Maple Share Library:  Science
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activ2.ms	FILE: science/active2.ms
		Maple worksheet for obtaining expressions for activity
		coefficients in liquid mixtures.  Parameter estimation is
		touched upon briefly.
                AUTHOR: Ross Taylor, taylor@sun.soe.clarkson.edu

AFA.ms		FILE: science/AFA.ms
		Algebraic Function Approximant Program
		Exactly reconstucts the expression for the Dirac energies
		from the series coefficients using a heuristic polynomial fit.
		AUTHORS: Tony Scott, Greg Fee, tcscott@maths.ox.ac.uk

biology.ms      FILE: plots/biology.ms
                Application of the plots/ODE package to a problem from biology
                where two populations compete with each other for resources to
                survive.  The biological system is modeled by two first order
                differential equations, and phase plots of the solutions are
                plotted showing examples of stable and unstable populations.
                AUTHOR: Daniel Schwalbe, schwalbe@macalstr.edu

chain.ms        FILE: science/chain.ms
		(classical mechanics)
                A uniform chain lies on the edge of a smooth table and starts
                falling over the edge.  What is the acceleration of the chain?
                Because the mass of the chain over the edge increases in time,
                a more general version of Newton's first law is needed.
                This leeds to a second order non-linear ODE to be solved.
                Tony Scott, tcscott@maths.ox.ac.uk

chemcomp.ms     FILE: science/chemcomp.ms
		(phsyical chemistry - thermodynamics)
                Given a simple system of steam reforming reactions the
                temperature dependence of the reaction extents and the chemical
                compositions at equilibrium are calculated. A system of
                nonlinear equations is constructed, using the molecular mass
                balance equations and the law's of Kirchhoff and van't Hoff,
                and then solved.
                AUTHORS: Johannes Grotendorst and Juergen Dornseiffer
                j.grotendorst@kfa-juelich.de

doubpend.ms     FILE: plots/doubpend.ms
                This worksheet uses the ODE package to approximate the
                solution to the differential equation associated to a
                double pendulum, i.e. a pendulum attached to a pendulum.
                The motion of the double pendulum is then animated.
                AUTHOR: Daniel Schwalbe, schwalbe@macalstr.edu

education	FILES:  science/bohratom.ms, science/chemeqn.ms,
			science/heatcap.ms,  science/Maxgas.ms,
			science/planck.ms,   science/quantopt.ms,
			science/wheatsto.ms

                These seven worksheets show different capabilities of Maple
		in solving seven problems in science at the educational level.
   bohratom.ms	1 (chemistry): shows Maple solving three non-linear equations
		symbolically arising from semi-classical mechanics, namely the
		Bohr theory applied to the Hydrogen atom.
   chemeqn.ms	2 (chemistry): shows Maple used to balance the coefficients in
		a chemical reaction.  We are given a chemical equation and
		Maple's isolve command is used to find an integral solution.
   heatcap.ms	3 (statistical mechanics): obtains the mean energy and heat
		capacity of an Einstein solid.  Maple is used to compute a
		symbolic infinite sum and compute symbolic limits.
   Maxgas.ms	4 (statistical mechanics): uses Maple to find the most probable
		speed of the Maxwell-Boltzman distribution.  This involves
		differentiation and solving symbolically a non-linear equation.
   planck.ms	5 (statistical mechanics): uses Maple to compute a definite
		integral, the Stefan-Boltzman Law (of Blackbody radiation).
   quantopt.ms	6 (quantum optics): uses Maple to symbolically integrate a
		triple integral and factor (simplify) the resulting formula.
   wheatsto.ms  7 (electronics): uses Maple to solve six linear equations
		(from applying Kirchoff's laws to the ``Wheatstone Bridge''
                electrical circuit) symbolically for the currents which are
		functions of the resistances R1, R2, R3, R3, R5.
		AUTHORS: Tony Scott, tcscott@maths.ox.ac.uk
		AUTHORS: Darren Redfern, Richard Pavelle,

flash.ms	FILE: science/flash.ms
		(phsyical chemistry - thermodynamics)
                Flash calculations are used to determine the phase condition of
                a mixture at a specified temperature and pressure.  Such
                computations lie at the heart of many process engineering
                calculations and are of central importance in many other
                applications as well (oil reservoir simulation for example).
                AUTHOR: Ross Taylor, taylor@sun.soe.clarkson.edu

