Computing Groebner Fans

This paper presents algorithms for computing the Groebner fan of an arbitrary polynomial ideal. The computation involves enumeration of all reduced Groebner bases of the ideal. Our algorithms are based on a uniform definition of the Groebner fan that applies to both homogeneous and non-homogeneous ideals and a proof that this object is a polyhedral complex. We show that the cells of a Groebner fan can easily be oriented acyclically and with a unique sink, allowing their enumeration by the memory-less reverse search procedure. The significance of this follows from the fact that Groebner fans are not always normal fans of polyhedra in which case reverse search applies automatically. Computational results using our implementation of these algorithms in the software package Gfan are included.Comment: 26 page

Dynamics of large anisotropic spin in a sub-ohmic dissipative environment close to a quantum-phase transition

We investigate the dynamics of a large anisotropic spin whose easy-axis component is coupled to a bosonic bath with a spectral function J(\w)\propto \omega^s. Such a spin complex might be realized in a single-molecular magnet. Using the non-perturbative renormalization group, we calculate the line of quantum-phase transitions in the sub-ohmic regime ($s<1$). These quantum-phase transitions only occur for integer spin $J$. For half-integer $J$, the low temperature fixed-point is identical to the fixed-point of the spin-boson model without quantum-tunneling between the two levels. Short-time coherent oscillations in the spin decay prevail even into the localized phase in the sub-ohmic regime. The influence of the reorganization energy and the recurrence time on the decoherence in the absence of quantum-tunneling is discussed.Comment: 14 pages,7 figure

Time-reversible Born-Oppenheimer molecular dynamics

We present a time-reversible Born-Oppenheimer molecular dynamics scheme, based on self-consistent Hartree-Fock or density functional theory, where both the nuclear and the electronic degrees of freedom are propagated in time. We show how a time-reversible adiabatic propagation of the electronic degrees of freedom is possible despite the non-linearity and incompleteness of the self-consistent field procedure. Time-reversal symmetry excludes a systematic long-term energy drift for a microcanonical ensemble and the number of self-consistency cycles can be kept low (often only 2-4 cycles per nuclear time step) thanks to a good initial guess given by the adiabatic propagation of the electronic degrees of freedom. The time-reversible Born-Oppenheimer molecular dynamics scheme therefore combines a low computational cost with a physically correct time-reversible representation of the dynamics, which preserves a detailed balance between propagation forwards and backwards in time.Comment: 4 pages, 4 figure

ALFA & 3D: integral field spectroscopy with adaptive optics

One of the most important techniques for astrophysics with adaptive optics is the ability to do spectroscopy at diffraction limited scales. The extreme difficulty of positioning a faint target accurately on a very narrow slit can be avoided by using an integral field unit, which provides the added benefit of full spatial coverage. During 1998, working with ALFA and the 3D integral field spectrometer, we demonstrated the validity of this technique by extracting and distinguishing spectra from binary stars separated by only 0.26". The combination of ALFA & 3D is also ideally suited to imaging distant galaxies or the nuclei of nearby ones, as its field of view can be changed between 1.2"x1.2" and 4"x4", depending on the pixel scale chosen. In this contribution we present new results both on galactic targets, namely young stellar objects, as well as extra-galactic objects including a Seyfert and a starburst nucleus.Comment: SPIE meeting 4007 on Adaptive Optical Systems Technology, March 200

Density Matrix Perturbation Theory

An expansion method for perturbation of the zero temperature grand canonical density matrix is introduced. The method achieves quadratically convergent recursions that yield the response of the zero temperature density matrix upon variation of the Hamiltonian. The technique allows treatment of embedded quantum subsystems with a computational cost scaling linearly with the size of the perturbed region, O(N_pert.), and as O(1) with the total system size. It also allows direct computation of the density matrix response functions to any order with linear scaling effort. Energy expressions to 4th order based on only first and second order density matrix response are given.Comment: 4 pages, 2 figure

Wilson chains are not thermal reservoirs

Wilson chains, based on a logarithmic discretization of a continuous spectrum, are widely used to model an electronic (or bosonic) bath for Kondo spins and other quantum impurities within the numerical renormalization group method and other numerical approaches. In this short note we point out that Wilson chains can not serve as thermal reservoirs as their temperature changes by a number of order Delta E when a finite amount of energy Delta E is added. This proves that for a large class of non-equilibrium problems they cannot be used to predict the long-time behavior.Comment: 2 page

Spin wave dispersion in La2CuO4

We calculate the antiferromagnetic spin wave dispersion in the half-filled Hubbard model for a two-dimensional square lattice and find it to be in excellent agreement with recent high-resolution inelastic neutron scattering performed on La2CuO4 [Phys. Rev. Lett. 86, 5377 (2001)].Comment: typos correcte

Advances in methods for determining fecundity: application of the new methods to some marine fishes

Estimation of individual egg production (realized fecundity) is a key step either to understand the stock and recruit relationship or to carry out fisheries-independent assessment of spawning stock biomass using egg production methods. Many fish are highly fecund and their ovaries may weigh over a kilogram; therefore the work time can be consuming and require large quantities of toxic fixative. Recently it has been shown for Atlantic cod (Gadus morhua) that image analysis can automate fecundity determination using a power equation that links follicles per gram ovary to the mean vitellogenic follicular diameter (the autodiametric method). In this article we demonstrate the precision of the autodiametric method applied to a range of species with different spawning strategies during maturation and spawning. A new method using a solid displacement pipette to remove quantitative fecundity samples (25, 50, 100, and 200 milligram [mg]) is evaluated, as are the underlying assumptions to effectively fix and subsample the ovary. Finally, we demonstrate the interpretation of dispersed formaldehyde-fixed ovarian samples (whole mounts) to assess the presence of atretic and postovulatory follicles to replace labor intensive histology. These results can be used to estimate down regulation (production of atretic follicles) of fecundity during maturation

Analysing observed star cluster SEDs with evolutionary synthesis models: systematic uncertainties

The definitive version is available at www.blackwell-synergy.com. Copyright Blackwell Publishing DOI : 10.1111/j.1365-2966.2004.07197.xWe discuss the systematic uncertainties inherent to analyses of observed (broad-band) Spectral Energy Distributions (SEDs) of star clusters with evolutionary synthesis models. We investigate the effects caused by restricting oneself to a limited number of available passbands, choices of various passband combinations, finite observational errors, non-continuous model input parameter values, and restrictions in parameter space allowed during analysis. Starting from a complete set of UBVRIJH passbands (respectively their Hubble Space Telescope/WFPC2 equivalents) we investigate to which extent clusters with different combinations of age, metallicity, internal extinction and mass can or cannot be disentangled in the various evolutionary stages throughout their lifetimes and what are the most useful passbands required to resolve the ambi- guities. We find the U and B bands to be of the highest significance, while the V band and near-infrared data provide additional constraints. A code is presented that makes use of luminosities of a star cluster system in all of the possibly available passbands, and tries to find ranges of allowed age-metallicity-extinction-mass combinations for individual members of star cluster systems. Numerous tests and examples are pre- sented. We show the importance of good photometric accuracies and of determining the cluster parameters independently without any prior assumptions.Peer reviewe