A NEW APPROACH FOR CALCULATING AVERAGE CROSS SECTIONS IN THE UNRESOLVED ENERGY REGION
|
|
- Lesley Lang
- 6 years ago
- Views:
Transcription
1 Nuclear Matheatical Coputational Sciences: A Century in Review, A Century Anew Gatlinburg, Tennessee, April 6-, 2003, on CD-ROM, Aerican Nuclear Society, LaGrange Park, IL (2003) A NEW APPROACH FOR CALCULATING AVERAGE CROSS SECTIONS IN THE UNRESOLVED ENERGY REGION L. C. Leal M. E. Dunn Oak Ridge National Laboratory Oak Ridge, TN 3783 US LealLC@ornl.gov; DunnME@ornl.gov ABSTRACT A novel approach for calculating average cross sections in the unresolved resonance region is proposed. The ethodology is based on the well-known probability table technique. Two new features are added to the probability table ethod in the way the energy level spacing is sapled: firstly, a constraint is iposed in the sapling of the energy level spacing, that is, in addition to sapling fro a Wigner distribution the 3 statistic test of Mehta-Dyson is also added; secondly, instead of generating a sequence of level spacing in a energy range (ladders) in the present ethod the level of spacing is sapled around a reference energy. The ethodology was ipleented tested in a coputer code naed URR (Unresolved Resonance Region). It has also been incorporated in the codes RACER AMPX. Key Words: cross section, unresolved, probability table. INTRODUCTION The foralis developed based on the R-atrix theory for treating the resonance in the resolved resonance region cannot be utilized when the average resonance width is of the order or larger than the average level spacing. One cannot deterine suitably the resonance paraeter for an individual resonance but rather resonance paraeter, which would represent a cluster of resonance. For instance, for the fissile fertile nuclides the unresolved energy region starts in the kev region extends up to few hundreds kev. An alternative for representing the cross section in the unresolved region would be to use a pointwise tabulation. However this approach would iply an overwheling aount of data storage. The foralis ostly used for calculating cross sections in the unresolved energy region is based on calculations done using average resonance paraeters. The calculation is expected to include the Doppler the self-shielding effects, which are iportant effects in the deterination of reactor ultiplication factors. The calculation of average resonance paraeters is based on the statistical distributions of the resonance paraeters. A coputer code naed URR (Unresolved Resonance Region) [] was developed to study the effect of various assuptions on the statistical distributions of unresolved resonance paraeters on the calculation of self-shielding factors self-indication ratios. The code uses the Monte Carlo ethod to generate probability tables for calculating of average cross sections. The self-shielding factors are calculated using the Bondarenko foralis. All cross section calculations are done based on the single-level Breit-Wigner approxiation. The calculations can be done at a specified energy, teperature cross section dilution. The ain characteristic of the URR code is that, contrary
2 L.C Leal M. E. Dunn to existing probability table codes, the resonance energies are not sapled fro consecutive points on a statistical ladder, but rather pairs of resonance are generated around the energy of interest. This ethod has been ipleented in the coputer codes RACER [2,3] AMPX [4]. In addition to the odification in the sapling of the energy level spacing the resonance energies generated are also copared with the corresponding energy levels on the 3 statistic test of Mehta-Dyson. 2. BRIEF OVERVIEW OF THE THEORETICAL DISTRIBUTIONS OF THE RESONANCE PARAMETERS 2. LEVEL SPACING DISTRIBUTION LAW The spacing between two consecutive resonance energies for the sae total angular oentu parity exhibits ro behavior. For a set of n resonance energy levels, E, E 2,..., E n, where the level spacing between two consecutive energies, E k E k-, is D k, the average level spacing is <D>, the probability distribution function predicted by the Wigner law[5] is p(x) dx ' π x 2 2 π x exp (& ) dx, () 4 where x ' D k /<D>, <D> is the average level spacing. The Wigner probability distribution function has the following property: 0 4 p(x) dx ' 0 4 xp(x)dx '. (2) The second oent of the Wigner distribution is given by x 2 ' 0 4 x 2 p(x)dx ' 4 π. (3) Equation () was the first atheatical prediction of the level spacing distribution to provide excellent agreeent with experiental results; it has triggered a series of investigations on the subject of the statistical distribution of resonance paraeters. Although other accurate level spacing distributions have been proposed, Wigner s law is the ost widely used is suitable for practical applications. 2.2 RESONANCE WIDTH DISTRIBUTION LAW Systeatic easureents of the resonance widths show strong fluctuations aong resonances of the sae angular oentu parity. The definition of resonance width involves two other quantities, naely the reduced widths, γ λc, the penetration factor, P c, which are related according to the equation Aerican Nuclear Society Topical Meeting in Matheatics & Coputations, Gatlinburg, TN, /9
