On some topological properties of the systems of compartments
Topological properties of compartment systems used for tracer and drug kinetics
DRUG↗
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Some topological properties of halfgroupoids technical report no. 8
Some topological properties of halfgroupoids
MATHEMATICS↗
The Universe at Moderate Redshift
The report covers the work done in the past year and a wide range of fields including properties of clusters of galaxies; topological properties of galaxy distributions in terms of galaxy types; patterns of gravitational nonlinear clustering process; development of a ray tracing algorithm to study the gravitational lensing phenomenon by galaxies, clusters and large-scale structure, one of whose applications being the effects of weak gravitational lensing by large-scale structure on the determination of q(0); the origin of magnetic fields on the galactic and cluster scales; the topological properties of Ly(alpha) clouds the Ly(alpha) optical depth distribution; clustering properties of Ly(alpha) clouds; and a determination (lower bound) of Omega(b) based on the observed Ly(alpha) forest flux distribution. In the coming year, we plan to continue the investigation of Ly(alpha) clouds using larger dynamic range (about a factor of two) and better simulations (with more input physics included) than what we have now. We will study the properties of galaxies on 1 - 100h(sup -1) Mpc scales using our state-of-the-art large scale galaxy formation simulations of various cosmological models, which will have a resolution about a factor of 5 (in each dimension) better than our current, best simulations. We will plan to study the properties of X-ray clusters using unprecedented, very high dynamic range (20,000) simulations which will enable us to resolve the cores of clusters while keeping the simulation volume sufficiently large to ensure a statistically fair sample of the objects of interest. The details of the last year's works are now described.
Cen, Renyue↗
Topologies on directed graphs
Given a directed graph, a natural topology is defined and relationships between standard topological properties and graph theoretical concepts are studied. In particular, the properties of connectivity and separatedness are investigated. A metric is introduced which is shown to be related to separatedness. The topological notions of continuity and homeomorphism. A class of maps is studied which preserve both graph and topological properties. Applications involving strong maps and contractions are also presented.
Lieberman, R. N.↗
Finite elements of nonlinear continua.
The finite element method is extended to a broad class of practical nonlinear problems, treating both theory and applications from a general and unifying point of view. The thermomechanical principles of continuous media and the properties of the finite element method are outlined, and are brought together to produce discrete physical models of nonlinear continua. The mathematical properties of the models are analyzed, and the numerical solution of the equations governing the discrete models is examined. The application of the models to nonlinear problems in finite elasticity, viscoelasticity, heat conduction, and thermoviscoelasticity is discussed. Other specific topics include the topological properties of finite element models, applications to linear and nonlinear boundary value problems, convergence, continuum thermodynamics, finite elasticity, solutions to nonlinear partial differential equations, and discrete models of the nonlinear thermomechanical behavior of dissipative media.
Oden, J. T.↗
Hamiltonian indices and rational spectral densities
Several (global) topological properties of various spaces of linear systems, particularly symmetric, lossless, and Hamiltonian systems, and multivariable spectral densities of fixed McMillan degree are announced. The study is motivated by a result asserting that on a connected but not simply connected manifold, it is not possible to find a vector field having a sink as its only critical point. In the scalar case, this is illustrated by showing that only on the space of McMillan degree = /Cauchy index/ = n, scalar transfer functions can one define a globally convergent vector field. This result holds both in discrete-time and for the nonautonomous case. With these motivations in mind, theorems of Bochner and Fogarty are used in showing that spaces of transfer functions defined by symmetry conditions are, in fact, smooth algebraic manifolds.
Byrnes, C. I.↗
Magnetic helicity of the Parker field
The topological properties of the interplanetary magnetic field are discussed based on a calculation of the magnetic helicity of the Parker field. The most striking feature of the helicity is that it is negative north of the heliospheric current sheet and positive south of the current sheet, regardless of the sign of the solar poloidal magnetic field. Informal arguments based on MHD turbulence theory suggest that the magnetic helicity of turbulence in the interplanetary medium may be related to the large-scale Parker helicity. Because charged particle scattering in certain types of magnetic turbulence (such as slab turbulence) depends strongly upon helicity, the existence of such a relationship could have important implications to cosmic-ray transport in the heliosphere.
