The diameter of random Cayley digraphs of given degree

We consider random Cayley digraphs of order $n$ with uniformly distributed generating set of size $k$. Specifically, we are interested in the asymptotics of the probability such a Cayley digraph has diameter two as $n\to\infty$ and $k=f(n)$. We find a sharp phase transition from 0 to 1 at around $k = \sqrt{n \log n}$. In particular, if $f(n)$ is asymptotically linear in $n$, the probability converges exponentially fast to 1.Comment: 11 page

The structure of flame filaments in chaotic flows

The structure of flame filaments resulting from chaotic mixing within a combustion reaction is considered. The transverse profile of the filaments is investigated numerically and analytically based on a one-dimensional model that represents the effect of stirring as a convergent flow. The dependence of the steady solutions on the Damkohler number and Lewis number is treated in detail. It is found that, below a critical Damkohler number Da(crit), the flame is quenched by the flow. The quenching transition appears as a result of a saddle-node bifurcation where the stable steady filament solution collides with an unstable one. The shape of the steady solutions for the concentration and temperature profiles changes with the Lewis number and the value of Da(crit) increases monotonically with the Lewis number. Properties of the solutions are studied analytically in the limit of large Damkohler number and for small and large Lewis number.Comment: 17 pages, 13 figures, to be published in Physica

Why the lowest Landau level approximation works in strongly type II superconductors

Higher than the lowest Landau level contributions to magnetization and specific heat of superconductors are calculated using Ginzburg - Landau equations approach. Corrections to the excitation spectrum around solution of these equations (treated perturbatively) are found. Due to symmetries of the problem leading to numerous cancellations the range of validity of the LLL approximation in mean field is much wider then a naive range and extends all the way down to $H = {H_{c2}(T)}/13$. Moreover the contribution of higher Landau levels is significantly smaller compared to LLL than expected naively. We show that like the LLL part the lattice excitation spectrum at small quasimomenta is softer than that of usual acoustic phonons. This enhanses the effect of fluctuations. The mean field calculation extends to third order, while the fluctuation contribution due to HLL is to one loop. This complements the earlier calculation of the LLL part to two loop order.Comment: 20 pages, Latex file, three figure

Anisotropic Release of the Residual Zero-point Entropy in the Spin Ice Compound Dy2Ti2O7: Kagome-ice Behavior

We report the specific heat and entropy of single crystals of the spin ice compound Dy2Ti2O7 at temperatures down to 0.35 K. We apply magnetic fields along the four characteristic directions: [100], [110], [111] and [112]. Because of Ising anisotropy, we observe anisotropic release of the residual zero-point entropy, attributable to the difference in frustration dimensionality. In the high magnetic field along these four directions, the residual entropy is almost fully released and the activation entropy reaches Rln2. However, in the intermediate field region, the entropy in fields along the [111] direction is different from those for the other three field directions. For the [111] direction the frustration structure changes from that of three-dimensional(3D) pyrochlore to that of two-dimensional(2D) Kagome-like lattice with constraint due to the ice rule, leading to different values of zero-point entropy.Comment: 4 pages, 4 figures, to appear in Phys. Rev.

A world of cobenefits : solving the global nitrogen challenge

Houlton, Benjamin Z. University of California. John Muir Institute of the Environment. Davis, CA, USA.Houlton, Benjamin Z. University of California. Department of Land, Air and Water Resources. Davis, CA, USA.Almaraz, Maya. University of California. Department of Land, Air and Water Resources. Davis, CA, USA.Aneja, Viney. North Carolina State University at Raleigh. Department of Marine, Earth, and Atmospheric Sciences. Raleigh, NC, USA.Austin, Amy T. Universidad de Buenos Aires. Facultad de Agronomía. Instituto de Investigaciones Fisiológicas y Ecológicas Vinculadas a la Agricultura (IFEVA). Buenos Aires, Argentina.Austin, Amy T. CONICET – Universidad de Buenos Aires. Instituto de Investigaciones Fisiológicas y Ecológicas Vinculadas a la Agricultura (IFEVA). Buenos Aires, Argentina.Bai, Edith. Chinese Academy of Sciences. Institute of Applied Ecology. CAS Key Laboratory of Forest Ecology and Management. Shenyang, China.Bai, Edith. Northeast Normal University. School of Geographical Sciences. Changchun, China.Cassman, Kenneth. University of Nebraska – Lincoln. Department of Agronomy and Horticulture. Lincoln. NE, USA.Compton, Jana E. Environmental Protection Agency. Western Ecology Division. Washington, DC, USA.Davidson, Eric A. University of Maryland Center for Environmental Science. Appalachian Laboratory. Cambridge, MD, USA.865-872Nitrogen is a critical component of the economy, food security, and planetary health. Many of the world's sustainability targets hinge on global nitrogen solutions, which, in turn, contribute lasting benefits for (i) world hunger; (ii) soil, air, and water quality; (iii) climate change mitigation; and (iv) biodiversity conservation. Balancing the projected rise in agricultural nitrogen demands while achieving these 21st century ideals will require policies to coordinate solutions among technologies, consumer choice, and socioeconomic transformation

A Spitzer Study of Comets 2P/Encke, 67P/Churyumov-Gerasimenko, and C/2001 HT50 (LINEAR-NEAT)

We present infrared images and spectra of comets 2P/Encke, 67P/Churyumov-Gerasimenko, and C/2001 HT50 (LINEAR-NEAT) as part of a larger program to observe comets inside of 5 AU from the sun with the Spitzer Space Telescope. The nucleus of comet 2P/Encke was observed at two vastly different phase angles (20 degrees and 63 degrees). Model fits to the spectral energy distributions of the nucleus suggest comet Encke's infrared beaming parameter derived from the near-Earth asteroid thermal model may have a phase angle dependence. The observed emission from comet Encke's dust coma is best-modeled using predominately amorphous carbon grains with a grain size distribution that peaks near 0.4 microns, and the silicate contribution by mass to the sub-micron dust coma is constrained to 31%. Comet 67P/Churyumov-Gerasimenko was observed with distinct coma emission in excess of a model nucleus at a heliocentric distance of 5.0 AU. The coma detection suggests that sublimation processes are still active or grains from recent activity remain near the nucleus. Comet C/2001 HT50 (LINEAR-NEAT) showed evidence for crystalline silicates in the spectrum obtained at 3.2 AU and we derive a silicate-to-carbon dust ratio of 0.6. The ratio is an order of magnitude lower than that derived for comets 9P/Tempel 1 during the Deep Impact encounter and C/1995 O1 (Hale-Bopp).Comment: Accepted for publication in the Astrophysical Journal 48 pages, 15 figures, 10 table