Monte Carlo Simulation of Transmission Experiement

Monte Carlo Simulation of Transmission Experiement Fluid Densitometer Design based on Transmission and Scattering Gamma Ray Method using Monte Carlo Approach R.Wirawan, M. Djamal, A.Waris, G. Handayani,  H.J. Kim Abstract. Non-destructive testing is one method in the material testing that was applied and developed for many purposes in the industrial field. Gamma spectrometer is a one method that can be applied for the fluid densitometer. It was studied the potential of the use of transmission and scattering gamma ray measurements in order to evaluate the fluid density using GEANT4 Monte Carlo simulation toolkit. Keywords: Non-destructive testing, scattering gamma, Monte Carlo, GEANT4. PACS: 29.40.-n Introduction Gamma-ray spectrum measurement is one of promising developing method in the non-destructive test application especially for an online measurement. It’s applicable for many industrial applications such as in medical, mining and oil industry, homeland security. The quality of the material can be differentiating from another one based on its density. In the application of gamma spectrometry, it’s influence the gamma ray energies spectrum detection result. Ball et al. (1998) have investigated the response of gamma backscatter to the spatial density in bulk sample [1]. In the fluid product analysis especially for the oil product density measurement, it’s a promising method for a densitometer. Hussein (2011) has developed investigation of the fluid flow in the pipe using gamma spectrometry [2]. Khorsandi and Feghhi have analyzed the transmission mode in densitometer application for the petroleum products monitoring applications [3]. The combination of transmission and scattering measurement modes are good approaching for a better analysis method in the detector response measurement due to the fluid density inside the pipe. For this purpose, simulation using Monte Carlo method can be conducted. Monte Carlo methods have capabilities in the implementation of the several of physics models and give the predicting result in the radiation physics application [4, 5]. In the present study we investigated the potential of the combination of these measurements using the Monte Carlo radiation transport from GEANT4 simulation toolkit. Theory Gamma ray energy spectrum characteristic that detected from its interaction with the material have information to identify the material characteristics involved. In the gamma ray spectrum measurement, there are two kinds of measurement type i.e. transmission and scattering. In the transmission, the gamma ray beams have an attenuated intensity because of energy absorption by material. The mass attenuation coefficient à ¯Ã‚ Ã‚ ­ of photon is a function of photon energy. The attenuated intensity was described by the Beer–Lambert formula: (1) where I0 incident gamma rays intensities, x is material absorption thickness, is mass absorption coeficient and its proportional to the total cross-section as follows , NA is the Avogadro’s number (6.021023 atom/mole) and A is atomic mass number of material[8]. For the scattering measurement, the detected photon beam is the result of deflecting with an electrons material. Scattering interactions that may occur is the single scattering or multiple scattering.The photon beam intensity has attenuation in the path before the scattering point interaction and in the path to the detector after the scattering point interaction. Figure 1 shows the single scattering interaction of photon with an element volume dV. Figure 1 Schematic diagram of photon single scattering interaction with an element volume in the material (adopted from Devlin and Taylor) [9]. According to the Compton scattering interaction, the photon with an energy Eà ¯Ã‚ Ã‚ § will be deflected with scattering angles à ¯Ã‚ Ã‚ ± to the origin direction after collision with an atomic electron. The scattered photon energy (EScatt) is expressed by the formula: (2) The intensity of detected gamma photon are influence of attenuation along primary photon, number of electron in element volume, differential cross-section, attenuation of scattered photon path and the solid angle subtended by detector at the element volume. For the single scattering interaction, the intensity of detected photon as depicted in the formula: (3) where S is the source activity (photon s-1), dV is element volume interaction, n is the electron density of the material, r1 and r2 are the length path of the primary photon before interaction and after scattering respectively. The density à ¯Ã‚ Ã‚ ² of the material is related to the electron density by (4) where NA is the Avogadro number, Z is the atomic number and M is the atomic mass. For the Compton interaction probabilities of the photon beam when it interact with an electron of the material was describe in differential form by Klein-Nishina formula, (5) where r0 is clasical electron radius (2,82 fm) and P parameter as function of incident photon energy and scattering angles à ¯Ã‚ Ã‚ ± as the formula (6) where constant [1,8]. Using the equation (4) and (5) to substitute parameter n and in the equation (3), we have the relation of intensity with the material density: (7) Solution of the equation (7) can be expressed in the simple form: (8) where A and B are constant. Method The simulation setup was developed based on the transmission configuration which conducted experimentally done by Khorsandi [3]. Four detectors are placed in two type positions where two detectors in the same side with source and two others in the opposite site as shown in Figure 2. The spatial distance between two detector d10 and d30 from the collimated source axis are about axis 27.5cm. For detector d20 is placed 20 cm far away