Improved solution for potential flow about arbitrary axisymmetric bodies by the use of a higher-order surface source method. Part 1. Theory and results

The surface-source method of calculating potential flow is improved by refining the underlying numerical analysis. The analysis uses parabolic elements and linearly-varying source density. The result is a large increase in computing speed and accuracy. The theory is described, and the effectiveness of the modification is illustrated

Controlling the accuracy of the density matrix renormalization group method: The Dynamical Block State Selection approach

We have applied the momentum space version of the Density Matrix Renormalization Group method ($k$-DMRG) in quantum chemistry in order to study the accuracy of the algorithm in the new context. We have shown numerically that it is possible to determine the desired accuracy of the method in advance of the calculations by dynamically controlling the truncation error and the number of block states using a novel protocol which we dubbed Dynamical Block State Selection (DBSS). The relationship between the real error and truncation error has been studied as a function of the number of orbitals and the fraction of filled orbitals. We have calculated the ground state of the molecules CH$_2$, H$_2$O, and F$_2$ as well as the first excited state of CH$_2$. Our largest calculations were carried out with 57 orbitals, the largest number of block states was 1500--2000, and the largest dimensions of the Hilbert space of the superblock configuration was 800.000--1.200.000.Comment: 12 page

Quantitative nanoscale vortex-imaging using a cryogenic quantum magnetometer

Microscopic studies of superconductors and their vortices play a pivotal role in our understanding of the mechanisms underlying superconductivity. Local measurements of penetration depths or magnetic stray-fields enable access to fundamental aspects of superconductors such as nanoscale variations of superfluid densities or the symmetry of their order parameter. However, experimental tools, which offer quantitative, nanoscale magnetometry and operate over the large range of temperature and magnetic fields relevant to address many outstanding questions in superconductivity, are still missing. Here, we demonstrate quantitative, nanoscale magnetic imaging of Pearl vortices in the cuprate superconductor YBCO, using a scanning quantum sensor in form of a single Nitrogen-Vacancy (NV) electronic spin in diamond. The sensor-to-sample distance of ~10nm we achieve allows us to observe striking deviations from the prevalent monopole approximation in our vortex stray-field images, while we find excellent quantitative agreement with Pearl's analytic model. Our experiments yield a non-invasive and unambiguous determination of the system's local London penetration depth, and are readily extended to higher temperatures and magnetic fields. These results demonstrate the potential of quantitative quantum sensors in benchmarking microscopic models of complex electronic systems and open the door for further exploration of strongly correlated electron physics using scanning NV magnetometry.Comment: Main text (5 pages, 4 figures) plus supplementary material (5 pages, 6 figures). Comments welcome. Further information under http://www.quantum-sensing.c

Excitons in a Photosynthetic Light-Harvesting System: A Combined Molecular Dynamics/Quantum Chemistry and Polaron Model Study

The dynamics of pigment-pigment and pigment-protein interactions in light-harvesting complexes is studied with a novel approach which combines molecular dynamics (MD) simulations with quantum chemistry (QC) calculations. The MD simulations of an LH-II complex, solvated and embedded in a lipid bilayer at physiological conditions (with total system size of 87,055 atoms) revealed a pathway of a water molecule into the B800 binding site, as well as increased dimerization within the B850 BChl ring, as compared to the dimerization found for the crystal structure. The fluctuations of pigment (B850 BChl) excitation energies, as a function of time, were determined via ab initio QC calculations based on the geometries that emerged from the MD simulations. From the results of these calculations we constructed a time-dependent Hamiltonian of the B850 exciton system from which we determined the linear absorption spectrum. Finally, a polaron model is introduced to describe quantum mechanically both the excitonic and vibrational (phonon) degrees of freedom. The exciton-phonon coupling that enters into the polaron model, and the corresponding phonon spectral function are derived from the MD/QC simulations. It is demonstrated that, in the framework of the polaron model, the absorption spectrum of the B850 excitons can be calculated from the autocorrelation function of the excitation energies of individual BChls, which is readily available from the combined MD/QC simulations. The obtained result is in good agreement with the experimentally measured absorption spectrum.Comment: REVTeX3.1, 23 pages, 13 (EPS) figures included. A high quality PDF file of the paper is available at http://www.ks.uiuc.edu/Publications/Papers/PDF/DAMJ2001/DAMJ2001.pd

Vortex precession in Bose-Einstein condensates: observations with filled and empty cores

