Scalar Diffusion Equation Based Model to Predict 2-D Film Cooling Effectiveness of Shaped Hole

One-dimensional laterally averaged adiabatic film cooling effectiveness η¯lat based correlations have been widely employed in the cooling design of the modern gas turbine and aero-engine; however, the flow field of the discrete film cooling is fully three-dimensional and thus the cooling effectiveness distribution on the solid surface is two-dimensional. Accurate prediction of the cooling effectiveness distribution in the lateral direction would help to optimize the film cooling design but few paid attention to this issue in the literature. In this work, a simple yet accurate scalar diffusion equation based model is proposed to extend the one-dimensional correlation into two-dimensional. The effective diffusion coefficient is modeled to represent the balance between the diffusion and the passive transportation by the main flow. Analyses conducted within typical experimental range show that the effective diffusion coefficient is only dependent on the velocity ratio and the main-flow turbulence. The current model can be efficiently solved within one second and the results have been validated against a series of experimental data. According to the accuracy analysis, the R2 value larger than 0.9 is obtained for all cases and the source of the prediction error is also analyzed. The proposed model is proved to be accurate and efficient, and results show that the 2-D distribution of coolant can be reasonably predicted with this simple model.

Pulsating and Rotating Spirals in a Delayed Feedback Diffractive Nonlinear Optical System

We study spiral waves in a mathematical model of a nonlinear optical system with a feedback loop. Starting from a delayed scalar diffusion equation in a thin annulus with oblique derivative boundary conditions, we shrink the annulus and derive the limiting equation on a circle. Based on the explicitly constructed normal form of the Hopf bifurcation for the one-dimensional delayed scalar diffusion equation, we make predictions about the existence and stability of two-dimensional spirals that we verify in direct numerical simulations, observing pulsating and rotating spiral waves.

Some results on optimal stopping under phase-type distributed implementation delay

We study optimal stopping of strong Markov processes under random implementation delay. By random implementation delay we mean the following: the payoff is not realised immediately when the process is stopped but rather after a random waiting period. The distribution of the random waiting period is assumed to be phase-type. We prove first a general result on the solvability of the problem. Then we study the case of Coxian distribution both in general and with scalar diffusion dynamics in more detail. The study is concluded with two explicit examples.

Heritability of the Mouse Brain Connectome

SUMMARYGenome-wide association studies have demonstrated significant links between human brain structure and common DNA variants. Similar studies with rodents have been challenging because of smaller brain volumes. Using high field MRI (9.4T) and compressed sensing, we have achieved microscopic resolution and sufficiently high throughput for rodent population studies. We generated whole brain structural MRI and diffusion connectomes for four diverse isogenic lines of mice (C57BL/6J, DBA/2J, CAST/EiJ, and BTBR) at spatial resolution 20,000 times higher than human connectomes. We derived volumes, scalar diffusion metrics, and estimates of residual technical error for 166 regions in each hemisphere and connectivity between the regions. Volumes of discrete brain regions had the highest mean heritability (0.71 ± 0.23 SD, n = 332), followed by fractional anisotropy (0.54 ± 0.26), radial diffusivity (0.34 ± 0.022), and axial diffusivity (0.28 ± 0.19). Connection profiles were statistically different in 280 of 322 nodes across all four strains. Nearly 150 of the connection profiles were statistically different between the C57BL/6J, DBA/2J, and CAST/EiJ lines.