Katmanlı Beslemeli Sinir Ağı ile Gama Işını Açısal Dağılım Katsayıları için Tutarlı Ampirik Fiziksel Formül Eldesi
Abstract
Gama ışınlarının multipolariteleri ve nükleer
durumların spinleri, genelliklle, nükleer reaksiyonlarla oluşturulan hizalanmış
durumlardan yayılan gama ışınlarının açısal dağılımı ile incelenir. Geçişlerin
farklı multipolarite değerleri için, dağılım farklı özellikler göstermektedir.
Dağıtım, farklı spinler ve çok kutupluluklar için literatürdeki tablolanmış
katsayılarve açısal dağılım formülü kullanılarak elde edilir. Bununla birlikte,
bu katsayılar r katlı tensör çarpımları içerir ve yapıları oldukça doğrusal
olmayan şekildedir. Dahası, bu katsayıların hesaplanması karmaşık integraller
içerdiğinden, daha büyük r değerleri için açıkça ele alınması çok zordur. Bu
bağlamda, daha önceki bir çalışmamızla teorik olarak ispatlandığımız gibi,
doğrusal olmayan fiziksel fenomenler için, tutarlı, ampirik fiziksel formüller
(EPF'ler) oluşturmak için, evrensel doğrusal olmayan bir katmanlı beslemeli
sinir ağı (LFNN) kullanılabilir. Bu makalede, nükleer durumların tamsayı
spinlerine ve geçişlerin dipol ve kuadrupol multipolaritelerine odaklanarak,
uygun LFNN'leri inşa ederek katsayıları tutarlı bir şekilde tahmin ettik.
LFNN-EPF'ler, literatür katsayısı verisini çok iyi bir şekilde fitledi. Ayrıca,
daha önce görülmemiş veriler üzerinde yapılan LFNN test seti tahminleri, katsayıların
belirlenmesi için tutarlı LFNN-EPF'leri doğrulamıştır. Bu bağlamda, LFNN'nin,
gama ışınlarının açısal dağılımını yöneten doğrusal olmayan fiziksel yasalara
tutarlı bir şekilde uyduğu sonucuna varabiliriz. Bu da, geleneksel katsayı
hesaplama yöntemleri ile elde edilmesi zor olan bir sonuçtur.
References
- [1]. Yildiz N., N, Layered feedforward neural network is relevant to empirical physical formula construction: a theoretical analysis and some simulation results. Phys. Lett. A 345-13 (2005) 69-87.
- [2]. Yildiz N., and Akkoyun S. Neural network consistent empirical physical formula construction for neutron–gamma discrimination in gamma ray tracking, Annals of Nuclear Energy 51 (2013) 10-17.
- [3]. Akkoyun S., Bayram T., and Turker T. Estimations of beta-decay energies through the nuclidic chart by using neural network, Radiation Physics and Chemistry 96 (2014) 186-189.
- [4]. Bass S.A., Bischoff A., Maruhn J.A., Stöcker H., Greiner W. Neural networks for impact parameter determination. Phys. Rev. C 53-5 (1996) 2358–2363.
- [5]. Haddad F., Hagel K., Li J., Mdeiwayeh N., Natowitz J.B., Wada R., Xiao B., David C., Freslier M., Aichelin J. Impact parameter determination in experimental analysis using a neural network. Phys. Rev. C 55-3 (1997) 1371-1375.
- [6]. Medhat M.E. Artificial intelligence methods applied for quantitative analysis natural radioactive sources. Ann. Nucl. Energy 45 (2012) 73–79.
- [7]. Akkoyun S., Bayram T., Kara S.O., Sinan A., An artificial neural network application on nuclear charge radii. J. Phys. G Nucl. Part. 40 (2013) 055106.
- [8]. Costiris N., Mavrommatis E., Gernoth K.A., Clark J.W., A global model of beta decay half-lives using neural networks. arXiv:nucl-th/0701096v1 (2007).
- [9]. Ferguson A.J. Angular correlation methods in gamma-ray spectroscopy. North- Holland Publishing Co., Amsterdam (1965).
- [10]. Yamazaki T. Tables of coefficients for angular distribution of gamma rays from aligned nuclei. Nuclear Data Section A (1967) 3-1.
- [11]. Mateosian E. der, and Sunyar A.W. Table of attenuation coefficients for angular distribution of gamma rays from partially aligned nuclei. Atomic Data and Nuclear Data Tables 13 (1974) 391.
- [12]. Ferentz M., and Rosenzweig N., Table of F coefficients. ANL-5324.
- [13]. Haykin S. Neural networks: A comprehensive foundation. Prentice-Hall Inc., Englewood Cliffs, NJ, USA (1999).