Bieber, J. W.↗
N-body models
The experimental discovery of an overstability in the central regions of galaxies is briefly discussed, and numerical methods for integrating orbits are briefly addressed. The overstability manifests itself as a growing amplitude in the orbit of a galaxy's nucleus about its mass centroid. This finding may complicate studies of the topological properties of orbits and studies of the bifurcation structure of orbits. A sample problem is used to illustrate the importance of a Liouville theorem in N-body calculations.
Miller, R. H.↗
A study of the turbulence structures of wall-bounded shear flows
This project extends the study of the structure of wall-bounded flows using the topological properties of eddying motions as developed by Chong et al. (1990), Soria et al. (1992, 1994), and as recently extended by Blackburn et al. (1996) and Chacin et al. (1996). In these works, regions of flow which are focal in nature are identified by being enclosed by an isosurface of a positive small value of the discriminant of the velocity gradient tensor. These regions resemble the attached vortex loops suggested first by Theodorsen (1955). Such loops are incorporated in the attached eddy model versions of Perry & Chong (1982), Perry et al. (1986), and Perry & Marusic (1995), which are extensions of a model first formulated by Townsend (1976). The DNS data of wall bounded flows studied here are from the zero pressure gradient flow of Spalart (1988) and the boundary layer with separation and reattachment of Na & Moin (1996). The flow structures are examined from the viewpoint of the attached eddy hypothesis.
Chong, M. S.↗
The UAH Spinning Terrella Experiment: A Laboratory Analog for the Earth's Magnetosphere
The UAH Spinning Terrella Experiment has been modified to include the effect of a second magnet. This is a simple laboratory demonstration of the well-known double-dipole approximation to the Earth's magnetosphere. In addition, the magnet has been biassed $\sim$-400V which generates a DC glow discharge and traps it in a ring current around the magnet. This ring current is easily imaged with a digital camera and illustrates several significant topological properties of a dipole field. In particular, when the two dipoles are aligned, and therefore repel, they emulate a northward IMF Bz magnetosphere. Such a geometry traps plasma in the high latitude cusps as can be clearly seen in the movies. Likewise, when the two magnets are anti-aligned, they emulate a southward IMF Bz magnetosphere with direct feeding of plasma through the x-line. We present evidence for trapping and heating of the plasma, comparing the dipole-trapped ring current to the cusp-trapped population. We also present a peculiar asymmetric ring current produced in by the plasma at low plasma densities. We discuss the similarities and dissimilarities of the laboratory analog to the collisionless Earth plasma, and implications for the interpretation of IMAGE data.
Sheldon, R. B.↗
Introduction to Radiation Issues for International Space Station Extravehicular Activities
The International Space Station (ISS) provides significant challenges for radiation protection of the crew due to a combination of circumstances including: the extended duration of missions for many crewmembers, the exceptionally dynamic nature of the radiation environment in ISS orbit, and the necessity for numerous planned extravehicular activities (EVA) for station construction and maintenance. Radiation protection requires accurate radiation dose measurements and precise risk modeling of the transmission of high fluxes of energetic electrons and protons through the relatively thin shielding provided by the space suits worn during EVA. Experiments and analyses have been performed due to the necessity to assure complete radiation safety for the EVA crew and thereby ensure mission success. The detailed characterization described of the material and topological properties of the ISS space suits can be used as a basis for design of space suits used in future exploration missions. In radiation protection practices, risk from exposure to ionizing radiation is determined analytically by the level of exposure, the detrimental quality of the radiation field, the inherent radiosensitivity of the tissues or organs irradiated, and the age and gender of the person at the time of exposure. During low Earth orbit (LEO) EVA, the relatively high fluxes of low-energy electrons and protons lead to large variations in exposure of the skin, lens of the eye, and tissues in other shallow anatomical locations. The technical papers in this publication describe a number of ground-based experiments that precisely measure the thickness of the NASA extravehicular mobility unit (EMU) and Russian Zvezda Orlan-M suits using medical computerized tomography (CT) X-ray analysis, and particle accelerator experiments that measure the minimum kinetic energy required by electrons and photons to penetrate major components of the suits. These studies provide information necessary for improving the understanding of the current ISS space suits and provide insights into improved approaches for the design of future suits. This chapter begins with a summary of the dynamic ionizing radiation environment in LEO space and introduces the concepts and quantities used to quantify exposure to space radiation in LEO. The space suits used for EVA and the experimental partial human phantom are described. Subsequent chapters report results from measured charged particle fields before and after incident protons and secondary particles are transported through the space suits and into organs and tissues.
