VOLUME 2 │ISSUE 1│YEAR 2023│JAN - MAR 2023

REVISED DATE

18/11/2022

Article Type: Research Article

Available online: www.tmp.twistingmemoirs.com

ISSN: 2583-7214

EVOLUTIONARY ALGORITHMS MOLECULAR EFFECT MODEL OPTIMIZATION FOR HIGH TEMPERATURE SUPERCONDUCTORS CUPRATES AND REVIEW OF TIN AND THALLIUM CLASSES

*Francisco Casesnoves

*PhD Engineering, MSc Physics-Mathematics, Physician. Independent Research Scientist. International Association of Advanced Materials, Sweden. Uniscience Global Scientific Member, Wyoming, USA

ABSTRACT

CORRESPONDING AUTHOR

Name: Francisco Casesnoves

Affiliation: PhD Engineering, MSc Physics-Mathematics, Physician. Independent Research Scientist. International Association of Advanced Materials, Sweden. Uniscience Global Scientific Member, Wyoming, USA

Email: casesnoves.research.emailbox@gmail.com

INTRODUCTION

The objective of this continuing study is to apply Artificial Intelligence by using Evolutionary Algorithms for modelling of several HTSCs classes. Namely, Hg-Cuprates, [ Hg-Ba-Ca-Cu-O ] constrained to [ T C > 0° ], and improve/review Tin ( Sn ) group with [ T C > 0° ], and Thallium ( Tl

) class subject to [ T C ˂ 0° , T C > 0° ] in Molecular Effect Model (MEM). The methods applied are 2D/3D Graphical Optimization and Genetic Algorithm techniques. All the software developed constitutes improvements/applications of previous research publications [3-9,48,49,50], not limited to Superconductors field. Along the GA optimization series published, Evolutionary Algorithms have proven be accurate and practical, with many programming options. Given any HTSCs class, if differences of molecular weight as a result of proportion/isotopic-variation in the molecule occur, the MEM, as an hypothesis to approximate/predict the T C magnitude changes may be useful/efficacious. MEM was initially created on the basis of largely proven Isotope Effect. Inverse Methods, [3-9,48,49,50], could also be applied to select a desired T C with optimal molecular weight composition in MEM. The innovations of this following research are given by the software for AI-GA methods. As was presented in [51], the advance consists in setting at Z axis the absolute difference between MEM T C and experimental T C . The software method applied in this study is set with GA Matlab tools and Imaging Processing programming. Results cogency involve GA MEM for Hg-Cuprates , and review with further explanations for Tin and Thallium HTSCs classes. 2D/3D GA Graphics of program performance, and final T C polynomial predictive equations [3-5,48-51]. Succintly, the article shows an evolutionary algorithm method with 2D/3D Graphical Optimization for several HTSCs classes. The aim is to continue the improvements for MEM in search for refinements and precision. Applications in Electronics Physics new materials are explored.

MATHEMATICAL AND COMPUTATIONAL METHOD

At Tables 1-4, the software programming setting data for Equation (1) the programming algorithm made [3-5,48-51]. The Tikhonov Functional is implemented/improved with Chebyshev L 1 norm from previous research [48-51], Equation 1. As in [51], the difference with previous publications is the setting of MEM algorithm objective function at Z axis [ abs (T C Experimental- T C MEM ] ) in Figures 2-17. The dataset was applied in single and/or multifunctional charts into GA program. For Hg-Cuprates, first stage method, Figure 1, comprises the polynomial fit to obtain approximations for GA further programming constraints. Second stage is direct application of GA to get single/multifunctional graphics. Third stage is more difficult, consists in implementation of GA results into 3D Graphical optimization charts. With GA program, the refinements to obtain the MEM optimal fitness sectors are got.

Table: 1- Numerical Data for Cr and HTSC Hg-Cuprates. Note the 97 Kelvin temperature corresponds to two different compounds. This fact gives to the 2D and 3D MEM plots a parabolic-like analytic geometry shape. Hg-Cuprates T C is expressed in Kelvin usually.