We have observed and characterized the dynamics of singly quantized vortices in dilute-gas Bose-Einstein condensates. Our condensates are produced in a superposition of two internal states of 87Rb, with one state supporting a vortex and the other filling the vortex core. Subsequently, the state filling the core can be partially or completely removed, reducing the radius of the core by as much as a factor of 13, all the way down to its bare value. The corresponding superfluid rotation rates, evaluated at the core radius, vary by a factor of 150, but the precession frequency of the vortex core about the condensate axis changes by only a factor of two.Comment: 4 pages, 3 figure

Self-Similar Interpolation in Quantum Mechanics

An approach is developed for constructing simple analytical formulae accurately approximating solutions to eigenvalue problems of quantum mechanics. This approach is based on self-similar approximation theory. In order to derive interpolation formulae valid in the whole range of parameters of considered physical quantities, the self-similar renormalization procedure is complimented here by boundary conditions which define control functions guaranteeing correct asymptotic behaviour in the vicinity of boundary points. To emphasize the generality of the approach, it is illustrated by different problems that are typical for quantum mechanics, such as anharmonic oscillators, double-well potentials, and quasiresonance models with quasistationary states. In addition, the nonlinear Schr\"odinger equation is considered, for which both eigenvalues and wave functions are constructed.Comment: 1 file, 30 pages, RevTex, no figure

The Interstellar Environment of our Galaxy

We review the current knowledge and understanding of the interstellar medium of our galaxy. We first present each of the three basic constituents - ordinary matter, cosmic rays, and magnetic fields - of the interstellar medium, laying emphasis on their physical and chemical properties inferred from a broad range of observations. We then position the different interstellar constituents, both with respect to each other and with respect to stars, within the general galactic ecosystem.Comment: 39 pages, 12 figures (including 3 figures in 2 parts

Classification tree analysis of second neoplasms in survivors of childhood cancer

BACKGROUND: Reports on childhood cancer survivors estimated cumulative probability of developing secondary neoplasms vary from 3,3% to 25% at 25 years from diagnosis, and the risk of developing another cancer to several times greater than in the general population. METHODS: In our retrospective study, we have used the classification tree multivariate method on a group of 849 first cancer survivors, to identify childhood cancer patients with the greatest risk for development of secondary neoplasms. RESULTS: In observed group of patients, 34 develop secondary neoplasm after treatment of primary cancer. Analysis of parameters present at the treatment of first cancer, exposed two groups of patients at the special risk for secondary neoplasm. First are female patients treated for Hodgkin's disease at the age between 10 and 15 years, whose treatment included radiotherapy. Second group at special risk were male patients with acute lymphoblastic leukemia who were treated at the age between 4,6 and 6,6 years of age. CONCLUSION: The risk groups identified in our study are similar to the results of studies that used more conventional approaches. Usefulness of our approach in study of occurrence of second neoplasms should be confirmed in larger sample study, but user friendly presentation of results makes it attractive for further studies

Drought-Adaptation Potential in Fagus sylvatica: Linking Moisture Availability with Genetic Diversity and Dendrochronology

<div><h3>Background</h3><p>Microevolution is essential for species persistence especially under anticipated climate change scenarios. Species distribution projection models suggested that the dominant tree species of lowland forests in Switzerland, European beech (<em>Fagus sylvatica</em> L.), might disappear from most areas due to expected longer dry periods. However, if genotypes at the moisture boundary of the species climatic envelope are adapted to lower moisture availability, they can serve as seed source for the continuation of beech forests under changing climates.</p> <h3>Methodology/Principal Findings</h3><p>With an AFLP genome scan approach, we studied neutral and potentially adaptive genetic variation in <em>Fagus sylvatica</em> in three regions containing a dry and a mesic site each (<em>n</em>_ind. = 241, <em>n</em>_markers = 517). We linked this dataset with dendrochronological growth measures and local moisture availabilities based on precipitation and soil characteristics. Genetic diversity decreased slightly at dry sites. Overall genetic differentiation was low (<em>F</em>_st = 0.028) and Bayesian cluster analysis grouped all populations together suggesting high (historical) gene flow. The Bayesian outlier analyses indicated 13 markers with three markers differing between all dry and mesic sites and the others between the contrasting sites within individual regions. A total of 41 markers, including seven outlier loci, changed their frequency with local moisture availability. Tree height and median basal growth increments were reduced at dry sites, but marker presence/absence was not related to dendrochronological characteristics.</p> <h3>Conclusion and Their Significance</h3><p>The outlier alleles and the makers with changing frequencies in relation to moisture availability indicate microevolutionary processes occurring within short geographic distances. The general genetic similarity among sites suggests that ‘preadaptive’ genes can easily spread across the landscape. Yet, due to the long live span of trees, fostering saplings originating from dry sites and grown within mesic sites might increase resistance of beech forests during the anticipated longer dry periods.</p> </div