Alternating Quark Model: First Principles to Fusion

<div> <div> <p>A subnucleonic structure of light nuclei comprises an alternating up and down quark sequence (AQS) that accounts for the measured RMS charge radii with an agreement of >99% and statistical correlation of ρ = 0.99, p<0.001. An interpretation of the uncertainty principle in terms of uncertainty in energy and time, coupled with Chaos theory as relates to linked harmonic oscillators, allows localization of average quark position. Structures incorporate equally spaced quarks around regular polyhedron geometries. The distance between neighboring quarks in a sequence is constant and equal to the radius of the proton. Light nuclei from H-3 to Li-7 conform to ring structures whose radii are calculated from the formula of a regular polygon having <i>n</i> sides, each side equal to the radius of the proton, and <i>n</i> vertices, each occupied by a quark. Quark-quark interactions link nucleons to maintain a continuous sequence of alternating equally spaced quarks. Parallel strands of quark sequences overlap so that protons overlap with neutrons. Regular polyhedron structures yield better radius predictions; larger nuclei tend to be less regular and less predictable (with the exception of C-12). The relative certainty in the accepted radius of helium-4, and its geometric relationship tithe proton radius, allow a prediction for the proton radius of 0.8673±0.0014 fm.<br></p> </div> </div>

An Alternating Quark Sequence Predicts Nuclear Radius from Quark Number

<div> <div> <p>A subnucleonic structure of light nuclei comprises an alternating up and down quark sequence (AQS) that accounts for the measured RMS charge radii with an agreement of >99% and statistical correlation of ρ = 0.99, p<0.001. An interpretation of the uncertainty principle in terms of uncertainty in energy and time, coupled with Chaos theory as relates to linked harmonic oscillators, allows localization of average quark position. Structures incorporate equally spaced quarks around regular polyhedron geometries. The distance between neighboring quarks in a sequence is constant and equal to the radius of the proton. Light nuclei from H-3 to Li-7 conform to ring structures whose radii are calculated from the formula of a regular polygon having <i>n</i> sides, each side equal to the radius of the proton, and <i>n</i> vertices, each occupied by a quark. Quark-quark interactions link nucleons to maintain a continuous sequence of alternating equally spaced quarks. Parallel strands of quark sequences overlap so that protons overlap with neutrons. Regular polyhedron structures yield better radius predictions; larger nuclei tend to be less regular and less predictable (with the exception of C-12). The relative certainty in the accepted radius of helium-4, and its geometric relationship tithe proton radius, allow a prediction for the proton radius of 0.8673±0.0014 fm.<br></p> </div> </div>

An Alternating Quark Sequence Subnucleonic Structure of Stable Light Nuclei H-1 Through Li-7

<div> <div> <div> <p>Structures of stable light nuclei incorporate an alternating up and down quark sequence (AQS) of equally spaced quarks around regular polyhedron geometries. AQS is a ball-and-stick model in which the ball represents the average center of cur- rent quark mass, and the stick length is constant and equal to the radius of the proton. AQS radius predictions of H-1 through Li-7 demonstrate 99.3% average agreement (SD 4%) and statistical correlation of ρ = 0.96, p<0.001, with accepted RMS charge radii. Light nuclei above deuterium conform to ring structures whose radii are calculated from the formula of a regular polygon having n sides, each side equal to the radius of the proton, and n vertices, each occupied by a quark. Quark-quark interactions link nucleons to maintain a continuous sequence of alternating equally spaced quarks. Parallel strands of quark sequences overlap so that protons overlap with neutrons. Regular polyhedron structures yield better radius predictions; larger nuclei tend to be less regular and less predictable (with the exception of C-12). The relative certainty in the accepted radius of helium-4, and its geometric relationship tithe proton radius, allow a prediction for the proton radius of 0.8673±0.0014 fm. ASQ localizes average quark position, and the high statistical correlation of ASQ with experimental radii thus warrants an expression of the uncertainty principle as the product of uncertainty in energy and time rather than position and momentum. This view is consistent with the quark as a harmonic oscillator. </p> </div> </div> </div>

Generating Function for the Figurative Numbers of Regular Polyhedron

In this paper, we are going to demonstrate a method for determining the generating functions of tetrahedral, hexahedral, octahedral, dodecahedral, and icosahedral figurative numbers. The method is based on the differences between the members of the series of the mentioned figurative numbers, as well as on the previously specified generating functions for the sequence ∑n≥0n+1xn and geometric sequence ∑n≥0xn.

Geometric realizations of abstract regular polyhedra with automorphism group H 3

A geometric realization of an abstract polyhedron {\cal P} is a mapping that sends an i-face to an open set of dimension i. This work adapts a method based on Wythoff construction to generate a full rank realization of an abstract regular polyhedron from its automorphism group Γ. The method entails finding a real orthogonal representation of Γ of degree 3 and applying its image to suitably chosen (not necessarily connected) open sets in space. To demonstrate the use of the method, it is applied to the abstract polyhedra whose automorphism groups are isomorphic to the non-crystallographic Coxeter group H 3.

Theoretical and Experimental Study of Viscoelastic Damper Based on Fractional Derivative Approach and Micromolecular Structures

Viscoelastic dampers are one of the most popular earthquake mitigation devices for building structures with a large number of applications in civil engineering. The seismic performance of viscoelastic dampers is greatly affected by viscoelastic materials. The present paper addresses the theoretical and experimental studies of the viscoelastic damper. The regular polyhedron chain network models for viscoelastic materials are proposed based on the molecular chain network microstructures and the temperature–frequency equivalent principle. Several dynamic property tests for the viscoelastic damper at different temperatures, frequencies, and displacements are carried out, and the proposed models are verified by comparing the numerical and experimental results. The comparisons show that the viscoelastic damper has perfect energy dissipation capacity, and the regular polyhedron chain network models can well describe the mechanical properties of the viscoelastic damper at different environmental temperatures and excitation frequencies.