Hi, I'm Akhilan

Extracted Boltzmann's constant from Johnson noise measurements in resistors, achieving 5.9% agreement with the accepted value through gain-corrected signal chain analysis, bandwidth-controlled filtering, and statistical averaging of mean-square voltage data.

Applied FFT techniques to decompose periodic and noisy electrical signals, verified harmonic power-law relationships, and recovered weak sinusoidal signals buried 20 dB below broadband noise through spectral averaging and resolution optimization.

Designed and executed an optical measurement pipeline to extract a material constant from polarization rotation data, including systematic error characterization of instruments, Malus's Law validation, and linear regression analysis yielding agreement within 7.25% of published values.

Extracted discrete atomic excitation energies from current-voltage characteristic curves, applying oscilloscope-based data acquisition, scale-factor calibration, and uncertainty propagation to achieve measurements consistent with accepted values for neon (19.0 ± 2.0 eV) and mercury (4.9 ± 0.5 eV).

Implemented lock-in amplifier techniques to isolate a weak Faraday rotation signal from noise, demonstrating modulation-based measurement, signal chain calibration, and systematic error identification through comparison with independent reference data.

Measured magnetic dipole moments using three independent methods (force-balance, static torque, and harmonic oscillation) demonstrating multi-method experimental design, Helmholtz coil field calibration, and linear model fitting across distinct physical regimes.

Analyzed simulation output of the Hubbard model on a cubic lattice, extracting energy and density as functions of temperature and chemical potential through array slicing, interpolation, and function inversion on large datasets.

Investigated machine epsilon, overflow limits, and catastrophic cancellation in floating-point arithmetic. Demonstrated how mathematically equivalent expressions diverge numerically and derived stable alternatives for the quadratic formula.

Computed Bessel functions via Simpson's rule integration to model the Airy diffraction pattern of a circular aperture, generating 2D intensity density plots optimized through circular symmetry exploitation.

Solved the nonlinear pendulum ODE using Euler, Euler-Cromer, and Verlet integration schemes. Compared energy conservation and period accuracy across methods, benchmarking against elliptic integral solutions.

Implemented fourth-order Runge-Kutta and adaptive step-size solvers for the Lorenz and Lotka-Volterra systems. Visualized deterministic chaos through strange attractor phase-space plots and population oscillation dynamics.

Solved the 1D diffusion equation using FTCS finite-difference methods with Dirichlet and von Neumann boundary conditions. Validated against Gaussian analytical solutions and visualized temperature evolution in 3D surface and contour plots.

Implemented FTCS, Lax, and Lax-Wendroff schemes for the advection and transport equations. Analyzed numerical stability criteria and demonstrated how physical diffusion stabilizes advective transport.

Solved the 2D Laplace equation for a parallel-plate capacitor geometry using iterative relaxation on a 100×100 grid to 10⁻⁶ V precision. Generated electric field quiver plots from numerical gradient computation.

Modeled a polymer chain as a coupled spring-mass system, formulating and solving the resulting linear system to find equilibrium positions as a function of spring constant ratios.

Built a Metropolis Monte Carlo simulation of the 2D Ising model on a 20×20 lattice. Observed spontaneous magnetization, phase transition behavior across temperatures, and optimized energy computation for million-step runs.

Applied linear regression and FFT-based filtering to NOAA atmospheric CO₂ data from Mauna Loa and Barrow, extracting long-term growth rates and removing annual periodicity through frequency-domain processing.

Exploring real-time audio classification and processing on XMOS multicore hardware. Using the XU316 dev board to prototype DSP pipelines that detect and respond to audio characteristics in real time. Written in C, leveraging hardware concurrency for low-latency signal processing. Work in progress.

Identified a security gap in how developers use AI coding agents — by default, agents inherit full user permissions including access to SSH keys, credentials, and system files. Built and published an open-source CLI tool that wraps Claude Code in disposable Docker containers, mounting only the project directory, installing the agent fresh each session, running as a non-root user, and self-destructing on exit. The container is the security boundary, not the agent’s own permission system.