Writer

Modeling EM waves using cellular automata

Can cellular automata models be used to analyze EM propagation behaviors in building with multipath propagations? I would like to understand how much wireless data rate dense radio environments could support. I am considering an area like the Media Lab cube where every single item in the area has an RF connection with people carrying around devices like mobile phones that may also relay RF signals. I would like to understand how EM waves behave and propagate in such environments by modeling them in numerical simulators. Such invesgtigation will allow how much data rate can be consistently supported in such environments and what kind of multiple access mechanism could be used for all the distributed radios to constantly communicate with each other.

Goal

For the PIT class, my goal is to understand how EM modeling works and build a simple cellular automata based EM modeler that can model simple EM waves and dipoles.

Evaluation

There are too many EM modeling tools that exist that are used for different problems with differing constraints. I will be focusing on understanding time domain based modelers such as finite difference time domain (FDTD) and transmission line matrix (TLM) models, since the CA model will also be time domain based.

Work Plan

Understand how FDTD and LGA models work

Open source simulators can be found at fdtd.org. Meep uses scheme interface and was created at MIT.
EM Solver Background

Implement a CA model

Simple wave propagation LGA wave
For simple dipole propagation
Differing boundary conditions Square center, Slit
For multiple sources of radio

Prove that it models Maxwell's equations

Hint: Simple Lattice Gas Models for Waves [Chen, Chen, Doolen, Lee]
There must be + and - particles that cancel each other when they meet.
Total wave energy and total wave momentum needs to be conserved.
Speed cannot exceed c.
Linear wave equation is recovered after making an ensemble averaging and a Taylor expansion in time and space.

Final Presentation

References

Numerical solution of inital boundary value problems involving maxwell's equations in isotropic media

A Lattice Gas Automaton Capable of Modelling 3D-EM Fields

Integer Lattice Gas Automata for Computational Electromagnetics

Extremely Low-Precision Integer Cellular Array Algorithm for Computational Electromagnetics

Application of Cellular Automata to Modeling Mobility and Radio Communication in Wireless Networks

Crystalline Computation

Cellular Automata Methods in Mathematical Physics

Integer Lattice Gases at Equilibrium

Cellular Automata Theory and Physics: A new Paradigm for the Unification of Physics

Statistical Mechanics and Cellular Automata

Cellular Automata and Discrete Physics

Book: Microwave Circuit Modeling Using Electromagnetic Field Simulation [Swanson, Hoefer]

Book: Lattice Gas Methods for Partial Differential Equations [Ed. Doolen]

FEM Maxwell Eqns

FDTD.org Home

Microwave Circuit Modeling Using EM Field Simulators

EM Explorer

UMR EMC LAB: Commercial EM Codes

EM Simulators Reveal Contents Of Crystal Ball

Elmer FEM solver - Wikipedia, the free encyclopedia

Overview of EM Modeling Techniques


	.	Kwan's PIT Project Modeling EM waves using cellular automata Can cellular automata models be used to analyze EM propagation behaviors in building with multipath propagations? I would like to understand how much wireless data rate dense radio environments could support. I am considering an area like the Media Lab cube where every single item in the area has an RF connection with people carrying around devices like mobile phones that may also relay RF signals. I would like to understand how EM waves behave and propagate in such environments by modeling them in numerical simulators. Such invesgtigation will allow how much data rate can be consistently supported in such environments and what kind of multiple access mechanism could be used for all the distributed radios to constantly communicate with each other. Goal For the PIT class, my goal is to understand how EM modeling works and build a simple cellular automata based EM modeler that can model simple EM waves and dipoles. Evaluation There are too many EM modeling tools that exist that are used for different problems with differing constraints. I will be focusing on understanding time domain based modelers such as finite difference time domain (FDTD) and transmission line matrix (TLM) models, since the CA model will also be time domain based. Work Plan Understand how FDTD and LGA models work Open source simulators can be found at fdtd.org. Meep uses scheme interface and was created at MIT. EM Solver Background Implement a CA model Simple wave propagation LGA wave For simple dipole propagation Differing boundary conditions Square center, Slit For multiple sources of radio Prove that it models Maxwell's equations Hint: Simple Lattice Gas Models for Waves [Chen, Chen, Doolen, Lee] There must be + and - particles that cancel each other when they meet. Total wave energy and total wave momentum needs to be conserved. Speed cannot exceed c. Linear wave equation is recovered after making an ensemble averaging and a Taylor expansion in time and space. Final Presentation References Numerical solution of inital boundary value problems involving maxwell's equations in isotropic media A Lattice Gas Automaton Capable of Modelling 3D-EM Fields Integer Lattice Gas Automata for Computational Electromagnetics Extremely Low-Precision Integer Cellular Array Algorithm for Computational Electromagnetics Application of Cellular Automata to Modeling Mobility and Radio Communication in Wireless Networks Crystalline Computation Cellular Automata Methods in Mathematical Physics Integer Lattice Gases at Equilibrium Cellular Automata Theory and Physics: A new Paradigm for the Unification of Physics Statistical Mechanics and Cellular Automata Cellular Automata and Discrete Physics Book: Microwave Circuit Modeling Using Electromagnetic Field Simulation [Swanson, Hoefer] Book: Lattice Gas Methods for Partial Differential Equations [Ed. Doolen] FEM Maxwell Eqns FDTD.org Home Microwave Circuit Modeling Using EM Field Simulators EM Explorer UMR EMC LAB: Commercial EM Codes EM Simulators Reveal Contents Of Crystal Ball Elmer FEM solver - Wikipedia, the free encyclopedia Overview of EM Modeling Techniques	.