3 A New Approach for Calculating Average Cross Sections Γ λ ' jc (2P c ) γ 2 λc, (4) where λ refers to the energy levels in the copound nucleus c refers to the particle channel. One should expect that the fluctuations are connected to either the reduced widths, γ λc, or to the penetration factors, P c. However, it is iprobable that the fluctuations are due to the penetration factors since they are sooth functions of energy. Therefore, the observed fluctuations are caused by the reduced widths, γ λc ; these, in turn, are related to the projection of the eigenfunctions of the Hailtonian of the copound nucleus on the nuclear surface. This projection involves an integration of any uncorrelated contributions, positive negative, over the high-diensional phase space of the copound nucleus. It then follows fro the central liit theore that the distributions of γ 2 λchave a Gaussian distribution with zero-ean. Therefore, the distribution function of the reduced widths can be written as P(γ λc ) d γ λc ' γ 2 λc exp(& ) d γ 2 π <γ 2 λc > 2<γ 2 λc > λc, (5) where <γ 2 λc > is the average value of γ2 λ c. The probability distribution function of the resonance widths, Γ λ,can be derived fro Eq. (3) as follows: The statistical theore states that if y is a variable that is the su of squares of ν norally distributed zero-ean independent variables, then y is distributed according to a χ 2 distribution with ν degrees of freedo. Therefore, the distribution of Γ λ is p ν (x) dx ' ν 2 G(ν/2) (ν x/2) ν 2 & exp(&νx/2) dx, (6) where x ' Γ λ /<Γ >, G(ν/2) is the atheatical gaa function, <Γ > is the average value of the width taken over a given energy range. For ν ', Eq. (6) is the well known as the Porter- Thoas[6] distribution law of the neutron width. It is generally accepted that fission is a fewchannel process, that there are only a liited nuber of effectively open channels; 2 or 3 degrees of freedo (ν ' 2orν ' 3) are usually assued in the fission width distribution. In the neutron capture event, a large nuber of capture channels are opened; the gaa width distribution is represented by a χ 2 distribution with a large nuber of degrees of freedo ( ν64),which corresponds to a Dirac-delta function centered at Γ γ ' < Γ >. The χ 2 distribution function has the following property: Aerican Nuclear Society Topical Meeting in Matheatics & Coputations, Gatlinburg, TN, /9
4 L.C Leal M. E. Dunn 0 4 pν (x) dx ' 0 4 xpν (x) dx '. (7) The second oent of a χ 2 distribution with νdegrees of freedo is given as x 2 ' 0 4 x 2 p ν (x) dx ' 2 ν %. (8) 2.3 DYSON AND MEHTA LONG-RANGE CORRELATION OF 3 STATISTICS TEST The 3 statistics test, introduced by Dyson Mehta, [7] provides a easure of the ean-square deviation between the nuber of observed energy levels in the energy interval to the best fit to the straight line, as a function of energy, given as ae% b. Strictly speaking, the definition is 3 ' Min (a, b) N(E) & ae&b 2 de, (9) 2 L where N(E) is the corresponding cuulative nuber of energy levels as a function of energy. The Dyson Mehta 3 test predicts that the theoretical average value < 3 > is given as < 3 > ' π 2 ln(n) & , (0) with variance V 3 '.69/π 4. Here n is the nuber of energy levels observed in the interval to. For practical applications, the coefficients a b in Eq. (9) are deterined according to the following conditions: M 3 M a ' 0, () Aerican Nuclear Society Topical Meeting in Matheatics & Coputations, Gatlinburg, TN, /9
5 A New Approach for Calculating Average Cross Sections M 3 Mb ' 0. (2) These conditions lead to the following equations: a E 2 de % b EdE ' N(E) de, (3) a EdE % b de ' N(E) de. (4) The following identities will be used in evaluating a b: de ' E f &, (5) EdE ' (E 2 f & E 2 i )/2, (6) E 2 de ' ( E 3 f & E 3 i )/3. (7) If the energy levels in the range to are nubered fro l '&L to l ', then the following relations also hold: N(E) de ' j E l% E l lde' j l (E l% & E l ), (8) Aerican Nuclear Society Topical Meeting in Matheatics & Coputations, Gatlinburg, TN, /9
6 L.C Leal M. E. Dunn N(E) EdE ' j E l% E l lede ' j l ( E 2 l% & E 2 l )/2, (9) N 2 (E) EdE ' j l 2 (E l% & E l ). (20) The syste of Eqs. (3) (4) can be written as α a % β b ' γ (2) α 2 a % β 2 b ' γ 2, (22) in which the Greek sybols are defined as α ' (E 3 f & E 3 i )/3, (23) α 2 ' β ' (E 2 f & E 2 i )/2, (24) β 2 ' &, (25) γ ' jl l (E 2 l% & E 2 l )/2, (26) γ 2 ' jl l (E l% & E l ). (27) Aerican Nuclear Society Topical Meeting in Matheatics & Coputations, Gatlinburg, TN, /9
7 The solution for a b is then A New Approach for Calculating Average Cross Sections a ' γ & γ 2 β / β 2 α & α 2 β / β 2, (28) b ' γ 2 β 2 & α 2 β 2 γ & γ 2 β / β 2 α & α 2 β / β 2. (29) Substituting these definitions into Eq. (9) leads to the expression for the 3 test: 3 ' & N 2 (E) de & γ a & γ 2 b, (30) or 3 ' & j &L l 2 (E l% &E l ) & γ a & γ 2 b, (3) where a b are given by Eqs. (28) (29), γ γ 2 by Eqs. (26) (27). 3. SAMPLING TECHNIQUE TO GENERATE RESONANCE ENERGY AROUND THE REFERENCE ENERGY For a reference energy E, as tabulated in the Evaluated Nuclear Data Files (ENDF), series of resonance surrounding the reference energy is selected fro the probability distribution P(x)dx'xW(x)dx (32) where W( x) is the level spacing distribution law given in Eq. (Wigner distribution). The saple variable x is defined as the ratio between the level spacing D the average level spacing <D> ( x = D/ < D > ). The separation between the first two resonances around s sapled fro Eq. (32) pair of resonances are assigned above below E respectively as, E+ sd E+ ( s ) D. The value s is a ro nuber between 0 is deterined fro a unifor distribution as p(x)' dx s (33) Aerican Nuclear Society Topical Meeting in Matheatics & Coputations, Gatlinburg, TN, /9
