Finite-system statistical mechanics for nucleons, hadrons and partons Scott Pratt, Michigan State University
|
|
|
- Geraldine Belinda Foster
- 5 years ago
- Views:
Transcription
1 Fnte-system sttstcl mechncs for nucleons hdrons nd prtons Scott Prtt RECURSIVE TECHNIQUES THE BCK ND FORTHS OF STTISTICL NUCLER PHYSICS Collbortors: S. Ds Gupt McGll W. Buer MSU S. Cheng UCSF S. Petrcon MSU J. Ruppert Frnfurt M. Soby U.Mnn.Morrs o Mult-Frgmentton o Level Denstes o Hdron Gs o QGP
2 The OTHER method for cnoncl ensembles GC C β α β Q Tr exp βh dα e 2π αq + αq GC β α Cn even be ppled to non-ddtve chrges: H.-T. Elze nd W. Grener PR86 PLB86 Hs been ppled to QGP
3 Trnsformng GC vs. Recursve Technues Old methods: Cn be performed nlytclly for smple systems Recursve technues: Bose nd Ferm sttstcs rbtrry level denstes Multplcty dstrbutons Exct dscrete sums not ntegrls
4 Scott Prtt Fundmentl Relton Fundmentl Relton K. Chse &. K. Chse &. Mejn Mejn PRC 995 S.P. & S.Ds Gupt PRC 2 PRC 995 S.P. & S.Ds Gupt PRC 2 Consder Speces wth mss n n n! ω n n n n ω ω! Q Q ω One cn dd other chrges
5 Populton of speces Multfrgmentton n ω Mss Dstrbuton 25
6 Multplcty dstrbutons P Tret the number N N N ω s chrge N n
7 Mcrocnoncl ensembles Dscretze E nd tret t s chrge N E E ω Eε FLUCTUTIONS n IMF PRODUCTION Cnoncl Mcrocnoncl No Coulomb Coulomb
8 Scott Prtt Ferm Ferm systems systems S.P. PLB 93 PRL 2 Prevous form ω n /n! neglects degenerte sttes. rrnge permuttons nto cycles P N P H P e! 2 β ccount for symmetrzton wth permuttons + E H e e C C β β 2 2
9 Level denstes Usng mcrocnoncl ensemble clculte N E 56 N
10 ngulr momentum. Clculte M 2. J MJ - MJ+
11 pplcton: Rre sotope producton Incorporte: FRLDM ground sttes Excted sttes Frgment nto ll possble prttons Seuentl decy S.P. P.Underhll W.Buer PRC 2
12 Hdron gs Sme formlsm Conserve B S I I 3 Q Symmetrzton for pons Isospn treted le ngulr momentum Monte Crlo prtcles
13 Hdron gs Monte Crlo MONTE CRLO PROCEDURE:. Pc Q nd ccordng to weght ~ 2. For nd Q: Clculte weght w /- Q- /Q Choose speces ccordng to weght Reduce sze: ->- Q->Q- Repet 3. Cn not nclude Ferm/Bose sttstcs
14 Blnce functons S.P. S. Petrcon nd M. Soby PRC 23. Chrge conservton s locl Wdth determned lrgely by T ccounts for lost chrge π + π blnce functon
15 Scott Prtt Isospn Isospn dstrbutons: bcground dstrbutons: bcground 2 / 2 2 N N P N η DCC stte: sosnglet n one untum level Rndom stte: 3 2 3!!! N N N N N P Bose-Gs wth no sospn constrnts: Brod dstrbuton t hgh phse spce densty Prwse sospn conservton further brodens dstrbuton S.P. nd V.elevnsy PRL 94
16 Isospn dstrbutons: chllenges Include ll rrngements Conservng I Bose Ensten sttstcs Resonnces Number of neutrl pons N -- does not commute wth I
