Variable order integrators for the numerical solution of ordinary differential equations

Series of computer subroutines integrates systems of ordinary differential equations and is used for numerical quadrature

Multi-dimensional real Fourier transform

Four subroutines compute one-dimensional and multi-dimensional Fourier transforms for real data, multi-dimensional complex Fourier transforms, and multi-dimensional sine, cosine and sine-cosine transforms. Subroutines use Cooley-Tukey fast Fourier transform. In all but one-dimensional case, transforms are calculated in up to six dimensions

University Innovation and the Professor’s Privilige

Publisher PD

High precision U-PB geochronology and implications for the tectonic evolution of the Superior Province

The underlying mechanisms of Archean tectonics and the degree to which modern plate tectonic models are applicable early in Earth's history continue to be a subject of considerable debate. A precise knowledge of the timing of geological events is of the utmost importance in studying this problem. The high precision U-Pb method has been applied in recent years to rock units in many areas of the Superior Province. Most of these data have precisions of about + or - 2-3 Ma. The resulting detailed chronologies of local igneous development and the regional age relationships furnish tight constraints on any Archean tectonic model. Superior province terrains can be classified into 3 types: (1) low grade areas dominated by meta-volcanic rocks (greenstone belts); (2) high grade, largely metaplutonic areas with abundant orthogneiss and foliated to massive I-type granitoid bodies; and (3) high grade areas with abundant metasediments, paragneiss and S-type plutons. Most of the U-Pb age determinations have been done on type 1 terrains with very few having been done in type 3 terrains. A compilation of over 120 ages indicates that the major part of igneous activity took place in the period 2760-2670 Ma, known as the Kenoran event. This event was ubiquitous throughout the Superior Province

Recurrence relations for computing with modified divided differences

Modified divided differences (MDD) provide a good way of representing a polynomial passing through points with unequally spaced abcissas. Recurrence relations for computing coefficients in either the monomial or Chebyshev basis from the MDD coefficients, and for computing the MDD coefficients for either the differentiated or the integrated polynomial are given. The latter operation is likely to be useful if MDD are used in a method for solving stiff differential equations

U-Pb isotopic results for single shocked and polycrystalline zircons record 550-65.5-Ma ages for a K-T target site and 2700-1850-Ma ages for the Sudbury impact event

The refractory mineral zircon develops distinct morphological features during shock metamorphism and retains these features under conditions that would anneal them in other minerals. In addition, weakly shocked zircon grains give primary ages for the impact site, while highly reconstituted (polycrystalline) single grains give ages that approach the age of the impact event. Data for a series of originally coeval grains will define a mixing line that gives both of these ages providing that no subsequent geological disturbances have overprinted the isotopic systematics. In this study, we have shown that the three zircon grain types described by Bohor, from both K-T distal ejecta (Fireball layer, Raton Basin, Colorado) and the Onaping Formation, represent a progressive increase in impact-related morphological change that coincides with a progressive increase in isotopic resetting in zircons from the ejecta and basement rocks. Unshocked grains are least affected by isotopic resetting while polycrystalline grains are most affected. U-Pb isotopic results for 12 of 14 single zircon grains from the Fireball layer plot on or close to a line recording a primary age of 550 +/- 10 Ma and a secondary age of 65.5 +/- 3 Ma. Data for the least and most shocked grains plot closest to the primary and secondary ages respectively. The two other grains each give ages between 300 and 350 Ma. This implies that the target ejecta was dominated by 550-Ma rocks and that the recrystallization features of the zircon were superimposed during the impact event at 65.5 Ma. A predominant age of 550 Ma for zircons from the Fireball layer provides an excellent opportunity to identify the impact site and to test the hypothesis that multiple impacts occurred at this time. A volcanic origin for the Fireball layer is ruled out by shock-related morphological changes in zircon and the fact that the least shocked grains are old. Basement Levack gneisses north of the Sudbury structure have a primary age of 2711 Ma. Data for three single zircons from this rock, which record a progressive increase in shock features, are displaced 24, 36, and 45 percent along a Pb-loss line toward the 1850 +/- 1 Ma minimum age for the impact as defined by the age of the norite. Southeast of the structure three shocked grains from the Murray granite record a primary age of 2468 Ma and are displaced 24, 41, and 56 percent toward the 1853 +/- 4 Ma even as defined by coexisting titanite

Basic linear algebra subprograms for FORTRAN usage

A package of 38 low level subprograms for many of the basic operations of numerical linear algebra is presented. The package is intended to be used with FORTRAN. The operations in the package are dot products, elementary vector operations, Givens transformations, vector copy and swap, vector norms, vector scaling, and the indices of components of largest magnitude. The subprograms and a test driver are available in portable FORTRAN. Versions of the subprograms are also provided in assembly language for the IBM 360/67, the CDC 6600 and CDC 7600, and the Univac 1108

Laminar flow of two miscible fluids in a simple network

When a fluid comprised of multiple phases or constituents flows through a network, non-linear phenomena such as multiple stable equilibrium states and spontaneous oscillations can occur. Such behavior has been observed or predicted in a number of networks including the flow of blood through the microcirculation, the flow of picoliter droplets through microfluidic devices, the flow of magma through lava tubes, and two-phase flow in refrigeration systems. While the existence of non-linear phenomena in a network with many inter-connections containing fluids with complex rheology may seem unsurprising, this paper demonstrates that even simple networks containing Newtonian fluids in laminar flow can demonstrate multiple equilibria. The paper describes a theoretical and experimental investigation of the laminar flow of two miscible Newtonian fluids of different density and viscosity through a simple network. The fluids stratify due to gravity and remain as nearly distinct phases with some mixing occurring only by diffusion. This fluid system has the advantage that it is easily controlled and modeled, yet contains the key ingredients for network non-linearities. Experiments and 3D simulations are first used to explore how phases distribute at a single T-junction. Once the phase separation at a single junction is known, a network model is developed which predicts multiple equilibria in the simplest of networks. The existence of multiple stable equilibria is confirmed experimentally and a criteria for their existence is developed. The network results are generic and could be applied to or found in different physical systems

Nonperturbative dynamics for abstract (p,q) string networks

We describe abstract (p,q) string networks which are the string networks of Sen without the information about their embedding in a background spacetime. The non-perturbative dynamical formulation invented for spin networks, in terms of causal evolution of dual triangulations, is applied to them. The formal transition amplitudes are sums over discrete causal histories that evolve (p,q) string networks. The dynamics depend on two free SL(2,Z) invariant functions which describe the amplitudes for the local evolution moves.Comment: Latex, 12 pages, epsfig, 7 figures, minor change

String Junctions and Bound States of Intersecting Branes

We study four-dimensional black hole configurations which result from wrapping M5-branes on a Calabi-Yau manifold, as well as U-dual realizations. Our aim is to understand the microscopic degrees of freedom responsible for the existence of bound states of multiple branes. The details depend on the chosen U-frame; in some cases, they are massless string junctions. We also identify a perturbative description in which these states correspond to twisted strings of intersecting D3-branes at an orbifold singularity. In each case, these are the preponderant states of the spacetime infrared conformal field theory and account for the entropy of the blackhole.Comment: 14 pages; 2 figures; uses latex with epsf and hyperref package