The Generation of Fullerenes

We describe an efficient new algorithm for the generation of fullerenes. Our implementation of this algorithm is more than 3.5 times faster than the previously fastest generator for fullerenes -- fullgen -- and the first program since fullgen to be useful for more than 100 vertices. We also note a programming error in fullgen that caused problems for 136 or more vertices. We tabulate the numbers of fullerenes and IPR fullerenes up to 400 vertices. We also check up to 316 vertices a conjecture of Barnette that cubic planar graphs with maximum face size 6 are hamiltonian and verify that the smallest counterexample to the spiral conjecture has 380 vertices.Comment: 21 pages; added a not

Transient Emission From Dissipative Fronts in Magnetized, Relativistic Outflows. II. Synchrotron Flares

The time dependent synchrotron emission from relativistic jets, and the relation between the synchrotron and ERC emission is considered within the framework of the radiative front model. The timescale and profile of the optically thin emission are shown to be determined, in this model, by the shock formation radius, the thickness of expelled fluid slab and the variation of the front's parameters due to its transverse expansion. For a range of reasonable conditions, a variety of flare shapes can be produced, varying from roughly symmetric with exponential rises and decays, as often seen in blazars, to highly asymmetric with a fast rise and a much slower, power law decay, as seen in GRB afterglows. The onset, duration, and fluence of low-frequency (below the initial turnover frequency) and hard gamma-ray (above the initial gamma-spheric energy) outbursts are limited by opacity effects; the emission at these energies is quite generally delayed and, in the case of sufficiently short length outbursts, severely attenuated. The observational consequences are discussed. One distinctive prediction of this model is that in a single, powerful source, the upper cutoff of the gamma-ray spectrum should be correlated with the timescale of the outburst and with the amplitude of variations at long wavelengths (typically radio to millimeter).Comment: AAS LaTex, 14 pgs, accepted to A

e+e−→bbˉudˉμ−νˉμe^+e^- \to b \bar{b} u \bar{d} \mu^- \bar{\nu}_\mu with a ttˉt\bar{t} production

The cross section of $e^+e^- \to b \bar{b} u \bar{d} \mu^- \bar{\nu}_\mu$ process with a complete set of tree diagrams, 232 diagrams in the unitary gauge, was calculated at the energy range of $\sqrt{s}$ = 340 - 500 GeV by using GRACE system. A main contribution to the cross section comes from $t\bar{t}$ production, where $t$ and $\bar{t}$ decay into $bu\bar{d}$ and $\bar{b} \mu^- \bar{\nu}_{\mu}$, respectively. It was found that the interference between the diagrams with $t\bar{t}$ production and those with single-$t$ through $WW$ pair production amounts to 10% at the $t \bar{t}$ threshold energy region. In the energy region above twice of the top quark mass, more than 95% of the cross section comes from the $t\bar{t}$ diagrams.Comment: 17 pages, 8 PostScript figures, LateX; To appear in Phys. Lett.

Thermal X-ray emission from shocked ejecta in Type Ia Supernova Remnants. Prospects for explosion mechanism identification

The explosion mechanism behind Type Ia supernovae is a matter of continuing debate. The diverse attempts to identify or at least constrain the physical processes involved in the explosion have been only partially successful so far. In this paper we propose to use the thermal X-ray emission from young supernova remnants originated in Type Ia events to extract relevant information concerning the explosions themselves. We have produced a grid of thermonuclear supernova models representative of the paradigms currently under debate: pure deflagrations, delayed detonations, pulsating delayed detonations and sub-Chandrasekhar explosions, using their density and chemical composition profiles to simulate the interaction with the surrounding ambient medium and the ensuing plasma heating, non-equilibrium ionization and thermal X-ray emission of the ejecta. Key observational parameters such as electron temperatures, emission measures and ionization time scales are presented and discussed. We find that not only is it possible to identify the explosion mechanism from the spectra of young Type Ia Supernova Remnants, it is in fact necessary to take the detailed ejecta structure into account if such spectra are to be modeled in a self-consistent way. Neither element line flux ratios nor element emission measures are good estimates of the true ratios of ejected masses, with differences of as much as two or three orders of magnitude for a given model. Comparison with observations of the Tycho SNR suggests a delayed detonation as the most probable explosion mechanism. Line strengths, line ratios, and the centroid of the Fe Kalpha line are reasonably well reproduced by a model of this kind.Comment: 11 pages, 8 figures (5 of them color), accepted for publication by the Ap

Exhaustive generation of kk-critical H\mathcal H-free graphs

We describe an algorithm for generating all $k$-critical $\mathcal H$-free graphs, based on a method of Ho\`{a}ng et al. Using this algorithm, we prove that there are only finitely many $4$-critical $(P_7,C_k)$-free graphs, for both $k=4$ and $k=5$. We also show that there are only finitely many $4$-critical graphs $(P_8,C_4)$-free graphs. For each case of these cases we also give the complete lists of critical graphs and vertex-critical graphs. These results generalize previous work by Hell and Huang, and yield certifying algorithms for the $3$-colorability problem in the respective classes. Moreover, we prove that for every $t$, the class of 4-critical planar $P_t$-free graphs is finite. We also determine all 27 4-critical planar $(P_7,C_6)$-free graphs. We also prove that every $P_{10}$-free graph of girth at least five is 3-colorable, and determine the smallest 4-chromatic $P_{12}$-free graph of girth five. Moreover, we show that every $P_{13}$-free graph of girth at least six and every $P_{16}$-free graph of girth at least seven is 3-colorable. This strengthens results of Golovach et al.Comment: 17 pages, improved girth results. arXiv admin note: text overlap with arXiv:1504.0697

Stringy multifield quintessence and the Swampland

We consider quintessence models within 4D effective descriptions of gravity coupled to two scalar fields. These theories are known to give rise to viable models of late-time cosmic acceleration without any need for flat potentials, and so they are potentially in agreement with the dS Swampland conjecture. In this paper we investigate the possibility of consistently embedding such constructions in string theory. We identify situations where the quintessence fields are either closed string universal moduli or non-universal moduli such as blow-up modes. We generically show that no trajectories compatible with today’s cosmological parameters exist, if one starts from matter-dominated initial conditions. It is worth remarking that universal trajectories compatible with observations do appear, provided that the starting point at early times is a phase of kinetic domination. However, justifying this choice of initial conditions on solid grounds is far from easy. We conclude by studying Q-ball formation in this class of models and discuss constraints coming from Q-ball safety in all cases analyzed here

Investigation of the Spin-Peierls transition in CuGeO_3 by Raman scattering

Raman experiments on the spin-Peierls compound CuGeO$_3$ and the substituted (Cu$_{1- x}$,Zn$_x$)GeO$_3$ and Cu(Ge$_{1-x}$,Ga$_x$)O$_3$ compounds were performed in order to investigate the response of specific magnetic excitations of the one-dimensional spin-1/2 chain to spin anisotropies and substitution-induced disorder. In pure CuGeO$_3$, in addition to normal phonon scattering which is not affected at all by the spin-Peierls transition, four types of magnetic scattering features were observed. Below T$_{SP}$=14 K a singlet-triplet excitation at 30 cm$^{-1}$, two-magnon scattering from 30 to 227 cm$^{-1}$ and folded phonon modes at 369 and 819 cm$^{-1}$ were identified. They were assigned by their temperature dependence and lineshape. For temperatures between the spin-Peierls transition T$_{SP}$ and approximately 100 K a broad intensity maximum centered at 300 cm$^{-1}$ is observed.Comment: 7 pages, LaTex2e, including 3 figures (eps) to be published in Physica B (1996