Table: 2 - The literature optimization of classic parameters for [ Sn-Sb-Te-Ba-Mn-Cu-O ]

class implemented [1,3-5,12-15,48-51]. This table is taken from [1,3-5,12-15,48-51] as the numerical initial data is the same for different mathematical-computational task.

Table 3.- The optimization of classic parameters for Thallium Molecular HTSC Group, [ Tl- Sn-Pb-Ba-Si-Mn-Mg-Cu-O ] implemented, [1,3-5,12-15,48-50], subject to [ T C > 0° C ].

Table 4.- The classical optimization parameters for Thallium Molecular HTSC Class, [ Tl-

Sn-Pb-Ba-Si-Mn-Mg-Cu-O ] implemented in this research [1,3-5,12-15,48-51] subject to [ T C

˂ 0° C ].

Algorithms and GA-Programming Method

Tikhonov algorithms have been extensively set in previous contributions [3-6, 48-51], both with L 1 Chevyshev norm and L 2 one. For this Molecular Model, the constraints values for parameters are shown in Tables 1-4. Sketch 1 shows the programming method for the following formula. The algorithms set for GA Molecular Effect, combined with a polynomial p(MO i ) fits read,

The programming techniques are related to previous research [3-9,48-51] and dual-program

design [50,51]. In [49-51], software and imaging processing details with explanations are included. With the 2D polynomial fit data, it is possible to get approximations for further setting of GA constraints and lower/upper boundaries. Sketch 1 shows the software method base.

Sketch 1.-Programming method that was applied in the study

RESULTS FOR Hg-CUPRATES CLASS

Results for Hg-Cuprates are presented in Figs 1-9. By observing and guessing data from the figures series, it is easy going to learn and deduce all the graphical and numerical results. Hg- Cuprates MEM show get the most accurate results at present hypothesis stage.

Figure 1.-Among all the HTSCs studied in publication series, Hg-Cuprates MEM shows the best analytic geometry results. Note the close coincidence among splines and polynomial model. The GA programming multifunctional 2D graph. 2D Sn polynomial fit parameters intervals set into GA program with Matlab. As it was found in previous contributions, for Sn class the MEM shows in [48-51] an approximate 2D parabolic shape [3-5,48-51]. But Thallium class has a 2D sigmoid analytic geometry.

Figure 2.-Best Fit, with 5 optimization parameters, the most important chart of GA method. Generations Number is 300. As it was found in previous contributions, for Sn and Thallium classes the MEM shows in [50,51] an approximate 2D parabolic shape in 3D charts, Figs 8-9, [3- 5,48-51].

Figure 3.-The second most important 2D GA programming graph, note ( % criteria met ). Generations Number is 300. As it was found in previous contributions, for Sn and Thallium classes, the MEM shows in [50-51] acceptable results [3-5,48-51].

Figure 4. - A multifunctional 2D GA programming graph. Generations Number is 300. Complementary data for scores and best individuals

Figure 5.- A 2D GA programming graph. Generations Number is 300. Complementary data for children generations and best individuals

Figure 6.- A 2D GA programming complementary graph showing fitness of every individual. Generations Number is 300.

Figure 7.- A 2D GA programming complementary graph showing score histograms. Generations Number is 300.

Figure 8.- Optimal MEM sector for Hg-Cuprates HTSCs class. Generations Number is 300. Green arrow zone, the almost exact fit, red arrow, inset, shows the approximately acceptable fit. Hg- Cuprates MEM shows be the best at this stage. Model fits approximately well between molecular weights interval [ 500 , 1400 ] for all values of T C .

Figure 9.- Additional grayscale perspective for optimal MEM sector of Hg-Cuprates HTSCs class. Generations Number is 300. Hg-Cuprates MEM shows be the best at this stage. Model fits approximately well between molecular weights interval [ 500 , 1400 ] for all values of T C .