- [14]. Hornik K., Stinchcombe M., White H. Multilayer feedforward networks are universal approximator. Neural Networks 2 (1989) 359-366.
Consistent Empirical Physical Formula Construction for Gamma Ray Angular Distribution Coefficients by Layered Feedforward Neural Network
Abstract
Multipolarities of gamma rays and
spins-parities of nuclear states are usually investigated by the angular
distribution of gamma rays emitted from aligned states formed by nuclear
reactions. For different multipolarities of the transitions, the distribution
shows different characteristics. The distribution is obtained by using angular
distribution formula which has literature tabulated coefficients for different
spins and multipolarities. However,
these coefficients involve -fold tensor products and they are highly nonlinear in nature.
Furthermore, as the calculation of these coefficients implicitly involves
highly complicated integral quantities, they are very difficult to handle
explicitly for larger values. In this respect, as
we theoretically proved in a previous paper, universal nonlinear function
approximator layered feedforward neural network (LFNN) can be applied to
construct consistent empirical physical formulas (EPFs) for nonlinear physical
phenomena. In this paper, by concentrating on the integer spins of nuclear
states and dipole and quadrupole type multipolarities of the transitions, we
consistently estimated the coefficients by constructing suitable LFNNs. The
LFNN-EPFs fitted the literature coefficient data very well. Moreover, magnificent
LFNN test set forecastings over previously unseen data confirmed the consistent
LFNN-EPFs for the determination of coefficients. In this sense, we can conclude that the LFNN
consistently infers nonlinear physical laws governing the angular distribution
of gamma rays, which are otherwise difficult to obtain by conventional
coefficient calculation methods.
Keywords
Angular distribution multipolarity nuclear spin layered feed-forward neural network layered feed-forward neural network
References
- [1]. Yildiz N., N, Layered feedforward neural network is relevant to empirical physical formula construction: a theoretical analysis and some simulation results. Phys. Lett. A 345-13 (2005) 69-87.
- [2]. Yildiz N., and Akkoyun S. Neural network consistent empirical physical formula construction for neutron–gamma discrimination in gamma ray tracking, Annals of Nuclear Energy 51 (2013) 10-17.
- [3]. Akkoyun S., Bayram T., and Turker T. Estimations of beta-decay energies through the nuclidic chart by using neural network, Radiation Physics and Chemistry 96 (2014) 186-189.
- [4]. Bass S.A., Bischoff A., Maruhn J.A., Stöcker H., Greiner W. Neural networks for impact parameter determination. Phys. Rev. C 53-5 (1996) 2358–2363.
- [5]. Haddad F., Hagel K., Li J., Mdeiwayeh N., Natowitz J.B., Wada R., Xiao B., David C., Freslier M., Aichelin J. Impact parameter determination in experimental analysis using a neural network. Phys. Rev. C 55-3 (1997) 1371-1375.
- [6]. Medhat M.E. Artificial intelligence methods applied for quantitative analysis natural radioactive sources. Ann. Nucl. Energy 45 (2012) 73–79.
- [7]. Akkoyun S., Bayram T., Kara S.O., Sinan A., An artificial neural network application on nuclear charge radii. J. Phys. G Nucl. Part. 40 (2013) 055106.
- [8]. Costiris N., Mavrommatis E., Gernoth K.A., Clark J.W., A global model of beta decay half-lives using neural networks. arXiv:nucl-th/0701096v1 (2007).
- [9]. Ferguson A.J. Angular correlation methods in gamma-ray spectroscopy. North- Holland Publishing Co., Amsterdam (1965).
- [10]. Yamazaki T. Tables of coefficients for angular distribution of gamma rays from aligned nuclei. Nuclear Data Section A (1967) 3-1.
- [11]. Mateosian E. der, and Sunyar A.W. Table of attenuation coefficients for angular distribution of gamma rays from partially aligned nuclei. Atomic Data and Nuclear Data Tables 13 (1974) 391.
- [12]. Ferentz M., and Rosenzweig N., Table of F coefficients. ANL-5324.
- [13]. Haykin S. Neural networks: A comprehensive foundation. Prentice-Hall Inc., Englewood Cliffs, NJ, USA (1999).
- [14]. Hornik K., Stinchcombe M., White H. Multilayer feedforward networks are universal approximator. Neural Networks 2 (1989) 359-366.
Details
| Primary Language | English |
|---|---|
| Journal Section | Natural Sciences |
| Authors | |
| Publication Date | December 24, 2018 |
| Submission Date | October 31, 2018 |
| Acceptance Date | December 9, 2018 |
| Published in Issue | Year 2018Volume: 39 Issue: 4 |