Sujit K. Ray

Clinical use of a concomitant boost technique using a gypsum compensator

PURPOSE To develop a clinical procedure to treat field within a field (concomitant boost) portals with a single compensated field. METHODS AND MATERIALS An ordinary manual cerrobend block former was used to produce styrofoam molds from simulator film data. A special gypsum compound was poured into the molds. The compensator block is independently mounted to the treatment machine via a custom-made compensator holder. RESULTS Measurements confirm that the inhomogeneous dose distribution has been reliably delivered via this technique. The accuracy of placement of the high dose region is sufficient for clinical use. CONCLUSION The procedure enables the concomitant boost effect to be easily implemented in the clinic without increasing clinical setup time.

Determination of differential scatter-air ratios (dSAR) for three-dimensional scatter integration.

Scatter dose may be calculated by summing the scatter contribution from individual volume elements. These contributions may be represented by differential scatter-air ratios (dSAR). Determination of dSAR from measured data is only approximately correct for second and higher orders of scatter and yields values often limited to one significant figure. Monte Carlo calculation, on the other hand, is time intensive, requires some knowledge of the beams x-ray spectrum, and mastering the complexities of a program such as EGS4. Total scatter dose at a point may be determined by measuring depth dose or tissue-air ratios and partitioning the dose into its primary and scatter components. Scatter may be represented by scatter-air ratios, which can be characterized by the sum of first, second, and higher orders of scatter. The first scatter dose may be computed exactly by summing the first scatter contribution from individual elements, determined from the first principle. Separation of dSAR into primary attenuation and depth-independent terms allows the latter to be precomputed once for a given energy and stored in tabular form. Second scatter may be treated in a similar manner. The higher orders of scatter are computed by subtracting the sum of calculated first and second scatter doses from the total scatter dose. Elements close to and approximately 1 cm above the point of calculation contribute most heavily to the first scatter dose. Compared to the first scatter dose, the second scatter dose contribution is lower, particularly for elements close to the point of calculation.(ABSTRACT TRUNCATED AT 250 WORDS)

A numerical simulation to verify the stress-free growth of silicon crystal ribbon

Abstract Thermal stresses developed during the growth of silicon crystal ribbon have been shown to be negligible, thus eliminating residual stresses and dislocations, if the temperature profile satisfies a second-order partial differential equation inside the ribbon. This has been numerically verified through a finite element model, an outline of which is presented here. This model shows that, for homogeneous isotropic material with temperature independent thermal expansion co-efficients, thermal stresses will vanish if the temperature profile satisfies the Laplacian. A comparison of stresses due to uniform and non-uniform temperature gradients in the plane of the ribbon is also presented. The strategies employed to control the round-off error and to validate the computer model are discussed.

On control of stresses in silicon web growth

It has been observed that the residual stresses and dislocations during the silicon crystal growth for photovoltaic applications are caused by thermal stresses. The temperatures along the boundaries of the silicon crystal ribbon are prescribed to meet the requirements of the crystal growth. It is shown that by allowing the temperatures to satisfy a second-order partial differential equation in the ribbon, all thermal stresses, and others induced by them, may be eliminated for the stress-free growth of the silicon crystal.

Effects of viscosity on the continuous growth of dendritic silicon crystal ribbon

Abstract This paper investigates the effects of viscosity on the thermal stresses developed in a silicon ribbon during its continuous growth. Kelvin models are used to study the viscous behavior of silicon. A specialization of the general three dimensional model for the plane stress conditions is presented. Results of the numerical studies, based on the assumed constants of the Kelvin models, indicate that the viscosity of silicon reduces peak elastic thermal stresses and does notcause any residual stress in the ribbon. The instability of the numerical solution process is also studied and various alternatives are proposed to avoid divergence of the numerical solution.

Computer program for the design of laterally unsupported angle beams

Abstract Based on the theory developed by Leigh, Thomas and Lay, a FORTRAN77 computer program for the design of laterally unsupported steel angle beams is developed. The program can be used for any span length and superimposed load. All available angle sections may be built into the database of the program. For a given set of input data, the program prints out a complete list of available sections that are safe against the bending and shear stresses. To make the program more useful, the deflection due to the superimposed load is also calculated and the sections are checked against the allowable deflections. For the convenience of the users, the input to this program is in the form of DATA statements and, therefore, is free from formats. The computer program has been tested extensively and a good correlation with the published work has been obtained.

Generalization of rectangular element stiffness matrix and thermal load vector associated with a0 + a1x + a2y + a3xy type interpolation rule

Abstract Explicit expressions for the element stiffness matrix K and element load vector p for the rectangular plane-stress and plane-strain finite elements associated with Ψ ( x , y ) = a 0 + a 1 x + a 2 y + a 3 xy type interpolation rule are given for the general anisotropic material in xy -planc subjected to non-uniform temperature increases. The expressions are optimized with respect to the numerical operations required for the computation of K and p , and they are valid for special cases of material properties and thermal loading.

An algorithm for the simulation of continuous growth of dendritic silicon crystal ribbon and its finite element implementation

Abstract A displacement-based algorithm for the simulation of continuous growth of dendritic silicon crystal ribbon is described. The discretization in the time domain has been directly linked to the finite element mesh. At every time step, a predetermined number of elements have been grown at the interface and moved in to the finite element mesh while an equal number of elements are moved out of the mesh at the other end. This growth algorithm can be used for studying viscous and elasto-plastic behaviors of the material. The flowcharts for a finite element implementation of this algorithm are also presented.