REVIEW WITH EXTENSIVE RESULTS FOR TIN AND THALLIUM MEM

This section is a review with further explanations from [51] database for Tin ( Sn ) and Thallium HTSCs classes. First part is Tin 2D/3D Graphical Optimization results, Figures 10-12 (erratum, at images is written Thallium in Figs 11-12, but the image correspond to Sn class). Second part corresponds to Thallium 2D/3D imaging charts, Figures 13-16. Multifunctional GA charts are shown for every HTSCs class. Brief of numerical results for both HTSCs classes is included in Table 6.

2D/3D Review of Results Sn GA Optimization

Figure 11 shows the 2D GA polynomial model in a multifunctional chart like in [48-51]. Figure 12 presents the optimal model sector for this MEM. The optimal zones for model are marked inset with arrows. Figure 12 represents MEM Tin HTSCs model in simple grayscale. The accuracy of these results are acceptable approximately, but Hg-Cuprates MEM fits better. This parabolic analytic geometry for Tin class was obtained in previous research with ILS method [3- 5,48,49,50], Figures 2-3. The Thallium class show a sigmoidal analytic geometry, [3-5,48-50, and references in those papers]. Figures 10 and 13 verify the GA program performance in a multifunctional chart. The most important graphs are the Best Fit that gives the fitness optimality, and the percentage of criteria met. The other parts show complementary information, such as best, worst and mean scores, stopping criteria and children number evolution, as in Figures 2-7. This type of software was initially developed in [48-51].

Figure 10.-The Sn GA programming multifunctional 2D graph. 2D Sn polynomial fit parameters intervals set into GA program. Generations Number is 800. As it was found in previous contributions, for Sn class the MEM shows in [50,51] an approximate 2D parabolic shape [3- 5,48,49,50,51].

Figure 11.-Optimal MEM sector for Tin HTSC class. It was set as in [50,51] a 2-Degree polynomial MEM model, Table 6 . 2D polynomial fit parameters intervals were obtained from GA program. Generations Number is 500-800 for getting these polynomial coefficients. As it was found in previous contributions, for Sn class the MEM shows get an approximate 2D parabolic shape [3-5,48,49,50,51]. Model fits approximately well between molecular weights interval [ 3200 , 4700 ] for all values of T C . (erratum, at images is written Thallium in Figs 11-12, but the image correspond to Sn class) .

Figure 12.- Grayscale imaging processing for Optimal MEM sector for Tin HTSC class. It was set as in previous study, [50], a 2-Degree polynomial MEM model. 2D polynomial fit parameters intervals were obtained from GA program. Generations Number is 500-800 for getting these polynomial coefficients. As it was found in previous contributions, for Tin ( Sn ) class the MEM shows get an approximate 2D parabolic shape [3-5,48,49,50,51]. Model fits approximately well between molecular weights interval [ 3200 , 4700 ] for all values of T C . (erratum, at images is written Thallium in Figs 11-12, but the image correspond to Sn class) .

2D/3D Review of Results Thallium ( Tl ) class with best-fitness in 3 th Degree Polynomial

Figures 13-16 show Thallium AI programming results. Best sectors for MEM in Thallium class

are marked inset along the images.

Figure 13.- Similar method than Figs 2-7, but in multifunctional graph. The Thallium HTSCs class GA programming multifunctional 2D graph shows the most important GA optimization dataset. 2D Tl polynomial fit parameters intervals set into GA program. Generations Number is 800. Best fit with 3-Degrees polynomial line, Table 6, inset first graph. As it was found in previous contributions, for Tl class the MEM shows in [50,51] an approximate 2D sigmoidal analytic geometry shape [3-5,48-51].

Figure 14.- Optimal MEM sector for Thallium HTSC class. It was set as in [48-51] a 3-Degree polynomial MEM model. 2D polynomial fit parameters intervals were obtained from GA program. Generations Number is 500-800 for getting these polynomial coefficients. For Tl class the MEM shows get an approximate 2D sigmoidal shape [3-5,48-51]. Model fits approximately well between MEM temperatures interval [ 0 , 75 ] Centigrades for all values of Molecular Mass.

