Marching algorithm

The initial value problem, Eqs. 1-3, can be integrated by any marching algorithm which is based on the Runge-Kutta or Adams-Moulton techniques. Based on the calculated space profiles of C,... 

The marching algorithm mainly takes care of two tasks. Firstly, it updates the index matrix whether a node is outside ( 0 ), at the front ( 1 ), or inside 2 ) the object. The other task is to update the travel-time value for the current node and its neighboring nodes. In addition, we want the algorithm to do this fast as well. Two important reasons for why a group marching-based method works fast are ... 

Marching Cubes A High Resolution 3D Surface Construction Algorithm, Computer Graphics 21(4), pp 163-169 (1987)... 

Figure 24. Fourteen cases of the polygonal approximation for the isosurface inside a cube used by the marching cube algorithm [211].

Fan, Y. S. Sarkar and L. Lasdon. Experiments with Successive Quadratic Programming Algorithms. J Optim Theory Appli 56 (3), 359-383 (March 1988). 

Elirman, L.M. and Lanterman, A.D. A robust algorithm for automatic target recognition using passive radar Proceedings of the Thirty-Sixth Southeastern Symposium on System Theory, 2004 pp 102-106, March 14-16, 2004. 

Werde, Bill, We Got Algorithm, But How About Soul New York Times, Section 4, page 12, March 21,2004. (Describes the Dia proj ect to assess the most desired painting.)... 

De Beek, R., R. Hoogen, V. Rozanov and J.P. Burrows (1998) Ozone profile from GOME satellite data I algorithm development Proceedings of the third ERS Symposium Florence lS "1 of March 1997. Report ESA SP 414, pp. 749-754. 

Figure 7.17 Moore s hardware implementation of Land s algorithm (Reproduced by permission of IEEE. Moore A and Allman J and Goodman RM 1991 A real-time neural system for color constancy. IEEE Transactions on Neural Networks, IEEE, 2(2), 237-247, March). The output of the camera is smoothed using three separate resistive grids (a). A single resistive grid is shown in (b). The smoothed image is then subtracted from the original image.

The change in velocity vt is equal to the integral of acceleration over time. In MolD, one numerically and iteratively integrates the classical equations of motion for every explicit atom N in the system by marching forward in time by tiny time increments, At. A number of algorithms exist for this purpose (Brooks et al., 1988 McCammon and Harvey, 1987), and the simplest formulation is shown below ... 

The most important one is that the model should be appropriately validated to confirm the reliability of its predictions. First rules of the validation were worked out in March 2002 at an international workshop held in Setubal, Portugal ( Setubal Rules ). In November 2004, the rules were discussed and modified by the OECD Work Program on QSAR they are now known as the OECD Principles. According to these principles, each QSAR model should be associated with (a) a well-defined endpoint (b) an unambiguous algorithm (c) a defined domain of applicability (d) appropriate measures of goodness-of-fit, robustness and predic-tivity and (v) a mechanistic interpretation, if possible [15, 16]. 

Yet another, quite different, approach to solving a system of odes, such as one obtains as an intermediate step when using, for example, MOL or OC, is the eigenvalue-eigenvector method. Its use for electrochemical simulations was described in two papers in 1989 and 1990 [255,332]. The method has some drawbacks, and does not appear to have seen much use since these two papers. It does have one unique feature there is no discretisation of time. A solution is generated by the algorithm, at any chosen time. So, although the method may at times be fairly inefficient, if one wants a current or concentrations at only one or a few time points, this could be faster than a time march with the usually small time intervals. 

FIGURE 4.37 Joint time-frequency domains of the AE signal for slurry 1 (a) and slurry 2 (b). The AE signal was filtered by a Debouche 05 wavelet filter. Only middle bands were selected and processed by the marching pursuit joint time-frequency domain algorithm (from Ref 27). 

This algorithm performs flawlessly for the twentieth and twenty-first centuries, up to the year 2100. If you really want to be meticulous beyond that, you can make further modifications by reducing D1 by 1 after March 2100, and repeating that every 100 years. You must do this because the century years like 2100 and 2200 which are not divisible by 400 are not leap years, but the algorithm treats them as if they were. 

Another semiempirical PCM formulation has been presented by Rauhut et al. (1993). They use a marching-cube algorithm to define tesserae (Lorensen and Cline, 1987). The flat mesh thus obtained is then projected on a van der Waals surface (factor Z =1.15). These authors point out that the full NDDO (Neglect of Diatomic Differential Overlap) expression of the (xm VBf xJ elements is convenient in order to have good results, when combined with the original PCM procedure for the surface charge renormalization. 

The marching-cube algorithm has been used also by Kolle and Jug (1995) to define the tesserae of isodensity surfaces. The procedure is implemented in the semiempirical SINDOl program (INDO with Slater-type orbitals, Li et al., 1992). To compute AS charges the asymptotic density model ADM (Koster et al., 1993) is used. This is an approximation to the calculation of molecular electrostatic potentials based on the cumulative atomic multipole moment procedure (CAMM, Sokalski et al., 1992). 

---