The Partition Function of Multicomponent Log-Gases

We give an expression for the partition function of a one-dimensional log-gas comprised of particles of (possibly) different integer charge at inverse temperature {\beta} = 1 (restricted to the line in the presence of a neutralizing field) in terms of the Berezin integral of an associated non- homogeneous alternating tensor. This is the analog of the de Bruijn integral identities [3] (for {\beta} = 1 and {\beta} = 4) ensembles extended to multicomponent ensembles.Comment: 14 page

Dynamics of Enceladus and Dione inside the 2:1 Mean-Motion Resonance under Tidal Dissipation

In a previous work (Callegari and Yokoyama 2007, Celest. Mech. Dyn. Astr. vol. 98), the main features of the motion of the pair Enceladus-Dione were analyzed in the frozen regime, i.e., without considering the tidal evolution. Here, the results of a great deal of numerical simulations of a pair of satellites similar to Enceladus and Dione crossing the 2:1 mean-motion resonance are shown. The resonance crossing is modeled with a linear tidal theory, considering a two-degrees-of-freedom model written in the framework of the general three-body planar problem. The main regimes of motion of the system during the passage through resonance are studied in detail. We discuss our results comparing them with classical scenarios of tidal evolution of the system. We show new scenarios of evolution of the Enceladus-Dione system through resonance not shown in previous approaches of the problem.Comment: 36 pages, 12 figures. Accepted in Celestial Mechanics and Dynamical Astronom

Detecting and Characterizing Small Dense Bipartite-like Subgraphs by the Bipartiteness Ratio Measure

We study the problem of finding and characterizing subgraphs with small \textit{bipartiteness ratio}. We give a bicriteria approximation algorithm \verb|SwpDB| such that if there exists a subset $S$ of volume at most $k$ and bipartiteness ratio $\theta$, then for any $0<\epsilon<1/2$, it finds a set $S'$ of volume at most $2k^{1+\epsilon}$ and bipartiteness ratio at most $4\sqrt{\theta/\epsilon}$. By combining a truncation operation, we give a local algorithm \verb|LocDB|, which has asymptotically the same approximation guarantee as the algorithm \verb|SwpDB| on both the volume and bipartiteness ratio of the output set, and runs in time $O(\epsilon^2\theta^{-2}k^{1+\epsilon}\ln^3k)$, independent of the size of the graph. Finally, we give a spectral characterization of the small dense bipartite-like subgraphs by using the $k$th \textit{largest} eigenvalue of the Laplacian of the graph.Comment: 17 pages; ISAAC 201

Quenched QCD at finite density

Simulations of quenched $QCD$ at relatively small but {\it nonzero} chemical potential $\mu$ on $32 \times 16^3$ lattices indicate that the nucleon screening mass decreases linearly as $\mu$ increases predicting a critical chemical potential of one third the nucleon mass, $m_N/3$, by extrapolation. The meson spectrum does not change as $\mu$ increases over the same range, from zero to $m_\pi/2$. Past studies of quenched lattice QCD have suggested that there is phase transition at $\mu = m_\pi/2$. We provide alternative explanations for these results, and find a number of technical reasons why standard lattice simulation techniques suffer from greatly enhanced fluctuations and finite size effects for $\mu$ ranging from $m_\pi/2$ to $m_N/3$. We find evidence for such problems in our simulations, and suggest that they can be surmounted by improved measurement techniques.Comment: 23 pages, Revte

Pathologies of Quenched Lattice QCD at non--zero Density and its Effective Potential

We simulate lattice QCD at non--zero baryon density and zero temperature in the quenched approximation, both in the scaling region and in the infinite coupling limit. We investigate the nature of the forbidden region -- the range of chemical potential where the simulations grow prohibitively expensive, and the results, when available, are puzzling if not unphysical. At weak coupling we have explored the sensitivity of these pathologies to the lattice size, and found that using a large lattice ($64 \times 16^3$) does not remove them. The effective potential sheds considerable light on the problems in the simulations, and gives a clear interpretation of the forbidden region. The strong coupling simulations were particularly illuminating on this point.Comment: 49 pages, uu-encoded expanding to postscript;also available at ftp://hlrz36.hlrz.kfa-juelich.de/pub/mpl/hlrz72_95.p

