Porter, Carlos

The workhorse for the calculation of cross sections in full collisions is the so-called Monte Carlo technique (Schreider 1966 Porter and Raff 1976 Pattengill 1979). The application to photodissociation proceeds in an identical fashion. Within the Monte Carlo method an integral over a function f(x) is approximated by the average of the function over N values Xk randomly selected from a uniform distribution,... 

These experiments are important because they are performed on a reaction for which a priori calculations of V(rAB, rBC, rCA) are likely to have their best chance of success as only three electrons are involved. Even here the accurate computation of V, frequently termed the potential-energy hypersurface, is extremely difficult. Porter and Karplus [19] have determined a semiempirical hypersurface, and Karplus, Porter, and Sharma [20] have calculated classical trajectories across it. This type of computer experiment has been mentioned before and will be described in greater detail later. The objective of Karplus et al. was to calculate aR(E) and E0. Collisions were therefore simulated at selected values of E, with other collision parameters selected by Monte Carlo procedures, and the subsequent trajectories were calculated using the classical equations of motion. Above E0, oR was found to rise to a maximum value, of the same order of magnitude as the gas-kinetic cross section, and then gradually to decrease to greater energies. 

This article is an abridged and modified version of the chapter on The Gas Chambers in the book by Carlo Mattogno and Jurgen Graf on the Concentration Camp Majdanek. A historical and technical Study, Theses Dissertations Press, Chicago 2003 (online vho.org/GB/Books/ccm), translated and edited by Carlos Porter and Russ Granata. 

Some years later, aided by considerably more rapid computers than available to Wall and co-workers, Karplus, Porter, and Sharma reinvestigated the exchange reaction between H2 and H [24]. As with the earlier work, the twelve classical equations of motion were solved. In addition, discrete quantum-mechanical vibrational and rotation states were included in the total energy so that the trajectories were examined as a function of the initial relative velocity of the atom and molecule and the rotational and vibrational quantum numbers j and v of the molecule. The more sophisticated potential energy surface of Porter and Karplus was used [7], and the impact parameter, orientation and momentum of the reactants, and vibration phase were selected at random from appropriate distribution functions. This Monte Carlo approach was used to examine 200-400 trajectories for each set of VyJ, and v. The reaction probability P can be written as... 

PORTER, M., SCHWAB, K., SALA-I-MARTIN, X., LOPEZ-CARLOS, A., The Global Competitiveness Report 2004-2005, World Economic Forum, published by Pal grave Macmillan, New York, NY (2004). 

The technical answer is the Monte Carlo theorem. We will not state it but paraphrase to say that if there are more than four variables, a systematic sampling is not the most economic route. See Porter and Raff (1976), Truhlar and Muckerman (1979). 

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