The reflected slab and sphere criticality problem with anisotropic scattering in one-speed neutron transport theory

Lineer-Kuadratik Anizotropik Saçılma için Kritiklik Probleminde Yansıtıcı Özdeğerleri

“…Kritiklik probleminde amaç, ikincil nötron sayısı ile reaktörün kalınlığı arasında matematiksel bir bağıntı elde etmektir. Problem birçok araştırmacının üzerinde çalıştığı sayısal çözümleme açısından zor bir problemdir [22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38].…”

The influence of linear anisotropic scattering of one-speed neutrons on the critical size of a slab with reflective boundary conditions

“…More over, the re sults ob tained from the pres ent method are tab ulated in the ta bles to gether with the re sults ob tained from the tra di tional P N method and the ones from lit era tures for com par i son. While the ex act re sults presented in lit er a ture are quoted from Lee-Dias and Aranson [15,16], the other re sults are from the study of Atalay [10].…”

“…In this ta ble, the re sults ob tained by the pres ent method, as well as the re sults ob tained for the iso tro pic scat ter ing quoted from refs. [15,16], by Case's sin gu lar eigenfunction method quoted from Atalay [10] and by the tra di tional P N method, are given. There fore, a com pre hen sive com par i son can be done be tween the re sults ob tained from the pres ent T N method and the re sults that al ready ex ist in lit er a ture.…”

“…The nu mer i cal re sults for the crit i cal thick ness of the slab are given in the ta bles to gether with the re sults ob tained by the con ven tional P N method, and the ones ob tained by Atalay us ing Case's sin gu lar eigenfunctions method [10]. It can eas ily be seen from the der i va tions of the equa tions and the re sults in the ta bles that this method has prac ti cal ex e cut able equa tions with its rapid con vergence.…”

U[sub N] Method For The Critical Slab Problem In One-Speed Neutron Transport Theory

“…In transport theory, criticality problems in different geometries with different scattering kernels have been studied by polynomial expansion based techniques [7][8][9][10][11]. Among these methods, although the Legendre polynomials expansion is the most commonly used method, it is not the unique one valid for all cases.…”