physics-visualization

# Physics Visualization ## Overview Generate publication-quality figures for physics: vector fields, streamlines, contour plots, 3D surfaces, phase diagrams, spectrograms, and animations. All plots use LaTeX rendering, proper colormaps, and journal-ready formatting. ## When to Use - Any physics result that needs a figure - Vector fields (E&M, fluid flow, gravitational fields) - Contour/heatmap plots (potential fields, temperature distributions, wavefunctions) - Phase space plots (trajectories, Poincare sections) - 3D surface plots (energy landscapes, wavefunctions) - Animations (time-evolving systems) - Multi-panel comparison figures ## Setup ```python import numpy as np import matplotlib matplotlib.use('Agg') # non-interactive backend for scripts import matplotlib.pyplot as plt from matplotlib import cm from mpl_toolkits.mplot3d import Axes3D # Publication-quality defaults plt.rcParams.update({ 'font.size': 12, 'axes.labelsize': 14, 'axes.titlesize': 15, 'xtick.labelsize': 11, 'ytick.labelsize': 11, 'legend.fontsize': 11, 'figure.dpi': 150, 'savefig.dpi': 300, 'savefig.bbox': 'tight', 'axes.grid': True, 'grid.alpha': 0.3, 'lines.linewidth': 1.5, }) # Enable LaTeX if available try: plt.rcParams.update({ 'text.usetex': True, 'font.family': 'serif', }) except: pass # fallback to mathtext ``` ## Core Plot Types ### 1. Vector Field ```python def plot_vector_field(ax, X, Y, U, V, title='', normalize=True, cmap='viridis'): """Plot a 2D vector field with magnitude coloring.""" magnitude = np.sqrt(U**2 + V**2) if normalize: U_n = U / (magnitude + 1e-10) V_n = V / (magnitude + 1e-10) else: U_n, V_n = U, V q = ax.quiver(X, Y, U_n, V_n, magnitude, cmap=cmap, alpha=0.8) plt.colorbar(q, ax=ax, label='|F|') ax.set_title(title) ax.set_aspect('equal') return q # Example: Electric dipole field x = np.linspace(-3, 3, 20) y = np.linspace(-3, 3, 20) X, Y = np.meshgrid(x, y) # Dipole at (±0.5, 0) def dipole_field(X, Y, d=0.5): r_plus = np.sqrt((X-d)**2 + Y**2) r_minus = np.sqrt((X+d)**2 + Y**2) Ex = (X-d)/r_plus**3 - (X+d)/r_minus**3 Ey = Y/r_plus**3 - Y/r_minus**3 return Ex, Ey Ex, Ey = dipole_field(X, Y) fig, ax = plt.subplots(figsize=(8, 8)) plot_vector_field(ax, X, Y, Ex, Ey, title='Electric Dipole Field') ax.set_xlabel('x [m]') ax.set_ylabel('y [m]') plt.savefig('vector_field.png', dpi=150, bbox_inches='tight') ``` ### 2. Streamlines ```python fig, ax = plt.subplots(figsize=(10, 8)) x_fine = np.linspace(-3, 3, 100) y_fine = np.linspace(-3, 3, 100) X_f, Y_f = np.meshgrid(x_fine, y_fine) Ex_f, Ey_f = dipole_field(X_f, Y_f) magnitude = np.sqrt(Ex_f**2 + Ey_f**2) strm = ax.streamplot(X_f, Y_f, Ex_f, Ey_f, color=np.log10(magnitude+1e-3), cmap='inferno', density=2, linewidth=1, arrowsize=1.5) plt.colorbar(strm.lines, ax=ax, label=r'$\log_{10}|E|$') ax.plot([-0.5, 0.5], [0, 0], 'ro', markersize=10, label='Charges') ax.set_xlabel('x [m]') ax.set_ylabel('y [m]') ax.set_title('Electric Field Streamlines') ax.legend() plt.savefig('streamlines.png', dpi=150, bbox_inches='tight') ``` ### 3. Contour / Heatmap ```python def plot_contour(ax, X, Y, Z, title='', levels=20, cmap='RdBu_r', symmetric=True): """Contour plot with optional symmetric colorbar (good for potentials).""" if symmetric: vmax = np.max(np.abs(Z)) vmin = -vmax else: vmin, vmax = Z.min(), Z.max() cf = ax.contourf(X, Y, Z, levels=levels, cmap=cmap, vmin=vmin, vmax=vmax) cs = ax.contour(X, Y, Z, levels=levels, colors='k', linewidths=0.3, alpha=0.5) plt.colorbar(cf, ax=ax, label=title) ax.clabel(cs, inline=True, fontsize=8, fmt='%.1f') ax.set_aspect('equal') return