Developing Theoretical Mathematics to Solve Problems in Turbulence

General Physics spends a lot of time understanding the strategic directions of science research, policy, and manufacturing. Instruments of advanced study involve Fourier analysis, distributions to fit data, and connected diagrams to run machine learning models. It has been said that we live in the modern era, and the information age, will lead to a new cyberage, one where things like programming, agents, LLMs, BIM, the IoT, apps, and UI or UX connections will be manipulated by general A.I. What is critical is understanding the physical nature of these systems in order to analyze their deterministic and regularized behavior. Turbulence, chaos, volatility, stochastic motion, Brownian diffusion, and many words are developed to describe the randomness of these systems. General Physics works at the heart of the isomorphism between the adaptive information content of the chaotic or turbulent system and the physical nature of the ensemble. The work is centered around the connections between the description of turbulence and the essential non-linear motion itself.

Self-similar behavoiur is observed in fractals, waves, periodic structures in biology, and in geographic features. The mountains beyond mountains approach, finding the arroyos of brooks and creeks in dried valley areas, which resemble the larger hill structure and the even larger mountain range, mean that there is a physical law that is scale invariant. We believe turbulence is scale invariant and formulated at the quantum scale, really below the Planck length. What is happening is the connection between natural and logical causation. The pre-ordained mathematical language of physics is beholden to the physical world and the isomorphism extends all the way down. At the Planck scale, the quantum foam allows for tunneling and Aharonov-Bohm hyperspace, regions where classical mechanics breaks down, even classical electromagnetic theory. Strange things happen. Photon number is not conserved, particles hop into existence, fields exist where there is no way for the photons to penetrate. What this behavior indicates is the fundamental problems with symmetry, and regularized behavior in the universe.

At the heart of turbulence is the fractional dimensional approach. Calculus tackles the dimensional problem through the integration and derivation approach and understanding through polynomial representation of dimension. We can further understand the dimension through a rigorous differential equation expansion, like a Taylor expansion, around every point with a infinite amplitude function which is well known to string theorists. Chaotic motion is a consequence of some physical-mathematical transition between a basis of Riemann zeta primes and a natural numbers. Critical to a description of anything from mathematics is the isomorphism to the physical state. This is why quantum computers, quantum systems, and understanding quantum mechanics is critical to develop isomorphic electronic systems capable of running advanced efficient turbulent dynamics code to model things like weather patterns and fusion plasma instabilities.

General Physics usually posts notes to describe the mathematical structure of zeta calculus and we have spent much time working to develop this theory. It started at the simple point where all ideas begin. It starts from play. Tesla just tacked on a sine and a cosine eikonal to the DC electric current of Edision. The idea was to make current time varying. What could be further developed is a Riemann zeta current beyond sine and cosine. Even Huygens curves can be modified with new zeta calculus. These are just two examples of how we can manipulate physical systems with turbulent prime basis states to generate new phenomena and new experiments. General Physics plans to develop higher dimensional phased array radar, even Aharonov-Bohm radar to better detect subtle magnetic perturbations. The future has to involve an expansion of turbulent convolutions onto existing functions and then the metadata or higher dimensional approach to this paradigm.