Figure 15.- From [51], a reviewed image processing with different perspective and optimal sector marked inset. Optimal MEM sector for Thallium HTSC class is approximately wide. It was set as in [48-51] a 3-Degree polynomial MEM model. 2D polynomial fit parameters intervals were obtained from GA program in Figure 4. Generations Number is 500-800 for getting these polynomial coefficients. Model fits approximately well between MEM temperatures interval [ 0 , 75 ] Centigrades for all values of Molecular Mass.

Figure 16.- From [51], a reviewed image with other image processing perspective and optimal sector elliptic-marks inset. Optimal MEM sector for Thallium HTSC class is approximately wide. It was set as in [48,49,50] a 3-Degree polynomial MEM model. For Tl class the MEM shows get an approximate 2D sigmoidal shape [3-5,48,49,50]. Model fits approximately well between MEM temperatures interval [ 0 , 75 ] Centigrades for all values of Molecular Mass.

Numerical Results for Hg-Cuprates and Review of Sn and Tl Classes

Tables 5-6 show all the dual numerical results with errors for every HTSCs classes. Hg-Cuprates formula is almost quadratic. Errors can be considered acceptable. Number of GA generations is 300-800. Usually, polynomial coefficients of magnitude order about 10 -9 are discarded for setting images.

Table 5.- From [51], brief of Numerical results for both HTSCs classes MEM optimization ( polynomial ) in 2D/3D Graphical GA implementation of software. For Sn class, error is higher in GA because for GA the program was done for 800 generations, and for polynomial fit was made for 200 functions. For Thallium class residual can be considered acceptable.

Table 6. - From [51], brief of Numerical results for both HTSCs classes MEM optimization ( polynomial ) in 2D/3D Graphical GA implementation of software. In contrast with Hg- Cuprates, the formula obtained was approximated to quadratic. For Sn class, error is higher in GA because for GA the program was done for 800 generations, and for polynomial fit was made for 200 functions. For Thallium class residuals can be considered acceptable.

ELECTRONICS PHYSICS APPLICATIONS

From [51], Table 7 shows overview of applications for MEM one. Molecular Effect applications are guessed and developed from experimental literature database [3-5,38-51]. From Table 7, the following points can be considered important:

1. Every HTSCs class shows get a proper 2D algorithm according to Molecular Mass.

2. The most frequent analytic geometry shape obtained is inverse-parabolic.

3. Inverse methods can be applied for engineering design of Superconducting Multifunctional Transmission Lines [Casanovas, 2021].

4. Applications are at this stage theoretically deduced [3-5, 14, 15, 28, 48-51] . MEM usages were also detailed in previous contributions [48-51].

Table 7.-From [48-51], brief of applications for the MEM that were explained in former contribution series [3-5,48-51].

DISCUSSION AND CONCLUSIONS

This research objective was multiple. Firstly, to apply the Artificial Intelligence GA MEM on Hg- Cuprates HTSCs class, following the former study [51]. Secondly, review, improve, and compare this Hg-Cuprates class to Tin HTSCs class, subject to [ T C > 0° ], and Thallium one, for [ T C ˂ 0° , T C > 0° ] . As in [51], the innovation of this study is the GA application following results got in previous contributions [3-5,48-51] . The GA optimization for Hg-Cuprates was performed with 5 parameters.

Results comprise Hg-Cuprates HTSCs class 2D/3D MEM polynomial Objective Function Graphical and Numerical Optimization database. These 3D imaging processing prove close similarities in MEM with the Tin class approximately parabolic-shaped curvatures and numerical- graphical extrapolations for T C . The best results for MEM are got with the Hg-Cuprates group.

