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Vestnik YuUrGU. Ser. Mat. Model. Progr., 2012, Issue 14, Pages 172–176 (Mi vyuru94)  

Short communications

Restoring Orientational Distribution Function of Particles

N. A. Evdokimovaa, D. V. Lukyanenkob, A. G. Yagolab

a South Ural State University (Chelyabinsk, Russian Federation)
b M. V. Lomonosov Moscow State University (Moscow, Russian Federation)

Abstract: 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.

Keywords: orientation distribution function, Tikhonov regularization functional, two-dimensional Fredholm integral of the first kind, task parallelizing.

Full text: PDF file (201 kB)
References: PDF file   HTML file
UDC: 519.6
MSC: 45Q05
Received: 08.08.2012

Citation: N. A. Evdokimova, D. V. Lukyanenko, A. G. Yagola, “Restoring Orientational Distribution Function of Particles”, Vestnik YuUrGU. Ser. Mat. Model. Progr., 2012, no. 14, 172–176

Citation in format AMSBIB
\Bibitem{EvdLukYag12}
\by N.~A.~Evdokimova, D.~V.~Lukyanenko, A.~G.~Yagola
\paper Restoring Orientational Distribution Function of Particles
\jour Vestnik YuUrGU. Ser. Mat. Model. Progr.
\yr 2012
\issue 14
\pages 172--176
\mathnet{http://mi.mathnet.ru/vyuru94}


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