8 L.C Leal M. E. Dunn This procedure is repeated ore resonances are included around the reference energy. The total nuber of resonances (pairs of resonances) around the reference energy is arbitrary. While this ethod is very efficient for generation of the values needed for creating probability tables for cross section calculations it was originally developed for testing interference effects of the elastic channel in the cross sections. The long range interference effect in the elastic channel ay require large nubers of resonance pairs around the energy of interest for the deterination of the average cross sections. The resonance energy sequence saple as described is also tested with the Dyson Mehta 3 test as indicated in Eqs. (3) (4). The 3 test was successfully used in the evaluation of the 235 U cross sections.[8] It is also included in the coputer code SAMDIST[9] which is used for calculating statistical distribution of R-Matrix resonance paraeters. To test the unresolved resonance ethodology in the coputer code URR, coparisons of the experiental average neutron cross section for 235 U in the energy region fro 3 kev to 20 kev is shown is Figure. The upper curve represents the total cross section easured by Harvey et al.[0], whereas the iddle botto curves are respectively the fission capture cross sections of Weston et. al.[] Solid curves are the average calculations with URR the vertical lines are the experiental data. The average input data used in the calculations are of an ongoing 235 U unresolved evaluation done at ORNL. The URR result are excellent. Figure. Coparisons of average cross sections calculated with the URR coputer code with experiental data for 235 U. Upper curve is the total cross section, iddle botto curves are respectively fission capture cross sections. Aerican Nuclear Society Topical Meeting in Matheatics & Coputations, Gatlinburg, TN, /9
9 A New Approach for Calculating Average Cross Sections 3. CONCLUSIONS This work describe a novel approach for calculating average cross sections based on the probability table ethod. Two new features are established in the way the energy level spacing of the resonances are sapled. The ethod has been ipleented a coputer code naed URR has also been included in ajor coputer codes, such as RACER AMPX. Coparisons of the average cross sections calculated with URR for 235 U are copared with experiental results the results are excellent. ACKNOWLEDGMENTS This work was sponsored by the Office of Environental Manageent, U. S. Departent of Energy, under contract DE-AC05-00OR22725 with UT-Battelle, LLC. REFERENCES. L. C. Leal, G. desaussure, R. B. Perez, URR Coputer Code: A Code to Calculate Resonance Neutron Cross-Section Probability Tables, Bondarenko Self-Shielding Factors Self-Indication Ratios for Fissile Fertile Nuclides, ORNL/TM-297, Martin Marieta Energy Systes, Inc., Oak Ridge National Laboratory (August 989). 2. F. B. Brown T. M. Sutton, Monte Carlo Fundaentals, KAPL-4823, Departent of Energy - Office of Scientific Technical Inforation (996). 3. T. M. Sutton F. B. Brown, Ipleentation of the Probability Table Method in a Continuous-Energy Monte Carlo Code Syste, International Conference on the Physics of Nuclear Science Technology, p , Long Isl, New York, October 5-8, M. E. Dunn N. M. Greene, AMPX-2000: A Cross-Section Processing Syste for Generating Nuclear Data for Criticality Safety Applications, Trans. A. Nucl. Soc., 86, 8-9 (2002). 5. E. P. Wigner, Conf. On Neutron Physics by Tie-of-Flight, Gatlinburg, TN, 956, ORNL-2309, Union Carbide Corp., Nucl. Div., Oak Ridge National Laboratory, 957, pp C. E. Porter R. G. Thoas, Fluctuations of Nuclear Reaction Widths, Phys. Rev. 04, (956). 7. F. J. Dyson M. L. Mehta, Statistical Theory of the Energy Levels of Coplex Systes, J. Math. Phys. 4, 70 (963). 8. L. C. Leal, G. desaussure, R. B. Perez, An R-Matrix Analysis of the 235 U Neutron Induced Cross Sections up to 500 ev, Nucl. Sci. Eng. 09, -7 (99). 9. L. C. Leal N. M. Larson, SAMDIST: A Coputer Code for Calculating Statistical Distributions for R-Matrix Resonance Paraeters, ORNL/TM-3092, Lockheed Martin Energy Research Corporation, Oak Ridge National Laboratory (Septeber 995). 0. J. A. Harvey, N. W. Hill, F. G. Perey, G. L. Tweed, L. C. Leal, Proc. Int. Conf. On Nuclear Data for Science Technology, Mito, Japan (May 30-June 3, 988).. L. W. Weston, J. H. Todd, Nucl. Sci. Eng., 88, 567 (984). Aerican Nuclear Society Topical Meeting in Matheatics & Coputations, Gatlinburg, TN, /9
COVARIANCE DATA FOR 233 U IN THE RESOLVED RESONANCE REGION FOR CRITICALITY SAFETY APPLICATIONS
Mathematics and Computation, Supercomputing, Reactor Physics and Nuclear and Biological Applications Palais des Papes, Avignon, France, September 12-15, 2005, on CD-ROM, American Nuclear Society, LaGrange
More informationExtension of CSRSM for the Parametric Study of the Face Stability of Pressurized Tunnels
Extension of CSRSM for the Paraetric Study of the Face Stability of Pressurized Tunnels Guilhe Mollon 1, Daniel Dias 2, and Abdul-Haid Soubra 3, M.ASCE 1 LGCIE, INSA Lyon, Université de Lyon, Doaine scientifique
More information2 Q 10. Likewise, in case of multiple particles, the corresponding density in 2 must be averaged over all
Lecture 6 Introduction to kinetic theory of plasa waves Introduction to kinetic theory So far we have been odeling plasa dynaics using fluid equations. The assuption has been that the pressure can be either
More informationPhysics 139B Solutions to Homework Set 3 Fall 2009
Physics 139B Solutions to Hoework Set 3 Fall 009 1. Consider a particle of ass attached to a rigid assless rod of fixed length R whose other end is fixed at the origin. The rod is free to rotate about
