Mathematical models for phenomena in the physical sciences are typically parameter-dependent, and the estimation of parameters that optimally model the trends suggested by experimental observation depends on how model...Mathematical models for phenomena in the physical sciences are typically parameter-dependent, and the estimation of parameters that optimally model the trends suggested by experimental observation depends on how model-observation discrepancies are quantified. Commonly used parameter estimation techniques based on least-squares minimization of the model-observation discrepancies assume that the discrepancies are quantified with the L<sup>2</sup>-norm applied to a discrepancy function. While techniques based on such an assumption work well for many applications, other applications are better suited for least-squared minimization approaches that are based on other norm or inner-product induced topologies. Motivated by an application in the material sciences, the new alternative least-squares approach is defined and an insightful analytical comparison with a baseline least-squares approach is provided.展开更多
In the scope of material science, it is well understood that mechanical behavior of a material is temperature dependent. The converse is also true and for specific loading cases contributes to a unique thermal failure...In the scope of material science, it is well understood that mechanical behavior of a material is temperature dependent. The converse is also true and for specific loading cases contributes to a unique thermal failure mechanism known as “heat explosion”. The goal for this paper is to improve the mathematical models for predicting heat explosion by using a specific case of the Fourier heat transfer system that focuses on thermoviscoelastic properties of materials. This is done by using a computational analysis to solve for an internal heat parameter that determines thermal failure at a critical value. This critical value is calculated under conditions either accounting for or negating the effect of heat dissipated by the material. This model is an improvement on existing models because it accounts for material specific properties and in doing so limits mathematical assumptions of the system. By limiting the assumptions in the conditions of the model, the model becomes more accurate and useful in regards to material design.展开更多
文摘Mathematical models for phenomena in the physical sciences are typically parameter-dependent, and the estimation of parameters that optimally model the trends suggested by experimental observation depends on how model-observation discrepancies are quantified. Commonly used parameter estimation techniques based on least-squares minimization of the model-observation discrepancies assume that the discrepancies are quantified with the L<sup>2</sup>-norm applied to a discrepancy function. While techniques based on such an assumption work well for many applications, other applications are better suited for least-squared minimization approaches that are based on other norm or inner-product induced topologies. Motivated by an application in the material sciences, the new alternative least-squares approach is defined and an insightful analytical comparison with a baseline least-squares approach is provided.
文摘In the scope of material science, it is well understood that mechanical behavior of a material is temperature dependent. The converse is also true and for specific loading cases contributes to a unique thermal failure mechanism known as “heat explosion”. The goal for this paper is to improve the mathematical models for predicting heat explosion by using a specific case of the Fourier heat transfer system that focuses on thermoviscoelastic properties of materials. This is done by using a computational analysis to solve for an internal heat parameter that determines thermal failure at a critical value. This critical value is calculated under conditions either accounting for or negating the effect of heat dissipated by the material. This model is an improvement on existing models because it accounts for material specific properties and in doing so limits mathematical assumptions of the system. By limiting the assumptions in the conditions of the model, the model becomes more accurate and useful in regards to material design.
