Deconvolution of Mono-Energetic and Multi-Lines Gamma-Ray Spectra Obtained with NaI(Tl) Scintillation Detectors Using Direct Matrix Inversion Method

Performance of a NaI(Tl) scintillation detector based on the gamma-ray spectroscopy system is not satisfactory in retaining its original peak (which is delta like function) of various gamma ray spectrum. The method of achieving precise peak for the various gamma ray was conducted by converting the observed pulse-height distribution of the NaI(Tl) detector to a true photon spectrum. This method is obtained experimentally with the help of an inverse matrix deconvolution method. The method is based on response matrix generated by the Monte Carlo simulation based on Geant4 package of mono-energy gamma-ray photon ranging from 0.050 to 2.04 MeV in the interval of 10 keV. The comparison of the measured and simulated response function was also performed in order to authenticate the simulation response function. Good agreement was observed around the photo-peak region of the spectrum, but slight deviation was observed at low energy region especially below 0.2 MeV. The Compton backscattering and Compton continuum counts was significantly transferred into the corresponding photo-peak and consequently the peak to total(P/T) ratio was improved. The P/T ratio results obtained after application of the deconvolution method taken with three calibration sources with gamma-ray’s energies of 81 keV, 303 keV and 356 keV (for 133Ba), 662 keV (for 137Cs), 1173 keV and 1333keV (for 60Co), were improved from(to) 0.50(0.90), 0.40(0.83), 0.57(0.93), 0.31(0.92), 0.18(0.84) and 0.15(0.83), respectively.

Completion of Matrix Inversions Using Elementary Matrix Inverse Multiplication Method

Given a matrix A is ordo . Elementary matrix inverse multiplication produces inverse matrix A which is where I is an identity matrix and is an inverse matrix A. The problem discussed in this research is to find a solution the ordo of matrices by using inverse elementary matrix inversion method with the steps given in solving by completing the smallest ordo matrix first up until the ordo matrix . Keywords: Matrix, Inverse Matrix, Multiplication of Elementary Matrix.

A tool for designing digital filters for the Hankel and Fourier transforms in potential, diffusive, and wavefield modeling

The open-source code fdesign makes it possible to design digital linear filters for the Hankel and Fourier transforms used in potential, diffusive, and wavefield modeling. Digital filters can be derived for any electromagnetic (EM) method, such as methods in the diffusive limits (direct current, controlled-source EM [CSEM]) as well as methods using higher frequency content (ground-penetrating radar [GPR], acoustic and elastic wavefields). The direct matrix inversion method is used for the derivation of the filter values, and a brute-force minimization search is carried out over the defined spacing and shifting values of the filter basis. Included or user-provided theoretical transform pairs are used for the inversion. Alternatively, one can provide layered subsurface models that will be computed with a precise quadrature method using the EM modeler empymod to generate numerical transform pairs. The comparison of the presented 201 pt filter with previously presented filters indicates that it performs better for some standard CSEM cases. The derivation of a longer 2001 pt filter for a GPR example with a 250 MHz center frequency proves that the filter method works not only for diffusive EM fields but also for wave phenomena. The presented algorithm provides a tool to create problem specific digital filters. Such purpose-built filters can be made shorter and can speed up consecutive potential, diffusive, and wavefield inversions.

Mathematical Modeling of Photovoltaic Thermal-Thermoelectric (PVT-TE) Air Collector

Photovoltaic (PV) cell from solar energy is one of the most widely adopted renewable energy source and commercially available system that can be used in various applications. More appealing application of PV arrays used in thermoelectric (TE) device was it can convert solar thermal energy from temperature difference into electric energy to act as power generators. In this study, a theoretical model is developed by using conducting steady state energy analysis of a PVT-TE air collector. The matrix inversion method is used to obtain energy balance equation. The effect of various parameters also investigated. The mass flow rate of range 0.01 kg/s to 0.05 kg/s and solar intensity of 400 W/m2, 600 W/m2 and 800 W/m2 was used to obtain outlet temperature, To in the range about 28.9oC to 43.7oC and PV temperature, Tp about 35.3oC to 60oC.

Photovoltaic Thermal (PVT) System with and Without Fins Collector: Theoretical Approach

<span lang="EN-GB">The fins collector design for solar thermal has widely been used and it has a higher thermal efficiency than without Fins. Photovoltaic thermal (PV/T) system produced Electrical and thermal energy instantaneously. Mathematical modeling based on steady-state thermal analysis of PV/T system with and without fins was conducted with matrix inversion method. The value results show that the PV/T system with fins collector is higher thermal and electrical efficiency than without fins.</span>