MSc Physics | Computational Physics (PhD aspirant) Nepal

Physics educator and computational researcher focusing on the explicit numerical modeling of non-linear dynamical systems. My work evaluates the long-term phase-space stability of Hamiltonian, Lagrangian, and dissipative chaotic models.

I treat my code repositories as formal numerical laboratories. My methodology prioritizes mathematical rigor, strict physical conservation proofs, and custom algorithmic execution over pre-built library wrappers. I am systematically building a technical and mathematical foundation for a PhD in Computational Physics and Nonlinear Dynamics.

Alongside that research track, I've been applying the same engineering discipline — rigor, conservation of correctness, distrust of black boxes — to a different kind of hard problem: Nepal's exam-prep and school-operations infrastructure has had almost no serious software built for it. That work now runs as MCQplex, a NEB curriculum exam-prep platform, alongside a school routine/substitution planner and a handful of open-source utilities that came out of building them. It's not a departure from the physics — it's the same habit of building things from first principles instead of trusting a wrapper, pointed at a problem in front of me instead of a problem on a syllabus.

A computational framework designed to model, visualize, and analyze deterministic chaos within the three-dimensional, non-linear atmospheric flow model derived by Edward Lorenz.

$$ \frac{dx}{dt} = \sigma(y - x), \quad \frac{dy}{dt} = x(\rho - z) - y, \quad \frac{dz}{dt} = xy - \beta z $$

• Numerical Engine: Implemented a standard fourth-order Runge-Kutta (RK4) integrator with adaptive time-stepping to preserve trajectory integrity across high-gradient vector fields.
• Bifurcation Analysis: Mapped phase-space trajectories across a spectrum of Rayleigh numbers ($\rho$). Safely isolated the subcritical Hopf bifurcation ($\rho \approx 24.74$) where steady-state fixed points lose stability, giving rise to the iconic "butterfly" strange attractor.
• Chaos Quantification: Evaluated sensitive dependence on initial conditions (SDIC) by tracking twin trajectories with an initial perturbation of $\delta \sim 10^{-8}$, calculating the maximal Lyapunov exponent ($\lambda_{max} > 0$) to verify true deterministic chaos rather than numerical noise.
• Topology Mapping: Visualized 3D phase-space projections, plotting the dual-wing geometry to study trajectory ergodicity and fractal structure bounds.

An examination of multi-degree-of-freedom systems and the explicit onset of deterministic chaos through analytical mechanics.

• Euler-Lagrange Derivation: Formulated the coupled, highly non-linear transcendental equations of motion using generalized coordinates ($\theta_1, \theta_2$).
• Phase-Space Mapping: Isolated the transition boundaries where regular, low-energy invariant tori break apart into high-energy chaotic seas.
• Poincaré Sections: Generated state-space slices to visually map the breaking of system integrability and track coordinate divergence.

A high-precision study of gravitational stability, transition to chaos, and long-term orbital conservation.

• Symplectic Engineering: Developed a custom Velocity-Verlet (Leapfrog) engine in Python to eliminate numerical energy dissipation, maintaining a relative Hamiltonian error of $\sim 10^{-9}$.
• Chaos Quantification: Identified a critical velocity perturbation threshold ($\delta \approx 0.5$) for stellar ejection using Lyapunov divergence mapping.
• Astronomical Validation: Verified engine stability through a 12-year simulation of the Sun-Earth-Jupiter system using Astronomical Units and Solar Masses ($G = 4\pi^2$).
• Visualization: Authored a cinematic rendering suite to visualize "Butterfly Effect" divergence and total system collapse.

A structural migration of a 2023 procedural Fortran 90 dissertation into a high-performance, vectorized Python framework.

• Numerical Validation: Verified custom RK4 algorithms against SciPy, achieving a maximum residual error of $< 10^{-7}$.
• Legacy Cross-Validation: Achieved 100% trace overlap between modern Python outputs and legacy Fortran data.
• Performance Auditing: Benchmarked Python interpreter loops versus compiled Fortran for 1,000,000-step execution cycles.

An investigation of ballistics kinematics evaluating the transit from idealized vacuum baselines to dissipative media.

$$ m \frac{d\mathbf{v}}{dt} = m \mathbf{g} - b\mathbf{v} - c|\mathbf{v}|\mathbf{v} $$

• State-Space Vectorization: Implements array-based evaluations in NumPy to resolve non-linear quadratic drag terms where exact analytical solutions are unavailable.
• Error Benchmarking: Compares custom discrete step allocations against adaptive-step algorithms to map absolute spatial residuals.

