An effort has been made to present the various topics in the theory of graphs in a logical order, to indicate the historical background, and to clarify the exposition by including figures to illustrate concepts and results. In addition, there are three appendices which provide diagrams of graphs, directed graphs, and trees. The emphasis throughout is on theorems rather than algorithms or applications, which however are occasionally mentioned.

Topics: DTIC Archive, Harary, Frank, MICHIGAN UNIV ANN ARBOR DEPT OF MATHEMATICS, *GRAPHICS, COLORS,...

This young investigator award from the Air Force Office of Scientific Research to Daniel Forger played a pivotal role in his career. Many discoveries were made and are described in over 10 published papers or manuscripts in preparation. Some research highlights include: 1) discovering that timekeeping in mammals is more complex than originally thought, 2) discovering on how to optimally stimulate neuronal (and in particular the circadian) systems and 3) mathematical methods for studying...

Topics: DTIC Archive, MICHIGAN UNIV ANN ARBOR DEPT OF MATHEMATICS, *BIOLOGICAL RHYTHMS, *MAMMALS,...

A wake is modelled by a vortex sheet carrying positive and negative circulation. The sheet's evolution is computed by the vortex-blob method. Initial conditions and circulation density for the vortex sheet are chosen to simulate some of the wake patterns observed in the soap-film experiments of Couder et.al.(2,3).

Topics: DTIC Archive, Krasny, Robert, MICHIGAN UNIV ANN ARBOR DEPT OF MATHEMATICS, *VORTICES, *WAKE,...

The award supported Peter Bosler as a postdoc in the Department of Mathematics at the University of Michigan. The project developed a novel Lagrangian particle method (LPM) for geophysical fluid flow simulations on a rotating sphere. The method is potentially relevant to Naval operations that rely on accurate and efficient modeling of atmosphere and ocean dynamics. We developed new remeshing and refinement schemes to overcome the loss of accuracy due to distortion in the particle distribution....

Topics: DTIC Archive, MICHIGAN UNIV ANN ARBOR DEPT OF MATHEMATICS, *ALGORITHMS, *FLUID FLOW, *GEOPHYSICS,...

This project draws together a team of researchers to develop new grid-free tools for plasma simulations. The objectives are: (1) to develop a grid-free field solver, fluid model, and kinetic model, (2) to evaluate these tools in comparison with traditional mesh-based methods, and (3) to demonstrate the capability of the grid-free approach in an application of USAF interest. The field solver will use boundary integral methods and a recently developed tree code algorithm to compute the...

Topics: DTIC Archive, Krasny, Robert, MICHIGAN UNIV ANN ARBOR DEPT OF MATHEMATICS, *ALGORITHMS, *CHARGED...

During this period the nine scientists associated with the project produced 76 papers of which 35 have appeared in journals at this time. Many invited lectures, editorships and a chair in mathematics attest to the ability of the principal investigators. In the area of entrainment of frequency in the large involving oscillations of physical systems at resonance and across point of resonance 14 papers were produced. Pareto optimization theorems in optimal control theory account for three papers....

Topics: DTIC Archive, Cesari,Lamberto, MICHIGAN UNIV ANN ARBOR DEPT OF MATHEMATICS, *PLASMAS(PHYSICS),...

This paper gives a theory of spectral approximation for closed operators in Banach spaces. The perturbation theory developed in this paper is applied to the study of a finite element procedure for approximating the spectral properties of a differential system modeling a fluid in a rotating basin. (Author)

Topics: DTIC Archive, Luskin,Mitchell, MICHIGAN UNIV ANN ARBOR DEPT OF MATHEMATICS,...

This grant provided support for a postdoc at the University of Michigan to assist in developing a grid-free particle method for electrostatic plasma simulations. The aim of the work is to substantially improve the accuracy and efficiency of these simulations. The proposed method is an alternative to traditional mesh-based methods such as particle-in-cell (PlC). In the new approach, the standard Eulerian formulation of the Vlasov-Poisson equation is replaced by a Lagrangian formulation in which...

Topics: DTIC Archive, Krasny, Robert, MICHIGAN UNIV ANN ARBOR DEPT OF MATHEMATICS, *ENERGY CONSERVATION,...

