An analytic approximation to the Diffusion Coefficient for the periodic Lorentz Gas

An approximate stochastic model for the topological dynamics of the periodic triangular Lorentz gas is constructed. The model, together with an extremum principle, is used to find a closed form approximation to the diffusion coefficient as a function of the lattice spacing. This approximation is superior to the popular Machta and Zwanzig result and agrees well with a range of numerical estimates.Comment: 13 pages, 4 figure

Dust in Interstellar Clouds, Evolved Stars and Supernovae

Outflows of pre-main-sequence stars drive shocks into molecular material within 0.01 - 1 pc of the young stars. The shock-heated gas emits infrared, millimeter and submillimeter lines of many species including. Dust grains are important charge carriers and play a large role in coupling the magnetic field and flow of neutral gas. Some effects of the dust on the dynamics of oblique shocks began to emerge in the 1990s. However, detailed models of these shocks are required for the calculation of the grain sputtering contribution to gas phase abundances of species producing observed emissions. We are developing such models. Some of the molecular species introduced into the gas phase by sputtering in shocks or by thermally driven desorption in hot cores form on grain surfaces. Recently laboratory studies have begun to contribute to the understanding of surface reactions and thermally driven desorption important for the chemistry of star forming clouds. Dusty plasmas are prevalent in many evolved stars just as well as in star forming regions. Radiation pressure on dust plays a significant role in mass loss from some post-main-sequence stars. The mechanisms leading to the formation of carbonaceous dust in the stellar outflows are similar to those important for soot formation in flames. However, nucleation in oxygen-rich outflows is less well understood and remains a challenging research area. Dust is observed in supernova ejecta that have not passed through the reverse shocks that develop in the interaction of ejecta with ambient media. Dust is detected in high redshift galaxies that are sufficiently young that the only stars that could have produced the dust were so massive that they became supernovae. Consequently, the issue of the survival of dust in strong supernova shocks is of considerable interest.Comment: 4 pages, to be published in the proceedings of Fifth International Conference on Physics of Dusty Plasma

Validation of Observed Bedload Transport Pathways Using Morphodynamic Modeling

Phenomena related to braiding, including local scour and fill, channel bar development, migration and avulsion, make numerical morphodynamic modeling of braided rivers challenging. This paper investigates the performance of a Delft3D model, in a 2D depth-averaged formulation, to simulate the morphodynamics of an anabranch of the Rees River (New Zealand). Model performance is evaluated using data from field surveys collected on the falling limb of a major high flow, and using several sediment transport formulas. Initial model results suggest that there is generally good agreement between observed and modeled bed levels. However, some discrepancies in the bed level estimations were noticed, leading to bed level, water depth and water velocity estimation errors

Pyramidal micromirrors for microsystems and atom chips

Concave pyramids are created in the (100) surface of a silicon wafer by anisotropic etching in potassium hydroxide. High quality micromirrors are then formed by sputtering gold onto the smooth silicon (111) faces of the pyramids. These mirrors show great promise as high quality optical devices suitable for integration into micro-optoelectromechanical systems and atom chips. We have shown that structures of this shape can be used to laser-cool and hold atoms in a magneto-optical trap

Intercellular Ca²⁺ signalling in the adult mouse cochlea

We have investigated wave‐like cytoplasmic calcium (Ca²⁺) signalling in an ex vivo preparation of the adult mouse organ of Corti. Two types of intercellular Ca²⁺ waves that differ in propagation distance and speed were observed. One type was observed to travel up to 100 μm with an average velocity of 7 μm/s. Such waves were initiated by local tissue damage in the outer hair cell region. The propagation distance was decreased when the purinergic receptor antagonists pyridoxalphosphate‐6‐azophenyl‐2′,4′‐disulfonic acid (PPADS; 50 μm) or suramin (150 μm) were added to the extracellular buffer. Immunocytochemical analysis and experiments with calcium indicator dyes showed that both P2X and P2Y receptors were present in supporting cells. A second class of waves identified to travel longitudinally along the organ of Corti propagated at a lower velocity of 1–3 μm/s. These ‘slow’ Ca²⁺ waves were particularly evident in the inner sulcus and Deiters’ cells. They travelled for distances of up to 500 μm. The slow Ca²⁺ signalling varied periodically (approximately one wave every 10 min) and was maintained for more than 3 h. The slow waves were not affected by apyrase, or by the P2 receptor agonists suramin (150 μm) or PPADS (50 μm) but were blocked by the connexin channel blockers octanol (1 mm) and carbenoxolone (100 μm). It is proposed that the observed Ca²⁺ waves might be a physiological response to a change in extracellular environment and may be involved in critical gene regulation activities in the supporting cells of the cochlea

