A high-order full-discretization method using Hermite interpolation for periodic time-delayed differential equations

A high-order full-discretization method(FDM)using Hermite interpolation(HFDM) is proposed and implemented for periodic systems with time delay. Both Lagrange interpolation and Hermite interpolation are used to approximate state values and delayed state values in each discretization step. The transition matrix over a single period is determined and used for stability analysis. The proposed method increases the approximation order of the semidiscretization method and the FDM without increasing the computational time. The convergence, precision, and efficiency of the proposed method are investigated using several Mathieu equations and a complex turning model as examples. Comparison shows that the proposed HFDM converges faster and uses less computational time than existing methods.     

Absence of Anomalous Dissipation of Energy in Forced Two Dimensional Fluid Equations

We prove the absence of anomalous dissipation of energy for long time averaged solutions of the forced critical surface quasi-geostrophic equation in two spatial dimensions.     

Molecular dynamics simulation of poly(3‐hexylthiophene) helical structure In Vacuo and in amorphous polymer surrounding

The stability of poly(3‐hexylthiophene) (P3HT) helical structure has been investigated in vacuo and in amorphous polymer surrounding via molecular dynamics‐based simulations at temperatures below and above the P3HT melting point. The results show that the helical chain remains stable at room temperature both in vacuo and in amorphous surrounding, and promptly loses its structure at elevated temperatures. However, the amorphous surrounding inhibits the destruction of the helix at higher temperatures. In addition, it is shown that the electrostatic interactions do not significantly affect the stability of the helical structure. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016 , 54, 2448–2456     

Thermal measurements using ultrasonic acoustical pyrometry

Reflections from geometric discontinuities can be used with ultrasonic energy to predict the temperature of an interface where classical temperature measurement techniques are impractical because of physical access limitations or harsh environmental conditions. Additionally, these same ultrasonic measurements can be used with inversion methods commonly applied to ill-posed heat transfer problems to increase the accuracy of the measurement of surface temperature or heat flux at the surface of interest. Both methods for determining surface temperature are presented, along with a comparison of results both from a verification example and using data gathered in a field test of the methods. The results obtained with these two methods are shown to be in good agreement with an empirical relationship used in the design of large caliber guns.