More informationSpine Fin Efficiency A Three Sided Pyramidal Fin of Equilateral Triangular Cross-Sectional Area
Proceedings of the 006 WSEAS/IASME International Conference on Heat and Mass Transfer, Miai, Florida, USA, January 18-0, 006 (pp13-18) Spine Fin Efficiency A Three Sided Pyraidal Fin of Equilateral Triangular
More informationOBJECTIVES INTRODUCTION
M7 Chapter 3 Section 1 OBJECTIVES Suarize data using easures of central tendency, such as the ean, edian, ode, and idrange. Describe data using the easures of variation, such as the range, variance, and
More informationMultiscale Entropy Analysis: A New Method to Detect Determinism in a Time. Series. A. Sarkar and P. Barat. Variable Energy Cyclotron Centre
Multiscale Entropy Analysis: A New Method to Detect Deterinis in a Tie Series A. Sarkar and P. Barat Variable Energy Cyclotron Centre /AF Bidhan Nagar, Kolkata 700064, India PACS nubers: 05.45.Tp, 89.75.-k,
More informationBlock designs and statistics
Bloc designs and statistics Notes for Math 447 May 3, 2011 The ain paraeters of a bloc design are nuber of varieties v, bloc size, nuber of blocs b. A design is built on a set of v eleents. Each eleent
More informationWork, Energy and Momentum
Work, Energy and Moentu Work: When a body oves a distance d along straight line, while acted on by a constant force of agnitude F in the sae direction as the otion, the work done by the force is tered
More informationFeature Extraction Techniques
Feature Extraction Techniques Unsupervised Learning II Feature Extraction Unsupervised ethods can also be used to find features which can be useful for categorization. There are unsupervised ethods that
More informationESTIMATING AND FORMING CONFIDENCE INTERVALS FOR EXTREMA OF RANDOM POLYNOMIALS. A Thesis. Presented to. The Faculty of the Department of Mathematics
ESTIMATING AND FORMING CONFIDENCE INTERVALS FOR EXTREMA OF RANDOM POLYNOMIALS A Thesis Presented to The Faculty of the Departent of Matheatics San Jose State University In Partial Fulfillent of the Requireents
More informationTEST OF HOMOGENEITY OF PARALLEL SAMPLES FROM LOGNORMAL POPULATIONS WITH UNEQUAL VARIANCES
TEST OF HOMOGENEITY OF PARALLEL SAMPLES FROM LOGNORMAL POPULATIONS WITH UNEQUAL VARIANCES S. E. Ahed, R. J. Tokins and A. I. Volodin Departent of Matheatics and Statistics University of Regina Regina,
More informationResearch in Area of Longevity of Sylphon Scraies
IOP Conference Series: Earth and Environental Science PAPER OPEN ACCESS Research in Area of Longevity of Sylphon Scraies To cite this article: Natalia Y Golovina and Svetlana Y Krivosheeva 2018 IOP Conf.
More informationŞtefan ŞTEFĂNESCU * is the minimum global value for the function h (x)
7Applying Nelder Mead s Optiization Algorith APPLYING NELDER MEAD S OPTIMIZATION ALGORITHM FOR MULTIPLE GLOBAL MINIMA Abstract Ştefan ŞTEFĂNESCU * The iterative deterinistic optiization ethod could not
More informationAnisotropic reference media and the possible linearized approximations for phase velocities of qs waves in weakly anisotropic media
INSTITUTE OF PHYSICS PUBLISHING JOURNAL OF PHYSICS D: APPLIED PHYSICS J. Phys. D: Appl. Phys. 5 00 007 04 PII: S00-770867-6 Anisotropic reference edia and the possible linearized approxiations for phase
More informationSPECTRUM sensing is a core concept of cognitive radio
World Acadey of Science, Engineering and Technology International Journal of Electronics and Counication Engineering Vol:6, o:2, 202 Efficient Detection Using Sequential Probability Ratio Test in Mobile
More informationHee = ~ dxdy\jj+ (x) 'IJ+ (y) u (x- y) \jj (y) \jj (x), V, = ~ dx 'IJ+ (x) \jj (x) V (x), Hii = Z 2 ~ dx dy cp+ (x) cp+ (y) u (x- y) cp (y) cp (x),
SOVIET PHYSICS JETP VOLUME 14, NUMBER 4 APRIL, 1962 SHIFT OF ATOMIC ENERGY LEVELS IN A PLASMA L. E. PARGAMANIK Khar'kov State University Subitted to JETP editor February 16, 1961; resubitted June 19, 1961
More informationare equal to zero, where, q = p 1. For each gene j, the pairwise null and alternative hypotheses are,
Page of 8 Suppleentary Materials: A ultiple testing procedure for ulti-diensional pairwise coparisons with application to gene expression studies Anjana Grandhi, Wenge Guo, Shyaal D. Peddada S Notations
More informationNumerical Evaluation of Sn Isotope Cross Sections by Photoneutron Activation Method
Nuerical Evaluation of Sn Isotope Cross Sections by Photoneutron Activation Method C. Oprea ), A. Oprea ), A. Mihul ) ) Joint Institute for Nuclear Research, Frank Laboratory of Neutron Physics, 98 Dubna,
More informationProc. of the IEEE/OES Seventh Working Conference on Current Measurement Technology UNCERTAINTIES IN SEASONDE CURRENT VELOCITIES
Proc. of the IEEE/OES Seventh Working Conference on Current Measureent Technology UNCERTAINTIES IN SEASONDE CURRENT VELOCITIES Belinda Lipa Codar Ocean Sensors 15 La Sandra Way, Portola Valley, CA 98 blipa@pogo.co
More informationP (t) = P (t = 0) + F t Conclusion: If we wait long enough, the velocity of an electron will diverge, which is obviously impossible and wrong.
4 Phys520.nb 2 Drude theory ~ Chapter in textbook 2.. The relaxation tie approxiation Here we treat electrons as a free ideal gas (classical) 2... Totally ignore interactions/scatterings Under a static
More informationNeutron Cross-Section Measurements at ORELA
December 16, 2005 Paper for ORELA Proceedings Nuclear Science and Technology Division (94) Neutron Cross-Section Measurements at ORELA K. H. Guber, L. C. Leal, R. O. Sayer, P. E. Koehler, H. Derrien, D.
