Scaling Properties of Paths on Graphs

Let $G$ be a directed graph on finitely many vertices and edges, and assign a positive weight to each edge on $G$. Fix vertices $u$ and $v$ and consider the set of paths that start at $u$ and end at $v$, self-intersecting in any number of places along the way. For each path, sum the weights of its edges, and then list the path weights in increasing order. The asymptotic behaviour of this sequence is described, in terms of the structure and type of strongly connected components on the graph. As a special case, for a Markov chain the asymptotic probability of paths obeys either a power law scaling or a weaker type of scaling, depending on the structure of the transition matrix. This generalizes previous work by Mandelbrot and others, who established asymptotic power law scaling for special classes of Markov chains.Comment: 23 pages, 2 figure

Telegram, from Mr. and Mrs. J. E. Edwards, to President Dean W. Colvard, 1963

In this Western Union telegram, Mr. and Mrs. J.E. Edwards write to MSU President Dean W. Colvard, expressing their opposition to MSU playing Loyola Chicago, a team with Black players, in the NCAA tournament.https://scholarsjunction.msstate.edu/ua-msu-loyola-1963/1024/thumbnail.jp

Mass-spectrometric study of the rhenium-oxygen system

Rhenium, having the second highest melting point among the metals, is used for refractory containers. Thermodynamic values for rhenium oxide is determined by mass spectrometry and X ray diffraction

A new coordinate transformation for turbulent boundary layer flows

The transformation permits a uniform mesh to be used in the computational coordinate which extends across the layer. This coordinate transformation uses the local value of the skin friction coefficient to scale the thickness of the wall layer region, and the local maximum value of turbulent viscosity to scale the boundary-layer thickness. Results are presented for two dimensional boundary layers in both positive and negative pressure gradients and comparisons are made with experimental data and conventional variable-grid results for low speed turbulent boundary-layers. The cases chosen illustrate the capability of this new transformation to capture the boundary layer growth over the full extent of laminar, transitional, and turbulent flow with no grid adjustment as well as its ability to consistently enlarge the wall layer region for accurate shear stress representation. Results of mesh refinement studies using the new coordinate transformation are presented

Computer program grade 2 for the design and analysis of heat-pipe wicks

This user's manual describes the revised version of the computer program GRADE(1), which designs and analyzes heat pipes with graded porosity fibrous slab wicks. The revisions are: (1) automatic calculation of the minimum condenser-end stress that will not result in an excess-liquid puddle or a liquid slug in the vapor space; (2) numerical solution of the equations describing flow in the circumferential grooves to assess the burnout criterion; (3) calculation of the contribution of excess liquid in fillets and puddles to the heat-transport; (4) calculation of the effect of partial saturation on the wick performance; and (5) calculation of the effect of vapor flow, which includes viscousinertial interactions

Five-year financial analysis of two commercial farms converting to organic: 2000-2005

The financial performance including input and output costs were analysed for two commercial Scottish farms converting to organic production. A comparative analysis for a five year period is provided using data from the Scottish Farm Accounts scheme, and demonstrates that both conversions had positive financial outcomes. Both farms applied strategic changes to their businesses

Computer integration of hydrodynamics equations for heat pipes

Program has five operational modes that provide user flexibility in answering crucial heat-pipe design questions. User specifies heat input and rejection distribution