HMO.ms          FILE: science/HMO.ms
		(organic (quantum) chemistry)
                Huckel Molecular Orbital theory provides a simple approximation 
                to the electronic structure of molecules, i.e.
                1) The eigenvalues approximate the energy spectrum. 
                2) The eigenvectors approximate the states.
                This leeds to symbolic eigenvalue and eigenvector problems.
                These are computed for Butadiene and Naphthalene.
                AUTHOR: Tony Scott, tcscott@maths.ox.ac.uk

kinetics        > readshare(kinetics, science);
                SEE ALSO: science/kinetics.tex
                (routines: odes, laws, steady)
                Given a reaction scheme these Maple procedures determine the
                system of differential equations, the associated conservation
                laws, and some of the species that have a zero steady state.
                AUTHOR: Mark Holmes, holmem@rpi.edu

logistic.ms     FILE: plots/logistic.ms
                The worksheet solves the logistics law of population
                growth P' = a*P - b*P^2.  Given 3 populations P(t0),
                P(t0+delta), and P(t0+2*delta) Maple can solve for a and b.
                This is impressive.
                AUTHOR: Daniel Schwalbe, schwalbe@macalstr.edu

McConnel.ms     FILE: science/McConnel.ms
                A Maple worksheet on how to use matrix algebra, in particular
                matrix exponentials, for the symbolic solution of a system of
                first order differential equations in biochemistry, namely the
                McConnell equations.  The McConnell equations are used to
                analyse data obtained from solute-cell transport experiments
                using the nuclear magnetic resonance (NMR) technique.
                The formal parameters involved in the solutions
                are determined by nonlinear least-squares fitting.
                AUTHOR: Johannes Grotendorst, j.grotendorst@kfa-juelich.de
		AUTHORS: Paul Jansen, and Siegfried M. Schoberth

pendulum.ms	FILE: science/pendulum.ms
		Models the motion of a pendulum in a fluid as a second order
		ODE, solves the ODE analytically using Maple, and then plots
		the motion for different fluid resistances.
		AUTHOR: David Harper, D.Harper@qmw.ac.uk
		
phase1.ms	FILES: science/phase1.ms, science/phase2.ms
phase2.ms	(phsyical chemistry - thermodynamics)
		Simple Thermodynamic calculations including bubble and
		dew point determination, creating and plotting phase diagrams.
		AUTHOR: Ross Taylor, taylor@sun.soe.clarkson.edu

pof             > readshare(pof, science);  (41K)
		(phsical chemistry - nuclear magnetic resonance)
		WORKSHEETS: science/COSY.ms, science/JRes.ms,
			    science/nQF.ms, science/oneD.ms

                This package of procedures implements the product operator
                formalism approach for calculation and vizualization of the
                effect of an NMR pulse sequence. The implementation is written
                for weakly-coupled systems with nuclear spin of 1/2.  The four
		worksheets below are example applications of the package.
  COSY.ms	1: Homonuclear AX COSY spectrum
		Comparison of lineshape and phase pattern in diagonal-
		versus crosspeaks in a simple COSY spectrum
  JRes.ms	2: Homonuclear A2MX J-resolved spectrum, with hetero X.
		Determination of the differences between a homo-nuclear versus
		heter-nuclear coupling in a spin-echo experiment.
  nQF.ms	3: Multiple Quantum Filtered Spectra
		Establishing the requirements for observable cross-peaks and
		their phase pattern in DQF spectra. In addition to that, the
		effect of hetero- versus homonuclear coupling.
  oneD.ms	4: Homonuclear A2MX one-dimensional Spectrum.
 		Calculation of the spectrum from a single pulse-experiment, and
		the effect of accidental equality of coupling size on relative
		intensities in a multiplet.

                AUTHOR: Rene P.F. Kanters, KANTERS@urvax.urich.edu

shottraj.ms	FILE: science/shottraj.ms
		Uses Maple to solve symbolically and plot the solution of a
		second order ODE which describes the motion of a bullet shot
		straight up into the air.
		AUTHOR: Michael Monagan, monagan@inf.ethz.ch
