JaiHind15

Hi all! Archimedes proved that the crown was not pure gold by doing the following: 1. Measuring the volume of the crown using immersion in water (Archimedes's Principle) 2. Compare the density obtained from the volume and mass for the crown with that of pure gold D(crown) ≠ D(pure gold) Therefore the crown can not be pure gold! The events could be subject to speculation but, using density, he was able to prove that the crown was not gold. The density of the alloy is dependent on many factors such as composition, temperature, in some cases even pressure. Archimedes' work was a qualitative analysis based on the density - composition relationship. Any perturbations in the composition of an alloy will affect its density. Since, the mass percents of each constituent affects the density, this means that the information of constituents is already naturally "encoded" in the form of density, all we need to do is "decode" this information by understanding the dynamics of density-constituent relationship. The work of Archimedes as described above has been quantified already for binary alloys which utilizes conservation of mass from constituents to alloy and assumes conservation of volume. We extended this relationship further for ternary, quaternary etc. This produces the governing equation: V=v1+v2+v3... ---(1) M=m1+m2+m3... ---(2) Rewriting into density terms: D=M/(m1/d1 +m2/d2 +m3/d3 +....) In terms of mass percents, this shows a linear relationship. Since there are two equations (1) & (2), only two variables can be uniquely identified, i.e. binary alloys! Extending this for multi-component alloy makes this an underdetermined system. We tackled the problem of underdetermined system by first considering mass percents (M=100), so the alloy space (VAS) constricts to the area in ternary plot (3-metals), tetrahedral plot (4-metals) etc. Then we discretized. This is Density Decoding System (DDS). The results of this are the following: Test alloy: Produce a theoretical alloy density based on the governing equation e.g., Au90Ag5Cu3Zn2 -> 17.3928 [Au:19.32, Ag:10.5, Cu:8.96, Zn:7.14] 1) Calibrate DDS: Metal Densities, Iterative Step (used in convergence, dictates the discretization) e.g., selected: Au(19.32), Ag(10.5), Cu(8.96), Zn(7.14); i=1 2) Input: Alloy Density (Theoretical) e.g., Density: 17.3928 3) Output: Percent Composition for multi-component alloy e.g., Alloy: Au90Ag5Cu3Zn2 We have presented upto 8-metal alloy identification using density in the paper. I hope this clears things as this has been peer reviewed already in 2006. In this paper we delved deeper into the functioning of the algorithm and tried to understand why this method works. In this pursuit, we have found evidences of chromosomal structure of probability distributions of the probable iso-density compositions, butterfly effect stemming from alloy density, principle of vernier caliper in multi-dimensions etc. We wish to share these findings through this paper. Please take a look as we believe it is a fascinating find. Sincerely, Jai on behalf of research team