Acid catalyzed reactions of alpha and beta styryl azides

Acid degradation of alpha and beta styryl azide

The formation of 3,6-diphenylpyridazine and 2,5-diphenylpyrrole from alpha-styryl azide

Formation of 3,6-diphenylpyridazine and 2,5- diphenylpyrrole from alpha-styryl azid

Scaling Symmetries of Scatterers of Classical Zero-Point Radiation

Classical radiation equilibrium (the blackbody problem) is investigated by the use of an analogy. Scaling symmetries are noted for systems of classical charged particles moving in circular orbits in central potentials V(r)=-k/r^n when the particles are held in uniform circular motion against radiative collapse by a circularly polarized incident plane wave. Only in the case of a Coulomb potential n=1 with fixed charge e is there a unique scale-invariant spectrum of radiation versus frequency (analogous to zero-point radiation) obtained from the stable scattering arrangement. These results suggest that non-electromagnetic potentials are not appropriate for discussions of classical radiation equilibrium.Comment: 13 page

The Blackbody Radiation Spectrum Follows from Zero-Point Radiation and the Structure of Relativistic Spacetime in Classical Physics

The analysis of this article is entirely within classical physics. Any attempt to describe nature within classical physics requires the presence of Lorentz-invariant classical electromagnetic zero-point radiation so as to account for the Casimir forces between parallel conducting plates at low temperatures. Furthermore, conformal symmetry carries solutions of Maxwell's equations into solutions. In an inertial frame, conformal symmetry leaves zero-point radiation invariant and does not connect it to non-zero-temperature; time-dilating conformal transformations carry the Lorentz-invariant zero-point radiation spectrum into zero-point radiation and carry the thermal radiation spectrum at non-zero temperature into thermal radiation at a different non-zero-temperature. However, in a non-inertial frame, a time-dilating conformal transformation carries classical zero-point radiation into thermal radiation at a finite non-zero-temperature. By taking the no-acceleration limit, one can obtain the Planck radiation spectrum for blackbody radiation in an inertial frame from the thermal radiation spectrum in an accelerating frame. Here this connection between zero-point radiation and thermal radiation is illustrated for a scalar radiation field in a Rindler frame undergoing relativistic uniform proper acceleration through flat spacetime in two spacetime dimensions. The analysis indicates that the Planck radiation spectrum for thermal radiation follows from zero-point radiation and the structure of relativistic spacetime in classical physics.Comment: 21 page

Using the Tip of the Red Giant Branch as a Distance Indicator in the Near Infrared

The tip of the red giant branch (TRGB) is a well-established standard candle used to measure distances to nearby galaxies. The TRGB luminosity is typically measured in the I-band, where the luminosity has little dependency on stellar age or stellar metallicity. As the TRGB is brighter at wavelengths redder than the I-band, observational gains can be made if the TRGB luminosity can be robustly calibrated at longer wavelengths. This is of particular interest given the infrared capabilities that will be available with the James Webb Space Telescope and an important calibration consideration for using TRGB distances as part of an independent measurement of the Hubble constant. Here, we use simulated photometry to investigate the dependency of the TRGB luminosity on stellar age and metallicity as a function of wavelength (475 nm - 4.5 micron). We find intrinsic variations in the TRGB magnitude to increase from a few hundredths of a magnitude at 800-900 nm to ~0.6 mag by 1.5 micron. We show that variations at the longer infrared wavelengths can be reduced to 0.02-0.05 mag (1-2% accuracy in distance) with careful calibrations that account for changes in age and metal content. These represent the minimum uncertainties; observational uncertainties will be higher. Such calibration efforts may also provide independent constraints of the age and metallicity of stellar halos where TRGB distances are best measured. At 3.6 and 4.5 micron, the TRGB magnitude is predicted to vary up to ~0.15 mag even after corrections for stellar age and metallicity, making these wavelengths less suitable for precision distances.Comment: 11 pages, 7 figures, 1 table, Accepted to the Astrophysical Journa

Numerical study of domain coarsening in anisotropic stripe patterns

We study the coarsening of two-dimensional smectic polycrystals characterized by grains of oblique stripes with only two possible orientations. For this purpose, an anisotropic Swift-Hohenberg equation is solved. For quenches close enough to the onset of stripe formation, the average domain size increases with time as $t^{1/2}$. Further from onset, anisotropic pinning forces similar to Peierls stresses in solid crystals slow down defects, and growth becomes anisotropic. In a wide range of quench depths, dislocation arrays remain mobile and dislocation density roughly decays as $t^{-1/3}$, while chevron boundaries are totally pinned. We discuss some agreements and disagreements found with recent experimental results on the coarsening of anisotropic electroconvection patterns.Comment: 8 pages, 11 figures. Phys. Rev E, to appea

Twisted topological structures related to M-branes II: Twisted Wu and Wu^c structures

Studying the topological aspects of M-branes in M-theory leads to various structures related to Wu classes. First we interpret Wu classes themselves as twisted classes and then define twisted notions of Wu structures. These generalize many known structures, including Pin^- structures, twisted Spin structures in the sense of Distler-Freed-Moore, Wu-twisted differential cocycles appearing in the work of Belov-Moore, as well as ones introduced by the author, such as twisted Membrane and twisted String^c structures. In addition, we introduce Wu^c structures, which generalize Pin^c structures, as well as their twisted versions. We show how these structures generalize and encode the usual structures defined via Stiefel-Whitney classes.Comment: 20 page

Incremental Distance Transforms (IDT)

A new generic scheme for incremental implementations of distance transforms (DT) is presented: Incremental Distance Transforms (IDT). This scheme is applied on the cityblock, Chamfer, and three recent exact Euclidean DT (E2DT). A benchmark shows that for all five DT, the incremental implementation results in a significant speedup: 3.4×−10×. However, significant differences (i.e., up to 12.5×) among the DT remain present. The FEED transform, one of the recent E2DT, even showed to be faster than both city-block and Chamfer DT. So, through a very efficient incremental processing scheme for DT, a relief is found for E2DT’s computational burden

Wide-angle, circularly polarized, omnidirectional-array antenna

Modified conventional turnstile antenna features bifoliate pattern with relatively high gain and good circularity over solid area enclosed by the 0.26 and 1.31 radian angles of elevation. These antennas are intended for high altitude balloon use, their permissible weight is restricted to one pound

Classical interpretation of the Debye law for the specific heat of solids

We derive the Debye law for the specific heat of solids within the realm of stochastic electrodynamics (i.e., classical electrodynamics with the assumption of a real zero-point field). Random lattice vibrations are generated by the Planck radiation including zero point, which is absorbed by the ions. The equilibrium is accomplished by a fluctuation-dissipation mechanism due to the emission of radiation by the ions in accelerated motion