Mathematical Physics

Physics is interesting enough on its own, but the theories and strategies used to model different equations are equally fascinating.

The image for this category page is from an old assignment of mine to study the chaotic behavior of a solution to the Duffing equation, a well-known nonlinear differential equation:

\[\frac{d^2 x}{dt^2} + \delta \frac{dx}{dt} + \alpha x + \beta x^3 = \gamma \cos(\omega t)\]

The plot above shows a Poincaré section of the solution, in which each point corresponds to the position and velocity of the system at regular time intervals, determined by the drive frequency $\omega$. This is an illustration of the tight relationship between many nonlinear physical systems and fractal geometry.

  • The Physics of Maxwell's Equations
    [Mathematical Physics] Maxwell’s Equations govern the study of electromagnetism, one of the fundamental forces of nature. Here, I attempt to motivate these beautiful equations and present some of their more interesting consequences.