Current-distribution simulations, examples

Current-distribution simulations are valuable for the design and analysis of electrochemical processes. For example, such simulations are ubiquitous in the battery and fuel-cell literature. They are used for electrochemical metallization processes not only in reactor design but also in wafer design. " A great deal of effort has also been put into the development of analog solvers for cathodic protection systems. ... 

In order to highlight some possibilities and potential problems for current-distribution simulations, two examples from recent articles are discussed. The first example is concerned with copper deposition from a poorly supported electrolyte, but in well-defined, unsteady fluid flow, for which an analytical solution is available. The second example refers to ferri-cyanide reduction in the presence of an unsteady flow, for which CFD was required to interpret experimental measurements. ... 

BEM might be thought of as best suited to steady state problems, and has been used for this, for example in corrosion simulations [64] and current distributions [198], but recently also for time-marching problems [457]. 

The horizontal ice distribution simulated with such a low order ice model resembles the observed distributions of sea ice however, the storage of freshwater in the ice and the formation of a new water mass by freezing with brine release and by melting is neglected. To include these features, the three-level ice model of Winton (2000) is coupled with MOM-3.1 to provide an improved representation of sea ice for long-term simulations. The sea ice is vertically resolved by two ice layers and a snow cover, with different development of thickness and temperature. As shown in Fig. 19.3, this local thermodynamic description yields arealistic simulation of the interannual variation in the thickness and the spatial extent of the ice cover in the Baltic Sea. The transfer of wind momentum to the currents and to surface waves is exponentially damped out if the ice thickness exceeds a critical value, for example, 10 cm, assuming fast ice. 

Recently, two programs based on similar principles have been introduced BlocfiLib and SPINEVOLIJTTON. These programs should offer the same sort of flexibility as SIMPSON with similar or different procedures for fast execution of numerical simulations. Examples of the use of these programs can be found in the respective publications. In the following, we will show typical examples of numerical simulations primarily based on SIMPSON calculations, as it is our impression that SIMPSON is currently the most widely distributed and used program for calculation of solid-state NMR spectra. 

When axons are placed inside a volume conductor with a stimulation electrode, current flows according to equations derived in the previous section. Some of the current lines enter and exit the axon at different locations and will produce excitation or inhibition. An example of this current distribution is shown in Figure 28.5a for a monopolar anodic electrode. A length Ax of the axonal membrane can be modeled at rest by a capacitance Cm in parallel with a series combination of a battery ( ] ) for the resting potential and a resistance Rm simulating the combined resistance atrest of all the membrane channels (see Figure 28.5b). 

Figure 2. Examples of numerical solutions for the cathodic current distribution on a plate electrode immersed in a cell with the counter electrode at the bottom. Three cases are compared (a) (/ column) completely reversible kinetics (primary distribution) (b) center) irttermedrate kinetics (Ub 0.2) (c) (right column) irreversible kinetics (Wa 10). The top row provides a comparison of the current distribution or the deposit profile on the cathode (cross-hatched region). The center row provides the current distribution along the electrode ( stretched ). The bottom row provides the corresponding poterrtial distributions. It is evident that the current distribution uniformity increases as the electrode kinetics become more passivated (Cell-Design software simulations ).

The push to highlight performance on GPUs has meant that not one of the currently published papers on GPU implementations of MD actually provide any validation of the approximations made in terms of statistical mechanical properties. For example, one could include showing that converged simulations run on a GPU and CPU give identical radial distribution functions, order parameters, and residue dipolar couples to name but a few possible tests. 

The formulation of emission factors for mobile sources, the major sources of VOCs and NO, is based on rather complex emission estimation models used in conjunction with data from laboratory testing of representative groups of motor vehicles. Vehicle testing is performed with a chassis dynamometer, which determines the exhaust emission of a vehicle as a function of a specified ambient temperature and humidity, speed, and load cycle. The current specified testing cycle is called the Federal Test Procedure (FTP). Based on results from this set of vehicle emissions data, a computer model has been developed to simulate for specified speeds, temperatures, and trip profiles, for example, the emission factors to be applied for the national fleet average for all vehicles or any specified distribution of vehicle age and type. These data are then incorporated with activity data on vehicle miles traveled as a function of spatial and temporal allocation factors to estimate emissions. 

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