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We investigate the shallow flow of viscous fluid into and out of a channel whose gap width increases as a power-law ($x^n$), where $x$ is the downstream axis. The fluid flows slowly, while injected at a rate in the form of $t^\alpha$, where $t$ is time and $\alpha$ is a constant. The invading fluid has higher viscosity than the ambient fluid, thus avoiding Saffman-Taylor instability. Similarity solutions of the first kind for the outflow problem are found using approximations of lubrication theory. Zheng et al [2014] studied the deep-channel case and found divergent behaviour of the similarity variable as $n\rightarrow1$ and $n\rightarrow3$, when fluid flows into and out of the channel respectively. No divergence is found in the shallow case presented here. The characteristic equilibration time for the numerically simulated constant-volume flow to converge to the similarity solution is calculated assuming inverse dependence on the ratio disagreement between the current front using the method of lines (MOL). The inverse power dependence between equilibration time and ratio disagreement is found for channels of different powers. A similarity solution of the second kind for the inflow problem is found using the phase plane formalism and the bisection method. An exponential decay relationship is found between $n$ and the degree $\delta$ of the similarity variable $xt^{-\delta}$, which does not show any divergent behaviour for large $n$. An asymptotic behaviour is found for $\delta$ that approaches $1/2$ as $n\rightarrow\infty$.

Analysis of helicon wave heating and current drive capability in EXL-50 spherical torus plasmas has been conducted. It is found that the driven current increases with the launched parallel refractive index $n_{||}$ and peaks around $n_{||} = 4.0$ when the frequency of the helicon wave is between 300~MHz and 380~MHz. The helicon wave current drive efficiency shows a relatively stable upward trend with increasing plasma temperature. Moreover, the driven current decreases as the plasma density increases. We also analyzed the current drive with helicon waves of 150~MHz and 170~MHz and found that the driven current at a lower frequency was lower than that at a higher frequency. A positive proportional relationship exists between the driven current and $n_{||}$. Besides, as $n_{||}$ increases, the profile of the driven current becomes wider. Finally, the effect of the scrape-off layer (SOL) region on the helicon wave current drive was also investigated.

The effectiveness of multiple electron cyclotron resonance (ECR) harmonics has been thoroughly investigated in context of high current drive efficiency, generally observed in fully non-inductive operation of the low aspect ratio EXL-50 spherical tokamak (ST) powered by electron cyclotron (EC) waves. The Fokker-Plank equation is numerically solved to obtain electron distribution function, under steady state of the relativistic nonlinear Coulomb collision and quasi-linear diffusion operators, for calculating plasma current driven by the injected EC wave. For the extra-ordinary EC wave, simulation results unfold a mechanism by which electrons moving around the cold second harmonic ECR layer strongly resonate with higher harmonics via the relativistic Doppler shifted resonance condition. This feature is in fact evident above a certain value of input EC wave power in simulation, indicating it to be a non-linear phenomenon. Similar to the experimental observation, high efficiency in current drive (over 1 A/W) has indeed been found in simulation for a typical low density ($\sim 1\times10^{18}~m^{-3}$), low temperature ($\lesssim 100$ eV) plasma of EXL-50 by taking into account multi-pass absorptions in our simulation model. However, such characteristic is not found in the ordinary EC-wave study for both single-pass and multi-pass simulations, suggesting it as inefficient in driving current on our ST device., Comment: 22 pages, 15 figures. Submitted to the Nuclear Fusion journal

We present new data in the ongoing effort to bound the effect of proton angle of incidence on the single-event upset (SEU) rate in silicon-on-sapphire (SOS) and silicon-on-insulator (SOI) devices.

The numerical algorithms used to simulate the advection, diffusion, sedimentation, coagulation, and condensational growth of atmospheric aerosols are described. The model can be used in one, two, or three spatial dimensions. The continuity equation in a generalized horizontal and vertical coordinate system is developed, which allows the model to be quickly adapted to a wide variety of dynamical models of global or regional scale. Algorithms are developed to treat the various physical processes, and the results of simulations are presented, which show the strengths and weaknesses of these algorithms. Although the emphasis is on the modeling of aerosols, the work is also applicable to the simulations of the transport of gases.

A simulation is carried out of the evolution of an optically thick dust cloud in the earth's atmosphere, and calculations are made of the effects that such a dust cloud would have on the amount of visible light reaching the surface and the temperature at the earth's surface. It is found that large quantities of dust remain in the atmosphere for periods of only three to six months. This duration is fixed by the physical processes of coagulation; these cause the rapid formation of micron-sized particles and sedimentation that quickly removes the particles from the atmosphere. The duration of the event is found to be nearly independent of the initial altitude, initial particle size, initial mass, atmospheric vertical diffusive mixing rate, and rainout rate. It depends to a slight extent on the particle density and the probability that colliding particles stick together to form a larger particle. In addition, the duration is limited by the rate at which the debris spreads from the initial impact site. A doubling code is used to calculate the visible radiative transfer in the dust clouds. It is found that light levels are too low for vision for one to six months and too low for photosynthesis for two months to one year.