Numerical results for both HTSCs groups are approximately acceptable, Tables 5-6. These HTSC groups MEM [Casesnoves, 2020], 2D analytical geometry shapes and 3D MEM Objective Functions curvatures can be considered approximately satisfactory with low residuals, Figures 1-

16. Electronics Physics applications for MEM are explained, Table 7.

Advantages of this GA software method are the 2D/3D improved mathematical and geometrical numerical analysis for the MEM optimization. Further, the numerical coincidence with 2D polynomial fits proves the cogency of the Artificial intelligence method. Inconvenients with GA programming multifunctional 2D imaging processing was the increasing running time, about 2-4 minutes, when several GA optimization parameters and numerical statistics are implemented in a unique graph. The higher number of generations, the longer running gradient time in GA compared to other optimization Inverse Least Squares techniques used previously [3-6, 39,48-51]. MEM hypothesis algorithms are at primary development stage.

Software and programming methods arebased on previous contributions [3-9, 48-51]. Sketch 1 shows the basic technique stages. The programming for Figures 1-9 requires arranging of GA special commands, patterns, loops, optimal running time choice, and setting precise upper and lower boundary limits for constraints. Grosso modo , a 2D/3D GA methods for MEM subject to Hg-Cuprates and Tin and Thallium HTSCs classes have been developed for MEM. Primary applications in Electronics/ Electromagnetic are included.

REFERENCES

1. Aditya M. Vora. Modified Transition Temperature Equation for Superconductors. Chin.Phys.Lett. Vol. 25, No. 6 (2008) 2162.

2. Abramobitz, Stegun. Handbook of Mathematical Functions. Applied Mathematics Series. 55.1972.

4. Casesnoves, F. "Advanced Interior Optimization Methods with Electronics Applications", International Journal of Scientific Research in Science, Engineering and Technology (IJSRSET), Online ISSN : 2394-4099, Print ISSN : 2395-1990, Volume 7 Issue 5, pp. 97-

   110, September-October 2020. DOI : 10.32628/IJSRSET207518.

5. Casesnoves, F. "Multiobjective Interior Optimization Computational Methods for Electronics BCS Superconductivity", International Journal of Scientific Research in Computer Science, Engineering and Information Technology (IJSRCSEIT), ISSN : 2456- 3307, Volume 6 Issue 5, pp. 280-293, September-October 2020. Available at DOI : 10.32628/CSEIT206556.

6. Casesnoves, F. Mathematical Models and Optimization of Erosion and Corrosion. Ph.D.

   Thesis, Taltech University, Tallinn, Estonia. 14 December. 2018. ISSN 25856898.

7. Casesnoves, F. Die Numerische Reuleaux-Methode Rechnerische und Dynamische Grundlagen mit Anwendungen (Erster Teil); Sciencia Scripts: 2019; ISBN-13: 978-620-0- 89560-8, ISBN-10: 6200895600.

8. Casesnoves, F. Primary Modelling for Electromagnetic Waves Transmission in Extreme Weather Conditions. International Journal of Innovative Research in Science, Engineering, and Technology. Volume 7, Issue 10, 2018. ISSN Online:2319-8753. DOI: 10.15680/IJIRSET.2018.0710022.

9. Casesnoves, F. The Numerical Reuleaux Method, a computational and dynamical base with applications. First Part. Lambert Academic Publishing. ISBN-10 3659917478. 2019.

10. Darwin, C. The origin of species. Barnes & Noble Classics. 2004.

11. Haupt, R, Haupt, S. Practical Genetic Algorithms. Wiley. Second Edition. 2004.

12. Kazufumi, I; Bangti, J. Inverse Problems, Tikhonov Theory and Algorithms. Series on Applied Mathematics Volume 22. World Scientific. 2015.

13. [13]. Plakida, N. High-Temperature Cuprate Superconductors Experiment, Theory, and Applications. Springer Series in Solid-State Sciences ISSN 0171-1873. 2010.

14. Alexandrev, A S. Theory of Superconductivity, From Weak to Strong Coupling. Series in Condensed Matter Physics. Institute of Physics Publishing Philadelphia. 2003.

