mcrt: l0 - astronomy group – university of st andrews
TRANSCRIPT
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MCRT: L0
• Some background, what previous courses students should look over, gentle introduction/recap of probabilities
• Get an idea of computer programming experience of the class
• Overview of course structure and assessment
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Monte Carlo Radiation Transport Kenny Wood
[email protected] • A practical approach to the numerical simulation of
radiation transport • Develop programs for the random walks of photons and
neutrons using Monte Carlo techniques • Will refer to previous courses on optics, radiation,
neutrons, atomic physics, biological tissue structure, some hydrodynamics
• Guest lectures in week 3 from Prof Steve Jacques (Oregon) on Monte Carlo radiation transfer in biological tissue and medical physics
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Astrophysics Interpreting data via 3D radiation transfer modeling Heating of dust and gas, thermal pressure, radiation pressure Radiation-magneto-hydrodynamics
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Dusty Ultra Compact H II Regions
Indebetouw, Whitney, Johnson, & Wood (2006)
ONE 3D model can explain ALL UCHII SEDs!!
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Hierarchical Density Structure
Elmegreen (1997)
Fractal generating algorithm reproduces observed structure and fractal dimension, D, of clouds in interstellar medium 2D: P ~ AD/2 ; Circle: D =1 ISM clouds: D ~ 1.3 Radiation transfer in clouds…
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Mathis, Whitney, & Wood (2002)
3D density: viewing angle effects
NGC 7023 Reflection Nebula Monte Carlo scattered light
Simulations of fractal clouds
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Atmospheric Physics Clouds important for photon transport and temperature structure of atmosphere
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Medical Physics Light activated treatments such as photodynamic therapy: how deep does the radiation penetrate into skin and tissue? Imaging using x-ray, ultraviolet, optical, infrared, & polarised light Optical tweezers, photo-acoustic imaging, nuclear medicine, etc, etc
Monte Carlo simulations of computed topography (CT) x-ray imaging doses Rensselaer Polytechnic Institute
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Nuclear Physics & Neutron Transport Compute controlled criticality assemblies & geometries for nuclear fission reactors Nuclear safety – radioactive shielding calculations Uncontrolled reactions – critical masses for bombs
Chain reaction in 235U Chicago Pile 1, December 1942 World’s first artificial nuclear reactor
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Course Structure • Lectures on MCRT techniques and outline of
FORTRAN programs • Computer lab sessions for what you’ll need in
FORTRAN and to develop a code for photon random walks in a uniform density sphere
• Tutorial-style problems to do in groups • No final exam, 100% continuous assessment:
– 40% for two homework sheets of written problems and short programs & subroutines
– 40% for one large project – 20% for one short project
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Remind yourself of… • Refractive index, Snell’s Law, Fresnel reflection &
refraction (PH1011 Waves & Optics) • Polarization (PH3007 Electromagnetism & PH4035
Principles of Optics) • Ionization potentials, atomic term diagrams PH4037
(Physics of Atoms) • Equations of hydrodynamics, pressure & forces (PH4031
Fluids)
• Probability theory: probability distribution function (PDF) and cumulative distribution function (CDF)
• Numerical integration, Simpsons rule, quadrature
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• Intensity, luminosity, flux, radiation pressure (many astronomy courses)
• Biological tissue optics, skin structure, light-tissue interactions (PH5016 Biophotonics)
• Neutron cross sections: scattering, absorption, fission • Fission products, slow/fast & prompt/delayed neutrons • Chain reactions, critical mass, moderators • PH4022 or PH4040 (Nuclear & Particle Physics)
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Programming in FORTRAN77
• You’ll need: text editor; FORTRAN compiler (gfortran); graphics package for plotting lines, contours, 3D visualisation
• By Monday create file called hello.f • Compile it: gfortran hello.f • Run the executable: ./a.out
program hello implicit none print *, ‘Hello’ stop end
Note six spaces before text starts on each line!
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Buffon’s needles
What is the probability that a needle will cross a line?
Georges-Louis Leclerc Comte de Buffon
1707-1788
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Needles of length l Line separation s x = distance from needle centre to closest line Needle touches/crosses line if Probability density function: function of a variable that gives
probability for variable to take a given value Exponential distribution: p(x) = e-x , for x in range 0 to infinity Uniform distribution: p(x) = 1/L , for x in range 0 to L Normalised over all x:
€
x ≤l2sinθ
€
p(x)dx0
∞
∫ =1
s l
x θ
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Probability x lies in range a < x < b is ratio of “areas under the curve” x is distributed uniformly between (0, s/2), θ in range (0, π/2)
p(x) = 2/s, p(θ) = 2/π Variables x and θ independent, so joint probability is
p(x, θ) = 4/(s π)
€
P =p(x)dx
a
b∫p(x)dx
0
∞
∫
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Probability of a needle touching a line (l < s) is Drop lots of needles. Probability of needle crossing line is Can estimate π :
€
P =4sπ0
l / 2 sinθ∫0
π / 2∫ dx dθ =
2 lsπ
€
P =Number of needles crossing linesTotal number of needles dropped
€
π =2 lsP