describing the slow-light propagation in the MCR is established. Experimentally, the MCR slow-light element is fabricated and its relative slow-light time delay is measured. The group velocity of the ...

In this paper we disprove a conjecture stated in [4] on the equality of two notions of dimension for closed cones. Moreover, we answer in the negative to the following question, raised in the same paper. Given a compact family C of closed cones and a set S such that every blow-up of S at every point x ∈ S is contained in some element of C, is it true that the dimension of S is smaller then or e...

Coupling phenomena between artificial left-handed ~LH! transmission lines are explored on the basis of a transmission line approach of LH materials. A LH forward coupler in the form of an ideal lumped-element ladder network is presented and is shown to exhibit strong forward coupling that increases with decreasing of frequency. A quasi-lumped element microstrip implementation of a LH coupler is...

We analyze the use of edge finite element methods to approximate Maxwell’s equations in a bounded cavity. Using the theory of collectively compact operators, we prove h-convergence for the source and eigenvalue problems. This is the first proof of convergence of the eigenvalue problem for general edge elements, and it extends and unifies the theory for both problems. The convergence results are...

Integrated holographics is a novel photonics technology made possible by recent advances in semiconductor manufacturing technology and planar waveguide fabrication. The technology’s corner stone, the holographic Bragg reflector (HBR), is a slab-waveguide based, nanoscale, refractive-index structure that merges, for the first time, powerful features of holography, such as single-element spectral...

Consider the following two questions. (1) When does a compact Lie group G ⊂ U(n) have an element g ∈ G possessing exactly two eigenvalues? (2) When does a compact Lie group G ⊂ U(n) have a cocharacter U(1) → G such that the compositionU(1) → U(n) is a representation ofU(1)with exactly two weights? A solution to the second problem gives a family of solutions to the first, by choosing g to be alm...

This paper presents a low-cost compact planar microstrip-fed monopole antenna and its four-element array design for ultra-wideband (UWB) wireless communication and target detection applications, respectively, operating in the frequency span of 3 GHz to 11 GHz. A prototype was fabricated and then measured based on optimal parameters. The results of reflection coefficient (S11) and radiation patt...

In this paper the capability of Gurson-Tvergaard-Needleman (GTN) model in the prediction of ductile damage in 7075-T651 aluminum alloy is investigated. For this purpose, three types of specimens were tested: Standard tensile bars, Round notched bar (RNB) specimens and compact tension (C(T)) specimens. Standard tensile bar tests were used to obtain the mechanical properties of the material and t...