Lightning Solvers for Potential Flows

We present a method for computing potential flows in planar domains. Our approach is based on a new class of techniques, known as “lightning solvers”, which exploit rational function approximation theory in order to achieve excellent convergence rates. The method is particularly suitable for flows in domains with corners where traditional numerical methods fail. We outline the mathematical basis for the method and establish the connection with potential flow theory. In particular, we apply the new solver to a range of classical problems including steady potential flows, vortex dynamics, and free-streamline flows. The solution method is extremely rapid and usually takes just a fraction of a second to converge to a high degree of accuracy. Numerical evaluations of the solutions are performed in a matter of microseconds and can be compressed further with novel algorithms.

Influence of Calcium Nitrate on Microbial Community Structure of Acidophilic Microorganisms

The influence of different concentrations of calcium nitrate on the growth and activity of acidophilic microorganisms were studied and the microbial community structures were compared by 16S rRNA gene clone library analysis. The addition of Ca (NO3)2has a certain effect on the solution potential, and that the time needed to reach the steady potential were prolonged with the increase of Ca (NO3)2concentration but not obvious when it was above 1.64 g.L-1. It also can be observed that the cell numbers decreased with the increase of Ca (NO3)2concentration which can alter the cell osmolarity, and that the time entering the stationary phase of cell concentration was delayed with the addtion of Ca (NO3)2. With the addition of 0.41g.L-1Ca (NO3)2, the percentage ofLeptospirillum ferriphilumandAcidiphilium cryptumdidn’t have great changes, while the unculturedSulfobacillus sp.,Acidithiobacillus ferrooxidansandAlicyclobacillus toleranswere also detected. With the addition of 2.05 g.L-1Ca (NO3)2or more, theAcidithiobacillus ferrooxidansbecome the dominant bacterium (which accounted for more than 90%).

Conservation laws for plane steady potential barotropic flow

It is shown that the set of conservation laws for the nonlinear system of equations describing plane steady potential barotropic flow of gas is given by the set of conservation laws for the linear Chaplygin system. All the conservation laws of zero order for the Chaplygin system are found. These include both known and new nonlinear conservation laws. It is found that the number of conservation laws of the first order is not more than three, assuming that the laws do not depend on the velocity potential and are not non-obvious ones. The components of these conservation laws are quadratic with respect to the stream function and its derivatives. All the Chaplygin functions are found, for which the Chaplygin system has three non-obvious conservation laws of the first order that are independent of velocity potential. All such non-obvious first-order conservation laws are found.

Interaction of Waves With a Steady Intake/Discharge Flow Emanating From a 3D Body

It has been proposed that the warm surface-water intake pipes distributed around an OTEC plant can generate adequate momentum to globally position a platform to overcome the second-order drift forces, thereby eliminating the need for additional power for thrusters or for mooring lines. It is evident that if the intake rate of the flow is high, there will be interaction among the locally created steady flow due to the intake, the incoming wave, and the ensuing platform motions. In this work, we address such concerns by developing a linear theory for obtaining the motions (in the presence of incoming waves) of arbitrary 3D bodies from which there is a steady intake/discharge. The boundary-value problem is formulated within the assumption of the linear potential theory by decomposing the total potential into oscillatory and steady components. The steady potential is further decomposed into double-model and perturbation potentials. The time harmonic potential is coupled with the steady potential through the free-surface condition. The potentials are obtained using the quadratic boundary-element method. The effect of the steady flow on hydrodynamic force coefficients and response amplitude operators is studied.