Visualizations of some specific solutions of different differential equations.

Overview

Diff_sims

Visualizations of some specific solutions of different differential equations.

Heat Equation in 1 Dimension

(A very beautiful and elegant explanation for the heat equation and its solution is given here

  • The heat diffusion equation gives us the temperature at every part of a conducting 1 dimensional material (specific to the current discussion), given we specify the initial condition, and the boundary conditions.
  • The thing to be noted here is that the differential equation has a doble derivative with respect to position and a single derivative with respect to time.
  • Hence, one can say that the curvature of the position function and the slope of the time function (of course, assuming one is able to write the solution as independent functions of position and time, which we can) are the key playing factors which determine how the temperature gets diffused, so to speak.
  • The co-efficient D is the thermal diffusivity constant, and here, can be thought of to be some positive constant. (Let's henceforth assume D = 1)

heat_eqn

The Gaussian

  • If the initial temperature distribution were to be in the form of a gaussian:

gauss

This function looks like a bell shaped curve centred at the origin. In other words, it tells us that at the very centre of the rod, the temperature is the highest, and as we move along in either direction it decreases very fast, and some distance from the centre, the temperature is almost zero. This ditribustion might be due to a source which is in contact with the conductor initially, exactly at the centre.

Laying off rigor (we haven't discussed about the boundary conditions here, but a gaussian converges rather rapidly as the magnitude of x increases, so essentially we can assume that the function tends to zero at its boundaries), the solution can be written in the following manner (setting certain constats to 1):

Soln

The denominator in the exponential part, actually tells us how much spread out the bell shape is, the higher it's value, more spread out it will be. The factor multiplied in the beginning is a normalizing factor, which makes sure that the energy remains constant at all times.

Hence, intuitively, we can see that as time increases, the temperature function smooths out.

  • The above solution is by no means accurate but it helps us understand the behavior.

  • One more thing to be noted, is that as the heat starts spreading, it takes more and more time for it to move farther. This is because temperature is an axponentially decaying function of time. Link to simulation here

Custom Plotly Dash components based on Mantine React Components library

Dash Mantine Components Dash Mantine Components is a Dash component library based on Mantine React Components Library. It makes it easier to create go

Snehil Vijay 239 Jan 08, 2023
A simple, fast, extensible python library for data validation.

Validr A simple, fast, extensible python library for data validation. Simple and readable schema 10X faster than jsonschema, 40X faster than schematic

kk 209 Sep 19, 2022
Python toolkit for defining+simulating+visualizing+analyzing attractors, dynamical systems, iterated function systems, roulette curves, and more

Attractors A small module that provides functions and classes for very efficient simulation and rendering of iterated function systems; dynamical syst

1 Aug 04, 2021
PolytopeSampler is a Matlab implementation of constrained Riemannian Hamiltonian Monte Carlo for sampling from high dimensional disributions on polytopes

PolytopeSampler PolytopeSampler is a Matlab implementation of constrained Riemannian Hamiltonian Monte Carlo for sampling from high dimensional disrib

9 Sep 26, 2022
An adaptable Snakemake workflow which uses GATKs best practice recommendations to perform germline mutation calling starting with BAM files

Germline Mutation Calling This Snakemake workflow follows the GATK best-practice recommandations to call small germline variants. The pipeline require

12 Dec 24, 2022
The repository is my code for various types of data visualization cases based on the Matplotlib library.

ScienceGallery The repository is my code for various types of data visualization cases based on the Matplotlib library. It summarizes the code and cas

Warrick Xu 2 Apr 20, 2022
Create Badges with stats of Scratch User, Project and Studio. Use those badges in Github readmes, etc.

Scratch-Stats-Badge Create customized Badges with stats of Scratch User, Studio or Project. Use those badges in Github readmes, etc. Examples Document

Siddhesh Chavan 5 Aug 28, 2022
Visualization ideas for data science

Nuance I use Nuance to curate varied visualization thoughts during my data scientist career. It is not yet a package but a list of small ideas. Welcom

Li Jiangchun 16 Nov 03, 2022
python partial dependence plot toolbox

PDPbox python partial dependence plot toolbox Motivation This repository is inspired by ICEbox. The goal is to visualize the impact of certain feature

Li Jiangchun 723 Jan 07, 2023
This is a Cross-Platform Plot Manager for Chia Plotting that is simple, easy-to-use, and reliable.

Swar's Chia Plot Manager A plot manager for Chia plotting: https://www.chia.net/ Development Version: v0.0.1 This is a cross-platform Chia Plot Manage

Swar Patel 1.3k Dec 13, 2022
股票行情实时数据接口-A股,完全免费的沪深证券股票数据-中国股市,python最简封装的API接口

股票行情实时数据接口-A股,完全免费的沪深证券股票数据-中国股市,python最简封装的API接口,包含日线,历史K线,分时线,分钟线,全部实时采集,系统包括新浪腾讯双数据核心采集获取,自动故障切换,STOCK数据格式成DataFrame格式,可用来查询研究量化分析,股票程序自动化交易系统.为量化研究者在数据获取方面极大地减轻工作量,更加专注于策略和模型的研究与实现。

dev 572 Jan 08, 2023
Graphical visualizer for spectralyze by Lauchmelder23

spectralyze visualizer Graphical visualizer for spectralyze by Lauchmelder23 Install Install matplotlib and ffmpeg. Put ffmpeg.exe in same folder as v

Matthew 1 Dec 21, 2021
An interactive GUI for WhiteboxTools in a Jupyter-based environment

whiteboxgui An interactive GUI for WhiteboxTools in a Jupyter-based environment GitHub repo: https://github.com/giswqs/whiteboxgui Documentation: http

Qiusheng Wu 105 Dec 15, 2022
demir.ai Dataset Operations

demir.ai Dataset Operations With this application, you can have the empty values (nan/null) deleted or filled before giving your dataset to machine le

Ahmet Furkan DEMIR 8 Nov 01, 2022
Python script to generate a visualization of various sorting algorithms, image or video.

sorting_algo_visualizer Python script to generate a visualization of various sorting algorithms, image or video.

146 Nov 12, 2022
A customized interface for single cell track visualisation based on pcnaDeep and napari.

pcnaDeep-napari A customized interface for single cell track visualisation based on pcnaDeep and napari. 👀 Under construction You can get test image

ChanLab 2 Nov 07, 2021
Lightweight, extensible data validation library for Python

Cerberus Cerberus is a lightweight and extensible data validation library for Python. v = Validator({'name': {'type': 'string'}}) v.validate({

eve 2.9k Dec 27, 2022
PanGraphViewer -- show panenome graph in an easy way

PanGraphViewer -- show panenome graph in an easy way Table of Contents Versions and dependences Desktop-based panGraphViewer Library installation for

16 Dec 17, 2022
basemap - Plot on map projections (with coastlines and political boundaries) using matplotlib.

Basemap Plot on map projections (with coastlines and political boundaries) using matplotlib. ⚠️ Warning: this package is being deprecated in favour of

Matplotlib Developers 706 Dec 28, 2022
Create artistic visualisations with your exercise data (Python version)

strava_py Create artistic visualisations with your exercise data (Python version). This is a port of the R strava package to Python. Examples Facets A

Marcus Volz 53 Dec 28, 2022