## 4 Conclusions  
The results presented in this study underscore the sensitivity of the JWL EoS parameter fitting process to the choices of algorithm and parameter constraints. The non-uniqueness of the fitting solution highlights the critical need for carefully imposed constraints, particularly at the Chapman-Jouguet (CJ) point, to ensure physically meaningful and accurate parameters. Our detailed algorithm, which includes the explicit imposition of the CJ constraints and the separate treatment of the different terms in the JWL EoS, demonstrates a robust approach to achieving reliable fits. The sensitivity analysis from the open literature indicates that small variations in the input data or initial parameter guesses can lead to significant differences in the fitted parameters, emphasizing the importance of selecting appropriate ranges and constraints. These findings suggest that the success of the JWL EoS fitting is highly dependent on the specific choices made during the fitting process, including the handling of data and the definition of validity ranges for the parameters. Additionally, it is important to recognize that the JWL EoS requires a constant Gruneisen gamma. This assumption can be problematic, as real materials often experience phase transitions, such as the transition between diamond and graphite, which introduce discontinuities and invalidate the constant gamma assumption. This further complicates the fitting process and requires careful consideration when applying the JWL EoS to materials undergoing such transitions. Our comparative analysis with experimental data shows that, despite these sensitivities, the proposed algorithm can achieve high fidelity in modeling detonation phenomena when applied judiciously. However, users of the JWL EoS must remain cognizant of the potential for variability and the necessity of a methodical approach to parameter fitting. By providing a clear and detailed methodology for JWL EoS parameter fitting, this work contributes to the field by offering a more reliable and efficient approach to detonation modeling. In conclusion, this work provides a comprehensive methodology for the least-squares fitting of the JWL EoS parameters, offering clarity and guidance for future applications. By acknowledging and addressing the inherent sensitivities and potential for non-unique solu  
Figure 3: Plot of isentropic data from EXPLO5 and the 2 fitting procedures from the latter software and the one presented in this work: qualitatively, the difference between the results is not appreciable. tions, this study enhances the precision and reliability of detonation modeling, contributing valuable insights to the field. Conceptualization, Y.C. and A.C.; methodology, Y.C. ; software, Y.C., A.C. and F.V. ; validation, Y.C., A.C. and F.V. ; formal analysis, Y.C. and S.B. ; investigation, Y.C. ; resources, Y.C. ; data curation, Y.C. and A.C.; writing--original draft preparation, Y.C. ; writing--review and editing, Y.C., F.V. and S.B. ; visualization, Y.C. ; supervision, S.B. and F.V. ; project administration, S.B. and Y.C. All authors have read and agreed to the published version of the manuscript. * [PERSON] (1965) [PERSON]; [PERSON] Calculating the Singular Values and Pseudo-Inverse of a Matrix. _J. Soc. Ind. Appl. Math. Ser. B Numer. Anal._**1965**, \(2\), 205-224. * [PERSON] et al. (2023) [PERSON]; [PERSON] [PERSON]; [PERSON] [PERSON]; [PERSON] [PERSON] MATLAB code for highly energetic material. In Proceedings of the III Aerospace PhD-Days: International congress of PhD students in Aerospace Science and Engineering, Bertinoro, Italy, 16-19 April 2023; Volume 33. * [PERSON] et al. (2024) [PERSON] [PERSON]; [PERSON] [PERSON]; [PERSON] [PERSON] HEMSim: A new MATLAB software to simulate the behavior of highly energetic materials upon Chapman-Jouguet hypothesis. _J. Energetic Mater._**2024**, 1-16. [CrossRef]
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