17 Scott Prtt Isospn Isospn dstrbutons: soluton dstrbutons: soluton S.Cheng nd S.P. PRC 23 One cn show non-trvl Ρ α β α α ~ ; ; 2 n n e n m C M I m M I n N W n m C N W N W N P m E M I m M I M I I M I M I Isospn decomposton of cycle dgrm for pons n one untum stte Clculted brute force wth rsng/lowerng opertors
18 Isospn dstrbutons: results π ρ ω gs t T5 MeV Rndom Isosnglet + symmetry + resonnces Scott Prtt Bose effects broden dstrbuton Resonnces nrrow dstrbuton Resonnces wn
19 Conservng SU3 color ll systems re confned to color snglets Constrnt should lower entropy Color multplets re lbeled p Snglet s s nt- s gluon s Scott Prtt
20 ddng color multplets Scott Prtt
21 Scott Prtt Recurson reltons for gluons Recurson reltons for gluons ; p p p p p C p p p p p β From Young-tbleux ddton rules Must now Color decomposton of: Ρ p 3 2 2
22 Color decomposton of cycle dgrm Cycle dgrm wth no p projecton
23 Color decomposton of cycle dgrm Gluons: C Qurs: C
24 Clcultng for prton gs J.Ruppert nd S.P. PRC 23 Clculte p for gluons Clculte p for strnge urs Convolute strnge/ntstrnge ps P Q p p p p β p p ; P Q Clculte I p for up/down urs Convolute up/down p wth ntup/ntdown p Keep only I pece of up/down/ntup/ntdown Convolute both ur segments Convolute ur sector wth gluon sector Keep only p pece.
25 Prton gs: results Effects re mportnt for V < fm 3 Wht re effectve volumes t RHIC? 2 fm 3?
26 sde: Why re the constrnts so lrge for systems wth 5 prtons? Now consder the SU3 cse dd gluons p rndom wl n 2-d P p p + + p + pexp 2 2 p 2 Pp ~ -4 Entropy penlty ~ -4 log For 2 gluons:.53x 8 multplets chnce of snglet /22558
27 Summry We cn clculte nythng When you hve hmmer every problem loos le nl. -K.H. Interctons re gnored Men Feld or st-order perturbton theory s esy Itertve perturbton theory? or BBGKY herrchy?
Electrochemical Thermodynamics. Interfaces and Energy Conversion
CHE465/865, 2006-3, Lecture 6, 18 th Sep., 2006 Electrochemcl Thermodynmcs Interfces nd Energy Converson Where does the energy contrbuton F zϕ dn come from? Frst lw of thermodynmcs (conservton of energy):
4. More general extremum principles and thermodynamic potentials
4. More generl etremum prncples nd thermodynmc potentls We hve seen tht mn{u(s, X )} nd m{s(u, X)} mply one nother. Under certn condtons, these prncples re very convenent. For emple, ds = 1 T du T dv +
Chemistry 163B Absolute Entropies and Entropy of Mixing
Chemstry 163 Wnter 1 Hndouts for hrd Lw nd Entropy of Mxng (del gs, dstngushle molecules) PPENDIX : H f, G f, U S (no Δ, no su f ) Chemstry 163 solute Entropes nd Entropy of Mxng Hº f Gº f Sº 1 hrd Lw
6. Chemical Potential and the Grand Partition Function
6. Chemcl Potentl nd the Grnd Prtton Functon ome Mth Fcts (see ppendx E for detls) If F() s n nlytc functon of stte vrles nd such tht df d pd then t follows: F F p lso snce F p F we cn conclude: p In other
Applied Statistics Qualifier Examination
