Calculation of Generalized Polynomial-Chaos Basis Functions and Gauss Quadrature Rules in Hierarchical Uncertainty Quantification

Stochastic spectral methods are efficient techniques for uncertainty quantification. Recently they have shown excellent performance in the statistical analysis of integrated circuits. In stochastic spectral methods, one needs to determine a set of orthonormal polynomials and a proper numerical quadrature rule. The former are used as the basis functions in a generalized polynomial chaos expansion. The latter is used to compute the integrals involved in stochastic spectral methods. Obtaining such information requires knowing the density function of the random input {\it a-priori}. However, individual system components are often described by surrogate models rather than density functions. In order to apply stochastic spectral methods in hierarchical uncertainty quantification, we first propose to construct physically consistent closed-form density functions by two monotone interpolation schemes. Then, by exploiting the special forms of the obtained density functions, we determine the generalized polynomial-chaos basis functions and the Gauss quadrature rules that are required by a stochastic spectral simulator. The effectiveness of our proposed algorithm is verified by both synthetic and practical circuit examples.Comment: Published by IEEE Trans CAD in May 201

The top quark electric dipole moment in an MSSM extension with vector like multiplets

The electric dipole moment (EDM) of the top quark is calculated in a model with a vector like multiplet which mixes with the third generation in an extension of the MSSM. Such mixings allow for new CP violating phases. Including these new CP phases, the EDM of the top in this class of models is computed. The top EDM arises from loops involving the exchange of the W, the Z as well as from the exchange involving the charginos, the neutralinos, the gluino, and the vector like multiplet and their superpartners. The analysis of the EDM of the top is more complicated than for the light quarks because the mass of the external fermion, in this case the top quark mass cannot be ignored relative to the masses inside the loops. A numerical analysis is presented and it is shown that the top EDM could be close to $10^{-19} ecm$ consistent with the current limits on the EDM of the electron, the neutron and on atomic EDMs. A top EDM of size $10^{-19}ecm$ could be accessible in collider experiments such as the ILC.Comment: 21 pages and 5 figues. Accepted for publication in Physical Review

The Chromoelectric Dipole Moment of the Top Quark in Models with Vector Like Multiplets

The chromoelectric dipole moment of the top quark is calculated in a model with a vector like multiplet which mixes with the third generation in an extension of the MSSM. Such mixings allow for new CP violating phases. Including these new CP phases, the chromoelectric dipole moment that generates an electric dipole of the top in this class of models is computed. The top chromoelectric dipole moment operator arises from loops involving the exchange of the W, the Z as well as from the exchange involving the charginos, the neutralinos, the gluino, and the vector like multiplet and their superpartners. The analysis of the chromoelectric dipole moment operator of the top is more complicated than for the light quarks because the mass of the external fermion, in this case the top quark mass, cannot be ignored relative to the masses inside the loops. A numerical analysis is presented and it is shown that the contribution to the top EDM could lie in the range ($10^{-19}-10^{-18})$ ecm consistent with the current limits on the EDM of the electron, the neutron and on atomic EDMs. A top EDM of size $(10^{-19}-10^{-18})$ ecm could be accessible in collider experiments such as at the LHC and at the ILC.Comment: 17 pages, 6 figures. Accepted for publication in Phys. Rev.

