quark-energy

Explore how the energy of the quarks changes in different models.

Demo

https://quark-energy.netlify.app

Controls

• Left mouse button: select one quark
• Left mouse button + CTRL/SHIFT: add/remove from selection
• Right mouse button: add new quark (gray)
• Right mouse button + "1": add new quark (red)
• Right mouse button + "2": add new quark (green)
• Right mouse button + "3": add new quark (blue)
• Delete: Remove selected quark

Energy functions

Available fields:

• quark.x: returns the x component of position
• quark.y: returns the y component of position
• quark.angle: returns the angle in degrees between the x-axis and the vector
• quark.scale: returns quark's scale relative to the scene

Available custom functions:

• radians(degrees): converts the angle given in degrees to radians

Example energy functions:

1. Dot product $$E = \frac{E_0}{|v|^2} \sum_{i,j=1}^n \vec{v_i} \cdot \vec{v_j}$$ If we suppose that $|v_i| = 1$ for every $i$ in $\set{1, ..., n}$ and $E_0 = 1$, we have the following function:

function (quarks) {
  let sum = 0;
  for (const q1 of quarks) {
    for (const q2 of quarks) {
      sum += Math.cos(
        radians(q1.angle - q2.angle)
      )
    }
  }
  return sum;
};

2. Dot product + Coulomb-like potential $$E = \frac{E_0}{|v|^2} \sum_{i,j=1}^n \frac{\vec{v_i} \cdot \vec{v_j}}{a + d(\vec{v_i}, \vec{v_j})}$$ $d(v_1, v_2)$ is a distance function and $a$ is a positive constant so there is no division by zero. If we make the same assumptions as above, choose $a = 1$ and $d(v_1, v_2)$ as the euclidean distance metric, we have:

function (quarks) {
  let sum = 0;
  for (const q1 of quarks) {
    for (const q2 of quarks) {
      sum += Math.cos(
        radians(q1.angle - q2.angle)
      ) / (1 + Math.hypot(q1.x - q2.x, q1.y - q2.y));
    }
  }
  return sum;
};