Started as a way to apply the same first-principles habit to a problem in front of me rather than a problem on a syllabus, and grew into an ongoing project.

• MCQplex — an adaptive exam-prep and school-analytics platform for Nepal's NEB curriculum: a client-side exam engine tuned for low-end Android devices and patchy connectivity, a cognitive-level-tagged question bank with difficulty bands that adjust to a student's performance, assistive tooling for teachers (AI-assisted question drafting, quality review, class analytics), and real-time head-to-head practice duels. Most of what runs it is written in-house rather than assembled from a SaaS template, for the same reason the physics repos avoid library wrappers — the constraints (device class, network, curriculum structure) are specific enough that a generic tool doesn't fit them.
• Routine & Substitution Planner — a school-operations tool that generates a day's teaching schedule from a master timetable, resolves teacher absences through a tiered substitution engine, and publishes it to a page every teacher can check on their phone. Built offline-first, since that's the actual operating condition for most schools.
• Open curricula for Nepali schools — two openly licensed (CC BY 4.0 content, MIT code) teaching resources for Grades 8–12, published in October 2026. Both are v0.1 and have not yet been piloted in a classroom; classroom pilots are the next step before anything is called finished.
  • git-for-nepal — an offline-first curriculum for teaching Git and version control. Grade 8 is a full chapter (seven modules with teacher guides); Grades 9–12 are outlines plus core lessons. Modules are written to work from "no computer" up to internet-connected, with a school-LAN option using Forgejo. Mapping to the national curriculum is verified for Grades 10–12 and still unverified for Grades 8–9.
  • data-science-nepal — a bilingual (Nepali/English) data science curriculum built around Nepali datasets, with a no-code track (paper, spreadsheets, CODAP) and a code track (SQL, Python in the browser). It currently has 40 units and 28 notebooks across Grades 8–12, but only Grade 8 Unit 1 and Grade 9 Unit 3 have Nepali chapters so far; the other units are English-only, and real-data fetch links are still on the roadmap.
• Open-source utilities — infrastructure pieces that came out of building the above, extracted because they're generic enough to be useful outside this one project:
  • llm-free-cascade — cascades an LLM call across free-tier providers (Gemini, Groq, Cerebras, and others) with per-key rotation, reset-aware cooldowns, and support for custom providers (currently 0.9.0), so a small project can use AI-assisted content tooling without a paid API bill.
  • pdf-render-pool — a persistent, concurrency-capped Puppeteer render pool for HTML-to-PDF generation, avoiding the cost of launching a fresh headless Chromium per document.
  • mongo-job-lock — a MongoDB-backed advisory lock so a cron job registered on every instance of a clustered deployment only actually runs once.

The throughline across both tracks is the same: work things out from first principles, verify rather than assume, and don't reach for a black box when the underlying mechanism is knowable and worth knowing.

My technical stack maps directly to strict methodological requirements designed for reproducible execution on standard consumer hardware (16 GB RAM, CPU-only):

• Numerical Integration: Symplectic algorithms (Leapfrog/Verlet) and adaptive high-order solvers (RK45, DOP853).
• State-Space Modeling: Vectorized array operations using NumPy and SciPy for multi-variable ODEs.
• Chaotic Quantification: Implementation of phase-space metrics, including Lyapunov exponents and Poincaré mapping.
• Physics Validation: Test-driven workflows designed to verify structural invariants (e.g., energy and momentum conservation) during runtime.
• Environment Reproducibility: Strict adherence to deterministic random seed controls and continuous versioning for repository continuity.

Consolidated Knowledge I have verified my capacity to construct vectorized ODE solvers for many-body and chaotic systems. I can successfully track structural conservation laws directly within computation loops, quantify non-linear trajectories using established chaos indicators, and enforce mathematical accuracy over millions of integration steps.

Targeted PhD-Level Methodologies (Future Research Roadmap) To transition from standalone numerical simulations to high-performance, doctoral-level research, I have identified the following computational methodologies as the core technical objectives of my upcoming academic trajectory:

1. Compiled Acceleration: Migrating computationally intensive components from interpreted Python to compiled frameworks (Numba, native C++ extensions) to bypass interpreter overhead and execute high-speed multi-parameter sweeps.
2. Dimensional Scaling: Progressing from systems governed by Ordinary Differential Equations (ODEs) to high-dimensional Partial Differential Equations (PDEs) and large many-body lattice matrices.
3. Parallelization: Implementing multi-core CPU parallelization architectures to manage large-scale computational execution and high-density state-space mapping efficiently.

"Physics is the only profession in which prophecy is not only allowed but required." — This profile tracks my progress in mastering those prophecies through code.