More informationA Multi-Level Lorentzian Analysis of the Basic Structures of the Daily DJIA
A Multi-Level Lorentzian Analysis of the Basic Structures of the Daily DJIA Frank W. K. Firk Professor Emeritus of Physics, The Henry Koerner Center for Emeritus Faculty, Yale University, New Haven, CT
More informationBrief Review of the R-Matrix Theory
Brief Review of the R-Matrix Theory L. C. Leal Introduction Resonance theory deals with the description of the nucleon-nucleus interaction and aims at the prediction of the experimental structure of cross
More informationKeywords: Estimator, Bias, Mean-squared error, normality, generalized Pareto distribution
Testing approxiate norality of an estiator using the estiated MSE and bias with an application to the shape paraeter of the generalized Pareto distribution J. Martin van Zyl Abstract In this work the norality
More informationNumerical Studies of a Nonlinear Heat Equation with Square Root Reaction Term
Nuerical Studies of a Nonlinear Heat Equation with Square Root Reaction Ter Ron Bucire, 1 Karl McMurtry, 1 Ronald E. Micens 2 1 Matheatics Departent, Occidental College, Los Angeles, California 90041 2
More informationAn Approximate Model for the Theoretical Prediction of the Velocity Increase in the Intermediate Ballistics Period
An Approxiate Model for the Theoretical Prediction of the Velocity... 77 Central European Journal of Energetic Materials, 205, 2(), 77-88 ISSN 2353-843 An Approxiate Model for the Theoretical Prediction
More informationIN modern society that various systems have become more
Developent of Reliability Function in -Coponent Standby Redundant Syste with Priority Based on Maxiu Entropy Principle Ryosuke Hirata, Ikuo Arizono, Ryosuke Toohiro, Satoshi Oigawa, and Yasuhiko Takeoto
More informationBayesian Approach for Fatigue Life Prediction from Field Inspection
Bayesian Approach for Fatigue Life Prediction fro Field Inspection Dawn An and Jooho Choi School of Aerospace & Mechanical Engineering, Korea Aerospace University, Goyang, Seoul, Korea Srira Pattabhiraan
More informationThe Transactional Nature of Quantum Information
The Transactional Nature of Quantu Inforation Subhash Kak Departent of Coputer Science Oklahoa State University Stillwater, OK 7478 ABSTRACT Inforation, in its counications sense, is a transactional property.
More informationGeneral Properties of Radiation Detectors Supplements
Phys. 649: Nuclear Techniques Physics Departent Yarouk University Chapter 4: General Properties of Radiation Detectors Suppleents Dr. Nidal M. Ershaidat Overview Phys. 649: Nuclear Techniques Physics Departent
More informationSEISMIC FRAGILITY ANALYSIS
9 th ASCE Specialty Conference on Probabilistic Mechanics and Structural Reliability PMC24 SEISMIC FRAGILITY ANALYSIS C. Kafali, Student M. ASCE Cornell University, Ithaca, NY 483 ck22@cornell.edu M. Grigoriu,
More informationarxiv: v2 [hep-ph] 9 Jan 2014
Fluctuation induced equality of ulti-particle eccentricities for four or ore particles Ada Bzdak a, Piotr Bozek b,c, Larry McLerran d,a,e arxiv:1311.7325v2 [hep-ph] 9 Jan 2014 a RIKEN BNL Research Center,
More informationQualitative Modelling of Time Series Using Self-Organizing Maps: Application to Animal Science
Proceedings of the 6th WSEAS International Conference on Applied Coputer Science, Tenerife, Canary Islands, Spain, Deceber 16-18, 2006 183 Qualitative Modelling of Tie Series Using Self-Organizing Maps:
More informationMeasures of average are called measures of central tendency and include the mean, median, mode, and midrange.
CHAPTER 3 Data Description Objectives Suarize data using easures of central tendency, such as the ean, edian, ode, and idrange. Describe data using the easures of variation, such as the range, variance,
More informationMachine Learning Basics: Estimators, Bias and Variance
Machine Learning Basics: Estiators, Bias and Variance Sargur N. srihari@cedar.buffalo.edu This is part of lecture slides on Deep Learning: http://www.cedar.buffalo.edu/~srihari/cse676 1 Topics in Basics
More informationOptical Properties of Plasmas of High-Z Elements
Forschungszentru Karlsruhe Techni und Uwelt Wissenschaftlishe Berichte FZK Optical Properties of Plasas of High-Z Eleents V.Tolach 1, G.Miloshevsy 1, H.Würz Project Kernfusion 1 Heat and Mass Transfer
More informationMathematical Models to Determine Stable Behavior of Complex Systems
Journal of Physics: Conference Series PAPER OPEN ACCESS Matheatical Models to Deterine Stable Behavior of Coplex Systes To cite this article: V I Suin et al 08 J. Phys.: Conf. Ser. 05 0336 View the article
More information7. Renormalization and universality in pionless EFT
Renoralization and universality in pionless EFT (last revised: October 6, 04) 7 7. Renoralization and universality in pionless EFT Recall the scales of nuclear forces fro Section 5: Pionless EFT is applicable
More informationRECOVERY OF A DENSITY FROM THE EIGENVALUES OF A NONHOMOGENEOUS MEMBRANE
Proceedings of ICIPE rd International Conference on Inverse Probles in Engineering: Theory and Practice June -8, 999, Port Ludlow, Washington, USA : RECOVERY OF A DENSITY FROM THE EIGENVALUES OF A NONHOMOGENEOUS
More informationMeasuring orbital angular momentum superpositions of light by mode transformation
CHAPTER 7 Measuring orbital angular oentu superpositions of light by ode transforation In chapter 6 we reported on a ethod for easuring orbital angular oentu (OAM) states of light based on the transforation
More informationTABLE FOR UPPER PERCENTAGE POINTS OF THE LARGEST ROOT OF A DETERMINANTAL EQUATION WITH FIVE ROOTS. By William W. Chen
TABLE FOR UPPER PERCENTAGE POINTS OF THE LARGEST ROOT OF A DETERMINANTAL EQUATION WITH FIVE ROOTS By Willia W. Chen The distribution of the non-null characteristic roots of a atri derived fro saple observations
More informationThe Thermal Conductivity Theory of Non-uniform Granular Flow and the Mechanism Analysis
Coun. Theor. Phys. Beijing, China) 40 00) pp. 49 498 c International Acadeic Publishers Vol. 40, No. 4, October 5, 00 The Theral Conductivity Theory of Non-unifor Granular Flow and the Mechanis Analysis
More informationUfuk Demirci* and Feza Kerestecioglu**
1 INDIRECT ADAPTIVE CONTROL OF MISSILES Ufuk Deirci* and Feza Kerestecioglu** *Turkish Navy Guided Missile Test Station, Beykoz, Istanbul, TURKEY **Departent of Electrical and Electronics Engineering,
More informationPh 20.3 Numerical Solution of Ordinary Differential Equations
Ph 20.3 Nuerical Solution of Ordinary Differential Equations Due: Week 5 -v20170314- This Assignent So far, your assignents have tried to failiarize you with the hardware and software in the Physics Coputing
More informationChapter 1: Basics of Vibrations for Simple Mechanical Systems
Chapter 1: Basics of Vibrations for Siple Mechanical Systes Introduction: The fundaentals of Sound and Vibrations are part of the broader field of echanics, with strong connections to classical echanics,
More informationA Simplified Analytical Approach for Efficiency Evaluation of the Weaving Machines with Automatic Filling Repair
Proceedings of the 6th SEAS International Conference on Siulation, Modelling and Optiization, Lisbon, Portugal, Septeber -4, 006 0 A Siplified Analytical Approach for Efficiency Evaluation of the eaving
More informationTheory and Applications of the Indoor Noise Module (VDI 3760)
Fullerton, CA 9835 USA Theory and Applications of the Indoor Noise Module (VDI 3760) The following Technical Note suarizes the atheatical concepts used in the SoundPLAN Indoor Factory Noise Module. 1.
