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Register a new userConvergence of the discrete dipole approximation. I. Theoretical analysis
تجمع التقدير المطبق للطاقة المشتركة. أ. تحليل نظري
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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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We propose an extrapolation technique that allows accuracy improvement of the discrete dipole approximation computations. The performance of this technique was studied empirically based on extensive simulations for 5 test cases using many different d
iscretizations. The quality of the extrapolation improves with refining discretization reaching extraordinary performance especially for cubically shaped particles. A two order of magnitude decrease of error was demonstrated. We also propose estimates of the extrapolation error, which were proven to be reliable. Finally we propose a simple method to directly separate shape and discretization errors and illustrated this for one test case.
We present a review of the discrete dipole approximation (DDA), which is a general method to simulate light scattering by arbitrarily shaped particles. We put the method in historical context and discuss recent developments, taking the viewpoint of a
general framework based on the integral equations for the electric field. We review both the theory of the DDA and its numerical aspects, the latter being of critical importance for any practical application of the method. Finally, the position of the DDA among other methods of light scattering simulation is shown and possible future developments are discussed.
We present a method of incorporating the discrete dipole approximation (DDA) method with the point matching method to formulate the T-matrix for modeling arbitrarily shaped micro-sized objects. The emph{T}-matrix elements are calculated using point matching between fields calculated using vector spherical wave functions and DDA. When applied to microrotors, their discrete rotational and mirror symmetries can be exploited to reduce memory usage and calculation time by orders of magnitude; a number of optimization methods can be employed based on the knowledge of the relationship between the azimuthal mode and phase at each discrete rotational point, and mode redundancy from Floquets theorem. A reduced-mode T-matrix can also be calculated if the illumination conditions are known.
In this manuscript we investigate the capabilities of the Discrete Dipole Approximation (DDA) to simulate scattering from particles that are much larger than the wavelength of the incident light, and describe an optimized publicly available DDA compu
ter program that processes the large number of dipoles required for such simulations. Numerical simulations of light scattering by spheres with size parameters x up to 160 and 40 for refractive index m=1.05 and 2 respectively are presented and compared with exact results of the Mie theory. Errors of both integral and angle-resolved scattering quantities generally increase with m and show no systematic dependence on x. Computational times increase steeply with both x and m, reaching values of more than 2 weeks on a cluster of 64 processors. The main distinctive feature of the computer program is the ability to parallelize a single DDA simulation over a cluster of computers, which allows it to simulate light scattering by very large particles, like the ones that are considered in this manuscript. Current limitations and possible ways for improvement are discussed.
Elastic light scattering by mature red blood cells (RBCs) was theoretically and experimentally analyzed with the discrete dipole approximation (DDA) and the scanning flow cytometry (SFC), respectively. SFC permits measurement of angular dependence of light-scattering intensity (indicatrix) of single particles. A mature RBC is modeled as a biconcave disk in DDA simulations of light scattering. We have studied the effect of RBC orientation related to the direction of the incident light upon the indicatrix. Numerical calculations of indicatrices for several aspect ratios and volumes of RBC have been carried out. Comparison of the simulated indicatrices and indicatrices measured by SFC showed good agreement, validating the biconcave disk model for a mature RBC. We simulated the light-scattering output signals from the SFC with the DDA for RBCs modeled as a disk-sphere and as an oblate spheroid. The biconcave disk, the disk-sphere, and the oblate spheroid models have been compared for two orientations, i.e. face-on and rim-on incidence. Only the oblate spheroid model for rim-on incidence gives results similar to the rigorous biconcave disk model.
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