Rectangular Full Packed Format for Cholesky's Algorithm: Factorization, Solution and Inversion

We describe a new data format for storing triangular, symmetric, and Hermitian matrices called RFPF (Rectangular Full Packed Format). The standard two dimensional arrays of Fortran and C (also known as full format) that are used to represent triangular and symmetric matrices waste nearly half of the storage space but provide high performance via the use of Level 3 BLAS. Standard packed format arrays fully utilize storage (array space) but provide low performance as there is no Level 3 packed BLAS. We combine the good features of packed and full storage using RFPF to obtain high performance via using Level 3 BLAS as RFPF is a standard full format representation. Also, RFPF requires exactly the same minimal storage as packed format. Each LAPACK full and/or packed triangular, symmetric, and Hermitian routine becomes a single new RFPF routine based on eight possible data layouts of RFPF. This new RFPF routine usually consists of two calls to the corresponding LAPACK full format routine and two calls to Level 3 BLAS routines. This means {\it no} new software is required. As examples, we present LAPACK routines for Cholesky factorization, Cholesky solution and Cholesky inverse computation in RFPF to illustrate this new work and to describe its performance on several commonly used computer platforms. Performance of LAPACK full routines using RFPF versus LAPACK full routines using standard format for both serial and SMP parallel processing is about the same while using half the storage. Performance gains are roughly one to a factor of 43 for serial and one to a factor of 97 for SMP parallel times faster using vendor LAPACK full routines with RFPF than with using vendor and/or reference packed routines

Theoretical study of a cold atom beam splitter

A theoretical model is presented for the study of the dynamics of a cold atomic cloud falling in the gravity field in the presence of two crossing dipole guides. The cloud is split between the two branches of this laser guide, and we compare experimental measurements of the splitting efficiency with semiclassical simulations. We then explore the possibilities of optimization of this beam splitter. Our numerical study also gives access to detailed information, such as the atom temperature after the splitting

Noise limits in matter-wave interferometry using degenerate quantum gases

We analyze the phase resolution limit of a Mach-Zehnder atom interferometer whose input consists of degenerate quantum gases of either bosons or fermions. For degenerate gases, the number of atoms within one de Broglie wavelength is larger than unity, so that atom-atom interactions and quantum statistics are no longer negligible. We show that for equal atom numbers, the phase resolution achievable with fermions is noticeably better than for interacting bosons.Comment: 4 pages, 5 figure

Propagation of Bose-Einstein condensates in a magnetic waveguide

Gaseous Bose-Einstein condensates of 2-3 million atoms were loaded into a microfabricated magnetic trap using optical tweezers. Subsequently, the condensates were released into a magnetic waveguide and propagated 12 mm. Single-mode propagation was observed along homogeneous segments of the waveguide. Inhomogeneities in the guiding potential arose from geometric deformations of the microfabricated wires and caused strong transverse excitations. Such deformations may restrict the waveguide physics that can be explored with propagating condensates.Comment: 5 pages, 4 figure

Mach's Principle and the Origin of Inertia

The current status of Mach's principle is discussed within the context of general relativity. The inertial properties of a particle are determined by its mass and spin, since these characterize the irreducible unitary representations of the inhomogeneous Lorentz group. The origin of the inertia of mass and intrinsic spin are discussed and the inertia of intrinsic spin is studied via the coupling of intrinsic spin with rotation. The implications of spin-rotation coupling and the possibility of history dependence and nonlocality in relativistic physics are briefly mentioned.Comment: 14 pages. Dedicated to Carl Brans in honor of his 80th birthday. To appear in the Brans Festschrift; v2: typo corrected, published in: At the Frontier of Spacetime, edited by T. Asselmeyer-Maluga (Springer, 2016), Chapter 10, pp. 177-18

First electron beam polarization measurements with a Compton polarimeter at Jefferson Laboratory

A Compton polarimeter has been installed in Hall A at Jefferson Laboratory. This letter reports on the first electron beam polarization measurements performed during the HAPPEX experiment at an electron energy of 3.3 GeV and an average current of 40 $\mu$A. The heart of this device is a Fabry-Perot cavity which increased the luminosity for Compton scattering in the interaction region so much that a 1.4% statistical accuracy could be obtained within one hour, with a 3.3% total error

Transport of Bose-Einstein Condensates with Optical Tweezers

We have transported gaseous Bose-Einstein condensates over distances up to 44 cm. This was accomplished by trapping the condensate in the focus of an infrared laser and translating the location of the laser focus with controlled acceleration. Condensates of order 1 million atoms were moved into an auxiliary chamber and loaded into a magnetic trap formed by a Z-shaped wire. This transport technique avoids the optical and mechanical access constraints of conventional condensate experiments and creates many new scientific opportunities.Comment: 5 pages, 3 figure

Investigation Into the Humaneness of Slaughter Methods for Guinea Pigs (Cavia porcelus) in the Andean Region