Appled Sttstcs Qulfer Exmnton Qul_june_8 Fll 8 Instructons: () The exmnton contns 4 Questons. You re to nswer 3 out of 4 of them. () You my use ny books nd clss notes tht you mght fnd helpful n solvng
4. Eccentric axial loading, cross-section core
. Eccentrc xl lodng, cross-secton core Introducton We re strtng to consder more generl cse when the xl force nd bxl bendng ct smultneousl n the cross-secton of the br. B vrtue of Snt-Vennt s prncple we
Many-Body Calculations of the Isotope Shift
Mny-Body Clcultons of the Isotope Shft W. R. Johnson Mrch 11, 1 1 Introducton Atomc energy levels re commonly evluted ssumng tht the nucler mss s nfnte. In ths report, we consder correctons to tomc levels
Intro to Nuclear and Particle Physics (5110)
Intro to Nucler nd Prticle Physics (5110) Feb, 009 The Nucler Mss Spectrum The Liquid Drop Model //009 1 E(MeV) n n(n-1)/ E/[ n(n-1)/] (MeV/pir) 1 C 16 O 0 Ne 4 Mg 7.7 14.44 19.17 8.48 4 5 6 6 10 15.4.41
Partially Observable Systems. 1 Partially Observable Markov Decision Process (POMDP) Formalism
CS294-40 Lernng for Rootcs nd Control Lecture 10-9/30/2008 Lecturer: Peter Aeel Prtlly Oservle Systems Scre: Dvd Nchum Lecture outlne POMDP formlsm Pont-sed vlue terton Glol methods: polytree, enumerton,
Physics 9 Fall 2011 Homework 2 - Solutions Friday September 2, 2011
Physics 9 Fll 0 Homework - s Fridy September, 0 Mke sure your nme is on your homework, nd plese box your finl nswer. Becuse we will be giving prtil credit, be sure to ttempt ll the problems, even if you
19 Optimal behavior: Game theory
Intro. to Artificil Intelligence: Dle Schuurmns, Relu Ptrscu 1 19 Optiml behvior: Gme theory Adversril stte dynmics hve to ccount for worst cse Compute policy π : S A tht mximizes minimum rewrd Let S (,
Quantum Mechanics Qualifying Exam - August 2016 Notes and Instructions
Quntum Mechnics Qulifying Exm - August 016 Notes nd Instructions There re 6 problems. Attempt them ll s prtil credit will be given. Write on only one side of the pper for your solutions. Write your lis
Haddow s Experiment:
schemtc drwng of Hddow's expermentl set-up movng pston non-contctng moton sensor bems of sprng steel poston vres to djust frequences blocks of sold steel shker Hddow s Experment: terr frm Theoretcl nd
Lecture 36. Finite Element Methods
CE 60: Numercl Methods Lecture 36 Fnte Element Methods Course Coordntor: Dr. Suresh A. Krth, Assocte Professor, Deprtment of Cvl Engneerng, IIT Guwht. In the lst clss, we dscussed on the ppromte methods
Problem Set 3 Solutions
Chemistry 36 Dr Jen M Stndrd Problem Set 3 Solutions 1 Verify for the prticle in one-dimensionl box by explicit integrtion tht the wvefunction ψ ( x) π x is normlized To verify tht ψ ( x) is normlized,
13: Diffusion in 2 Energy Groups
3: Diffusion in Energy Groups B. Rouben McMster University Course EP 4D3/6D3 Nucler Rector Anlysis (Rector Physics) 5 Sept.-Dec. 5 September Contents We study the diffusion eqution in two energy groups
