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Articles
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Determining the stabilizability of the abelian sandpile model
The abelian sandpile model is a cellular automaton where each cell is a sandpile that can topple to put grains on neighboring cells when having enough grains. It is stable if none of the sandpiles can topple. A natural question to ask is whether it can become stable eventually. In this article, I will show that one can determine the stabilizibility usiung integer linear programming for the abelian sandpile model on an arbitrary finite graph.
- Categories: math
- Tags: graph theory, linear programming, long paper
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From Picard iteration to Feynman path integral
The Schrödinger equation is an ODE, so we can approach its solution through Picard iteration. This approach leads to a sum over walks on the graph formed by an orthonormal basis as vertices and the Hamiltonian matrix elements as edge weights. This sum is exactly the Feynman path integral if we choose the position basis and take the continuum limit.
- Categories: physics
- Tags: ode, quantum mechanics, graph theory, stochastic process, long paper
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Imperative programming in Nix language
Nix is a functional programming language primarily used for package management and system configuration. However, it may be interesting to emulate imperative programming constructs within Nix. This post explores how to achieve imperative-style programming in Nix.
- Categories: programming
- Tags: nix, functional programming
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Multi-pass Gaussian blur filter
According to the central limit theorem, the sum of some i.i.d. samples is normally distributed in the limit of large sample size. This fact can be used to implement a multi-pass Gaussian blur filter, where the total number of passes is equal to the number of samples used in the averaging. Through this, we can also see a nice relation to the heat equation, which is not surprising since the heat kernel is a Gaussian function.
- Categories: programming
- Tags: algorithm, shader, probability, pde
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The buildup kickroll in Time to beat the odds
There is a gradually-accelerating buildup kickroll at 1:18 in the song Time to beat the odds by 影虎。. In order to know the details of this rhythm, I have to analyze the sample using Python.
- Categories: music
- Tags: fourier transform, python
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Eigenfunctions of the Laplacian on an annulus with homogeneous Neumann boundary condition
Several features of the eigenfunctions of the Laplacian on an annulus with homogeneous Neumann boundary condition are discussed. The distribution of the eigenvalues is discussed in detail, making use of a phase angle function called . The limiting cases of a disk and a circle are discussed.
- Categories: math
- Tags: mathematical physics, pde, ode, long paper
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The role of particle indistinguishability in statistical mechanics
Indistinguishability plays an important role in enumerative problems in combinatorics. This article explains the concept and significance of particle indistinguishability in statistical mechanics.
- Categories: physics
- Tags: mathematical physics, statistical mechanics, probability, long paper, combinatorics, quantum mechanics
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Why it is a bad idea to use GitHub for submiting school homework
It is common for school courses to require students to submit their homework using GitHub. However, this is usually a bad idea for several reasons.
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How to use JavaScript in GitHub Actions without committing
node_modules
I was creating my first GitHub Action. According to the official documentation, I should commit the node_modulesto the repo or generate a script that bundles the wholenode_modulesif I want to create a JavaScript action. I think this is not good practice, so I try to find another way.- Categories: guide
- Tags: javascript, github
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Some understanding of Grassmann numbers out of intuition
I was briefly introduced to Grassmann numbers when I studied quantum field theory. I then had the natural question of how we can formally define them. In this article, I went with my intuition and tried to answer this question.
- Categories: math
- Tags: quantum field theory, linear algebra, abstract algebra
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