cf # Example: 2D wavefunction |ψ|² r = np.linspace(-5, 5, 200) X, Y = np.meshgrid(r, r) R = np.sqrt(X**2 + Y**2) # Hydrogen 2p orbital (simplified) psi = R * np.exp(-R/2) * X / R # p_x orbital psi_sq = np.abs(psi)**2 fig, ax = plt.subplots(figsize=(8, 7)) plot_contour(ax, X, Y, psi_sq, title=r'$|\psi_{2p}|^2$', symmetric=False, cmap='hot') ax.set_xlabel('x [a₀]') ax.set_ylabel('y [a₀]') ax.set_title(r'Hydrogen $2p_x$ Probability Density') plt.savefig('wavefunction.png', dpi=150, bbox_inches='tight') ``` ### 4. 3D Surface ```python fig = plt.figure(figsize=(10, 8)) ax = fig.add_subplot(111, projection='3d') # Energy landscape x = np.linspace(-2, 2, 100) y = np.linspace(-2, 2, 100) X, Y = np.meshgrid(x, y) Z = (X**2 - 1)**2 + Y**2 # double-well potential surf = ax.plot_surface(X, Y, Z, cmap='coolwarm', alpha=0.8, linewidth=0, antialiased=True) ax.set_xlabel('x') ax.set_ylabel('y') ax.set_zlabel('V(x,y)') ax.set_title('Double-Well Potential') fig.colorbar(surf, ax=ax, shrink=0.6, label='V') plt.savefig('surface_3d.png', dpi=150, bbox_inches='tight') ``` ### 5. Animation ```python from matplotlib.animation import FuncAnimation, PillowWriter def create_animation(update_func, n_frames, fig, interval=50, filename='animation.gif'): """Create and save an animation.""" anim = FuncAnimation(fig, update_func, frames=n_frames, interval=interval, blit=True) writer = PillowWriter(fps=1000/interval) anim.save(filename, writer=writer) print(f"Animation saved: {filename}") return anim # Example: wave propagation fig, ax = plt.subplots(figsize=(10, 4)) x = np.linspace(0, 10, 500) line, = ax.plot(x, np.sin(x), 'b-', linewidth=2) ax.set_ylim(-1.5, 1.5) ax.set_xlabel('x') ax.set_ylabel('u(x,t)') time_text = ax.text(0.02, 0.95, '', transform=ax.transAxes) def update(frame): t = frame * 0.05 y = np.sin(2*np.pi*(x - t)) * np.exp(-0.1*t) line.set_ydata(y) time_text.set_text(f't = {t:.2f}') return line, time_text create_animation(update, 200, fig, interval=33, filename='wave.gif') ``` ### 6. Multi-Panel Figure ```python def multi_panel(n_rows, n_cols, figsize=None, sharex=False, sharey=False): """Create a multi-panel figure with consistent styling.""" if figsize is None: figsize = (5*n_cols, 4*n_rows) fig, axes = plt.subplots(n_rows, n_cols, figsize=figsize, sharex=sharex, sharey=sharey) # Add panel labels (a), (b), (c), ... if n_rows * n_cols > 1: for i, ax in enumerate(np.atleast_1d(axes).flat): label = chr(ord('a') + i) ax.text(-0.12, 1.05, f'({label})', transform=ax.transAxes, fontsize=14, fontweight='bold', va='top') return fig, axes ``` ## Colormap Guide | Data Type | Recommended Colormap | Why | |---|---|---| | Sequential (magnitude, density) | `viridis`, `plasma`, `inferno` | Perceptually uniform, colorblind-safe | | Diverging (potential, temperature anomaly) | `RdBu_r`, `coolwarm` | Symmetric around zero | | Cyclic (phase, angle) | `twilight`, `hsv` | Wraps around | | Binary (positive/negative) | `bwr` | Clear sign distinction | **Never use** `jet` or `rainbow` — they are not perceptually uniform and mislead. ## Save Format Guide | Format | When to Use | |---|---| | PNG (300 dpi) | General use, presentations | | PDF | Journal submission, vector graphics | | SVG | Web, editable vector | | EPS | Legacy journals requiring EPS | Always save both PNG and PDF: ```python plt.savefig('figure.png', dpi=300, bbox_inches='tight') plt.savefig('figure.pdf', bbox_inches='tight') ```