Monthly Archives: March 2026

Problem: Consider a Landau-Ginzburg theory involving a single real scalar field \(\phi(\mathbf x)\) for \(\mathbf x\in\mathbf R^n\) governed by the canonically normalized free energy density: \[\mathcal F(\phi,\partial\phi/\partial\mathbf x,…)=\left(\frac{1}{2}\biggr|\frac{\partial\phi}{\partial\mathbf x}\biggr|^2+\frac{\phi^2}{2\xi^2}+…\right)\] Explain what the \(…\) means, and explain which terms have temperature … Continue reading →

CNNs_Part_1 $\textbf{Problem}$: Write functions that take an arbitrary grayscale image and convolve them with a Sobel edge detection kernel. Apply both functions to a grayscale image of your choice. $\textbf{Solution}$: In [1]: import numpy as np import matplotlib.pyplot as plt sobel_horizontal_kernel … Continue reading →