## 28 results

#### Seam Carving

Seam carving is an algorithm for content-aware resizing of an image. This notebook presents the algorithm and tries to provide some insight into its workings.

#### Neural Network From Scratch

Making a neural network from scratch and training the network using a dataset from scikit-learn.

#### A quick introduction to the Julia programming language

Julia has to some degree already cemented itself in the scientific community, and will most likely continue to expand in the coming years. It aims at taking the middle ground between Python on one side, and Fortran and C++ on the other. In this notebook we offer a quick introduction for those who wish to venture from Python to Julia.

#### Quantum computing - Basics

Uses the qiskit framework to run basic quantum circuits, both locally and on real quantum computers.

#### Bak-Sneppen model in Julia

The Bak-Sneppen model of evolution is a simple model describing the evolution of an ecosystem. It offers a surprising amount of insight given its simplicity. This notebook does not deep dive into the model, but illustrates the basics using the Julia programming language.

#### Euler's Method

A thorough walkthrough of the theoretical aspects of Euler's method. Also covers how to solve higher order ODEs.

#### Magnetic Mirror

The trajectory of a charged particle propagating in a non-uniform magnetic field is calculated by solving the Lorentz force law using an embedded Runge-Kutta pair. The results show that the particle is mirrored.

#### Simple implementation of Euler's method

Basic notebook covering how to implement Euler's method, without much focus on theory

#### Equilibrium Monte Carlo simulation of the 2D Ising model

Using the Metropolis algorithm to approximate the magnetization and specific heat for a 2D Ising lattice.

#### Uniform Magnetic Field

Solving Lorentz force law for a charged particle traveling in a uniform magnetic field using Euler's method.

#### Modeling Atoms, Molecules, and Crystals in One Dimension

Solving the time independent Schrödinger equation in one dimension using matrix diagonalisation for five different potentials.

#### Projectile motion

Computing the trajectory of a projectile moving through the air, subject to wind and air drag.

#### The Fate of Our Universe

Solving the Friedmann equations to model the expansion of our universe.

#### Precession of Mercury

Computes the precession of Mercury by linear extrapolation.

#### Double Pendulum and Chaos

Discusses the chaotic motion of the double pendulum using a phase-space diagram

#### Simple Pendulum

Simulates the simple pendulum and damped simple pendulum

#### General Relativity

Discussion of orbits in the Schwarzschild Geometry.

#### Cubic Splines

Uses cubic splines to interpolate a given set of data points

#### One-dimensional Stationary Heat Equation

Solving the one-dimensional stationary heat equation with a Gaussian heat source by approximating the solution as a sum of Lagrange polynomials.

#### The Fiber Bundle Bridge Model

Simulates the disentanglement of a polymer from a surface using an increasing electric field

#### Ising Model in 1D and 2D

Computing the internal energy, specific heat and magnetisation in the 1D and 2D Ising model. An analytical solution to the XY model is also provided.

#### Sloshing

Analyzing sloshing using a numerical approach based on a linear model, which reduces the problem to a Steklov eigenvalue problem.

#### Polynomial Interpolation

Using polynomial interpolation to interpolate a set of points and to approximate a function or a curve.

#### Ordinary Differential Equations 4

Solving a first-order ordinary differential equation using Runge-Kutta methods with adaptive step sizes.

#### Runge-Kutta Methods

Solving a first-order ordinary differential equation using the Runge-Kutta method.

#### Implicit Euler Method

Solving a first-order ordinary differential equation using the implicit Euler method (backward Euler method).

#### Verlet Integration

Solving a second-order ordinary differential equation (Newton's second law) using Verlet integration.

#### Lennard-Jones Potential

A simple physical model that approximates the interaction between a pair of neutral atoms or molecules.