Accurate Calculation Model Research Articles

A universal model for accurate calculation of electromagnetic transients on overhead lines and underground cables

This paper presents a transmission line model for the simulation of electromagnetic transients in power systems. The model can be applied to both overhead lines and cables, even in the presence of a strongly frequency dependent transformation matrix and widely different modal time delays. This has been achieved through a phase domain formulation where the modal characteristics have been utilized in the approximation for the propagation matrix. High computational efficiency is achieved by grouping modes with nearly equal velocities and by columnwise realization of the matrices for propagation and characteristic admittance.

A pencil-beam photon dose algorithm for stereotactic radiosurgery using a miniature multileaf collimator.

A computer-controlled miniature multileaf collimator (MMLC) with 4 mm leaf width and a maximum field size of 6 cm X 6 cm has been designed as a tertiary beam-shaping device for linac-based stereotactic radiosurgery. The purpose of this study is to develop an accurate and efficient dose calculation model for use with the MMLC. A pencil-beam based algorithm using a sum of three Gaussian kernels was developed to model the off-axis ratio of MMLC fields. Because the kernel integration over a rectangular field can be solved in closed form, dose to any point from an arbitrary MMLC field can be calculated efficiently by summing dose contribution from a set of rectangular apertures and transmission blocks that model individual leaf openings or leaf transmissions. The model uses an effective rectangular field and equivalent square method for determination of depth dose and dose output. Results showed that the calculated percentage depth dose was within 1% and output factor was within 1.5% of measured data. The parameters of the pencil beam kernels were extracted by fitting measured off-axis profiles for a few field sizes at a few depths. The accuracy of the calculated off-axis ratio was tested by comparison with measured data for a number of MMLC fields. The algorithm was shown to be accurate to within 1.5% or 1 mm for off-axis ratios. The algorithm computes at a speed of 34,600 data points per second on a DEC Alpha server model 2000/433 (Digital Equipment Corp., Maynard, MA), which is about 15 times faster than a Clarkson-type summation method.

Optimized Dose Distribution of a High Dose Rate Vaginal Cylinder

Purpose: To present a comparison of optimized dose distributions for a set of high-dose-rate (HDR) vaginal cylinders calculated by a commercial treatment-planning system with benchmark calculations using Monte-Carlo–calculated dosimetry data. Methods and Materials: Optimized dose distributions using both an isotropic and an anisotropic dose calculation model were obtained for a set of HDR vaginal cylinders. Mathematical optimization techniques available in the computer treatment-planning system were used to calculate dwell times and positions. These dose distributions were compared with benchmark calculations with TG43 formalism and using Monte-Carlo–calculated data. The same dwell times and positions were used for a quantitative comparison of dose calculated with three dose models. Results: The isotropic dose calculation model can result in discrepancies as high as 50%. The anisotropic dose calculation model compared better with benchmark calculations. The differences were more significant at the apex of the vaginal cylinder, which is typically used as the prescription point. Conclusion: Dose calculation models available in a computer treatment-planning system must be evaluated carefully to ensure their correct application. It should also be noted that when optimized dose distribution at a distance from the cylinder surface is calculated using an accurate dose calculation model, the vaginal mucosa dose becomes significantly higher, and therefore should be carefully monitored.

The calculation of signal stable ranges in combinational circuits

The estimation of signal stable ranges in a combinational circuit is an important issue for determining clock time in a synchronous system. An optimal clocking period time highly depends on the accuracy of the shortest path length as well as the longest path length in a combinational circuit. In this paper, a sensitization criterion for the short path is first proposed. Based on this sensitization criterion, an accurate model for calculation of signal stable range can be created. This will allow the output stable range of a gate to be the union of its inputs when the input leads hold a controlling value, rather than to be always the intersection. Then, an LS-algorithm for calculation of signal stable ranges is presented in which both the sensitizable shortest path and the sensitizable longest path are considered. It avoids the exhaustive search by tracing the path sensitization and eliminates some conservative restriction to get more accurate results in a more efficient way, compared to the previous approaches. The speedup and the improved accuracy of the proposed LS-algorithm showed promising experimental results. >

Novel model for accurate calculation of hardenability and continuous cooling transformation

The development of an accurate, yet simple, transformation and hardenability model for general use in the heat treatment and steelmaking industries is described. An empirical approach is used, based on both continuous cooling transformation (CCT ) diagrams and hardenability literature. For this purpose, an equation is developed relating hardenability and the critical time requiredfor transformation during continuous cooling. Existing hardenability models and CCT diagrams are analysed to determine a correct mathematical structure for the hardenability multiplication factor equation. The multiplication factor for a fixed weight percentage of an alloying element X isfound to be strongly dependent on carbon content (in wt– %) according to the equation ℳ=(K%Cn)X, where K and n are constantsfor a specific alloying element. Best values of K and nfor the various alloying elements are determined. Very strong interactions (high values of |n) between the carbide forming elements and carbon are reported. The multiplication factors for the carbide forming elements increase exponentially with carbon content. The accuracy of the model proposed is compared with that of existing models, in which a constant carbon effect on ℳ had been assumed, for a wide range of both low and medium carbon steels, and it is shown that significant improvements in accuracy are obtained using the new model. This is attributed to the use of the improved harden ability multiplication factor equation, which reflects the variable influence of carbon content.MST/992

Novel model for accurate calculation of hardenability and continuous cooling transformation

The development of an accurate, yet simple, transformation and hardenability model for general use in the heat treatment and steelmaking industries is described. An empirical approach is used, based on both continuous cooling transformation (CCT ) diagrams and hardenability literature. For this purpose, an equation is developed relating hardenability and the critical time requiredfor transformation during continuous cooling. Existing hardenability models and CCT diagrams are analysed to determine a correct mathematical structure for the hardenability multiplication factor equation. The multiplication factor for a fixed weight percentage of an alloying element X isfound to be strongly dependent on carbon content (in wt– %) according to the equation ℳ=(K%Cn)X, where K and n are constantsfor a specific alloying element. Best values of K and nfor the various alloying elements are determined. Very strong interactions (high values of |n) between the carbide forming elements and carbon are reported. The multiplication factors for the carbide forming elements increase exponentially with carbon content. The accuracy of the model proposed is compared with that of existing models, in which a constant carbon effect on ℳ had been assumed, for a wide range of both low and medium carbon steels, and it is shown that significant improvements in accuracy are obtained using the new model. This is attributed to the use of the improved harden ability multiplication factor equation, which reflects the variable influence of carbon content.MST/992

Simple model for accurate calculation of Coulomb-barrier penetration factors in molecular fusion rates.

We have developed a simple model that yields an approximate analytical expression for the Coulomb-barrier penetration factor in terms of the reduced mass M of the nucleon pair, the mass m of the particle that binds together the nuclei, the inner turning point ${\mathit{r}}_{\mathit{i}}$ for the state under consideration, and the variation in the electronic or muonic contribution ${\mathit{E}}_{\mathit{e}}$(r) to the total energy between r=0 and ${\mathit{r}}_{\mathit{i}}$. In the case of muon-catalyzed d+t\ensuremath{\rightarrow}\ensuremath{\alpha}+n fusion, our model yields fusion rates within 25% of those obtained from much more elaborate calculations. The remarkable accuracy of our simple model results from the fact that it is highly accurate for small r, the region that we demonstrate makes the predominant contribution to Coulomb-barrier penetration factors. Furthermore, we use this observation to explain the old puzzle of why the adiabatic approximation yields such accurate fusion rates.