Guinea pigs (Cavia porcelus) are an important source of nonhuman animal protein in the Andean region of South America. Specific guidelines regarding the welfare of guinea pigs before and during slaughter have yet to be developed. This study critically assessed the humaneness of 4 different stunning/slaughter methods for guinea pigs: cervical neck dislocation (n = 60), electrical head-only stunning (n = 83), carbon dioxide (CO(2)) stunning (n = 21), and penetrating captive bolt (n = 10). Following cervical neck dislocation, 97% of guinea pigs had at least 1 behavioral or cranial/spinal response. Six percent of guinea pigs were classified as mis-stunned after electrical stunning, and 1% were classified as mis-stunned after captive bolt. Increased respiratory effort was observed during CO(2) stunning. Apart from this finding, there were no other obvious behavioral responses that could be associated with suffering. Of the methods assessed, captive bolt was deemed the most humane, effective, and practical method of stunning guinea pigs. Cervical neck dislocation should not be recommended as a slaughter method for guinea pigs

Petrology and geochemistry of late-stage intrusions of the A-type, mid-Proterozoic Pikes Peak batholith (Central Colorado, USA): implications for petrogenetic models

The ~1.08 Ga anorogenic, A-type Pikes Peak batholith (Front Range, central Colorado) is dominated by coarse-grained, biotite ± amphibole syenogranites and minor monzogranites, collectively referred to as Pikes Peak granite (PPG). The batholith is also host to numerous small, late-stage plutons that have been subdivided into two groups (e.g. Wobus, 1976. Studies in Colorado Field Geology, Colorado School of Mines Professional Contributions, Colorado): (1) a sodic series (SiO2 = ~44–78 wt%; K/Na = 0.32–1.36) composed of gabbro, diabase, syenite/quartz syenite and fayalite and sodic amphibole granite; and (2) a potassic series (SiO2 = ~70–77 wt%; K/Na = 0.95–2.05), composed of biotite granite and minor quartz monzonite. Differences in major and trace element and Nd isotopic characteristics for the two series indicate different petrogenetic histories. Potassic granites of the late-stage intrusions appear to represent crustal anatectic melts derived from tonalite sources, based on comparison of their major element compositions with experimental melt products. In addition, Nd isotopic characteristics of the potassic granites [εNd (1.08 Ga) = −0.2 to −2.7] overlap with those for tonalites/granodiorites [ca 1.7 Ga Boulder Creek intrusions; εNd (1.08 Ga) = −2.4 to −3.6] exposed in the region. Some of the partial melts evolved by fractionation dominated by feldspar. The late-stage potassic granites share geochemical characteristics with most of the PPG, which is also interpreted to have an anatectic origin involving tonalitic crust. The origin of monzogranites associated with the PPG remains unclear, but mixing between granitic and mafic or intermediate magmas is a possibility. Syenites and granites of the sodic series cannot be explained as crustal melts, but are interpreted as fractionation products of mantle-derived mafic magmas with minor crustal input. High temperature and low oxygen fugacity estimates (e.g. Frost et al., 1988. American Mineralogist 73, 727–740) support a basalt fractionation origin, as do εNd values for sodic granitoids [εNd (1.08 Ga) = +2.2 to −0.7], which are higher than εNd values for Colorado crust at 1.08 Ga (ca −1.0 to −4.0). Enrichments in incompatible elements (e.g. rare earth elements, Rb, Y) and depletions in compatible elements (e.g. Cr, Sr, Ba) in the sodic granitoids compared to coeval mafic rocks are also consistent with fractionation. Accessory mineral fractionation, release of fluorine-rich volatiles and/or removal of pegmatitic fluids could have modified abundances of Ce, Nb, Zr and Y in some sodic granitoid magmas. Gabbros and mafic dikes associated with the sodic granitoids have εNd (1.08 Ga) of −3.0 to +3.5, which are lower than depleted mantle at 1.08 Ga, and their trace element characteristics suggest derivation from mantle sources that were previously affected by subduction-related processes. However, it is difficult to characterize the mantle component in these magmas, because assimilation of crust during magma ascent could also result in their observed geochemical features. The Pikes Peak batholith is composed of at least two petrogenetically different granite types, both of which exhibit geochemical characteristics typical of A-type granites. Models proposed for the petrogenesis of the granitoids imply the existence of mafic rocks at depth and addition of juvenile material to the crust in central Colorado at ~1.1 Ga

Eliminating the mean-field shift in multicomponent Bose-Einstein condensates

We demonstrate that the nonlinear mean-field shift in a multi-component Bose-Einstein condensate may be eliminated by controlling the two-body interaction coefficients. This modification is achieved by, e.g., suitably engineering the environment of the condensate. We consider as an example the case of a two-component condensate in a tightly confining atom waveguide. Modification of the atom-atom interactions is then achieved by varying independently the transverse wave function of the two components. Eliminating the density dependent phase shift in a high-density atomic beam has important applications in atom interferometry and precision measurement