from detector d10. Polyethylene pipe have an inner radius 5cm and thickness it’s about 2mm. Fluids under investigation inside the pipe (i.e. gasoline, gasoil and water) are assumed to be of uniform densityà ¯Ã‚ Ã‚ ². A disk gamma ray source model is used for Cs-137 source is collimated by the cylinder shielding lead with 5cm thickness. The 3in. x 3in. NaI(Tl) detector model reconstruction in the simulation is adopted from references [6, 7]. Simulation based on GEANT4 Penelope Monte Carlo using 5.0 x 107 of the gamma source beamon. Figure 2 Schematic visualization of GEANT4 simulation for the transmission and scattering measurements setup. Result and Discussion To examine the response function of transmission and scattering measurement, firstly we need to consider the setup designed for the detector construction according to the c gamma source energy spectrum. The Cesium 137 source was placed in front of the Pb collimated NaI(Tl) 3 in. x 3 in. scintillation detector. Figure 3 shows the detector response function spectrum of GEANT4 simulation result comparing to the measurement result of the 15uCi gamma source. There are a good agreement for photopeak energy between the simulation result and the experiment result. Figure 3 Response function of Cs137 15uCi gamma source for 3 in. x 3 in NaI(Tl) detector. Based on detector construction setup, then we analyzes the detector response function of transmission and scattering measurement. Figure 4 shows the response function result of detector that placed in the four different positions for three different type of density fluid i.e. gasoline, gasoil and water. Figure 4 Response function of detector NaI(Tl) 3in. x 3in. from GEANT4 simulation of four different detector positions for gasoline, gasoil and water fluids in pipe. In the all energy spectrum distribution above, density of fluid matter give an effect to the gamma energies spectrum. The gasoline has a lower density number, but it shows a higher intensity (number of events) of gamma ray energy detected compare to the gasoil and water. The increased density of fluid will increased the number of electrons at the scattering point interaction, attenuation of primary and scattered photons. So, it’s give an effect to the decreasing intensity or peak energy spectrum that detected by the detector. For transmission mode as shown at d0 detector position, the main peak of Cesium 137 gamma source is in the 0.662 MeV. The normalize peak intensity shows that the GEANT4 simulations result have a good agreement to the Khorsandi (2011) experiment result as shown in Figure 5. This result shows that the model can be used for predicting the fluid densitometer experiment. Figure 5 Normalize intensity curve of transmission mode (d0 detector position) from simulation and experiment results. Here in the Figure 6(a), we have the same trends that the decreasing of the photopeak height due to the fluids density increase. Figure 6 Gaussian height curves of photopeak at four different detector positions. Based on the intensity as density function equation (8), the proposed constant A and B for the curve fit in the Figure 6(a) are depicted in Table 1. Table 1. Curve fitting constant Based on the B constant of the four normalize count rates curves, d20 detector position have a higher decreasing slope than the others. In other side, the number of entry photon to the detector d20 position is too small, so for this configuration its need the higher activity source. Conclusions In this study, a Monte Carlo simulation of transmission and scattering measurements of gamma ray for the fluid densitometer was carried out using GEANT4. Due to an increase in the fluid density in the pipe, the peak heights of detected gamma ray intensity have decreased. The simulations for the gamma ray transmission investigation were conducted according to the experiment setup give the best fit curve result. Acknowledgments The author acknowledges the financial support of Directorate General of Indonesian Higher Education through the Sandwich-Like (PKPI) Program 2013. Refference [1] A.J. Ball, C.J. Solomon, J.C. Zarnecki, The response of gamma backscatter density gauges to spatial inhomogeneity An extension of the single scattering model, Nuclear Instruments and Methods in Physics Research B 140 (1998) 449-462. [2] Nagy M. Hussein, Investigation of Fluid Flow using Gamma Spectroscopy, World Academy of Science, Engineering and Technology 80 2011 1169-1174. [3] M. Khorsandi, S.A.H. Feghhi, Design and reconstruction of a prototype gamma-ray densitometer for petroleum products monitoring applications, Measurement 44 (2011) 1512-1515. [4] U.A. Tarim, E.N. Ozmutlu, O. Gurler, S. Yalcin, The Effect of the Housing Material on NaI(Tl) detector response function, J. Radioanalytical and Nucl. Chem. DOI 10.1007/s10967-012-1716-z (2012) 1-5. [5] A.F. Bielajew, Fundamentals of the Monte Carlo method for neutral and charged particle transport, Department of Nuclear Engineering and Radiological Sciences, The University of Michigan, 2001, pp.1-10. [6] Hu-Xia Shi, Bo-Xian Chen, Ti-Zhu Li, Di Yun: Precise Monte Carlo simulation of gamma-ray response functions for an NaI(Tl) detector, Applied Radiation and Isotopes 57 (2002) 517–524. [7] Abd-Elzaher, M., Badawi, M. S, El-Khatib, A. and Thabet, A. A.: Determination of Full Energy Peak Efficiency of NaI(Tl) Detector Depending on Efficiency Transfer Principle for Conversion From Experimental Values, World Journal of Nuclear Science and Technology, (2012), pp. 65-72. [8] Knoll, G.F., Radiation Detection and Measurement (Second Edition), Wiley and Sons, New York, 1989. [9] G. Devlin, D. Taylor: The Spatial Response Pattern of Gamma Backscatter Density Gauges, Journal of Soil Sciences Vol. 21 No. 2 (1970), pp. 297-303.

