On the nonexistence of Smith-Toda complexes

Let p be a prime. The Smith-Toda complex V(k) is a finite spectrum whose BP-homology is isomorphic to BP_*/(p,v_1,...,v_k). For example, V(-1) is the sphere spectrum and V(0) the mod p Moore spectrum. In this paper we show that if p > 5, then V((p+3)/2) does not exist and V((p+1)/2), if it exists, is not a ring spectrum. The proof uses the new homotopy fixed point spectral sequences of Hopkins and Miller.Comment: 10 pages, AMSLate

Liquid stability in a model for ortho-terphenyl

We report an extensive study of the phase diagram of a simple model for ortho-terphenyl, focusing on the limits of stability of the liquid state. Reported data extend previous studies of the same model to both lower and higher densities and to higher temperatures. We estimate the location of the homogeneous liquid-gas nucleation line and of the spinodal locus. Within the potential energy landscape formalism, we calculate the distributions of depth, number, and shape of the potential energy minima and show that the statistical properties of the landscape are consistent with a Gaussian distribution of minima over a wide range of volumes. We report the volume dependence of the parameters entering in the Gaussian distribution (amplitude, average energy, variance). We finally evaluate the locus where the configurational entropy vanishes, the so-called Kauzmann line, and discuss the relative location of the spinodal and Kauzmann loci.Comment: RevTeX 4, 8 pages, 8 eps figure

Accurate Ritz wavelengths of parity-forbidden [Fe II], [Ti II] and [Cr II] infrared lines of astrophysical interest

With new astronomical infrared spectrographs the demands of accurate atomic data in the infrared have increased. In this region there is a large amount of parity-forbidden lines, which are of importance in diagnostics of low-density astrophysical plasmas. We present improved, experimentally determined, energy levels for the lowest even LS terms of Fe II, Ti II and Cr II, along with accurate Ritz wavelengths for parity-forbidden transitions between and within these terms. Spectra of Fe II, Ti II and Cr II have been produced in a hollow cathode discharge lamp and acquired using high-resolution Fourier Transform (FT) spectrometry. The energy levels have been determined by using observed allowed ultraviolet transitions connecting the even terms with upper odd terms. Ritz wavelengths of parity-forbidden lines have then been determined. Energy levels of the four lowest Fe II terms (a$^{6}$D, a$^{4}$F, a$^{4}$D and a$^{4}$P) have been determined, resulting in 97 different parity-forbidden transitions with wavelengths between 0.74 and 87 micron. For Ti II the energy levels of the two lowest terms (a$^{4}$F and b$^{4}$F) have been determined, resulting in 24 different parity-forbidden transitions with wavelengths between 8.9 and 130 micron. Also for Cr II the energy levels of the two lowest terms (a$^{6}$S and a$^{6}$D) have been determined, in this case resulting in 12 different parity-forbidden transitions with wavelengths between 0.80 and 140 micron.Comment: Accepted for publication in A&A, 13 pages, 6 figures, 9 table

Investigation of the relation between local diffusivity and local inherent structures in the Kob-Andersen Lennard-Jones model

We analyze one thousand independent equilibrium trajectories of a system of 155 Lennard Jones particles to separate in a model-free approach the role of temperature and the role of the explored potential energy landscape basin depth in the particle dynamics. We show that the diffusion coefficient $D$ can be estimated as a sum over over contributions of the sampled basins, establishing a connection between thermodynamics and dynamics in the potential energy landscape framework. We provide evidence that the observed non-linearity in the relation between local diffusion and basin depth is responsible for the peculiar dynamic behavior observed in supercooled states and provide an interpretation for the presence of dynamic heterogeneities.Comment: minor text changes, references adde

Energy landscape of a simple model for strong liquids

We calculate the statistical properties of the energy landscape of a minimal model for strong network-forming liquids. Dynamics and thermodynamic properties of this model can be computed with arbitrary precision even at low temperatures. A degenerate disordered ground state and logarithmic statistics for the energy distribution are the landscape signatures of strong liquid behavior. Differences from fragile liquid properties are attributed to the presence of a discrete energy scale, provided by the particle bonds, and to the intrinsic degeneracy of topologically disordered networks.Comment: Revised versio