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75 lines
2.1 KiB
Python
75 lines
2.1 KiB
Python
import numpy as np
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import matplotlib.pyplot as plt
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from matplotlib.animation import FuncAnimation
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from IPython.display import HTML
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# --- Parameters ---
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N_particles = 350
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box_size = 50.0
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dt = 0.04
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steps = 200
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# Constants
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k_gravity = 100.0 # Attraction
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k_repel = 100.0 # Repulsion
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softening = 1.2 # Smoothness
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R_max = 10.0 # Interaction radius
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damping = 0.95 # Viscosity = 5
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max_vel = 12.0 # Velocity
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# --- Initialization ---
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pos = np.random.rand(N_particles, 2) * box_size
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vel = np.zeros((N_particles, 2))
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fig, ax = plt.subplots(figsize=(8, 8), facecolor='#000000')
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ax.set_xlim(0, box_size)
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ax.set_ylim(0, box_size)
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ax.set_title("Pulsating Superfluid Medium", color='white', fontsize=14)
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ax.set_axis_off()
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# Particle Size
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scatter = ax.scatter(pos[:, 0], pos[:, 1], s=30, c='#00f2ff', edgecolors='white', linewidth=0.1)
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def update(frame):
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global pos, vel
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forces = np.zeros((N_particles, 2))
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# Calculation of interactions
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for i in range(N_particles):
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delta = pos - pos[i]
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dist_sq = np.sum(delta**2, axis=1)
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dist = np.sqrt(dist_sq) + 0.001
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mask = (dist > 0) & (dist < R_max)
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for j in np.where(mask)[0]:
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d_sq = dist_sq[j]
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d_vec = delta[j] / dist[j]
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# Newton's gravity: 1/r^2
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f_grav = k_gravity / (d_sq + softening)
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# Repulsion: 1/r^4
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f_repel = -k_repel / (d_sq**2 + 0.1)
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forces[i] += d_vec * (f_grav + f_repel)
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# Physics
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vel = vel * damping + forces * dt
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# Speed limit
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v_speed = np.linalg.norm(vel, axis=1, keepdims=True)
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vel = np.where(v_speed > max_vel, vel * (max_vel / v_speed), vel)
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pos += vel * dt
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# Reflection from boundaries
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for d in range(2):
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out_min, out_max = pos[:, d] < 0, pos[:, d] > box_size
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if np.any(out_min): pos[out_min, d], vel[out_min, d] = 0, -vel[out_min, d] * 0.5
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if np.any(out_max): pos[out_max, d], vel[out_max, d] = box_size, -vel[out_max, d] * 0.5
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scatter.set_offsets(pos)
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return scatter,
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plt.close()
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anim = FuncAnimation(fig, update, frames=steps, interval=30, blit=True)
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HTML(anim.to_jshtml())
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