Continuous Evaluation of Shear Wave Velocity from Bender Elements during Monotonic Triaxial Loading.

Few researchers have attempted to experimentally evaluate the low-strain shear wave velocity (Vs) of specimens undergoing large strain deformations. They report that the Vs is practically unaffected by the strains, and the reasons behind this behavior are not fully understood. This study presents the continuous measurement of low-strain Vs with bender elements (BE) during monotonic shearing of two sand specimens in a triaxial device. The results are analyzed using a micro-mechanical model based on contact theory. The results of this study confirm that the Vs values from BE measurements are unaffected by an increase in axial strains that are induced by a separate mechanism. The micro-mechanical model predictions of Vs agree well with the results of this study and with the results of previous studies. They show that the mean effective stress and increase in inter-particle stiffness controls the low-strain stiffness despite a global increase in strains during monotonic loading.

Comprehensive Study of a Diabetes Mellitus Mathematical Model Using Numerical Methods with Stability and Parametric Analysis.

Diabetes is sweeping the world as a silent epidemic, posing a growing threat to public health. Modeling diabetes is an effective method to monitor the increasing prevalence of diabetes and develop cost-effective strategies that control the incidence of diabetes and its complications. This paper focuses on a mathematical model known as the diabetes complication (DC) model. The DC model is analyzed using different numerical methods to monitor the diabetic population over time. This is by analyzing the model using five different numerical methods. Furthermore, the effect of the time step size and the various parameters affecting the diabetic situation is examined. The DC model is dependent on some parameters whose values play a vital role in the convergence of the model. Thus, parametric analysis was implemented and later discussed in this paper. Essentially, the Runge-Kutta (RK) method provides the highest accuracy. Moreover, Adam-Moulton's method also provides good results. Ultimately, a comprehensive understanding of the development of diabetes complications after diagnosis is provided in this paper. The results can be used to understand how to improve the overall public health of a country, as governments ought to develop effective strategic initiatives for the screening and treatment of diabetes.

Modeling the Effects of Chemotherapy and Immunotherapy on Tumor Growth.

Mathematical modeling has been used to simulate the interaction of chemotherapy and immunotherapy drugs intervention with the dynamics of tumor cells growth. This work studies the interaction of cells in the immune system, such as the natural killer, dendritic, and cytotoxic CD8+ T cells, with chemotherapy. Four different cases were considered in the simulation: no drug intervention, independent interventions (either chemotherapy or immunotherapy), and combined interventions of chemotherapy and immunotherapy. The system of ordinary differential equations was initially solved using the Runge-Kutta method and compared with two additional methods: the Explicit Euler and Heun's methods. Results showed that the combined intervention is more effective compared to the other cases. In addition, when compared with Runge-Kutta, the Heun's method presented a better accuracy than the Explicit Euler technique. The proposed mathematical model can be used as a tool to improve cancer treatments and targeted therapy.