Shavers, M. R.↗
The Chaotic Long-Term X-Ray Variability of 4U 1705-44
The low-mass X-ray binary 4U1705-44 exhibits dramatic long-term X-ray time variability with a time-scale of several hundred days. The All-SkyMonitor (ASM) aboard the Rossi X-ray Timing Explorer (RXTE) and the Japanese Monitor of All-sky X-ray Image (MAXI) aboard the International Space Station together have continuously observed the source from 1995 December through 2014 May. The combined ASM-MAXI data provide a continuous time series over 50 times the length of the time-scale of interest. Topological analysis can help us identify 'fingerprints' in the phase space of a system unique to its equations of motion. The Birman-Williams theorem postulates that if such fingerprints are the same between two systems, then their equations of motion must be closely related. The phase-space embedding of the source light curve shows a strong resemblance to the double-welled non-linear Duffing oscillator. We explore a range of parameters for which the Duffing oscillator closely mirrors the time evolution of 4U1705-44. We extract low period, unstable periodic orbits from the 4U1705-44 and Duffing time series and compare their topological information. The Duffing and 4U1705-44 topological properties are identical, providing strong evidence that they share the same underlying template. This suggests that we can look to the Duffing equation to help guide the development of a physical model to describe the long-term X-ray variability of this and other similarly behaved X-ray binary systems.
Rossi X-ray Timing Explorer (RXTE)↗
Weak peripheral covering properties imply covering properties
Covering properties of topological space as function of set density
Traylor, D. R.↗
A study of the electric field in an open magnetospheric model
Recently, Svalgaard and Heppner reported two separate features of the polar electromagnetic field that correlate with the dawn-dusk component of the interplanetary magnetic field. This work attempts to explain these findings in terms of properties of the open magnetosphere. The topology and qualitative properties of the open magnetosphere are first studied by means of a simple model, consisting of a dipole in a constant field. Many such properties are found to depend on the separation line, a curve connecting neutral points and separating different field line regimes. In the simple model it turns out that the electric field in the central polar cap tends to point from dawn to dusk for a wide variety of external fields, but, near the boundary of the polar cap, electric equipotentials are deformed into crescents.
Stern, D. P.↗
Hierarchic models for laminated plates
Structural plates and shells are three-dimensional bodies, one dimension of which happens to be much smaller than the other two. Thus, the quality of a plate or shell model must be judged on the basis of how well its exact solution approximates the corresponding three-dimensional problem. Of course, the exact solution depends not only on the choice of the model but also on the topology, material properties, loading and constraints. The desired degree of approximation depends on the analyst's goals in performing the analysis. For these reasons models have to be chosen adaptively. Hierarchic sequences of models make adaptive selection of the model which is best suited for the purposes of a particular analysis possible. The principles governing the formulation of hierarchic models for laminated plates are presented. The essential features of the hierarchic models described models are: (1) the exact solutions corresponding to the hierarchic sequence of models converge to the exact solution of the corresponding problem of elasticity for a fixed laminate thickness; and (2) the exact solution of each model converges to the same limit as the exact solution of the corresponding problem of elasticity with respect to the laminate thickness approaching zero. The formulation is based on one parameter (beta) which characterizes the hierarchic sequence of models, and a set of constants whose influence was assessed by a numerical sensitivity study. The recommended selection of these constants results in the number of fields increasing by three for each increment in the power of beta. Numerical examples analyzed with the proposed sequence of models are included and good correlation with the reference solutions was found. Results were obtained for laminated strips (plates in cylindrical bending) and for square and rectangular plates with uniform loading and with homogeneous boundary conditions. Cross-ply and angle-ply laminates were evaluated and the results compared with those of MSC/PROBE. Hierarchic models make the computation of any engineering data possible to an arbitrary level of precision within the framework of the theory of elasticity.
Actis, Ricardo Luis↗
Quantitative analysis of voids in percolating structures in two-dimensional N-body simulations
We present in this paper a quantitative method for defining void size in large-scale structure based on percolation threshold density. Beginning with two-dimensional gravitational clustering simulations smoothed to the threshold of nonlinearity, we perform percolation analysis to determine the large scale structure. The resulting objective definition of voids has a natural scaling property, is topologically interesting, and can be applied immediately to redshift surveys.
Harrington, Patrick M.↗
On the flow outside a closed invariant set, stability, relative stability and saddle sets.
Stability, relative stability and saddle set concepts used to examine solutions, topological and dynamic properties of closed invariant sets
DYNAMIC STABILITY↗