Chapter V - Numeric Simulation of a Finite Grid in Numpy * Why Python, Why Numpy? * Basics of Working with Numpy * Slicing * Iterative Solution with Relaxation Method * Solution with Sparse Matrix Algebra
Chapter IV - Solving the Integral * Solving the Integral * Calculating a Resistance from its Neighbors
Detailed Material: gitlab.com/mooond/grid-of-1ohm-resistors03 - The Infinite Grid of 1 Ohm Resistors - Chapter 3: Finding the Solution with a Fourier Seriesfranz schaefer2024-01-28 | Chapter 3 - Finding a Solution for the Infinite Grid of Resistors with Fourier Series
Solutions of differential equations instead of difference equations. Why is it easier? What is a Green's Function and why do we want one? Constructing the Green's Function for our Equation Calculating the Resistance from the Potential
Playlist: youtube.com/playlist?list=PLoGRr8ff1uXESrWh6z0BNTYpc4Y-hlBOm02 - The Infinite Grid of 1 Ohm Resistors - Chapter 2: Generating Functions, Z-Transformfranz schaefer2024-01-27 | From our original problem: Finding the Resistance of the diagonal points in an infinite grid of 1 Ohm resistors we found that we need a method to solve difference equations. For this we are looking into Generating Functions and Z-Transform:
Topics Covered Here are:
Chapter II - Taming Infinity with Generating Functions, Z-Transform
The equations for our Infinit Grid of Resistors The discrete laplacian How to solve 1 dimensional difference equations Example: Fibonacci Numbers Powerful Tools: Generating Functions and Z-Transform Trigonometric Functions as Solutions The Characteristic Polynomial Our Resistor Network in 1D 2D Generating Functions
Playlist: youtu.be/org8stfCObw?si=wYHotnZEeU4Y3Rui01 - The Infinite Grid of 1 Ohm Resistors - Chapter 1: Basics of Electricity and Electric Resistancefranz schaefer2024-01-21 | Chapter I - Electrical Resistance and Simple Electrical Networks
Basics of Electricity: Voltage, Potential, Current Resistors: Ohm's Law Connecting Multiple Resistors together Kirchhoff's Law More Complicated Resistor Networks The Superposition Principle An easier Infinite Network of Resistors The Infinite Grid - Our First Victory
A while ago while I helped my son to study for an electrical engineering test and explained to him how to calculate the electrical resistance in some network of resistors. At some point I remembered what I heard some 40 years ago when I was studying this myself: That if you build an infinite grid of electrical resistors that the resulting resistance between two digonal points is 2/π Ω
So I started to google around on how this could be calculated. It turns out that with a simple trick it is easy to calculate the resistance between 2 nearby points. The resistance is just
0.5 Ω
But that the diagonal case is much harder and there where no real good explaination online on how to calculate it. So this is here to fill in the gap and I will try to provide an understandable explainations for the complicated calculation. If you do not know much about electrical resistance or advanced mathematics you should still be able to follow it. Even if you are not so interested in the electrical aspects: There are plenty of pure math aspects and many of the tools here have some use in many other fields as well. E.g. The same equations are used to approximate many other physical problems, e.g. heat equations or electrostratics. Also the same equations are used in computer graphics for dedection of edges in pictures. So it should be useful. Along the way I hope to be able to provide you with everything you will need. I want to provide a video with some nice animation and a python-jupyter notebook with some python code.
