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 kw25@st-andrews.ac.uk 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 ONE 3D model can explain ALL UCHII SEDs!! Indebetouw, Whitney, Johnson, & Wood (2006)
Hierarchical Density Structure Fractal generating algorithm reproduces observed structure and fractal dimension, D, of clouds in interstellar medium 2D: P ~ A D/2 ; Circle: D =1 ISM clouds: D ~ 1.3 Radiation transfer in clouds Elmegreen (1997)
Monte Carlo scattered light Simulations of fractal clouds NGC 7023 Reflection Nebula 3D density: viewing angle effects Mathis, Whitney, & Wood (2002)
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 235 U 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 Note six spaces before text starts on each line! print *, Hello stop end
Buffon s needles Georges-Louis Leclerc Comte de Buffon 1707-1788 What is the probability that a needle will cross a line?
θ l x s Needles of length l Line separation s x = distance from needle centre to closest line Needle touches/crosses line if x l 2 sinθ 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: p(x) dx =1 0
Probability x lies in range a < x < b is ratio of areas under the curve b p(x) dx a P = p(x) dx 0 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)
Probability of a needle touching a line (l < s) is P = π / 2 0 0 l / 2 sinθ 4 dx dθ = 2l sπ sπ Drop lots of needles. Probability of needle crossing line is P = Number of needles crossing lines Total number of needles dropped Can estimate π : π = 2 l sp