QED vertex form factors at two loops

We present the closed analytic expression of the form factors of the two-loop QED vertex amplitude for on-shell electrons of finite mass $m$ and arbitrary momentum transfer $S=-Q^2$. The calculation is carried out within the continuous $D$-dimensional regularization scheme, with a single continuous parameter $D$, the dimension of the space-time, which regularizes at the same time UltraViolet (UV) and InfraRed (IR) divergences. The results are expressed in terms of 1-dimensional harmonic polylogarithms of maximum weight 4.Comment: 53 pages, 3 figure

Master Integrals for the 2-loop QCD virtual corrections to the Forward-Backward Asymmetry

We present the Master Integrals needed for the calculation of the two-loop QCD corrections to the forward-backward asymmetry of a quark-antiquark pair produced in electron-positron annihilation events. The abelian diagrams entering in the evaluation of the vector form factors were calculated in a previous paper. We consider here the non-abelian diagrams and the diagrams entering in the computation of the axial form factors, for arbitrary space-like momentum transfer Q^2 and finite heavy quark mass m. Both the UV and IR divergences are regularized in the continuous D-dimensional scheme. The Master Integrals are Laurent-expanded around D=4 and evaluated by the differential equation method; the coefficients of the expansions are expressed as 1-dimensional harmonic polylogarithms of maximum weight 4.Comment: 38 pages, 6 figures, typos corrected, version accepted by Nucl. Phys.

Vertex diagrams for the QED form factors at the 2-loop level

We carry out a systematic investigation of all the 2-loop integrals occurring in the electron vertex in QED in the continuous $D$-dimensional regularization scheme, for on-shell electrons, momentum transfer $t=-Q^2$ and finite squared electron mass $m_e^2=a$. We identify all the Master Integrals (MI's) of the problem and write the differential equations in $Q^2$ which they satisfy. The equations are expanded in powers of $\epsilon = (4-D)/2$ and solved by the Euler's method of the variation of the constants. As a result, we obtain the coefficients of the Laurent expansion in $\epsilon$ of the MI's up to zeroth order expressed in close analytic form in terms of Harmonic Polylogarithms.Comment: A few misprints have been corrected. The results are now available at http://pheno.physik.uni-freiburg.de/~bhabha, as FORM input file

Experimental comparison of a DC PV cooker and a parabolic dish solar cooker under variable solar radiation conditions

Solar cookers are not all-weather cooking devices and operate poorly during cloudy and low sunshine conditions. Their performance is evaluated usually during high solar radiation conditions. The objective of this study is to compare two solar cookers under variable non-ideal weather conditions. The comparison is carried out under variable solar radiation conditions to compare the all-weather performance of these two cookers. This is a major novelty compared to previous work reported where solar cookers are tested under high and ideal solar radiation conditions. Experiments to compare a PV DC battery-powered solar cooker and a parabolic dish solar cooker are presented in this paper. A total of six water heating tests are carried out to comprehensively compare these two types of solar cookers under different solar radiation conditions. Also, four food cooking tests are carried out with different types of food. The PV solar cooker shows almost constant input electrical power in the range of 160–180 W during the experimental tests whereas the input thermal power for the parabolic dish is highly variable depending on the solar radiation conditions (200–1200 W). The output water heating powers obtained using the PV cooker (66–100 W) are comparable to those obtained with parabolic dish solar cookers (78–142 W), regardless of the significantly lower input heating power. Water is boiled in all the heating tests with the PV cooker, whereas water is boiled for tests with low solar radiation variability for the parabolic dish solar cooker. Higher water heating efficiencies within a small range (0.38–0.57) are obtained for the PV cooker compared to the parabolic dish solar cooker (0.11–0.42). The water heating efficiency of the parabolic dish solar cooker is highly affected by ambient solar radiation and windspeed conditions. Food was well cooked with the PV cooker in all four food cooking tests, whereas food in only two tests with low solar radiation variability was well cooked for the parabolic dish solar cooker. The PV cooker proves to be an all-weather cooker from the experimental results obtained. Future work will extend the use of the PV system for other domestic applications such as lighting and refrigeration together with solar cooking for a multipurpose DC decentralized system for communities without grid connectivity