Essex County College

This paper develops a unified phenomenological description of solidification by using a quaternionic orientational order parameter to represent local atomic rotations in undercooled liquids. The novelty of the work is that the same topological language is used to describe both crystallization and glass formation. In the crystalline pathway, quantized misorientation defects bind, order, and support long-range orientational and translational coherence. In the glassy pathway, those defects proliferate and remain frustrated, producing a rigid but non-periodic solid. The competition is organized by a non-thermal tuning parameter g = U/J that balances orientational stiffness J against localization U, in close analogy with duality ideas known from Josephson-junction arrays. Within this framework, geometrical frustration explains persistent defect skeletons in topologically close-packed phases and the opposite temperature dependences of thermal conductivity in crystals and glasses are linked to the presence or loss of coherent heat-carrying vibrational modes. The paper is intended as a materials-oriented topological phenomenology that complements, rather than replaces, atomistic and first-principles approaches.

We identify a local, gauge-invariant mechanism that generates a finite spectral scale in pure SU(3) Yang-Mills theory on a punctured three-ball. Fixing a Z3 center sector isolates a single gauge-invariant holonomy angle whose Berry shift produces a quantum rotor with strictly nonzero level spacing. Gauss law is enforced by a covariant Dirichlet Helmholtz projector built from the Dirichlet inverse of the covariant scalar Laplacian with relative boundary conditions. The slow holonomy mode is chosen variationally as the minimizer of transverse electric energy under the holonomy constraint, yielding an inertia independent of the gauge representative with linear domain-size scaling and a controlled commutator-dominated regime. We prove projector stability and derive an adiabatic variational upper bound on the first positive Yang-Mills eigenvalue, with error controlled by the transverse vector gap of the covariant Laplacian on divergence-free one-forms. A femtometer-scale benchmark at realistic coupling gives an upper bound at a hadronic (similar to 1 GeV) scale. In Wilczek's sense this realizes "mass without mass": no explicit mass term or Higgs field is introduced, and the nonzero level spacing is fixed by gauge invariance, topology, and the chosen center sector. The present results are derived on a finite domain; interpreting the length R in Minkowski space requires an additional physical input (e.g. as a local confinement length), which we make explicit.

Abstract We develop a theoretical proposal linking vacuum stability and brain dynamics through superconductivity-inspired coherence, symmetry reduction, and the thermodynamic stabilization of low-entropy regimes. We take an unbroken SU(3) structure as a candidate stable residue of the low-temperature vacuum. At the neural level, we formulate a coarse-grained analog in which a two-fluid model with dissipative and coherence-supporting components describes brain dynamics. Specifically, the coherence-supporting component is proposed as a possible basis for the efficient binding and integration required to sustain a stable, unified conscious state. The proposal offers a common geometric language for relating physics and neuroscience with falsifiable signatures in coherence and state-dependent transitions. The main technical contribution is a computational algebraic model of conscious-state dynamics, where neural data are mapped to reconstructed state trajectories. Effective generators are inferred from those trajectories, and the two-fluid split is tested as a Cartan-root decomposition of su (3), with a rank-two commuting sector for coherence-preserving balance and six root directions for state transitions. This structure can be tested on neural data and contrasted with alternative dynamical models.

The Greater Essex County District School Board (GECDSB) aims to support the initiatives of Early Childhood Educators (ECEs) in Ontario’s Full-Day Kindergarten program by providing ECEs with support and guidance to facilitate professional efficacy and student success. We applied the mentoring component of the New Teacher Induction Program to first year ECEs in FDK and investigated the program’s impact from the perspective of mentees and mentors. New ECEs were mentored by experienced ECEs working for the board. Study outcomes indicated the following themes among the participants: role as a mentor, professional development, reciprocal learning, and developing relationships. Challenges of the study were lack of proximity and time. Mentees also felt that the program did not change the existing relationship with their teaching partner. Overall, participants expressed an appreciation for the opportunity to engage in professional development and an interest in continuing the mentorship program.

In our previous work (Ali, Fortsch. Phys. 72(4), 2200210 (2024)), We outline an exploratory framework in which in which the 24-cell acts both as the quantum of spacetime and as a geometric representation of elementary particles. In this paper, we provide comprehensive mathematical and phenomenological evidence that deepens and refines this primary model. The remarkable symmetry of the 24-cell naturally yields a unified hypercharge functional that reproduces the observed Standard Model hypercharge assignments while ensuring anomaly cancellation. By projecting the 24-cell’s vertices onto a three-dimensional flavor subspace using a Minimal Distortion Principle, an emergent tetrahedral structure is revealed that gives rise to an effective A_4 symmetry in the neutrino sector. Moreover, extending this discrete symmetry to its binary double cover T' supplies the spinorial representations and intrinsic complex phases necessary for generating realistic quark Yukawa textures. Guided by the fundamental tenet that spacetime and matter are inextricably linked, our analysis shows that the intricate flavor mixing of the Standard Model may well be a residual imprint of the underlying quantum-geometric nature of spacetime.