More informationWarning System of Dangerous Chemical Gas in Factory Based on Wireless Sensor Network
565 A publication of CHEMICAL ENGINEERING TRANSACTIONS VOL. 59, 07 Guest Editors: Zhuo Yang, Junie Ba, Jing Pan Copyright 07, AIDIC Servizi S.r.l. ISBN 978-88-95608-49-5; ISSN 83-96 The Italian Association
More informationDepartment of Physics, Sri Venkateswara University, Tirupati Range Operations, Satish Dhawan Space Centre SHAR, ISRO, Sriharikota
Trajectory Estiation of a Satellite Launch Vehicle Using Unscented Kalan Filter fro Noisy Radar Measureents R.Varaprasad S.V. Bhaskara Rao D.Narayana Rao V. Seshagiri Rao Range Operations, Satish Dhawan
More informationNew Neutron-Induced Cross-Section Measurements for Weak s-process Studies
New Neutron-Induced Cross-Section Measurements for Weak s-process Studies Klaus H. Guber 1, D. Wiarda, L. C. Leal, H. Derrien, C. Ausmus, D. R. Brashear, J. A. White Nuclear Science and Technology Division,
More informationSolidification of Porous Material under Natural Convection by Three Phases Modeling
Solidification of Porous Material under Natural Convection by Three Phases Modeling Hassan Basirat Tabrizi, Meber, IAENG and F. Sadeghpour Abstract The perforance of natural convective flow over a rectangular
More informationInteractive Markov Models of Evolutionary Algorithms
Cleveland State University EngagedScholarship@CSU Electrical Engineering & Coputer Science Faculty Publications Electrical Engineering & Coputer Science Departent 2015 Interactive Markov Models of Evolutionary
More informationMassachusetts Institute of Technology Quantum Mechanics I (8.04) Spring 2005 Solutions to Problem Set 4
Massachusetts Institute of Technology Quantu Mechanics I (8.04) Spring 2005 Solutions to Proble Set 4 By Kit Matan 1. X-ray production. (5 points) Calculate the short-wavelength liit for X-rays produced
More informationBootstrapping Dependent Data
Bootstrapping Dependent Data One of the key issues confronting bootstrap resapling approxiations is how to deal with dependent data. Consider a sequence fx t g n t= of dependent rando variables. Clearly
More informationCovariance Generation using CONRAD and SAMMY Computer Codes
Covariance Generation using CONRAD and SAMMY Computer Codes L. Leal a, C. De Saint Jean b, H. Derrien a, G. Noguere b, B. Habert b, and J. M. Ruggieri b a Oak Ridge National Laboratory b CEA, DEN, Cadarache
More informationChapter 12. Quantum gases Microcanonical ensemble
Chapter 2 Quantu gases In classical statistical echanics, we evaluated therodynaic relations often for an ideal gas, which approxiates a real gas in the highly diluted liit. An iportant difference between
More informationTesting the lag length of vector autoregressive models: A power comparison between portmanteau and Lagrange multiplier tests
Working Papers 2017-03 Testing the lag length of vector autoregressive odels: A power coparison between portanteau and Lagrange ultiplier tests Raja Ben Hajria National Engineering School, University of
More informationDESIGN OF THE DIE PROFILE FOR THE INCREMENTAL RADIAL FORGING PROCESS *
IJST, Transactions of Mechanical Engineering, Vol. 39, No. M1, pp 89-100 Printed in The Islaic Republic of Iran, 2015 Shira University DESIGN OF THE DIE PROFILE FOR THE INCREMENTAL RADIAL FORGING PROCESS
More informationEstimation of the Mean of the Exponential Distribution Using Maximum Ranked Set Sampling with Unequal Samples
Open Journal of Statistics, 4, 4, 64-649 Published Online Septeber 4 in SciRes http//wwwscirporg/ournal/os http//ddoiorg/436/os4486 Estiation of the Mean of the Eponential Distribution Using Maiu Ranked
More informationScattering and bound states
Chapter Scattering and bound states In this chapter we give a review of quantu-echanical scattering theory. We focus on the relation between the scattering aplitude of a potential and its bound states
More informationThe proofs of Theorem 1-3 are along the lines of Wied and Galeano (2013).
A Appendix: Proofs The proofs of Theore 1-3 are along the lines of Wied and Galeano (2013) Proof of Theore 1 Let D[d 1, d 2 ] be the space of càdlàg functions on the interval [d 1, d 2 ] equipped with
More informationTesting equality of variances for multiple univariate normal populations
University of Wollongong Research Online Centre for Statistical & Survey Methodology Working Paper Series Faculty of Engineering and Inforation Sciences 0 esting equality of variances for ultiple univariate
More informationPULSE-TRAIN BASED TIME-DELAY ESTIMATION IMPROVES RESILIENCY TO NOISE
PULSE-TRAIN BASED TIME-DELAY ESTIMATION IMPROVES RESILIENCY TO NOISE 1 Nicola Neretti, 1 Nathan Intrator and 1,2 Leon N Cooper 1 Institute for Brain and Neural Systes, Brown University, Providence RI 02912.
