Ulysses' trip

Apr 28, 2020

Simulating a mechanical system using RGSS3

Hamiltonian mechanics gives us a good way to simulate mechanical systems as long as we can get its Hamiltonian and its initial conditions. I implemented this simulation in RGSS3, the game scripting system shipped with RPG Maker VX Ace.

Categories: physics
Tags: ruby, rgss, hamiltonian, calculus, ode

Apr 27, 2020

Writing a DSL with commands split by space

DSL means domain-specific language. Ruby is a powerful script language in terms of building DSLs (as sublanguages of Ruby). In this article, I implemented my idea of a DSL with commands split by space. For example, you may just write a b c to run the commands a, b, and c one after another! This trick is heavily applied in my project alda-rb. How do I achieve this?

Categories: programming
Tags: ruby, meta programming

Apr 14, 2020

Running Jekyll myself

I have got tired of letting GitHub Pages to run Jekyll for me. I cannot use custom plugins! I decide to run Jekyll myself and push the built result to GitHub repo. I wrote a script to do this.

Categories: programming
Tags: jekyll

Apr 13, 2020

Algebraic structure of chemicals

Regarding balancing chemical equations, actually we are trying to find a non-trivial linear combination of some chemicals to get zero. The interesting thing is that the coefficients can only be integers ( $\mathbb Z$ ), which is not a field, so the algebraic structure of chemicals is not linear space. They actually live in a free $\mathbb Z$ -module. See how I formalize this idea in mathematical language.

Categories: chemistry
Tags: linear algebra, abstract algebra

Apr 12, 2020

The concentration change of gas in reversible reactions

A reversible elementary reaction takes place inside a closed, highly thermally conductive container of constant volume, whose reactants are all gases. Given the reaction equations and the reaction rate constants, a natural question to ask is how the concentration of each gas changes w.r.t. time. In this article, I will answer this question by proposing a general approach to solve it.

Categories: chemistry
Tags: calculus, ode, chemical reaction, long paper

Apr 11, 2020

Snippet: O, ’tis too true!

O, ’tis too true!

Categories: literature
Tags: snippet, chinese

Apr 8, 2020

The structure of a basic RM game

In this article, I present minimal examples of a RM game. They only illustrate the basic concepts of how a RM game is structured and what is the running logic of it.

Categories: programming
Tags: ruby, javascript, rgss

Mar 27, 2020

The frequency assignment of musical notes

This article explores the concept which I call the frequency assignment, which is a mapping from $N$ (the set of notes) to $\mathbb R^+$ (the set of frequencies). Concepts such as octaves, intervals, and equal temperaments are introduced.

Categories: music
Tags: music theory, number sequence, long paper, abstract algebra

Mar 3, 2020

Normal vectors of a scalar field

This article gives the formula for the normal vectors of a surface defined by a scalar field on $\mathbb R^n$ . The normal vector of the graph of the function $y=f\!\left(\mathbf x\right)$ at $\left(\mathbf x_0,f\!\left(\mathbf x_0\right)\right)$ is $\left(\nabla f\!\left(\mathbf x_0\right),-1\right)$ . This also provides us a way to recover a scalar field from the normal vectors of its graph: normalizing the vectors so that the last component is $-1$ , and then integrate the rest components.