T-matrix, codes

From Table 1, we draw two important conclusions. First, these data support the above hypothesis (3.24). Second, the scattered intensity is more sensitive to cluster orientations than extinction is [50]. Therefore, one has to use a large ensemble of monodisperse clusters to eliminate fluctuations in the scattered intensity. The first conclusion leads to great simplifications, as we can use effective and fast GMM codes [66] for a cluster with a fixed orientation instead of T-matrix codes that require large RAM and CPU-time. 

The T-matrix codes developed by Mishchenko and Travis [167] and Mishchenko et al. [168,169] are efficient mmierical tools for computing electromagnetic scattering by homogeneous, axisjmimetric particles with size... 

A. Moroz, Improvement of Mishchenko s T-matrix code for absorbing particles, Appl. Opt. 44, 3604 (2005)... 

Mackowski DW, Mishchenko MI A multiple sphere T-matrix Fortran code for use on parallel computer clusters, Quant Spectrosc Radiat Transf 112(13) 2182—2192, 2011. 

Quantity xa t) of various products produced by N manufacturers in period t is coded below. We use A to present a coding matrix row vector ... 

Inventory quantities of various products of N manufacmrer located in the computational layer at period t are coded as follows. represents the row vector of the coding matrix ... 

Symmetry properties of the transition matrix can be derived for specific particle shapes. These symmetry relations can be used to test numerical codes as well as to simplify many equations of the T-matrix method and develop efEcient numerical procedures. In fact, the computer time for the numerical evaluation of the surface integrals (which is the most time consuming part of the T-matrix calculation) can be substantially reduced. The surface integrals are usually computed in spherical coordinates and for a surface defined by... 

Essentially, the code performs a convergence test and computes the T-matrix and the scattering characteristics of particles with uniform orientation distribution functions. 

The main drawback of the code is that the computer time requirements might by higher in comparison to other more optimized T-matrix programs. Our intention was to cover a large class of electromagnetic scattering problem and therefore we sacrifice the speed in favor of the flexibihty and code modularization. The code shares several modules which are of general use and are not devoted to a specific application. 

The Fortran code SCSMTM for computing the T-matrix of a sphere cluster and the orientation-averaged scattering matrix and optical cross-... 

TAXSYM routine and the program developed by Bohren [16]. This program was coded by Ute Comberg and is available from www.T-matrix.de. The scattering characteristics are computed in the azimuthal plane y> = 0° and for two polarizations of the incident wave. 

As I note in my hoo i A Passion for Mathematics, Ramanujan was a prophet who plucked mathematical ideas from another world. They came to him in a flash. He could read the codes in the mathematical matrix in the same way thatNeo, the lead character in the movie The Matrix, could access mathematical symbols cascading about him that formed the infrastructure of his perceived reality. I don t know if God is a cryptographer, but codes are all around us waiting to be deciphered. Some may take a thousand years to understand. Some may always be shrouded in mystery. 

The expression is easily coded, since T<0>, Eq. 41, and the r 1 are known. It simplifies for substitution on a principal plane or axis and for symmetrically equivalent multiple substitution, because several of the elements of the matrix T will then vanish. It is clear from Eq. 45 that the derivatives are nonvanishing only for those atoms a that have actually been substitued in the particular isotopomer s. Therefore, the Jacobian matrix X generated from these derivatives is, in general, a sparse matrix. 

A major goal of the human genome project is to determine the order of occurrence of the four bases, adenine (A), cytosine (C), guanine (G), and thymine (T), in DNA molecules. The sequence defines an individual s genetic code. The need for sequencing DNA has spawned the development of several new analytical instruments. Among the most attractive of these approaches is capillary array electrophoresis. In this technique, as many as 96 capillaries are operated in parallel. The capillaries are filled with a separation matrix, normally a linear polyacrylamide gel. The capillaries have inner diameters of 35 to 75 p,m and are 30 to 60 cm in length. 

---