A new finite element method is proposed for the numerical solution of a class of initial-boundary value problems for first order hyperbolic systems in one space dimension. An application of our procedure to a system modeling gas flow in a pipe is discussed. Asymptotic error estimates are derived in the L sq norm in space. (Author)

Topics: DTIC Archive, Luskin,Mitchell, MICHIGAN UNIV ANN ARBOR DEPT OF MATHEMATICS, *FINITE ELEMENT...

Eigenfunction expansions for nonselfadjoint operators are important for scalar and electromagnetic wave scattering. Two methods: the Singularity Expansion Method (SEM), and the Eigenmode Expansion Method (EEM) which had been developed separately were studied. Criteria for their validity were established; moreover, the poles of the Green's function of the SEM are in 1-1 correspondence with the zeros of the eigenvalues of the EEM. A constructive numerical process for determining the poles of the...

Topics: DTIC Archive, Dolph,Charles L, MICHIGAN UNIV ANN ARBOR DEPT OF MATHEMATICS, *ELECTROMAGNETIC...

In this paper we construct an analytic model of cache misses during matrix multiplication. The analysis in this paper applies to square matrices of size 2m where the array layout function is given in terms of a function that interleaves the bits in the binary expansions of the row and column indices. We first analyze the number of cache misses for direct-mapped caches and then indicate how to extend this analysis to A-way associative caches. The work in this paper accomplishes two things....

Topics: DTIC Archive, Hanlon, Philip J, MICHIGAN UNIV ANN ARBOR DEPT OF MATHEMATICS, *MATHEMATICAL MODELS,...

Several problems relevant in the application of mechanics to real-world problems were treated. The work included theoretical analysis of solutions of partial differential equations, detailed studies of numerical techniques for approximately solving differential equations arising in mechanics, as well as actual numerical computations using such numerical schemes to model experimental phenomena. Application areas impacted by this research include heat conduction and fluid mechanics. Also closely...

Topics: DTIC Archive, Scott,L Ridgway, MICHIGAN UNIV ANN ARBOR DEPT OF MATHEMATICS, *PARTIAL DIFFERENTIAL...

This document contains six papers entitled: 1) On some mathematical aspects of SEM(Singularity Expansion Method), EEM(Eigenmode Expansion Method) and scattering; 2) On the singularity and eigenmode expansion methods; 3) Mathematical foundations of the singularity and eigenmode expansion methods; 4) Convergence of the T-matrix approach to scattering theory; 5) Convergence of the T-matrix approach in scattering theory, II; and 6) Variational principles for resonances, II.

Topics: DTIC Archive, Dolph,C L, MICHIGAN UNIV ANN ARBOR DEPT OF MATHEMATICS, *NUMERICAL METHODS AND...

Research on both internal and free-surface flows related to experimental situations was continued. Part of this research was based on using a low-order code developed previously, jointly by Pritchard and Scott. Funds for the programmer allowed two substantial new programming projects to be initiated during this time. One concerned investigation of techniques for implementing a quartic finite element method for viscous, incompressible, two-dimensional flows. The other involved a...

Topics: DTIC Archive, Scott,L R, MICHIGAN UNIV ANN ARBOR DEPT OF MATHEMATICS, *FINITE ELEMENT ANALYSIS,...

The report summarizes progress made in several, areas, including: estimates for finite element methods, numerical simulation of nonlinear dispersive waves, numerical models for plasticity, numerical methods for the transport equation, and computation of fluid-flow problems. (Author)

Topics: DTIC Archive, Scott,L Ridgway, MICHIGAN UNIV ANN ARBOR DEPT OF MATHEMATICS, *PARTIAL DIFFERENTIAL...

An examination of the relationship between the scattering matrix (the Fourier transform of the scattering operator) and the integral equations used in the Singularity Expansion Method (SEM) established that only the complex poles off the axis are intrinsically associated with the scatterer. While it has been known in special cases that those on the axis do not contribute to the field, this appears to be the first time this relationship has been clearly exhibited. Since the scattering matrix can...

Topics: DTIC Archive, Dolph, Charles L, MICHIGAN UNIV ANN ARBOR DEPT OF MATHEMATICS, *ELECTROMAGNETIC...