Fermín FrancoMathematician and computational scientist
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Research

I begin with mathematical structure and physical questions, then develop computational methods and software that let other people inspect, test, and extend the result.

  1. Nonlinear systems and mathematical modeling

    Question. How do parameters change stability, and how accurately can we follow a solution?

    Approach. I work with discrete dynamical systems, stability analysis, and numerical methods for initial-value problems.

    2025 Runge-Kutta article

  2. Fluid mechanics and multiphase flow

    Question. How do nozzle geometry, interfaces, and entrainment shape a jet?

    Approach. I connect reduced-order jet theory with VOF and particle-based computational studies, keeping each solver and physical regime distinct.

    Rectangular-slot VOF study
    Oblique view of the rectangular-slot liquid–gas interface computed in OpenFOAM
    Reading a computed interface. The oblique view makes the rectangular inlet and emerging liquid–gas interface visible. This is an early-time laminar VOF computational study with implemented conditions and 25 native states; the case connects geometry, fields, native times, and phase-aware post-processing. Open the full-resolution figure

  3. Biomedical and active-matter modeling

    Question. How can collective cytoskeletal organization support mucociliary function?

    Approach. At Osaka University, I developed mathematical modeling and fluid-dynamics simulations in a JST-CREST project on cytoskeletal organization and mucociliary function.

    Osaka research context

  4. Scientific computing, HPC, and reproducible software

    Question. How can a computational result remain usable beyond the first calculation?

    Approach. I build scientific software around explicit inputs, deterministic planning, reproducible analysis, and readable outputs. CPU/MPI execution, Python, Jupyter, and TypeScript serve different parts of this work.

    Scientific work

Connecting methods to usable work

Across these domains, I move between mathematical structure, reference calculations, implementation, and interpretation.

  1. Equations, scales, and assumptions
  2. Analytical limits and numerical methods
  3. Deterministic tests and reproducible workflows
  4. Scientific figures and multilingual explanation

How I move from a computational problem to a result

I evaluate computational results and AI-assisted technical answers with a repeatable sequence: frame the physics, construct a reference, compare the proposed result, and leave a decision trail another technical reader can follow.

  1. Frame the physical problem

    State governing assumptions, dimensions, scales, and the physical regime before selecting a computational method.

  2. Construct a reference

    Use an analytical limit, a documented numerical solution, or a deliberately scoped reference case; implement analysis in Python, Jupyter, or Google Colab where appropriate.

  3. Evaluate the proposed solution or model output

    Compare it with reference quantities and check units, limiting behavior, invariants, numerical tolerances, and failure cases. For software, use deterministic contracts, synthetic fixtures, and automated checks.

  4. Report the decision trail

    Record the answer, method, reference, and validation criteria so another technical reader can reproduce or challenge the conclusion.

What the OpenFOAM case covers. The project documents boundary conditions, mesh and initialization, a laminar regime, 25 native states, and phase-aware post-processing. VisualOpenFOAM separately documents deterministic checkers and reference fixtures.

A worked model check: equal-density jet

What does the ideal momentum model predict when the ambient and injected fluids have the same density and the normalized area is four?

Use the existing model's equal-density limit: ρ* = 1. Its normalized laws reduce to v̂ = 1/√Â, ρ̂ = 1, and p̂ = 1/Â.

At  = 4, the calculated values are v̂ = 0.5, ρ̂ = 1, and p̂ = 0.25. Substitution into the normalized momentum invariant gives ρ̂  v̂² = 1 × 4 × 0.5² = 1.

This checks the implementation against a limiting solution of the prescribed-area model. The observable is algebraic consistency within that model; its inputs describe an illustrative model state.

Current directions

These four themes are the stable lines that organize my work. I am currently developing questions around jet and interface computation, scientific-software workflows, and multilingual scientific communication.

Applied connections

I have also used these methods in mucociliary and respiratory-epithelium modeling, wind-energy analysis, agrometeorology, industrial statistics, and scientific software.

Mucociliary and respiratory-epithelium modeling

Model mucociliary and respiratory-epithelium phenomena. Mathematical modeling and computational fluid dynamics.

Project context

Wind-farm wake interaction modeling

Study wake interaction in wind farms. Analytical wake modeling.

Project context

Wine-region microclimate analysis

Analyze regional wine-growing microclimate data. Applied data analysis.

Project context