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| viXra.org > Mathematical Physics > 2606 |
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[5] viXra:2606.0119 [pdf] submitted on 2026-06-30 20:53:55
Authors: Casey McGrath
Comments: 5 Pages. (Note by viXra Admin: Please cite and list scientific reference and submit article written with AI assistance to ai.viXra.org)
We introduce a Projected Node Model, in which quantized action ΔS = ℏ manifests at discrete event loci (nodes) via conjugate projections.From minimal axioms we rigorously derive the invariance of c, de Broglie relations, geometric uncertainty, Minkowski structure, massinertia,and the Planck scale. The framework recovers standard quantum and relativistic phenomenology with enhanced geometric clarity.
Category: Mathematical Physics
[4] viXra:2606.0116 [pdf] submitted on 2026-06-30 05:57:29
Authors: Kohji Suzuki
Comments: 16 Pages.
We present a model in which SING, a singularity-inspired notion (viXra:1812.0480 [v1]), plays some role in black hole merging to suggest that evaporation of black hole leaves something behind.
Category: Mathematical Physics
[3] viXra:2606.0109 [pdf] submitted on 2026-06-29 05:11:52
Authors: Payam Danesh, Raoul Bianchetti
Comments: 15 Pages.
We study a periodic kinetic Fokker—Planck equation in which free transport in position is coupled to Ornstein—Uhlenbeck relaxation in velocity. Our aim is to give a transparent weighted L^2 analysis of the relaxation mechanism and to test it by a modal approximation. The equation is written in Maxwellian variables, the generator is decomposed into a skew transport part and a dissipative velocity part and its contraction semigroup is considered on the natural weighted Hilbert space. Using Gaussian and torus Poincaré inequalities, we prove mass conservation, microscopic coercivity and exponential decay on the zero-mass subspace through a modified first-order energy containing a spatial—velocity cross term. For the homogeneous problem, the entropy identity gives decay from the Gaussian logarithmic Sobolev inequality. A Fourier—Hermite discretization is then derived, its semi-discrete L^2-stability is shown and truncation tests quantify convergence in the Hermite index and the spectral abscissa of the first nonzero Fourier block. The results give a compact account of how velocity relaxation enforces global return to Maxwellian equilibrium in this model.
Category: Mathematical Physics
[2] viXra:2606.0052 [pdf] submitted on 2026-06-13 23:16:58
Authors: Urs Frauenfelder, Joa Weber
Comments: 57 pages, 2 figures
In part I, [FW26a], we showed that collisional periodic orbits of twisted Zeeman systems can be detected variationally by a non-local Hamiltonian action functional. In this part II we show that the linearized gradient flow of this non-local functional is a Fredholm operator and prove a non-local elliptic regularity result. These results are obtained with the theory of almost extendability of weak Hessian fields introduced in [FW26c].
Category: Mathematical Physics
[1] viXra:2606.0005 [pdf] submitted on 2026-06-02 14:44:15
Authors: Ellie Richwine, Lucian M. Ionescu
Comments: Pages.
This article explores the mathematical structures underpinning crystalline materials, bridging the gap between pure mathematics and materials science. Building upon Toshikazu Sunada’s breakthrough framework of topological crystallography and subsequent formalizations by John C. Baez, we provide a rigorous yet accessible introduction to the geometric and topological modeling of crystals. The study examines polyhedral geometry, duality, and lattice arrangements such as the Eisenstein and triangular lattices, framing them within the context of covering maps and Abel-Jacobi maps. Furthermore, we advance this foundation by introducing a simplified formulation of Graph Cohomology based on short exact sequences of graphs. This homological approach provides a unifying architectural template capable of tracking lattice defects via integer cohomology and modeling macroscopic continuous phenomena from discrete microscopic networks. The paper concludes by discussing the broader applications of these tools in molecular biology, theoretical physics, and fault-tolerant quantum engineering.
Category: Mathematical Physics
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