FARKLI TİPTE ÜRETİLEN HARÇLARIN YARI-DEĞER KALINLIKLARININ TEORİK OLARAK İNCELENMESİ

Bu çalışmada, farklı kimyasal bileşene sahip beton örneklerinde gama ışınlarının soğurulması için deneysel ve teorik yarı-değer kalınlıkları arasındaki uyumsuzluk kesirsel matematik kullanılarak giderilmeye çalışılmıştır. Soğurulmayı temsil eden birinci mertebeden diferansiyel denklem Caputo kesirsel türevi kullanılarak yeniden tanımlanmıştır. Bu denklemin çözümü Mittag-Leffler fonksiyonu terimleri cinsinden elde edilmiştir. Enerjileri sırasıyla 59,9 keV ve 661 keV olan 241Am ve 137Cs gama ışını kaynakları kullanarak elde edilen deneysel ve teorik lineer soğurma katsayıları kullanılarak kesirsel hesaplamalar yapılmıştır. Elde edilen sonuçlar standart matematik ile yapılan hesaplamalar ve deneysel sonuçlarla karşılaştırılmıştır. Hesaplanan kesirsel türev mertebelerinin gama ışınının soğurucu malzemeden geçerken şiddetindeki değişime nasıl bir etki yaptığı belirlenmeye çalışılmıştır.

Anahtar Kelimeler:

Soğurulma katsayısı, yarı-değer kalınlık, kesirsel matematik

THEORETICAL INVESTIGATION OF HALF-VALUE THICKNESS OF MORTARS PRODUCED BY DIFFERENT TYPES

In this study, inconsistency between experimental and theoretical half-value thickness for the absoption of gamma rays in concrete materials with different chemical properties has been removed with the help of fractional calculus. The first order differential equation related to the absorption has been re-defined by using Caputo fractional derivative. The solution of this equation has been obtained in terms of Mittag-Leffler function. The fractional calculations have been done using experimental and theoretical attenuation coefficients data obtained from gamma ray sources 241Am and 137Cs with 59.9 keV and 661 keV, respectively. The obtained results have beeen compared with the experimental and standard ones. How the calculated fractional derivative orders affect the intensity of the gamma ray as it passes through the absorbent material has been attempted to determine.

Keywords:

Attenuation coefficients, half-value thickness, fractional calculus,

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