Experimental Tests of Charge Symmetry Violation in Parton Distributions

Recently, a global phenomenological fit to high energy data has included charge symmetry breaking terms, leading to limits on the allowed magnitude of such effects. We discuss two possible experiments that could search for isospin violation in valence parton distributions. We show that, given the magnitude of charge symmetry violation consistent with existing global data, such experiments might expect to see effects at a level of several percent. Alternatively, such experiments could significantly decrease the upper limits on isospin violation in parton distributions.Comment: 20 pages, 6 figure

Ultra-short pulses in linear and nonlinear media

We consider the evolution of ultra-short optical pulses in linear and nonlinear media. For the linear case, we first show that the initial-boundary value problem for Maxwell's equations in which a pulse is injected into a quiescent medium at the left endpoint can be approximated by a linear wave equation which can then be further reduced to the linear short-pulse equation. A rigorous proof is given that the solution of the short pulse equation stays close to the solutions of the original wave equation over the time scales expected from the multiple scales derivation of the short pulse equation. For the nonlinear case we compare the predictions of the traditional nonlinear Schr\"odinger equation (NLSE) approximation which those of the short pulse equation (SPE). We show that both equations can be derived from Maxwell's equations using the renormalization group method, thus bringing out the contrasting scales. The numerical comparison of both equations to Maxwell's equations shows clearly that as the pulse length shortens, the NLSE approximation becomes steadily less accurate while the short pulse equation provides a better and better approximation

Effects of temperature and ammonia flow rate on the chemical vapour deposition growth of nitrogen-doped graphene

We doped graphene in situ during synthesis from methane and ammonia on copper in a low-pressure chemical vapour deposition system, and investigated the effect of the synthesis temperature and ammonia concentration on the growth. Raman and X-ray photoelectron spectroscopy was used to investigate the quality and nitrogen content of the graphene and demonstrated that decreasing the synthesis temperature and increasing the ammonia flow rate results in an increase in the concentration of nitrogen dopants up to ca. 2.1% overall. However, concurrent scanning electron microscopy studies demonstrate that decreasing both the growth temperature from 1000 to 900 1C and increasing the N/C precursor ratio from 1/50 to 1/10 significantly decreased the growth rate by a factor of six overall. Using scanning tunnelling microscopy we show that the nitrogen was incorporated mainly in substitutional configuration, while current imaging tunnelling spectroscopy showed that the effect of the nitrogen on the density of states was visible only over a few atom distances

The Renormalization Group and Singular Perturbations: Multiple-Scales, Boundary Layers and Reductive Perturbation Theory

Perturbative renormalization group theory is developed as a unified tool for global asymptotic analysis. With numerous examples, we illustrate its application to ordinary differential equation problems involving multiple scales, boundary layers with technically difficult asymptotic matching, and WKB analysis. In contrast to conventional methods, the renormalization group approach requires neither {\it ad hoc\/} assumptions about the structure of perturbation series nor the use of asymptotic matching. Our renormalization group approach provides approximate solutions which are practically superior to those obtained conventionally, although the latter can be reproduced, if desired, by appropriate expansion of the renormalization group approximant. We show that the renormalization group equation may be interpreted as an amplitude equation, and from this point of view develop reductive perturbation theory for partial differential equations describing spatially-extended systems near bifurcation points, deriving both amplitude equations and the center manifold.Comment: 44 pages, 2 Postscript figures, macro \uiucmac.tex available at macro archives or at ftp://gijoe.mrl.uiuc.edu/pu

Wigner's Dynamical Transition State Theory in Phase Space: Classical and Quantum

A quantum version of transition state theory based on a quantum normal form (QNF) expansion about a saddle-centre-...-centre equilibrium point is presented. A general algorithm is provided which allows one to explictly compute QNF to any desired order. This leads to an efficient procedure to compute quantum reaction rates and the associated Gamov-Siegert resonances. In the classical limit the QNF reduces to the classical normal form which leads to the recently developed phase space realisation of Wigner's transition state theory. It is shown that the phase space structures that govern the classical reaction d ynamicsform a skeleton for the quantum scattering and resonance wavefunctions which can also be computed from the QNF. Several examples are worked out explicitly to illustrate the efficiency of the procedure presented.Comment: 132 pages, 31 figures, corrected version, Nonlinearity, 21 (2008) R1-R11

A Multipronged Comparative Study of the Ultraviolet Photochemistry of 2-, 3-, and 4-Chlorophenol in the Gas Phase

The S1(1ππ*) state of the (dominant) syn-conformer of 2-chlorophenol (2-ClPhOH) in the gas phase has a subpicosecond lifetime, whereas the corresponding S1 states of 3- and 4-ClPhOH have lifetimes that are, respectively, ∼2 and ∼3-orders of magnitude longer. A range of experimental techniques–electronic spectroscopy, ultrafast time-resolved photoion and photoelectron spectroscopies, H Rydberg atom photofragment translational spectroscopy, velocity map imaging, and time-resolved Fourier transform infrared emission spectroscopy–as well as electronic structure calculations (of key regions of the multidimensional ground (S0) state potential energy surface (PES) and selected cuts through the first few excited singlet PESs) have been used in the quest to explain these striking differences in excited state lifetime. The intramolecular O–H···Cl hydrogen bond specific to syn-2-ClPhOH is key. It encourages partial charge transfer and preferential stabilization of the diabatic 1πσ* potential (relative to that of the 1ππ* state) upon stretching the C–Cl bond, with the result that initial C–Cl bond extension on the adiabatic S1 PES offers an essentially barrierless internal conversion pathway via regions of conical intersection with the S0 PES. Intramolecular hydrogen bonding is thus seen to facilitate the type of heterolytic dissociation more typically encountered in solution studies