اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدتجمع التقدير المطبق للطاقة المشتركة. أ. تحليل نظري
Convergence of the discrete dipole approximation. I. Theoretical analysis
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نقوم بتحليل التكامل النظري الشديد لتقريب الذرات المتجمعة (DDA). نثبت أن أخطاء في أي كمية مقياسة محددة محدودة بمجموعة من الأحداث الخطية والأحادية في حجم الذرة d، عندما يكون هذا الآخر في مجال تطبيق DDA. بالإضافة إلى ذلك، الحدث الخطي هو أصغر بكثير للأشكال المربعة من الأشكال غير المربعة. لذلك، للذرات الصغيرة تكون الأخطاء للأشكال المربعة أصغر بكثير من الأشكال غير المربعة. ينخفض أهمية الحدث الخطي مع زيادة الحجم، لذلك يكون التكامل لDDA للذرات كبيرة بما فيه الكفاية أحادي الحجم في النطاق الشائع. تم القيام بالعديد من المحاكاة الرقمية لمجموعة واسعة من d. وأخيرا نناقش عددا من التطورات الجديدة في DDA وتأثيرها على التكامل.
We performed a rigorous theoretical convergence analysis of the discrete dipole approximation (DDA). We prove that errors in any measured quantity are bounded by a sum of a linear and quadratic term in the size of a dipole d, when the latter is in the range of DDA applicability. Moreover, the linear term is significantly smaller for cubically than for non-cubically shaped scatterers. Therefore, for small d errors for cubically shaped particles are much smaller than for non-cubically shaped. The relative importance of the linear term decreases with increasing size, hence convergence of DDA for large enough scatterers is quadratic in the common range of d. Extensive numerical simulations were carried out for a wide range of d. Finally we discuss a number of new developments in DDA and their consequences for convergence.
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