Review of linear algebra. Nuno Vasconcelos UCSD
Revew of lner lgebr Nuno Vsconcelos UCSD Vector spces Defnton: vector spce s set H where ddton nd sclr multplcton re defned nd stsf: ) +( + ) (+ )+ 5) λ H 2) + + H 6) 3) H, + 7) λ(λ ) (λλ ) 4) H, - + 8)
CALIBRATION OF SMALL AREA ESTIMATES IN BUSINESS SURVEYS
CALIBRATION OF SMALL AREA ESTIMATES IN BUSINESS SURVES Rodolphe Prm, Ntle Shlomo Southmpton Sttstcl Scences Reserch Insttute Unverst of Southmpton Unted Kngdom SAE, August 20 The BLUE-ETS Project s fnnced
DCDM BUSINESS SCHOOL NUMERICAL METHODS (COS 233-8) Solutions to Assignment 3. x f(x)
DCDM BUSINESS SCHOOL NUMEICAL METHODS (COS -8) Solutons to Assgnment Queston Consder the followng dt: 5 f() 8 7 5 () Set up dfference tble through fourth dfferences. (b) Wht s the mnmum degree tht n nterpoltng
Topological Quantum Compiling
Topologicl Quntum Compiling Work in collbortion with: Lyl Hormozi Georgios Zikos Steven H. Simon Michel Freedmn Nd Petrovic Florid Stte University Lucent Technologies Microsoft Project Q UCSB NEB, L. Hormozi,
arxiv: v1 [hep-ph] 21 Mar 2009
![arxiv: v1 [hep-ph] 21 Mar 2009](/thumbs/88/115553101.jpg "arxiv: v1 [hep-ph] 21 Mar 2009")
1 rxv:0903.3666v1 [hep-ph] 1 Mr 009 Producton Rte of Second KK Guge Bosons n UED Models t LHC Shgek Mtsumoto Deprtment of Physcs, Unversty of Toym, Toym 930-8555, Jpn E-ml: smtsu@sc.u-toym.c.jp Joe Sto
1) Silicon oxide has a typical surface potential in an aqueous medium of ϕ,0
1) Slcon oxde has a typcal surface potental n an aqueous medum of ϕ, = 7 mv n 5 mm l at ph 9. Whch concentraton of catons do you roughly expect close to the surface? What s the average dstance between
LOCAL FRACTIONAL LAPLACE SERIES EXPANSION METHOD FOR DIFFUSION EQUATION ARISING IN FRACTAL HEAT TRANSFER
Yn, S.-P.: Locl Frctonl Lplce Seres Expnson Method for Dffuson THERMAL SCIENCE, Yer 25, Vol. 9, Suppl., pp. S3-S35 S3 LOCAL FRACTIONAL LAPLACE SERIES EXPANSION METHOD FOR DIFFUSION EQUATION ARISING IN
THE COMBINED SHEPARD ABEL GONCHAROV UNIVARIATE OPERATOR
REVUE D ANALYSE NUMÉRIQUE ET DE THÉORIE DE L APPROXIMATION Tome 32, N o 1, 2003, pp 11 20 THE COMBINED SHEPARD ABEL GONCHAROV UNIVARIATE OPERATOR TEODORA CĂTINAŞ Abstrct We extend the Sheprd opertor by
PHY688, Statistical Mechanics
Department of Physcs & Astronomy 449 ESS Bldg. Stony Brook Unversty January 31, 2017 Nuclear Astrophyscs James.Lattmer@Stonybrook.edu Thermodynamcs Internal Energy Densty and Frst Law: ε = E V = Ts P +
We partition C into n small arcs by forming a partition of [a, b] by picking s i as follows: a = s 0 < s 1 < < s n = b.
![We partition C into n small arcs by forming a partition of [a, b] by picking s i as follows: a = s 0 < s 1 < < s n = b.](/thumbs/93/114277851.jpg "We partition C into n small arcs by forming a partition of [a, b] by picking s i as follows: a = s 0 < s 1 < < s n = b.")