Law of Diminishing Marginal Utility Essay

In economics, utility is a measure of personal satisfaction or level of meeting a need that a good or service meets. For example the initial cup of coffee in the morning meets a large need and provides a large amount of satisfaction (utility). Another example is go under water and hold your breath, keep holding it until you think you will pass out. Then come up out of the water, that first breath is wonderful — tremendous utility. That is utility – the meeting of a need or being satisfied. Now Marginal Utility is the change in utility from one more good or service being consumed. So the amount of utility from the first cup of coffee or that first breath is huge. Diminishing Marginal Utility is the fact that each addition good or service consumed, creates a smaller and smaller amount of additional utility. In the examples above, that second cup of coffee in the morning or the second breath after the first will provide additional satisfaction or need meeting, but it will not provide near as much satisfaction (utility) as the first one did. The third cup or third breath has even less additional satisfaction or need meeting ability (utility) as the second and the first. Some products or services may have some increasing marginal utility at first, but every good or service at some point provides decreasing additional utility (or diminishing marginal utility). When the total utility curve stops increasing at an increasing rate and starts increasing at a decreasing rate, that is the point where the marginal utility curve reaches its max and starts decreasing — this is the point of diminshing marginal utility. Let me give you another example, if you had no shoes and someone gave you only one shoe, you would receive some utility. You can now hop through the sticker patch. But a second shoe that completes the pair might actually give you more utility than the first shoe, because you are clumsy and you keep falling down with only one shoe. But with two shoes, you can run and hop and not worry about stickers and stones. So the second shoe actually has increasing marginal utility. Now going on, a second pair of shoes doesn’t add as much utility as the first pair; though it is still better to have two pair of shoes than just one. So total utility has increased with the second pair of shoes, but marginal utility has diminished with the additional shoes.