15. Khare, N. Handbook of High-Temperature Superconductor. Marcel Dekker USA. ISBN: 0-8247-0823-7. 2003.

16. Casesnoves F, Suzenkov A. Mathematical Models in Biotribology with 2D-3D Erosion Integral-Differential Model and Computational-Optimization/Simulation Programming. International Journal of Scientific Research in Computer Science, Engineering and Information Technology. 2017 IJSRCSEIT | Volume 2 | Issue 3 | ISSN : 2456-3307.

17. Casesnoves F, Antonov M, Kulu P. Mathematical models for erosion and corrosion in power plants. A review of applicable modelling optimization techniques. IEEE Xplore database and will be cross referred in SCOPUS. Proceedings of RUTCON2016 Power Engineering Conference.2016. Riga Technical University.

18. Casesnoves, F. 2D computational-numerical hardness comparison between Fe-based hardfaces with WC-Co reinforcements for Integral-Differential modelling. Key Engineering Materials Journal. Trans Tech publications 2018. Vol 762, pp 330-338. DOI: 10.4028/www.scie ntific.net/KEM.762.330.ISSN: 1662-9795. 2018.

19. Casesnoves F, Surzhenkov A. Inverse methods for computational simulations and optimization of erosion models in power plants. IEEE Proceedings of RUTCON2017 Power Engineering Conference.Riga Technical University. IEEExplore Publication in 5th December 2017. DOI:10.1109/RTUCON.2017.8125630. Electronic ISBN:978-1-5386- 3846-0. USB ISBN: 978-1-5386-3844-6.Print on Demand (PoD) ISBN: 978-1-5386-3847-

    7.

20. Casesnoves, F. 'Computational Simulations of Vertebral Body for Optimal Instrumentation Design'. ASME Journal of Medical Devices (Research Paper). Author: F Casesnoves .Journal of Medical Devices. June 2012. Volume 6. Issue 2/021014.11 pages. http://dx.doi.org/10.1115/1.4006670.

21. Casesnoves,F.'Large-Scale Matlab Optimization Toolbox (MOT) Computing Methods in Radiotherapy Inverse reatment Planning’. High Performance Computing Meeting. Nottingham University. January 2007.

22. Casesnoves, F. ‘A Monte-Carlo Optimization method for the movement analysis of pseudo-rigid bodies’. 10th SIAM Conference in Geometric Design and Computing, Texas, San Antonio, USA. Contributed Talk. November 2007.

23. Casesnoves, F. 'Applied Inverse Methods for Deformable Solid Dynamics/Kinematics in Numerical Reuleaux Method (NRM)'. International Journal of Numerical Methods and Applications. volume 9(2) 2013 .pages 109-131. peer-reviewed International Mathematical/Computation Journal Article. print/Online. http://www.pphmj.com/abstract/7688.htm. This article is specially innovative in Inverse Problems applications for deformable solids kinematics/dynamics, further publications are included in United States Congress Library and Numerical Reuleaux

    Method is accepted by scientific community as an innovative dynamics method in

    deformable solids with mechanical, biomechanical and aerospace applications. New applications of this method will be probably found significantly in future.

24. Casesnoves, F. Nonlinear comparative optimization for biomaterials wear in artificial implants technology. Presented in Applied Chemistry and Materials Science RTU2018 Conference Proceedings. 2018.

25. Huang X. Does the isotope effect of mercury support the BCS theory?. Condensed Matter. 2011.

26. Hummel, R E. Electronic Properties of Materials.

27. Kasap F, P. Capper (Eds.), Springer Handbook of Electronic and Photonic Materials, DOI 10.1007/978-3-319-48933-9_50ourth Edition. Springer. 2000.

28. Kessel W.On a General Formula for the Transition Temperature of Superconductors. Naturforsch. 29 a, 445 — 451 [1974] ; received 24 December 1973.

29. Kulou P, Casesnoves F, Simson T, Tarbe R. Prediction of abrasive impact wear of composite hardfacings. Solid State Phenomena, Proceedings of 26th International Baltic Conference on Materials Engineering. 2017. Solid State Phenomena Submitted: 2017-06-

    12. ISSN: 1662-9779, Vol. 267, pp 201-206.

    DOI:10.4028/www.scie ntific.net/SSP.267.201 2017 Trans Tech Publications, Switzerland Online: 2017-10-10.

