Awakening the Sleeping Giant: Rediscovering Archimedes' Density Method for Fingerprinting of Multicomponent Alloys

16 August 2024, Version 1
This content is a preprint and has not undergone peer review at the time of posting.

Abstract

If the matter is the manifestation of the God-particle, then density is its soul, as one cannot exist without the other. Hence, density inherently becomes mother of all properties of the matter. The Archimedes' density method presents a mathematically unsolvable, computationally non-recursive, and undecidable NP-Hard problem for non-binary alloys. Resolving underdetermined linear equations, discretizing infinite Probable Iso-density Compositions (PICs), solving NP-Hard problems, and achieving certainty from probabilities are key to its application. Non-binary alloy densities reveal multiple PIC series interconnected through "True Composition" (TC) in the Isopycnic Region (IR) of Vast Alloys Space (VAS), replicating as Concordant Compositions (CCs) similar to centromere replication during cell division. The Principle of Vernier coincidence in multiple dimensions echoes CCs as unique alloy fingerprints in geometrical superimposition. We modified Archimedes' equations for additional metals and developed Density Decoding System (DDS) (www.densityfingerprinting.com) to compute PICs using Successively increasing Predefined Imaginary Numerical values (SPIN-values) and standard metal densities, generating a real-time database. A perfectly symmetric C-band breaks the asymmetry of Density Genome fractals, visualizing Density Fingerprints to conclusively determine "True Composition" up to octonary alloys with absolute accuracy in polynomial time. The precision range of alloy density limits the chaotic Butterfly effect, creating a fractal composition space that enables self-authentication of True Compositions. The study uncovers the coexistence of chaos and order, the butterfly effect, the emergence of order from infinity, and the fractal nature of the composition space. The research reveals the manifestation of quantum-like phenomena in the classical realm of alloy compositions, challenging our understanding of the nature of matter. Our work unveils density as the genetic code for non-living matter, leading to a novel alloy classification into binary and non-binary alloys. Furthermore, it introduces the Density Fingerprinting and Density Genome framework, which enables comprehensive materials analysis, characterization, design, and discovery, marking a paradigm shift in our understanding about density and its pivotal role in shaping the future of material science.

Keywords

Density Decoding System (DDS)
Archimedes' Method
Multicomponent Alloys
Density Genome
Alloy Composition
Materials Characterization
Alloy Fingerprinting
Alloy Design
Alloy Analysis
Alloy Discovery
Composition Space
NP-Hard
Combinatorial Chemistry
Underdetermined Linear Equations
Probability
Quantum-like Phenomena
Composition Fractals
Chaos and Order
Butterfly Effect

Supplementary weblinks

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Comment number 1, Jai Hind Rathore: Sep 02, 2024, 18:42

Dear Readers, We, the authors of "Awakening the Sleeping Giant: Rediscovering Archimedes' Density Method for Fingerprinting of Multicomponent Alloys," have received several inquiries expressing doubts and scepticism about the findings presented in our research, particularly regarding the determination of compositions of multicomponent alloys up to octonary alloys with absolute accuracy. To address these concerns, we would like to bring the following information to the attention of the scientific community: 1. The mathematical expressions forming the core component of the computation of Probable Iso-density Compositions (PICs) series and the determination of True Compositions (TCs) from such series have undergone a rigorous peer-review process and were published in Materials Letters, Volume 61 (June 2007), pg. 2956-2960 under title “Theoretical Optimization of Constitution of Alloys by Decoding Their Densities" DOI: https://doi.org/10.1016/j.matlet.2006.10.052 (Reference No. 31). 2. All the results presented in the tables and figures of our manuscript are reproducible and can be instantly verified using Density Decoding System (DDS) Platform (http://www.densityfingerprinting.com/), accessible via the link provided in the manuscript under the "Data Availability" section. We encourage readers to utilize the DDS platform to decode the densities of known alloys and validate the accuracy of our findings. A short demonstration video is available at YouTube: https://www.youtube.com/watch?v=3HnqxP_sBhU 3. The authors had the opportunity to conduct a live demonstration of the proposed DDS Technology at the University of Pennsylvania, USA, on July 26, 2023, in a hybrid format attended by distinguished scholars in the field. A video recording of the live demonstration is available at YouTube: https://www.youtube.com/watch?v=qqxGCLbIS9o We hope that this additional information helps to address queries and concerns regarding our work. We remain committed to engaging in constructive discussions and welcome further inquiries from the scientific community. Sincerely, Jai Hind Rathore Corresponding Author