The Quadratic Constitutive Model Based on Partial Derivative and Taylor Series of Ti6242s Alloy and Predictability Analysis

To solve the problem of insufficient predictability in the classical models for the Ti6242s alloy, a new constitutive model was proposed, based on the partial derivatives from experimental data and the Taylor series. Firstly, hot compression experiments on the Ti6242s alloy at different temperatures and different strain rates were carried out, and the Arrhenius model and Hensel-Spittel model were constructed. Secondly, the partial derivatives of logarithmic stress with respect to temperature and logarithmic strain rate at low, medium and high strain levels were analyzed. Thirdly, two new constitutive models with first- and second-order approximation were proposed to meet the requirements of high precision. In this new model, by analyzing the high-order differential data of experimental data and combining the Taylor series theory, the minimum number of terms that can accurately approximate the experimental rheological data was found, thereby achieving an accurate prediction of flow stress with minimal material parameters. In the new model, by analyzing the high-order differential of the experimental data and combining the theory of the Taylor series, the minimum number of terms that can accurately approximate the experimental rheological data was found, thereby achieving an accurate prediction of flow stress with minimal material parameters. Finally, the prediction accuracies for the classical model and the new model were compared, and the predictabilities for the classical models and the new model were proved by mathematical means. The results show that the prediction accuracies of the Arrhenius model and the Hensel-Spittel model are low in the single-phase region and high in the two-phase region. In addition, second-order approximation is required between the logarithmic stress and logarithmic strain rate, and first-order approximation is required between logarithmic stress and temperature to establish a high-precision model. The order of prediction accuracy of the four models from high to low is the quadratic model, Arrhenius model, linear model and HS model. The prediction accuracy of the quadratic model in all temperatures and strain rates had no significant difference, and was higher than the other models. The quadratic model can greatly improve prediction accuracy without significantly increasing the material parameters.

Ti3 C2 -MXene Partially Derived Hierarchical 1D/2D TiO2 /Ti3 C2 Heterostructure Electrode for High-Performance Capacitive Deionization

Constructing faradaic electrode with superior desalination performance is important for expanding the applications of capacitive deionization (CDI). Herein, a simple one-step alkalized treatment for in situ synthesis of 1D TiO₂ nanowires on the surface of 2D Ti₃ C₂ nanosheets, forming a Ti₃ C₂ -MXene partially derived hierarchical 1D/2D TiO₂ /Ti₃ C₂ heterostructure as the cathode electrode is reported. Cross-linked TiO₂ nanowires on the surface help avoid layer stacking while acting as the protective layer against contact of internal Ti₃ C₂ with dissolved oxygen in water. The inner Ti₃ C₂ MXene nanosheets cross over the TiO₂ nanowires can provide abundant active adsorption sites and short ion/electron diffusion pathways. . Density functional theory calculations demonstrated that Ti₃ C₂ can consecutively inject electrons into TiO₂ , indicating the high electrochemical activity of the TiO₂ /Ti₃ C₂ . Benefiting from the 1D/2D hierarchical structure and synergistic effect of TiO₂ and Ti₃ C₂ , TiO₂ /Ti₃ C₂ heterostructure presents a favorable hybrid CDI performance, with a superior desalination capacity (75.62 mg g^-1 ), fast salt adsorption rate (1.3 mg g^-1 min^-1 ), and satisfactory cycling stability, which is better than that of most published MXene-based electrodes. This study provides a feasible partial derivative strategy for construction of a hierarchical 1D/2D heterostructure to overcome the restrictions of 2D MXene nanosheets in CDI.

In creatinine kinetics, the glomerular filtration rate always moves the serum creatinine in the opposite direction

INTRODUCTION

When the serum [creatinine] is changing, creatinine kinetics can still gauge the kidney function, and knowing the kinetic glomerular filtration rate (GFR) helps doctors take care of patients with renal failure. We wondered how the serum [creatinine] would respond if the kinetic GFR were tweaked. In every scenario, if the kinetic GFR decreased, the [creatinine] would increase, and vice versa. This opposing relationship was hypothesized to be universal.

METHODS

Serum [creatinine] and kinetic GFR, along with other parameters, are described by a differential equation. We differentiated [creatinine] with respect to kinetic GFR to test if the two variables would change oppositely of each other, throughout the gamut of all allowable clinical values. To remove the discontinuities in the derivative, limits were solved.

RESULTS

The derivative and its limits were comprehensively analyzed and proved to have a sign that is always negative, meaning that [creatinine] and kinetic GFR must indeed move in opposite directions. The derivative is bigger in absolute value at the higher end of the [creatinine] scale, where a small drop in the kinetic GFR can cause the [creatinine] to shoot upward, making acute kidney injury similar to chronic kidney disease in that regard.

CONCLUSIONS

All else being equal, a change in the kinetic GFR obligates the [creatinine] to change in the opposite direction. This does not negate the fact that an increasing [creatinine] can be compatible with a rising kinetic GFR, due to differences in how the time variable is treated.