Easy Preparation of 1,3-Di-tert-Butylbenzene and Some Derivatives Thereof

1,3-Di-tert-butylbenzene (4) can conveniently be prepared from 1-bromo-3,5-di-tert-butylbenzene (2) which, in turn, is obtained from the easily available 1,3,5-tri-tert-butylbenzene (1). The use of 4 is illustrated by the preparation of the arylphosphines 6 and 7.     

Soft and hard photon corrections for μ-pair production and Bhabha scattering in the presence of a resonance

In this paper previous calculations of radiative corrections to μ-pair production and Bhabha scattering are extended to the case where a resonance is present. In contrast to other investigations of radiative corrections to a narrow resonance this paper gives a complete discussion of Bhabha scattering and discusses both for μ-pair production and Bhabha scattering hard photon bremsstrahlung taking into account specific experimental conditions.     

Charge asymmetry in mu-pair production from electron-positron collisions at 30 GeV

Corrections to the lowest order cross-section for e⁺e^?→μ⁺μ^? are calculated. These corrections arise from higher order quantum electrodynamics, where attention is paid to include the effects of hard photons, exponentiation and hadronic terms, and from the lowest order weak interactions. It is found, that for the qed-corrections the deviation from the so-called soft photon approximation may be important for the charge symmetric part, while it is less important for the antisymmetric part. As an example, the corrected charge asymmetry is given in two different weak interaction models.     

1,4-Addition of a Terminal Phosphinidene Complex to [5]Metacyclophane

Three novel aspects emerge for the reaction of [5]metacyclophane ( 1 ) with the (intermediate) phenylphosphinidene complex 2 to give the 7-phosphanorbornadiene 3 . It is the first 1,4-addition of a phosphinidene complex to an unsaturated system, the first addition of a phosphinidene complex to a benzene ring, and the first [4+1] cycloaddition to an aromatic compound.     

Energy spectra for decaying 2D turbulence in a bounded domain

We use results derived in the framework of the replica approach to study the liquid-glass thermodynamic transition. The main results are derived without using replicas and applied to the study of the Lennard-Jones binary mixture introduced by Kob and Andersen. We find that there is a phase transition due to the entropy crisis. We compute both analytically and numerically the value of the phase transition point T(K) and the specific heat in the low temperature phase.     

Electron-positron annihilation into two and three photons around the ψ

We study the effect of the direct decay of a ψ into three photons on electron-positron annihilation into two and three photons. In a charmonium-like bound state model we find a clear effect in e⁺e^? → 3γ and a somewhat less pronounced effect in e⁺e^? → 2γ, the actual size depending strongly on the charge of the ψ constituents. The effect is reduced when we take initial state radiative corrections into account.     

Scaling behaviour of charged spin-one partons in a gauge model

In a hadron model in which the fermion constituents are bound by vector-isovector gauge fields, electromagnetism is introduced; by spontaneously breaking the strong (SU(2)) gauge symmetry, the gauge fields become massive. We identify the spinors and vectors with partons, and, assuming the naive parton model hypothesis, we calculate the cross section e⁺e^?→ hadrons and the structure functions of the nucleon; scaling is obtained desoite induces presence of an anomalous magnetic moment term in the coupling of the photon with the charged vector fields; the reason is that the spontaneous breaking of the symmetry indices a vector-meson dominance type of coupling between the photon and the neutral vector, which is just what is necessary to restore scaling.     

Towards a Direct Numerical Simulation of a Simplified Pressurized Thermal Shock

The aim of this research work is to perform high quality direct numerical simulations (DNS) of a simplified single phase pressurized thermal shock (PTS) scenario with and without buoyancy effects. In that context, the objectives of this paper are (i) to present the road towards the DNS of a PTS design without buoyancy effects and (ii) to demonstrate that the code NEK5000 is adequate for true DNS analyses. This DNS of the PTS design will serve as a reference to validate low order CFD approaches. The higher order spectral element code NEK5000 is selected to perform the high quality DNS computations. The capabilities of this code, in order to perform the DNS for PTS like geometries, have been extensively assessed for a well-known turbulent channel flow configuration with Re_τ =?180 (turbulent Reynolds number based on the wall friction velocity). Different numerical parameters of NEK5000 have been thoroughly tested and their influence has been studied to obtain high quality turbulence statistics. This assessment of NEK5000 is further extended for the application of highly skewed hexahedral (non-orthogonal) meshes in a turbulent channel flow. The obtained results have shown that NEK5000 is capable of producing high quality DNS solution for a PTS like complex flow configuration for skewed elements (meshes) up to 60 degrees. Finally, this tested numerical framework is adopted to perform the targeted DNS computations of the simplified PTS design.