Samples Legalizing Marijuana Essay - the Story

Samples Legalizing Marijuana Essay - the Story Details of Samples Legalizing Marijuana Essay The list of methods marijuana can make money is all but endless! Most weed arrests are minor offenses and do not demand prison time but should you get busted for a few grams or perhaps a joint here and there you can obtain a hefty record begin to pile up. More people will have the ability to use marijuana for medical purposes more freely without needing to hide it all of the time. There are several different ways marijuana can be ingested to reap the advantages of everything it has to offer you. Thus, the paper outlines the probable pros and cons linked with legalization of gambling. At our essay assistance, essays are always delivered in a brief moment. Still, opinions on the topic of legalization differ greatly and the amazing debate continues to rage. 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Marijuana for a drug shouldn't be legalized, although the benefits of legalizing it and taxing it are more than the expenses of attempting to keep it illegal. Marijuana legalization might even be a potent weapon in the struggle against the opioid crisis. Marijuana is thought to be considered a gateway drug to use different drugs. Marijuana is among the most frequently abused drugs in the United States of america and legalizing Marijuana has been a continuing controversial debate for decades. There are risks connected with legalizing marijuana. Marijuana is apparently somewhat illegal still but substances like tobacco and alcohol are completely legal to get, at a particular age that is. What to Expect From Samples Legalizing Marijuana Essay? Marijuana may also be put to use as a pain reliever, as its usage recues the degree of pain however high it is. Aside from relieving pain, marijuana has a number of other medical usages. As a result of adverse negative effects which marijuana has on the body, its usage for the medicinal goal is simply accepted if it's delivered by an experienced health practitioner. Legalizing marijuana is not going to make our problems disappear it is only going to create new ones. Getting in a position to more fully understand the medicinal advantages of marijuana could result in a decrease of using other, more addictive, narcotics for pain reduction, like opioids. The adolescent length of the brain has doubled. There might be a lot of pros as to why it ought to be legalized but in addition, there are cons as to why it shouldn't. The Start of Samples Legalizing Marijuana Essay You'll receive your high quality plagiarism-free paper based on your deadline! My purpose is to help you with your studies at no charge. Despite Marijuana legalized on a state level it's still hard to track revenue that ought to be taxed. It's apparent that marijuana is a powerful revenue stream that might help fund critical government programs at all levels. What You Should Do to Find Out About Samples Legalizing Marijuana Essay Before You're Left Behind Marijuana's prohibition has resulted in the presence of black markets where it's sold at a reduce price without prescription, and it has given criminals the monopoly on the lucrative marijuana trade. To summarize, marijuana shouldn't be legalized. In the Indian context, marijuana is largely considered as being of recreational usage, but it's not simply that. Determining whether legalizing marijuana is wise or not is a challenging call at best, with pros and cons on either side.

John Maynard Keynes Absolute Income Hypothesis - 1481 Words

The basis behind much of macroeconomic consumption theory rests with John-Maynard Keynes’ Absolute Income Hypothesis, described in The General Theory of Employment, Interest and Money (1936). His findings lead to the conclusion that aggregate consumption is highly dependent upon disposable income; but also, as total income increased, the proportions of savings would increase, meaning one’s marginal propensity to consume (MPC) would decrease. Leading to the assumption that consumers’ consumption decisions are made only by considering disposable income. Following Keynes Absolute Income Hypothesis, James Duesenberry developed the Relative Income Hypothesis (Duesenberry 1949). This theory asserts that consumption is not only based on one’s†¦show more content†¦Expanding upon the Life Cycle Hypothesis and the Permanent Income Hypothesis, Robert E Hall introduced the Random Walk model of Consumption (Hall 1978). Hall’s theory introduces rational expectations into the Life Cycle and Permanent Income Hypotheses. Stating that if rational expectations exist, then consumers will change their expectations as additional information becomes available to them. Variations in consumption are then only able to be explained by events that were unpredictable, as they would otherwise be smoothing consumption, which suggests that changes in consumption should be unpredictable as well. Evidence from Jesse Rothstein and Cecilia Rouse’s (Rothstein and Rouse 2007) research about how student loan debt affects post-college career choices suggests that recent college graduates behave in a manner that is not in accordance with life-cycle agents in. They create a regression-based estimator using difference-in-differences analysis (DID) combined with the Wald Test, with controls for variances that a simple version of DID/Wald would not be able to capture. The first of their results that can be of importance to consumption is that students wi th student loan debt were more likely to take higher-salary jobs over lower paying or â€Å"public interest† positions, which would result in higher pre-debt servicing disposable incomes. The claim that those with student loan debts are not life-cycle agents stems from data about the pledgesShow MoreRelatedDissertation Proposal1339 Words   |  6 Pagesstrategies has been a matter of controversy. Before Keynes (1936), many economists considered the interest to be the important factor to determine the propensity of saving. Keynes introduced ‘Absolute Income Hypothesis’ (AIH) in 1936 which demonstrated that fluctuations in the short run interest rate had no significant effect on spending decisions; rather the consumption behaviour is entirely dependent on current income. The theory asserts that as income rises, the consumption will also rise. 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