No. 40 (299), issue 14Pages 172 - 176

Restoring Orientational Distribution Function of Particles

N.A. Evdokimova, D.V. Lukyanenko, A.G. Yagola
This article deals with the problem of determining the orientation distribution function (ODF), which shows the fraction of particles oriented in the angular range. One effective method to determine the orientation distribution function of partially oriented molecules is the method of electron paramagnetic resonance (EPR). More detailed information about orientational distribution of paramagnetic particles can be obtained from the EPR spectra. Experimental tasks were related to searching orientation of particles in the samples of axial symmetry. The intensity of the resonance signal at each point in the spectrum of H is determined from the two-dimensional Fredholm integral of the first kind, in which the ODF is unknown. For solving the equation is necessary to minimize the Tikhonov regularization functional (using conjugate gradient method). Calculate the value of the functional and its gradient requires time-consuming. Therefore, the problem is parallelized, ie a program is written in such way that the independent parts of the program run on different processors. This enables the use of multi-processor system.
Full text
orientation distribution function, Tikhonov regularization functional, two-dimensional Fredholm integral of the first kind, task parallelizing
1. Tikhonov A.N., Leonov A.S., Yagola A.G. Nonlinear ill-posed problems. Moscow, Science, 1995. (in Russian)
2. Tikhonov A.N. Regularization of Ill-Posed Problems. DAN SSSR, 1963, vol. 153, no. 1, pp. 55-59. (in Russian)
3. Tikhonov A.N., Goncharsky A.V., Stepanov V.V., Yagola A.G. Numerical Methods for the Solution of Ill-Posed Problems. Kluwer Academic Publishers, Dor- drecht: 1995.
4. Voevodin V.V., Voevodin Vl.V. Parallel Computing, Sankt-Peterburg, BXV-Peterburg, 2002. (in Russian)