More informationState Estimation Problem for the Action Potential Modeling in Purkinje Fibers
APCOM & ISCM -4 th Deceber, 203, Singapore State Estiation Proble for the Action Potential Modeling in Purinje Fibers *D. C. Estuano¹, H. R. B.Orlande and M. J.Colaço Federal University of Rio de Janeiro
More informationBernoulli Wavelet Based Numerical Method for Solving Fredholm Integral Equations of the Second Kind
ISSN 746-7659, England, UK Journal of Inforation and Coputing Science Vol., No., 6, pp.-9 Bernoulli Wavelet Based Nuerical Method for Solving Fredhol Integral Equations of the Second Kind S. C. Shiralashetti*,
More informationChapter 6 1-D Continuous Groups
Chapter 6 1-D Continuous Groups Continuous groups consist of group eleents labelled by one or ore continuous variables, say a 1, a 2,, a r, where each variable has a well- defined range. This chapter explores:
More informationExample A1: Preparation of a Calibration Standard
Suary Goal A calibration standard is prepared fro a high purity etal (cadiu) with a concentration of ca.1000 g l -1. Measureent procedure The surface of the high purity etal is cleaned to reove any etal-oxide
More informationA note on the multiplication of sparse matrices
Cent. Eur. J. Cop. Sci. 41) 2014 1-11 DOI: 10.2478/s13537-014-0201-x Central European Journal of Coputer Science A note on the ultiplication of sparse atrices Research Article Keivan Borna 12, Sohrab Aboozarkhani
More informationPhysics 215 Winter The Density Matrix
Physics 215 Winter 2018 The Density Matrix The quantu space of states is a Hilbert space H. Any state vector ψ H is a pure state. Since any linear cobination of eleents of H are also an eleent of H, it
More informationSupplementary Information for Design of Bending Multi-Layer Electroactive Polymer Actuators
Suppleentary Inforation for Design of Bending Multi-Layer Electroactive Polyer Actuators Bavani Balakrisnan, Alek Nacev, and Elisabeth Sela University of Maryland, College Park, Maryland 074 1 Analytical
More informationUpper bound on false alarm rate for landmine detection and classification using syntactic pattern recognition
Upper bound on false alar rate for landine detection and classification using syntactic pattern recognition Ahed O. Nasif, Brian L. Mark, Kenneth J. Hintz, and Nathalia Peixoto Dept. of Electrical and
More informationNonmonotonic Networks. a. IRST, I Povo (Trento) Italy, b. Univ. of Trento, Physics Dept., I Povo (Trento) Italy
Storage Capacity and Dynaics of Nononotonic Networks Bruno Crespi a and Ignazio Lazzizzera b a. IRST, I-38050 Povo (Trento) Italy, b. Univ. of Trento, Physics Dept., I-38050 Povo (Trento) Italy INFN Gruppo
More information13 Harmonic oscillator revisited: Dirac s approach and introduction to Second Quantization
3 Haronic oscillator revisited: Dirac s approach and introduction to Second Quantization. Dirac cae up with a ore elegant way to solve the haronic oscillator proble. We will now study this approach. The
More informationPhys463.nb. Many electrons in 1D at T = 0. For a large system (L ), ΕF =? (6.7) The solutions of this equation are plane waves (6.
â â x Ψn Hx Ε Ψn Hx 35 (6.7) he solutions of this equation are plane waves Ψn Hx A exphä n x (6.8) he eigen-energy Εn is n (6.9) Εn For a D syste with length and periodic boundary conditions, Ψn Hx Ψn
More informationA method to determine relative stroke detection efficiencies from multiplicity distributions
A ethod to deterine relative stroke detection eiciencies ro ultiplicity distributions Schulz W. and Cuins K. 2. Austrian Lightning Detection and Inoration Syste (ALDIS), Kahlenberger Str.2A, 90 Vienna,
More informationTHERMAL ENDURANCE OF UNREINFORCED UNSATURATED POLYESTERS AND VINYL ESTER RESINS = (1) ln = COMPOSITES & POLYCON 2009
Aerican Coposites Manufacturers Association January 15-17, 29 Tapa, FL USA Abstract THERMAL ENDURANCE OF UNREINFORCED UNSATURATED POLYESTERS AND VINYL ESTER RESINS by Thore M. Klaveness, Reichhold AS In
More informationCh 12: Variations on Backpropagation
Ch 2: Variations on Backpropagation The basic backpropagation algorith is too slow for ost practical applications. It ay take days or weeks of coputer tie. We deonstrate why the backpropagation algorith
More informationBirthday Paradox Calculations and Approximation
Birthday Paradox Calculations and Approxiation Joshua E. Hill InfoGard Laboratories -March- v. Birthday Proble In the birthday proble, we have a group of n randoly selected people. If we assue that birthdays
More informationOn Conditions for Linearity of Optimal Estimation
On Conditions for Linearity of Optial Estiation Erah Akyol, Kuar Viswanatha and Kenneth Rose {eakyol, kuar, rose}@ece.ucsb.edu Departent of Electrical and Coputer Engineering University of California at
More informationNUMERICAL MODELLING OF THE TYRE/ROAD CONTACT
NUMERICAL MODELLING OF THE TYRE/ROAD CONTACT PACS REFERENCE: 43.5.LJ Krister Larsson Departent of Applied Acoustics Chalers University of Technology SE-412 96 Sweden Tel: +46 ()31 772 22 Fax: +46 ()31
More informationRecursive Algebraic Frisch Scheme: a Particle-Based Approach
Recursive Algebraic Frisch Schee: a Particle-Based Approach Stefano Massaroli Renato Myagusuku Federico Califano Claudio Melchiorri Atsushi Yaashita Hajie Asaa Departent of Precision Engineering, The University
