2023-Sustainable Industrial Processing Summit
SIPS2023 Volume 13. Intl. Symp on Physics, Mathematics and Multiscale Mechanics
| Editors: | F. Kongoli, A. B. Bhattacharya, A.C. Pandey, G. Sandhu, F. Quattrocchi, L. Sajo-Bohus, S. Singh, H.S. Virk, R.M. Santilli, M. Mikalajunas, E. Aifantis, T. Vougiouklis, P. Mandell, E. Suhir, D. Bammann, J. Baumgardner, M. Horstemeyer, N. Morgan, R. Prabhu, A. Rajendran |
| Publisher: | Flogen Star OUTREACH |
| Publication Year: | 2023 |
| Pages: | 298 pages |
| ISBN: | 978-1-989820-96-4 (CD) |
| ISSN: | 2291-1227 (Metals and Materials Processing in a Clean Environment Series) |
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THE USE OF A NUMERICALLY CONTROLLED SYSTEM OF ANALYTICS TABLE FOR SOLVING VARIOUS CASES OF THE NAVIER-STOKES EQUATIONS IN TERMS OF GENERALIZED ANALYTICAL SOLUTIONS ONLY
Mike Mikalajunas1;1CIME, iLe Perrot, Canada;
Type of Paper: Regular
Id Paper: 118
Topic: 38
Abstract:
The general application of Specialized Differential Forms in Science and Engineering has resulted into the creation of a very unique table called Numerically Controlled System of Analytics or (NCSA) for short by which any type of differential equation may now be completed integrated only in terms of generalized analytical solutions involving only the algebraic and elementary functions. Over time when such a new method of computational analysis is applied correctly then this would have the effect of reducing our excessive dependency on the use of many types of well known experimental based models in the Physical Sciences in favor of a more Universal Algebraic Theory.
In this talk I will begin by highlighting the importance of using a Numerically Controlled System of Analytics table in fluid dynamics and in mechanics of material for integrating the corresponding set of PDEs only in terms of generalized analytical solutions as a complete alternative to conventional methods of integration. I will be demonstrating how to correctly setup such a table that would lead to defining a very special type of database by which complete generalized analytical solutions to PDEs may be logically deduced only by computation.
I will also be revealing a very important mathematical property of Specialized Differential Forms that has led to redefining the whole concept of a composite function in terms of providing us with a very practical way of measuring its degree of composition regardless of whether or not they are defined in either explicit or in implicit form. This would make it possible while in the process of setting up our Numerically Controlled System of Analytics table for analysis on various cases of the Naiver-Stokes equations to extend the scope of new potential forms of analytical solutions to PDEs by including composite functions of various degree of compositions that can be defined in either explicit or in implicit form.
Under this new type of measure for the degree of composition for all composite functions, the simple wave equation for example that forms the basis of representation of solutions to the time dependent and independent Schrödinger equation for uni-electron and multi-electron structure may be elevated to include composite functions as well where the exact order of composition would have to be determined by computation only. This would have the potential of providing us with a much better understand on the exact physical structure of a wave when applied to many areas of the Physical and Biological Sciences as a result of solving for certain types of differential equations and systems of differential equations based on the method of Specialized Differential Form.
Keywords:
engineering; physics; quantum mechanics; mathematics; fluid dynamics; Mechanics of MaterialReferences:
Mikalajunas, M. (2022), “The Gradual Abandonment of many types of well known experimental based Physical Models in favor of a more Universal Algebraic Theory: A General Introduction”, Sustainability through Science and Technology (SIPS 2022), Nov 2022, Hilton Phuket Arcadia, Thailand.Mikalajunas, M. (2022), “The Gradual Abandonment of many types of well known experimental based Physical Models in favor of a more Universal Algebraic Theory: Part I - General Framework”, Sustainability through Science and Technology (SIPS 2022), Nov 2022, Hilton Phuket Arcadia, Thailand.
Mikalajunas, M. (2022), “The Gradual Abandonment of many types of well known experimental based Physical Models in favor of a more Universal Algebraic Theory: Part II - Specific Examples”, Sustainability through Science and Technology (SIPS 2022), Nov 2022, Hilton Phuket Arcadia, Thailand.
Mikalajunas, M. (2023), “On the use of Multivariate Polynomials and the differential of Multivariate Polynomials as a means of establishing a more Universal Algebraic Theory for solving Differential Equations”, American Mathematical Society Spring Southeastern Sectional Meeting, Georgia Institute of Technology, Atlanta, GA, March 18-19, 2023.