Side-information Scalable Source Coding

The problem of side-information scalable (SI-scalable) source coding is considered in this work, where the encoder constructs a progressive description, such that the receiver with high quality side information will be able to truncate the bitstream and reconstruct in the rate distortion sense, while the receiver with low quality side information will have to receive further data in order to decode. We provide inner and outer bounds for general discrete memoryless sources. The achievable region is shown to be tight for the case that either of the decoders requires a lossless reconstruction, as well as the case with degraded deterministic distortion measures. Furthermore we show that the gap between the achievable region and the outer bounds can be bounded by a constant when square error distortion measure is used. The notion of perfectly scalable coding is introduced as both the stages operate on the Wyner-Ziv bound, and necessary and sufficient conditions are given for sources satisfying a mild support condition. Using SI-scalable coding and successive refinement Wyner-Ziv coding as basic building blocks, a complete characterization is provided for the important quadratic Gaussian source with multiple jointly Gaussian side-informations, where the side information quality does not have to be monotonic along the scalable coding order. Partial result is provided for the doubly symmetric binary source with Hamming distortion when the worse side information is a constant, for which one of the outer bound is strictly tighter than the other one.Comment: 35 pages, submitted to IEEE Transaction on Information Theor

Geometrically nonlinear analysis of layered composite plates and shells

A degenerated three dimensional finite element, based on the incremental total Lagrangian formulation of a three dimensional layered anisotropic medium was developed. Its use in the geometrically nonlinear, static and dynamic, analysis of layered composite plates and shells is demonstrated. A two dimenisonal finite element based on the Sanders shell theory with the von Karman (nonlinear) strains was developed. It is shown that the deflections obtained by the 2D shell element deviate from those obtained by the more accurate 3D element for deep shells. The 3D degenerated element can be used to model general shells that are not necessarily doubly curved. The 3D degenerated element is computationally more demanding than the 2D shell theory element for a given problem. It is found that the 3D element is an efficient element for the analysis of layered composite plates and shells undergoing large displacements and transient motion

J/psi (psi') production at the Tevatron and LHC at O(\alpha_s^4v^4) in nonrelativistic QCD

We present a complete evaluation for \jpsi(\psip) prompt production at the Tevatron and LHC at next-to-leading order in nonrelativistic QCD, including color-singlet, color-octet, and higher charmonia feeddown contributions. The short-distance coefficients of \pj at next-to-leading order are found to be larger than leading order by more than an order of magnitude but with a minus sign at high transverse momentum $p_T$. Two new linear combinations of color-octet matrix elements are obtained from the CDF data, and used to predict \jpsi production at the LHC, which agrees with the CMS data. The possibility of \sa dominance and the \jpsi polarization puzzle are also discussed.Comment: Version published in PRL, 4 pages, 4 figure

Geometrically nonlinear analysis of laminated elastic structures

This final technical report contains three parts: Part 1 deals with the 2-D shell theory and its element formulation and applications. Part 2 deals with the 3-D degenerated element. These two parts constitute the two major tasks that were completed under the grant. Another related topic that was initiated during the present investigation is the development of a nonlinear material model. This topic is briefly discussed in Part 3. To make each part self-contained, conclusions and references are included in each part. In the interest of brevity, the discussions presented are relatively brief. The details and additional topics are described in the references cited

Decays of the Meson BcB_c to a PP-Wave Charmonium State χc\chi_c or hch_c

The semileptonic decays, $B_{c}{\longrightarrow}{\chi_c}(h_c)+{\ell}+{{\nu}}_{\ell}$, and the two-body nonleptonic decays, $B_{c}{\longrightarrow}{\chi_c}(h_c)+h$, (here $\chi_c$ and $h_c$ denote $(c\bar c[^3P_J])$ and $(c\bar c[^1P_1])$ respectively, and $h$ indicates a meson) were computed. All of the form factors appearing in the relevant weak-current matrix elements with $B_c$ as its initial state and a $P$-wave charmonium state as its final state for the decays were precisely formulated in terms of two independent overlapping-integrations of the wave-functions of $B_c$ and the $P$-wave charmonium and with proper kinematics factors being `accompanied'. We found that the decays are quite sizable, so they may be accessible in Run-II at Tevatron and in the foreseen future at LHC, particularly, when BTeV and LHCB, the special detectors for B-physics, are borne in mind. In addition, we also pointed out that the decays $B_c\to h_c+...$ may potentially be used as a fresh window to look for the $h_c$ charmonium state, and the cascade decays, $B_c\to \chi_c[^3P_{1,2}]+l+\nu_l$ ($B_c\to \chi_c[^3P_{1,2}]+h$) with one of the radiative decays $\chi_c[^3P_{1,2}] \to J/\psi+\gamma$ being followed accordingly, may affect the observations of $B_c$ meson through the decays $B_{c}\to {J/\psi}+{l}+\nu_{l}$ ($B_c\to J/\psi+h$) substantially.Comment: 24 pages, 3 figures, the replacement for improving the presentation and adding reference

Modeling Eddy Current Crack Signals of Differential and Reflection Probes

The efforts of past several years have resulted in development of an eddy current model [1–8], using the boundary element method (BEM). As of last year, the BEM algorithm based on the Hertz potential approach [1–3] was shown to be effective in dealing with complex part and probe geometry [4–6], and particularly in modeling crack signals [7–9]. Previously, the modeling capabilities were demonstrated mostly with absolute probes. This year, the focus has been shifted toward on crack signals of differential and reflection probes

"Teleparallel" Dark Energy

Using the "teleparallel" equivalent of General Relativity as the gravitational sector, which is based on torsion instead of curvature, we add a canonical scalar field, allowing for a nonminimal coupling with gravity. Although the minimal case is completely equivalent to standard quintessence, the nonminimal scenario has a richer structure, exhibiting quintessence-like or phantom-like behavior, or experiencing the phantom-divide crossing. The richer structure is manifested in the absence of a conformal transformation to an equivalent minimally-coupled model.Comment: 5 pages, 1 figure, Version published in PLB704 (2011) 384-38

Fourier mode dynamics for the nonlinear Schroedinger equation in one-dimensional bounded domains

We analyze the 1D focusing nonlinear Schr\"{o}dinger equation in a finite interval with homogeneous Dirichlet or Neumann boundary conditions. There are two main dynamics, the collapse which is very fast and a slow cascade of Fourier modes. For the cubic nonlinearity the calculations show no long term energy exchange between Fourier modes as opposed to higher nonlinearities. This slow dynamics is explained by fairly simple amplitude equations for the resonant Fourier modes. Their solutions are well behaved so filtering high frequencies prevents collapse. Finally these equations elucidate the unique role of the zero mode for the Neumann boundary conditions