Chapter I - Electrical Resistance and Simple Electrical Networks
Basics of Electricity: Voltage, Potential, Current Resistors: Ohm's Law Connecting Multiple Resistors together Kirchhoff's Law More Complicated Resistor Networks The Superposition Principle An easier Infinite Network of Resistors The Infinite Grid - Our First Victory
Chapter II - Taming Infinity with Generating Functions, Z-Transform
The equations for our Infinite Grid of Resistors The discrete Laplacian How to solve 1 dimensional difference equations Example: Fibonacci Numbers Powerful Tools: Generating Functions and Z-Transform Trigonometric Functions as Solutions The Characteristic Polynomial Our Resistor Network in 1D
Chapter III - Finding a Solution for the Infinite Grid of Resistors with Fourier Series
Solutions of differential equations instead of difference equations. Why is it easier? What is a Green's Function and why do we want one? Constructing the Green's Function for our Equation Calculating the Resistance from the Potential
Chapter IV - Solving the Integral
Solving the Integral Calculating a Resistance from its Neighbors
Bonus: Chapter V - Numeric Simulation with Python Numpy
Wir starten ab 9h mit einer Zumarsch-Demo über Rotensterngasse-Taborstraße-Schwedenplatz-Rotenturmstraße-Stephansplatz-Kärtnerstraße-Albertina. Dort ist die Zusammenkunft mit der großen 1. Mai-Demonstration am Ring.
Gerade in diesen Zeiten ist Widerstand enorm wichtig. Kämpfen wir gemeinsam und feiern wir den Feiertag aller lohnarbeitspflichtigen Menschen mit Forderungen zu einem besseren Leben!
#poldi #kpö #1mai #wien #1mai2023 #LeopoldstadtAverage Distance between 2 Points in a Circle - Exact Solution via sympyfranz schaefer2023-03-04 | Average Distance between 2 Points in a Circle
How to add Encryption Keys When You Join additional Clients with Matrix Chat #matrix #matrixchat #riot #privacy #encryptionnew year vienna 2022franz schaefer2023-01-01 | view 1020vienna new year 2023franz schaefer2022-12-31 | new year 2023UFO Landet im Bednar Park (Wien)franz schaefer2019-04-01 | UFO landet kurz im Park und fliegt dann wieder weg!Hover Puck (Air Hockey Puck - play air hockey on any surface)franz schaefer2018-08-19 | Another Video of our Air Hockey Puck:
thingiverse.com/thing:3055842Hover Puck (Air Hockey Puck provides its own Air)franz schaefer2018-08-19 | 3D Printed design of a Air Hockey Puck with integrated ventilation. Bring your old quadcopter motors to a new live.
Designed and invented by my 11 year old son.Fun with GNU Radio (free SDR) and an Oscilloscopefranz schaefer2015-11-15 | A tutorial on how to generate lissajous paterns on your Oscilloscope. Using a soundcard and GNU-Radio to generate to sine waves.Arduino based DIY game consolefranz schaefer2015-09-19 | Built with an arduino nano clone and a 12864 oled display sku145210 (4pin). Power supply is made with 3 AAA rechargeable battery connected to the 5V input and a transistor and a small speaker for the sound.
code: http://mond.at/~schaefer/arduino/console-nano-pong.tgz XavBot an Arduino Robot with HC-06 Bluetoothfranz schaefer2014-11-24 | Robot Chassis: SKU115409 € 8.90 L298N Dual H Bridge: SKU113918 € 2.75 Arduino Nano Clone: SKU147298 € 2.78 HC-06 Bluetooth Transceiver: SKU106868 € 4.70 Mini Breadboard: SKU: SKU047552 € 1.29
BrickPi: http://www.dexterindustries.com/BrickPibrickPi in action (raspberry pi with brickPi)franz schaefer2013-11-29 | Raspberry pi with lego. Our 1st experiment.Bob jumpfranz schaefer2013-02-17 | This video was uploaded from an Android phone.lego merry go roundfranz schaefer2013-01-06 | This video was uploaded from an Android phone.Dancing lego robotfranz schaefer2013-01-05 | This video was uploaded from an Android phone.Lego machine which changes its own directionfranz schaefer2012-12-26 | Lego machine that changes its own running direction. This is our first machine (besides a small car). I was curious whether or not the thing could change its own running direction. The tricky part is that it needs to have enough momentum to switch over the middle position (where the current is turned off). But we got it right the first time. enjoy. xaver & mond.ACTA 22 march 2010 stakeholder meeting 9/10franz schaefer2010-03-23 | ACTA 22 march 2010 stakeholder meeting 9 or 10