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

Yıl 2018, Cilt: 6 Sayı: 1, 36 - 44, 21.04.2018

Abdullah Engin Çalık , Hüseyin Şirin

https://doi.org/10.20290/aubtdb.346219

Cited By: 2

Öz

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.

Anahtar Kelimeler

Attenuation coefficients, half-value thickness, fractional calculus

FARKLI TİPTE ÜRETİLEN HARÇLARIN YARI-DEĞER KALINLIKLARININ TEORİK OLARAK İNCELENMESİ

Öz

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

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