More informationAn Improved Particle Filter with Applications in Ballistic Target Tracking
Sensors & ransducers Vol. 72 Issue 6 June 204 pp. 96-20 Sensors & ransducers 204 by IFSA Publishing S. L. http://www.sensorsportal.co An Iproved Particle Filter with Applications in Ballistic arget racing
More informationKinetic Theory of Gases: Elementary Ideas
Kinetic Theory of Gases: Eleentary Ideas 9th February 011 1 Kinetic Theory: A Discussion Based on a Siplified iew of the Motion of Gases 1.1 Pressure: Consul Engel and Reid Ch. 33.1) for a discussion of
More informationPaul M. Goggans Department of Electrical Engineering, University of Mississippi, Anderson Hall, University, Mississippi 38677
Evaluation of decay ties in coupled spaces: Bayesian decay odel selection a),b) Ning Xiang c) National Center for Physical Acoustics and Departent of Electrical Engineering, University of Mississippi,
More informationMODIFIED SERIES RESISTANCE MODEL - DETERMINATION OF MEAN CONCENTRATION BY INTEGRAL TRANSFORMATION
MODIFIED SERIES RESISTANCE MODEL - DETERMINATION OF MEAN CONCENTRATION BY INTEGRAL TRANSFORMATION A. L. Venezuela a, R. F. Cantão a, R. S. Ongaratto b, and R. N. Haneda c a Universidade Federal de São
More informationDoes the quark cluster model predict any isospin two dibaryon. resonance? (1) Grupo defsica Nuclear
FUSAL - 4/95 Does the quark cluster odel predict any isospin two dibaryon resonance? A. Valcarce (1), H. Garcilazo (),F.Fernandez (1) and E. Moro (1) (1) Grupo defsica uclear Universidad de Salaanca, E-37008
More informationUniform Approximation and Bernstein Polynomials with Coefficients in the Unit Interval
Unifor Approxiation and Bernstein Polynoials with Coefficients in the Unit Interval Weiang Qian and Marc D. Riedel Electrical and Coputer Engineering, University of Minnesota 200 Union St. S.E. Minneapolis,
More informationPart I: How Dense Is It? Fundamental Question: What is matter, and how do we identify it?
Part I: How Dense Is It? Fundaental Question: What is atter, and how do we identify it? 1. What is the definition of atter? 2. What do you think the ter ass per unit volue eans? 3. Do you think that a
More informationEvaluation of the 235 U resonance parameters to fit the standard recommended values
Evaluation of the 235 U resonance parameters to fit the standard recommended values Luiz Leal 1,a, Gilles Noguere 2, Carlos Paradela 3, Ignacio Durán 4, Laurent Tassan-Got 5, Yaron Danon 6, and Marian
More informationEFFECT OF SURFACE ASPERITY TRUNCATION ON THERMAL CONTACT CONDUCTANCE
EFFECT OF SURFACE ASPERITY TRUNCATION ON THERMAL CONTACT CONDUCTANCE Fernando H. Milanez *, M. M. Yovanovich, J. R. Culha Microelectronics Heat Transfer Laboratory Departent of Mechanical Engineering University
More informationTwo New Unbiased Point Estimates Of A Population Variance
Journal of Modern Applied Statistical Methods Volue 5 Issue Article 7 5--006 Two New Unbiased Point Estiates Of A Population Variance Matthew E. Ela The University of Alabaa, ela@baa.ua.edu Follow this
More informationAnalysis of Impulsive Natural Phenomena through Finite Difference Methods A MATLAB Computational Project-Based Learning
Analysis of Ipulsive Natural Phenoena through Finite Difference Methods A MATLAB Coputational Project-Based Learning Nicholas Kuia, Christopher Chariah, Mechatronics Engineering, Vaughn College of Aeronautics
More informationClassical systems in equilibrium
35 Classical systes in equilibriu Ideal gas Distinguishable particles Here we assue that every particle can be labeled by an index i... and distinguished fro any other particle by its label if not by any
More informationIdentical Maximum Likelihood State Estimation Based on Incremental Finite Mixture Model in PHD Filter
Identical Maxiu Lielihood State Estiation Based on Increental Finite Mixture Model in PHD Filter Gang Wu Eail: xjtuwugang@gail.co Jing Liu Eail: elelj20080730@ail.xjtu.edu.cn Chongzhao Han Eail: czhan@ail.xjtu.edu.cn
More informationCOS 424: Interacting with Data. Written Exercises
COS 424: Interacting with Data Hoework #4 Spring 2007 Regression Due: Wednesday, April 18 Written Exercises See the course website for iportant inforation about collaboration and late policies, as well
More informationKinetic Theory of Gases: Elementary Ideas
Kinetic Theory of Gases: Eleentary Ideas 17th February 2010 1 Kinetic Theory: A Discussion Based on a Siplified iew of the Motion of Gases 1.1 Pressure: Consul Engel and Reid Ch. 33.1) for a discussion
More informationAlgebraic Montgomery-Yang problem: the log del Pezzo surface case
c 2014 The Matheatical Society of Japan J. Math. Soc. Japan Vol. 66, No. 4 (2014) pp. 1073 1089 doi: 10.2969/jsj/06641073 Algebraic Montgoery-Yang proble: the log del Pezzo surface case By DongSeon Hwang
More informationRESTARTED FULL ORTHOGONALIZATION METHOD FOR SHIFTED LINEAR SYSTEMS
BIT Nuerical Matheatics 43: 459 466, 2003. 2003 Kluwer Acadeic Publishers. Printed in The Netherlands 459 RESTARTED FULL ORTHOGONALIZATION METHOD FOR SHIFTED LINEAR SYSTEMS V. SIMONCINI Dipartiento di
More informationSemicircle law for generalized Curie-Weiss matrix ensembles at subcritical temperature
Seicircle law for generalized Curie-Weiss atrix ensebles at subcritical teperature Werner Kirsch Fakultät für Matheatik und Inforatik FernUniversität in Hagen, Gerany Thoas Kriecherbauer Matheatisches
More information