30. Luenberger, G D. Linear and Nonlinear Programming. Fourth Edition. Springer.2008.

31. Moysés Luiz, Adir. Superconductivity – Theory and Applications, Edited by ISBN 978- 953-307-151-0. 2010.

32. Reynolds C A, Serin, Nesbitt. The Isotope Effect in Superconductivity. I. Mercury. The Isotope Eff'ect in Superconductivity'. Mercury. Physical review volume 84, Number 4, November. 1951.

33. Seri B., C. A. Reynolds, and B. Nesbitt. Mass Dependence of the Superconducting Transition Temperature of Mercury. Letters to Editor. Phys. Rev 80-761. Page 761. 1950.

34. Todinov, M. Reliability and Risk Models. Wiley. 2005.

35. Vidyasagar M. Nonlinear Systems Analysis.Second Edition. Prentice Hall.1993.

36. Wesche, R. Chapter 50. High-Temperature Superconductors. Springer Handbook of Electronic and Photonic Materials. 2017.

37. ‘European Textbook on Ethics in Research’. European Commission, Directorate-General for Research. Unit L3. Governance and Ethics. European Research Area. Science and Society. EUR 24452 EN.

38. The European Code of Conduct for Research Integrity. Revised Edition. ALLEA. 2017.

39. Buschow, K. Magnetic & superconducting materials. Second edition. Elsevier. 2003.

40. Seidel, P. Applied superconductivity. Volume 1 and 2. Wiley-VCH. 2015.

41. Drechsler, S ; Mishonov, T. High-T c Superconductors and Related Materials Material Science, Fundamental Properties, and Some Future Electronic applications. Springer science media, B.V. 1998.

42. Parinov, I. Microstructure and Properties of High-Temperature Superconductors. Second Edition. Springer. 2017.

43. Plakida, N. High-Temperature Cuprate Superconductors Experiment, Theory, and Applications. Springer Series in Solid-State Sciences. 2010.

44. Fossheim, K ; Sudbø, A. Superconductivity Physics and Applications. Wiley. 2004.

45. Wang, Y. F. Fundamental elements of applied superconductivity in electrical engineering. Wiley. 2013.

46. [46]. Pia, M, and Colls. The Geant4 Simulation Toolkit. IEEE Nuclear Science Symposium and Medical Imaging Conference. Seoul. 2013.

47. Allison, K, and Colls. Geant4 Developments and Applications. IEEE Transactions on Nuclear Science, vol. 53, no. 1. February 2006.

48. Casesnoves, F. "Mathematical-Computational Optimization Methods on Primary Molecular Effect Model for Selected High Temperature Superconductors with Electronics Physics Applications". International Journal of Scientific Research in Computer Science, Engineering and Information Technology (IJSRCSEIT). ISSN : 2456-3307, Volume 8

    Issue 2, pp. 159-167, March-April 2022. DOI: [https://doi.org/10.32628/CSEIT228220].

49. Casesnoves, F. Genetic Algorithms for Interior Comparative Optimization of Standard BCS Parameters in Selected Superconductors and High-Temperature Superconductors. Standards 2022, 2, 430–448. [ https://doi.org/10.3390/standards2030029 ] .

50. Casesnoves, F. Genetic Algorithms Optimization for High Temperature Superconductors Sn Class Molecular Effect Model with Electronics Applications. International Journal on Recent Technologies in Mechanical and Electrical Engineering .ISSN: 2349-7947 Volume: 9 Issue: 3. 2022 .

51. Casesnoves, F. Genetic Algorithms Molecular Effect Model Optimization for High Temperature Superconductors Tin and Thallium Classes. Recent Trends in Programming Languages. 2022; 9(3): 1–16p. DOI (Journal): 10.37591/RTPL .