mcrt: l0 - astronomy group – university of st andrews
TRANSCRIPT
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
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
Astrophysics Interpreting data via 3D radiation transfer modeling Heating of dust and gas, thermal pressure, radiation pressure Radiation-magneto-hydrodynamics
Dusty Ultra Compact H II Regions
Indebetouw, Whitney, Johnson, & Wood (2006)
ONE 3D model can explain ALL UCHII SEDs!!
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…
Mathis, Whitney, & Wood (2002)
3D density: viewing angle effects
NGC 7023 Reflection Nebula Monte Carlo scattered light
Simulations of fractal clouds
Atmospheric Physics Clouds important for photon transport and temperature structure of atmosphere
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
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
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
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
• 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)
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!
Buffon’s needles
What is the probability that a needle will cross a line?
Georges-Louis Leclerc Comte de Buffon
1707-1788
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
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
∞
∫
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