On moduli of rings and quadrilaterals: algorithms and experiments

Moduli of rings and quadrilaterals are frequently applied in geometric function theory, see e.g. the Handbook by K\"uhnau. Yet their exact values are known only in a few special cases. Previously, the class of planar domains with polygonal boundary has been studied by many authors from the point of view of numerical computation. We present here a new $hp$-FEM algorithm for the computation of moduli of rings and quadrilaterals and compare its accuracy and performance with previously known methods such as the Schwarz-Christoffel Toolbox of Driscoll and Trefethen. We also demonstrate that the $hp$-FEM algorithm applies to the case of non-polygonal boundary and report results with concrete error bounds

NO2 Suppression of Autoxidation–Inhibition of Gas-Phase Highly Oxidized Dimer Product Formation

Atmospheric autoxidation of volatile organic compounds (VOC) leads to prompt formation of highly oxidized multifunctional compounds (HOM) that have been found crucial in forming ambient secondary organic aerosol (SOA). As a radical chain reaction mediated by oxidized peroxy (RO2) and alkoxy (RO) radical intermediates, the formation pathways can be intercepted by suitable reaction partners, preventing the production of the highest oxidized reaction products, and thus the formation of the most condensable material. Commonly, NO is expected to have a detrimental effect on RO2 chemistry, and thus on autoxidation, whereas the influence of NO2 is mostly neglected. Here it is shown by dedicated flow tube experiments, how high concentration of NO2 suppresses cyclohexene ozonolysis initiated autoxidation chain reaction. Importantly, the addition of NO2 ceases covalently bound dimer production, indicating their production involving acylperoxy radical (RC(O)OO•) intermediates. In related experiments NO was also shown to strongly suppress the highly oxidized product formation, but due to possibility for chain propagating reactions (as with RO2 and HO2 too), the suppression is not as absolute as with NO2. Furthermore, it is shown how NOx reactions with oxidized peroxy radicals lead into indistinguishable product compositions, complicating mass spectral assignments in any RO2 + NOx system. The present work was conducted with atmospheric pressure chemical ionization mass spectrometry (CIMS) as the detection method for the highly oxidized end-products and peroxy radical intermediates, under ambient conditions and at short few second reaction times. Specifically, the insight was gained by addition of a large amount of NO2 (and NO) to the oxidation system, upon which acylperoxy radicals reacted in RC(O)O2 + NO2 → RC(O)O2NO2 reaction to form peroxyacylnitrates, consequently shutting down the oxidation sequence. Keywords: acylperoxy radicals; Autoxidation; dimers; Highly oxidized multifunctional compounds; Highly oxygenated molecules; HOM; nitrogen oxides; peroxyacylnitratePeer reviewe

Single Spin Asymmetry at Large x_F and k_T

The large single spin asymmetries observed at high momentum fractions x_F and transverse momenta k_T in p^\uparrow p -> \pi(x_F,k_T)+X as well as in pp -> \Lambda^\uparrow(x_F,k_T)+X suggest that soft helicity flip processes are coherent with hard scattering. Such coherence can be maintained if x_F -> 1 as k_T -> \infty, while k_T^2(1-x_F) \sim \Lambda_QCD^2 stays fixed. The entire hadron wave function, rather than a single quark, then contributes to the scattering process. Analogous coherence effects have been seen experimentally in the Drell-Yan process at high x_F. We find that the p^\uparrow p -> \pi(x_F,k_T)+X production amplitudes have large dynamic phases and that helicity flip contributions are unsuppressed in this limit, giving rise to potentially large single spin asymmetries.Comment: 11 pages, 2 figures. v2: References and a preprint number added. Calculation of section 4 modified. v3: Minor changes in text. Version to be published in JHE

Positive-energy D-bar method for acoustic tomography: a computational study

A new computational method for reconstructing a potential from the Dirichlet-to-Neumann map at positive energy is developed. The method is based on D-bar techniques and it works in absence of exceptional points -- in particular, if the potential is small enough compared to the energy. Numerical tests reveal exceptional points for perturbed, radial potentials. Reconstructions for several potentials are computed using simulated Dirichlet-to-Neumann maps with and without added noise. The new reconstruction method is shown to work well for energy values between $10^{-5}$ and $5$, smaller values giving better results

Gravitational Techniwaves

We investigate the production and possible detection of gravitational waves stemming from the electroweak phase transition in the early universe in models of minimal walking technicolor. In particular we discuss the two possible scenarios in which one has only one electroweak phase transition and the case in which the technicolor dynamics allows for multiple phase transitions.Comment: 30 pages, 5 figures. v2: minor changes, references added, title changed in journa

Experimental Investigation of Angular Stackgram Filtering for Noise Reduction of SPECT Projection Data: Study with Linear and Nonlinear Filters

We discuss data filtering prior to image reconstruction. For this kind of filtering, the radial direction of the sinogram is routinely employed. Recently, we have introduced an alternative approach to sinogram data processing, exploiting the angular information in a novel way. This new stackgram representation can be regarded as an intermediate form of the sinogram and image domains. In this experimental study, we compare the radial sinogram and angular stackgram filtering methods using physical SPECT phantoms. Our study is carried out by employing simple linear and nonlinear filters with ten different Gaussian kernels, in order to provide a comparable investigation. According to our results, angular stackgram filtering with the nonlinear filters provides the best resolution-noise tradeoff of the compared methods. Besides, stackgram filtering with these filters seems to preserve the resolution in an exceptional way. Visually, noise in the reconstructed images after stackgram filtering appears more “powdery” in comparison with radial sinogram filtering

Electroweak phase transition in technicolor

Several phenomenologically viable walking technicolor models have been proposed recently. I demonstrate that these models can have first order electroweak phase transitions, which are sufficiently strong for electroweak baryogenesis. Strong dynamics can also lead to several separate transitions at the electroweak scale, with the possibility of a temporary restoration and an extra breaking of the electroweak symmetry. First order phase transitions will produce gravitational waves, which may be detectable at future experiments.Comment: 6 pages, 4 figures. Talk at PASCOS 2010 conference, Valencia, 19-23 July 201

Complexity Results and Algorithms for Extension Enforcement in Abstract Argumentation

Peer reviewe