An adaptive pseudo-spectral method for reaction diffusion problems

The spectral interpolation error was considered for both the Chebyshev pseudo-spectral and Galerkin approximations. A family of functionals I sub r (u), with the property that the maximum norm of the error is bounded by I sub r (u)/J sub r, where r is an integer and J is the degree of the polynomial approximation, was developed. These functionals are used in the adaptive procedure whereby the problem is dynamically transformed to minimize I sub r (u). The number of collocation points is then chosen to maintain a prescribed error bound. The method is illustrated by various examples from combustion problems in one and two dimensions

Heavy Dynamical Fermions in Lattice QCD

It is expected that the only effect of heavy dynamical fermions in QCD is to renormalize the gauge coupling. We derive a simple expression for the shift in the gauge coupling induced by $N_f$ flavors of heavy fermions. We compare this formula to the shift in the gauge coupling at which the confinement-deconfinement phase transition occurs (at fixed lattice size) from numerical simulations as a function of quark mass and $N_f$. We find remarkable agreement with our expression down to a fairly light quark mass. However, simulations with eight heavy flavors and two light flavors show that the eight flavors do more than just shift the gauge coupling. We observe confinement-deconfinement transitions at $\beta=0$ induced by a large number of heavy quarks. We comment on the relevance of our results to contemporary simulations of QCD which include dynamical fermions.Comment: COLO-HEP-311, 26 pages and 6 postscript figures; file is a shar file and all macros are (hopefully) include

The beta function and equation of state for QCD with two flavors of quarks

We measure the pressure and energy density of two flavor QCD in a wide range of quark masses and temperatures. The pressure is obtained from an integral over the average plaquette or psi-bar-psi. We measure the QCD beta function, including the anomalous dimension of the quark mass, in new Monte Carlo simulations and from results in the literature. We use it to find the interaction measure, E-3p, yielding non-perturbative values for both the energy density E and the pressure p. uuencoded compressed PostScript file Revised version should work on more PostScript printers.Comment: 24 page

Scaling of Pseudo-Critical Couplings in Two-Flavour QCD

We study the scaling behaviour of the pseudo-critical couplings for the chiral phase transition in two-flavour QCD. We show that all existing results from lattice simulations on lattices with temporal extent $N_\tau = 4$, 6 and 8 can be mapped onto a universal scaling curve. The relevant combination of critical exponents, $\beta\delta$, is consistent with the scaling behaviour expected for a second order phase transition with $O(4)$ exponents. At present, scaling according to the $O(2)$ symmetry group can, however, not be ruled out.Comment: 8 pages, NSF-ITP 93-12

Rotational Spectroscopy of PAHs: Acenaphthene, Acenaphthylene and Fluorene

Pure rotational spectra of three polycyclic aromatic hydrocarbons - acenaphthene, acenaphthylene and fluorene - have been obtained by Fourier transform microwave spectroscopy of a molecular beam and subsequently by millimeter wave absorption spectroscopy for acenaphthene and fluorene. The data presented here will be useful for deep radio astronomical searches for PAHs employing large radio telecopes.Comment: 2 pages, 1 figure (uses iaus.sty), to appear in IAU Symposium No. 231, Astrochemistry - Recent Successes and Current Challenges, eds. D. C. Lis, G. A. Blake & E. Herbst (Cambridge Univ. Press

The Traveling Salesman Problem: Low-Dimensionality Implies a Polynomial Time Approximation Scheme

The Traveling Salesman Problem (TSP) is among the most famous NP-hard optimization problems. We design for this problem a randomized polynomial-time algorithm that computes a (1+eps)-approximation to the optimal tour, for any fixed eps>0, in TSP instances that form an arbitrary metric space with bounded intrinsic dimension. The celebrated results of Arora (A-98) and Mitchell (M-99) prove that the above result holds in the special case of TSP in a fixed-dimensional Euclidean space. Thus, our algorithm demonstrates that the algorithmic tractability of metric TSP depends on the dimensionality of the space and not on its specific geometry. This result resolves a problem that has been open since the quasi-polynomial time algorithm of Talwar (T-04)

Laboratory And Astronomical Detection Of The Negative Molecular Ion C3N-

The negative molecular ion C3N- has been detected at millimeter wavelengths in a low-pressure laboratory discharge, and then with frequencies derived from the laboratory data in the molecular envelope of IRC+10216. Spectroscopic constants derived from laboratory measurements of 12 transitions between 97 and 378 GHz allow the rotational spectrum to be calculated well into the submillimeter-wave band to 0.03 km s(-1) or better in equivalent radial velocity. Four transitions of C3N- were detected in IRC+10216 with the IRAM 30 m telescope at precisely the frequencies calculated from the laboratory measurements. The column density of C3N- is 0.5% that of C3N, or approximately 20 times greater than that of C4H- relative to C4H. The C3N- abundance in IRC+10216 is compared with a chemical model calculation by Petrie & Herbst. An upper limit in TMC-1 for C3N- relative to C3N (< 0.8%) and a limit for C4H- relative to C4H (< 0.004%) that is 5 times lower than that found in IRC+10216, were obtained from observations with the NRAO 100 m Green Bank Telescope (GBT). The fairly high concentration ofNRFKorean government MEST 2012R1A1A1014646, 2012M4A2026720Southeast Physics Network (SEP-Net)Science and Technology Facilities Council ST/F002858/1, ST/I000976/1Swedish Research Council 2009-4088U.S. NSF AST-0708176, AST-1009799NASA NNX07AH09G, NNG04G177G, NNX11AE09GChandra grant SAO TM8-9009XBiochemistr

Two-Flavor Staggered Fermion Thermodynamics at N_t = 12

We present results of an ongoing study of the nature of the high temperature crossover in QCD with two light fermion flavors. These results are obtained with the conventional staggered fermion action at the smallest lattice spacing to date---approximately 0.1 fm. Of particular interest are a study of the temperature of the crossover a determination of the induced baryon charge and baryon susceptibility, the scalar susceptibility, and the chiral order parameter, used to test models of critical behavior associated with chiral symmetry restoration. From our new data and published results for N_t = 4, 6, and 8, we determine the QCD magnetic equation of state from the chiral order parameter using O(4) and mean field critical exponents and compare it with the corresponding equation of state obtained from an O(4) spin model and mean field theory. We also present a scaling analysis of the Polyakov loop, suggesting a temperature dependent ``constituent quark free energy.''Comment: LaTeX 25 pages, 15 Postscript figure