High Octane Number Gasoline-ether Blend

Gasoline produced in Egypt is a low-grade gasoline that contains high concentration of harmful components that are having a toll on our environment. In addition, those pollutants cause countless diseases and deaths annually to the Egyptian population. This paper targets two main sectors in the production of commercial gasoline. The improvement engine efficiency through the upgrading of octane number is first experimented by using a blend stock that ranges from gasoline fractions and Isomerates. An optimum was then chosen depending on the results obtained from different tests. Through those experiments, it was determined which samples obeyed the EU regulation for transportation emissions. Having an excellent gasoline with a high-octane number but produced large quantities of harmful emissions was unacceptable. This leads to the section aim of this research, which was to produce an environmental gasoline. This meant that once the gasoline sample is combusted, it should produce limited amounts of emissions such as 1% benzene since benzene is carcinogenic. A sample with euro 3 specification was produced and showed excellent gasoline properties such as an RON value of around 95 without the use of octane enhancers. A second sample showed better results satisfied euro 5 regulations and produced an even higher-octane number than the euro 3 sample. This sample was the optimum environmental ETBE-gasoline high octane number blend. By understanding the composition of those samples, maximum yield of commercial gasoline could be produced. This would also lead to the reduction of pollutants in the environment. Completing this task with successful results means that this environmental high octane number gasoline could be produced and used in Egypt. Such blends should be produced on a large scale by exercising euro 3 and/or 5 regulations

Selective Spectrophotometric and Spectrofluorometric Methods for the Determination of Amantadine Hydrochloride in Capsules and Plasma via Derivatization with 1,2-Naphthoquinone-4-sulphonate

New selective and sensitive spectrophotometric and spectrofluorometric methods have been developed and validated for the determination of amantadine hydrochloride (AMD) in capsules and plasma. The methods were based on the condensation of AMD with 1,2-naphthoquinone-4-sulphonate (NQS) in an alkaline medium to form an orange-colored product. The spectrophotometric method involved the measurement of the colored product at 460  nm. The spectrofluorometric method involved the reduction of the product with potassium borohydride, and the subsequent measurement of the formed fluorescent reduced AMD-NQS product at 382  nm after excitation at 293  nm. The variables that affected the reaction were carefully studied and optimized. Under the optimum conditions, linear relationships with good correlation coefficients (0.9972–0.9974) and low LOD (1.39 and 0.013 μg mL−1) were obtained in the ranges of 5–80 and 0.05–10  μg mL−1 for the spectrophotometric and spectrofluorometric methods, respectively. The precisions of the methods were satisfactory; RSD ≤2.04%. Both methods were successfully applied to the determination of AMD in capsules. As its higher sensitivity, the spectrofluorometric method was applied to the determination of AMD in plasma; the recovery was 96.3–101.2 ± 0.57–4.2%. The results obtained by the proposed methods were comparable with those obtained by the official metho

Weak Isospin Violations in Charged and Neutral Higgs Couplings from SUSY Loop Corrections

Supersymmetric QCD and supersymmetric electroweak loop corrections to the violations of weak isospin to Yukawa couplings are investigated. Specifically it involves an analysis of the supersymmetric loop corrections to the Higgs couplings to the third generation quarks and leptons. Here we analyze the SUSY loop corrections to the charged Higgs couplings which are then compared with the supersymmetric loop corrections to the neutral Higgs couplings previously computed. It is found that the weak isospin violations can be quite significant, i.e, as much as 40-50% or more of the total loop correction to the Yukawa coupling. The effects of CP phases are also studied and it is found that these effects can either enhance or suppress the weak isospin violations. We also investigate the weak isospin violation effects on the branching ratio $BR(H^-\to\bar t b)/ BR(H^-\to \bar\nu_{\tau}\tau^-)$ and show that the effects are sensitive to CP phases. Thus an accurate measurement of this branching ratio along with the branching ratio of the neutral Higgs boson decays can provide a measure of weak isospin violation along with providing a clue to the presence of supersymmetry.Comment: 20 pages, 9 figure

Mixing of the CP Even and the CP Odd Higgs Bosons and the EDM Constraints

The mixing among the CP even and the CP odd neutral Higgs bosons of MSSM by one loop induced effects in the presence of CP phases is investigated using three different mechanisms to satisfy the EDM constraints, i.e., a fine tuning of phases, a heavy sparticle spectrum, and the cancellation mechanism. It is shown that if a mixing effect among the CP even and the CP odd Higgs bosons is observed experimentally, then it is only the cancellation mechanism that can survive under the naturalness constraint.Comment: 14 pages, Latex and 4figures. A new paragraph is added and few more references. One figure is modified. To appear in Phys. Rev.