Towards the electron EDM search: Theoretical study of HfF+

We report first ab initio relativistic correlation calculations of potential curves for ten low-lying electronic states, effective electric field on the electron and hyperfine constants for the ^3\Delta_1 state of cation of a heavy transition metal fluoride, HfF^+, that is suggested to be used as the working state in experiments to search for the electric dipole moment of the electron. It is shown that HfF^+ has deeply bound ^1\Sigma^+ ground state, its dissociation energy is D_e=6.4 eV. The ^3\Delta_1 state is obtained to be the relatively long-lived first excited state lying about 0.2 eV higher. The calculated effective electric field E_eff=W_d|\Omega| acting on an electron in this state is 5.84*10^{24}Hz/(e*cm)Comment: 4 page

New Cretaceous empidoids and the Mesozoic dance fly revolution (Diptera: Empidoidea)

Dance flies and relatives (Empidoidea) are a diverse and ecologically important group of Diptera in nearly all modern terrestrial ecosystems. Their fossil record, despite being scattered, attests to a long evolutionary history dating back to the early Mesozoic. Here, we describe seven new species of Empidoidea from Cretaceous Kachin amber inclusions, assigning them to the new genus Electrochoreutes gen.n. (type species: Electrochoreutes trisetigerus sp.n.) based on unique apomorphies among known Diptera. Like many extant dance flies, the males of Electrochoreutes are characterized by species-specific sexually dimorphic traits, which are likely to have played a role in courtship. The fine anatomy of the fossils was investigated through high-resolution X-ray phase-contrast microtomography to reconstruct their phylogenetic affinities within the empidoid clade, using cladistic reasoning. Morphology-based phylogenetic analyses including a selection of all extant family- and subfamily-ranked empidoid clades along with representatives of all extinct Mesozoic genera, were performed using a broad range of analytical methods (maximum parsimony, maximum-likelihood and Bayesian inference). These analyses converged in reconstructing Electrochoreutes as a stem-group representative of the Dolichopodidae, suggesting that complex mating rituals evolved in this lineage during the Cretaceous

Investigation of the soil properties that affect Olsen P critical values in different soil types and impact on P fertiliser recommendations

Optimization of phosphorus (P) fertiliser use is desired to ensure more sustainable use of fertiliser, economic food production and reduction of eutrophication of water bodies. Presently, the Olsen P values on which fertiliser recommendations are based to achieve optimum yield are frequently the same for all soils. The aim of this study was to identify the properties of different soils that affect their critical Olsen P values in order to develop better, soil specific P fertiliser recommendations. A pot experiment using 10 soils with low available P with different P additions was carried out to investigate the impact of wide-ranging soil properties on the relationship between P addition, resultant Olsen P values and yield response of ryegrass to Olsen P values. The relationship between added P and Olsen P varied greatly between the individual soils. These relationships were affected by pH, manganese oxide, crystalline aluminium oxide and amorphous iron oxide contents of the soil. Different soils had widely varying critical Olsen P values for ryegrass. However, these could not be related to the measured soil properties. Fertiliser recommendations and critical values for optimum yield of ryegrass based on the Olsen P test should be soil specific. The complexity and lack of clarity over which combination of soil properties governs critical Olsen P values calls for further investigation with more soil types and additional soil property measurements to elucidate the different factors controlling critical Olsen P values in different soils

Random polynomials, random matrices, and LL-functions

We show that the Circular Orthogonal Ensemble of random matrices arises naturally from a family of random polynomials. This sheds light on the appearance of random matrix statistics in the zeros of the Riemann zeta-function.Comment: Added background material. Final version. To appear in Nonlinearit