Hierarchical Computational Modeling of Physical Structure Across Quark, Nuclear, and Atomic Scales

Year : 2026 | Volume : 15 | 01 | Page :
    By

    Pedro Portugal,

  • Kshitija Gadge,

  1. Independent Researcher, Tecnologico de Monterrey, Queretaro, Mexico
  2. Independent Researcher, University of Mumbai, Maharashtra, India

Abstract

We present a modular, multi-scale computational framework that integrates physical modeling and visualization across quark, nuclear, and atomic scales within a unified pipeline. Developed to address the traditional fragmentation between sub-nucleonic, nuclear, and electronic representations, the system provides a continuous data flow and visualization bridge spanning from femtometers to ångströms. The framework consists of three primary modules: a particle-level module illustrating nucleons as confined quark-triplets with effective flux-tube geometries; a nuclear module utilizing the semi-empirical mass formula (SEMF) to estimate binding energies and radii; and an atomic module that computes hydrogenic orbitals with Slater-corrected effective nuclear charges. To achieve high-fidelity visual representations, scalar fields for each scale are sampled on uniform Cartesian grids and rendered as marching-cubes isosurfaces. This technique enables the simultaneous visualization of quark confinement, nuclear volumes, and electron probability densities within a coherent spatial environment.

Validation of the nuclear and atomic modules against empirical mass and charge-radius data confirms that the framework accurately reproduces macroscopic stability trends and volumetric scaling behavior, such as the binding energy saturation near iron. While the particle-scale outputs are currently illustrative rather than quantitatively coupled to higher-scale calculations, the modular Python-based architecture is specifically designed for clarity and the future integration of high-fidelity ab-initio solvers. Beyond its technical implementation, the platform serves as a powerful pedagogical tool, transforming mathematical abstractions into spatially intuitive objects that clarify the hierarchical organization of matter. We demonstrate that this integrated approach effectively bridges conceptual gaps between quantum chromodynamics, nuclear physics, and atomic structure, providing a versatile, extensible foundation for both educational exploration and multi-scale computational research.

Keywords: Multi-scale modeling. Quark confinement. Nuclear structure. Nuclear charge radii. Semi-empirical mass formula. Atomic orbitals. Computational visualization. Computa-tional physics

How to cite this article:
Pedro Portugal, Kshitija Gadge. Hierarchical Computational Modeling of Physical Structure Across Quark, Nuclear, and Atomic Scales. Research & Reviews : Journal of Physics. 2026; 15(01):-.
How to cite this URL:
Pedro Portugal, Kshitija Gadge. Hierarchical Computational Modeling of Physical Structure Across Quark, Nuclear, and Atomic Scales. Research & Reviews : Journal of Physics. 2026; 15(01):-. Available from: https://journals.stmjournals.com/rrjophy/article=2026/view=236370


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Ahead of Print Subscription Review Article
Volume 15
01
Received 13/12/2025
Accepted 12/01/2026
Published 15/01/2026
Publication Time 33 Days
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