Welcome to AfricArXiv
This initiative showcases UbuntuNet's commitment to fostering knowledge sharing, collaboration, and accessibility within the African research community. With AfricArxiv, researchers across the continent have a dedicated platform to disseminate their findings, making them accessible to a global audience. By facilitating open access to scholarly work, UbuntuNet Alliance plays a pivotal role in advancing the principles of open science, enhancing research visibility, and driving innovation across Africa.
Communities in AfricArXiv
Select a community to browse its collections.
- The general repository is open for individual submissions by researchers, librarians and research administrators.
- Showcase of project activities, presentations, and scholarly contributions curated by the AfricArXiv initiative.
- Scholarly items sorted by country > Institution > Department
- A Rapid Grant Fund to address research questions and implement science engagement activities associated with COVID-19
Recent Submissions
Schrödinger–Navier–Stokes–Quantum-π: A Unified Model and Hybrid Numerical Method for Quantum Fluids with π-Phase Structure
(Publisher, 2025-11-30) Barack Ndenga
I present a unified theoretical and numerical framework that couples quantum wave dynamics (Schrödinger) with classical viscous flow (Navier–Stokes) through an emergent quantum-π field (π_q) that encodes phase-topology and coherence. The model reproduces Schrödinger dynamics in the conservative limit, Navier–Stokes turbulence in the dissipative limit, and novel intermediate regimes where quantum coherence and fluid turbulence coexist and interact. I derive the governing equations by (i) applying a Madelung decomposition to a complex field ψ, (ii) introducing a controlled viscous regularization and non-linear coupling terms, and (iii) coupling a dynamically evolving π_q scalar (or tensor) field that modulates local coherence, effective mass, and information flux. I then present a robust hybrid numerical method (QHFVM — Quantum Hydrodynamic Finite-Volume Method) combining split-step spectral propagation for dispersive quantum terms and conservative finite-volume solvers for advective, viscous and pressure dynamics. I validate the approach on a set of canonical problems (quantum vortex shedding in a viscous background, π-phase revival in confined geometries, and turbulence spectra with quantum corrections), show numerical convergence and conservation properties, and outline applications spanning quantum fluids, nanoscale bio-fluids, materials, and hybrid QEC architectures. Flash explanations highlight intuition and immediate experimental tests.
Resolving Nanoscale Reaction Kinetics: A Unified Framework from Classical Chemistry to Quantum Collectivity
(Publisher, 2025-11-28) Barack Ndenga
At the nanoscale, the classical separation between molecular reactivity and quantum collective behavior collapses. Conventional chemical kinetics—grounded in transition-state theory, Arrhenius scaling, and continuum thermodynamics—fails to describe reactions occurring in domains where particle numbers are small, energy landscapes are strongly quantized, and coherence competes with dissipation. In this work, I propose a unified theoretical framework that seamlessly bridges classical kinetics with emergent quantum collectivity in nanosystems.
My approach integrates:
discrete-state stochastic kinetics,
quantum master equations,
collective vibrational/photonic coupling,
topological constraints,
and non-extensive thermodynamic corrections unique to nanoscale systems.
I demonstrate how nanoscale reaction rates deviate systematically from classical predictions and how quantum correlations, confinement, and collective coherent modes reshape both reaction pathways and energy transfer. This framework resolves long-standing inconsistencies observed in nanocatalysis, reaction dynamics in quantum dots, plasmonic hot-electron chemistry, and molecular clusters. I conclude that nanoscale chemistry is neither “classical” nor “molecular quantum” but an intermediate regime governed by quantized collectivity, requiring a new kinetic law that I derive in closed form.
The Complete Solution to the Glass Transition: A Unified Energy–Topology Landscape (ETL) Framework
(Publisher, 2025-11-27) Barack Ndenga
The glass transition — the dramatic dynamical arrest of supercooled liquids into amorphous solids — remains one of the deepest unsolved problems in condensed-matter physics. Competing paradigms (thermodynamic Random First-Order Transition [RFOT], kinetically constrained/facilitation models, frustration-based approaches, and energy landscape viewpoints) each capture facets of the phenomenon but fail to produce a single, predictive, experimentally falsifiable theory. Here I propose the Energy–Topology Landscape (ETL) Unification, a theoretical and computational framework that synthesizes thermodynamics, topology of configuration space, and dynamical facilitation into a single continuum theory. In ETL the glass transition is not a single mechanism but an emergent consequence of (1) a proliferation of high-dimensional topological bottlenecks in the potential-energy landscape as cooling proceeds, (2) a finite but vanishingly small measure of accessible configuration-space pathways that enforce hierarchical facilitation, and (3) a thermodynamic drift toward deep meta-basins whose internal ruggedness controls low-temperature vibrational anomalies. ETL yields closed-form scaling relations for relaxation times, a microscopic origin for the boson peak and non-linear elastic response, and precise experimental signatures (specific heat, non-linear susceptibility, ultrastable glass fingerprints). I provide a mathematical formalism, numerical algorithmic recipes, and a program of decisive experiments. I argue that, once the proposed predictions are verified (or falsified) by the community, the ETL framework will constitute a comprehensive resolution to the glass problem.
Correlated Quantum Matter Beyond Band Theory: A Continuum-Interaction Formalism for Strongly Coupled Electrons
(Publisher, 2025-11-26) Barack Ndenga
The failure of conventional band theory to describe strongly correlated materials—high-Tc superconductors, Mott insulators, and strange metals—reveals a fundamental incompleteness in our current understanding of electron–electron interactions. In this work, I propose a unified continuum-interaction formalism that treats electronic behavior not as a perturbation around independent quasiparticles, but as an emergent quantum collective governed by non-local correlations. Using an extended Hubbard–Landau functional, a correlation-driven spectral reconstruction model, and a tensor-network-inspired coarse-graining operator, I derive a framework capable of capturing insulating, metallic, and incoherent regimes within a single mathematical structure. This approach suggests that the breakdown of band theory is not an anomaly but an inevitable manifestation of collective entanglement. I discuss analytical consequences, numerical implications, limitations, and future research directions toward a full predictive theory of correlated quantum matter.
Quantum π-Unification II: Definition, Mathematical Structure, and Foundational Properties of the Quantum π for Molecular Systems
(Publisher, 2025-11-25) Barack Ndenga
The second article in the Quantum π-Unification Series establishes a fully defined, operational, and mathematically rigorous formulation of the Quantum π for molecular systems.
Unlike classical π-electron theory—which only describes delocalized electrons—the Quantum π introduced here represents a phase-information invariant governing chemical stability, resonance, symmetry, and reactivity.
This work develops:
1. the conceptual foundations of the Quantum π,
2. its mathematical structure (phase operator, symmetry factor, information contribution),
3. the connection with chemical resonance, electronegativity flow, and energy minimization,
4. prediction rules for molecular stability and reactivity.
The article also introduces the π-Stability Index (PSI) and the Quantum π-Symmetry Number, two new descriptors that unify chemical information, electronic delocalization, and energetic behavior.