Latest post

My Book and SanDisk portable. Feb 25, 2024, 15:43:16

I have owned two 2TB external hard drives for some time, and I lately was seeking new storage devices. Three weeks ago, I bought a #MyBook (8TB #HDD) and a #SanDisk #portable (2TB #ssd with $300 in total from #WesternDigital. They seem decent!

#harddrive #storage #disk

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Articles

  • Normal vectors of a scalar field

    This article gives the formula for the normal vectors of a surface defined by a scalar field on Rn\mathbb R^n. The normal vector of the graph of the function y=f ⁣(x)y=f\!\left(\mathbf x\right) at (x0,f ⁣(x0))\left(\mathbf x_0,f\!\left(\mathbf x_0\right)\right) is (f ⁣(x0),1)\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 1-1, and then integrate the rest components.

  • It is Feb 29 today!

    It is Feb 29 today. The date appears once for as long as 4 years!

  • Monkey-patching graciously

    Monkey-patching is a powerful tool in programming. In this article, I used techniques of Ruby metaprogramming to define a series of methods def_after, def_before, etc. to help monkey-patching. They look graciously in that we can use it to shorten the codes for monkey-patching (avoiding aliasing and repeating codes).

  • Amazing Siteleaf

    I have been using Siteleaf to manage my blog. It is just convenient and amazing.

  • Hyperellipsoids in barycentric coordinates

    In this article, I introduce the barycentric coordinates: it is an elegant way to represent geometric shapes related to a simplex. By using it, given a simplex, we can construct a hyperellipsoid with the properties: its surface passes every vertex of the simplex, and its tangent hyperplane at each vertex is parallel to the hyperplane containing all other vertices.

  • Use complex numbers as canonical variables

    In this article, I try exploring an idea: using complex numbers to combine pairs of canonical variables into complex variables: cαq+iβp\mathbf c\coloneqq\alpha\mathbf q+\mathrm i\beta\mathbf p. It turns out that we can write canonical equations dcdt=2iαβHc\frac{\mathrm d\mathbf c}{\mathrm dt}=-2\mathrm i\alpha\beta\frac{\partial\mathcal H}{\partial\mathbf c^*}, Poisson brackets {f,g}=2iαβ(fcgcfcgc)\left\{f,g\right\}=-2\mathrm i\alpha\beta \left(\frac{\partial f}{\partial\mathbf c}\cdot \frac{\partial g}{\partial\mathbf c^*}- \frac{\partial f}{\partial\mathbf c^*}\cdot \frac{\partial g}{\partial\mathbf c}\right), and canonical transformations cc=cc,cc=cc\frac{\partial\mathbf c^*}{\partial\mathbf c'^*}= \frac{\partial\mathbf c'}{\partial\mathbf c}, \frac{\partial\mathbf c}{\partial\mathbf c'^*}= -\frac{\partial\mathbf c'}{\partial\mathbf c^*} in these complex numbers. Finally, I show two examples of using them in real problems: a free particle, and a harmonic oscillator.

  • Giving birth to my own blog

    This is my first blog! I will share interesting things in my life here.

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