Mth 255 - Vector lculus II Notes 4.2 Pth nd Line Integrls We begin with discussion of pth integrls (the book clls them sclr line integrls). We will do this for function of two vribles, but these ides cn
Energy Bands Energy Bands and Band Gap. Phys463.nb Phenomenon
Phys463.nb 49 7 Energy Bnds Ref: textbook, Chpter 7 Q: Why re there insultors nd conductors? Q: Wht will hppen when n electron moves in crystl? In the previous chpter, we discussed free electron gses,
Planar maps and continued fractions
Batz 2010 p. 1/4 Planar maps and contnued fractons n collaboraton wth Jéréme Boutter 1 3 3 2 0 3 1 maps and dstances: generaltes Batz 2010 p. 2/4 Batz 2010 p. 3/4 degree of a face = number of ncdent edge
Name Solutions to Test 3 November 8, 2017
Nme Solutions to Test 3 November 8, 07 This test consists of three prts. Plese note tht in prts II nd III, you cn skip one question of those offered. Some possibly useful formuls cn be found below. Brrier
Strong Gravity and the BKL Conjecture
Introducton Strong Grvty nd the BKL Conecture Dvd Slon Penn Stte October 16, 2007 Dvd Slon Strong Grvty nd the BKL Conecture Introducton Outlne The BKL Conecture Ashtekr Vrbles Ksner Sngulrty 1 Introducton
CS667 Lecture 6: Monte Carlo Integration 02/10/05
CS667 Lecture 6: Monte Crlo Integrtion 02/10/05 Venkt Krishnrj Lecturer: Steve Mrschner 1 Ide The min ide of Monte Crlo Integrtion is tht we cn estimte the vlue of n integrl by looking t lrge number of
Name: SID: Discussion Session:
Nme: SID: Dscusson Sesson: hemcl Engneerng hermodynmcs -- Fll 008 uesdy, Octoer, 008 Merm I - 70 mnutes 00 onts otl losed Book nd Notes (5 ponts). onsder n del gs wth constnt het cpctes. Indcte whether
Lecture 8. Band theory con.nued
Lecture 8 Bnd theory con.nued Recp: Solved Schrodinger qu.on for free electrons, for electrons bound in poten.l box, nd bound by proton. Discrete energy levels rouse. The Schrodinger qu.on pplied to periodic
Introduction to Numerical Integration Part II
Introducton to umercl Integrton Prt II CS 75/Mth 75 Brn T. Smth, UM, CS Dept. Sprng, 998 4/9/998 qud_ Intro to Gussn Qudrture s eore, the generl tretment chnges the ntegrton prolem to ndng the ntegrl w
UNIVERSITY OF IOANNINA DEPARTMENT OF ECONOMICS. M.Sc. in Economics MICROECONOMIC THEORY I. Problem Set II
Mcroeconomc Theory I UNIVERSITY OF IOANNINA DEPARTMENT OF ECONOMICS MSc n Economcs MICROECONOMIC THEORY I Techng: A Lptns (Note: The number of ndctes exercse s dffculty level) ()True or flse? If V( y )
Jens Siebel (University of Applied Sciences Kaiserslautern) An Interactive Introduction to Complex Numbers
Jens Sebel (Unversty of Appled Scences Kserslutern) An Interctve Introducton to Complex Numbers 1. Introducton We know tht some polynoml equtons do not hve ny solutons on R/. Exmple 1.1: Solve x + 1= for
Physics 121 Sample Common Exam 2 Rev2 NOTE: ANSWERS ARE ON PAGE 7. Instructions:
Physcs 121 Smple Common Exm 2 Rev2 NOTE: ANSWERS ARE ON PAGE 7 Nme (Prnt): 4 Dgt ID: Secton: Instructons: Answer ll 27 multple choce questons. You my need to do some clculton. Answer ech queston on the
On Hypercomplex Extensions of Quantum Theory
Journl of Modern Physcs, 5, 6, 698-79 Publshed Onlne Aprl 5 n ScRes. http://www.scrp.org/ournl/mp http://dx.do.org/.436/mp.5.6575 On Hypercomplex Extensons of Quntum Theory Dnel Sepunru RQE Reserch enter
ftp.fe?a:fmmmhm Quickly get policy ) long generally equilibrium independent steady P # steady E amp= : Dog steady systems Every equilibrium by density
Introduction fle SI 3 61 Non equilibrium Sttisticl Mechnics 2520 1 Techer : Tens It Brdrsonbrdrson@kthse Office 174 : 1049 ( open door policy Lecture 1 & The second lw nd origin of irreversibility Wht
Lecture 21: Order statistics
Lecture : Order sttistics Suppose we hve N mesurements of sclr, x i =, N Tke ll mesurements nd sort them into scending order x x x 3 x N Define the mesured running integrl S N (x) = 0 for x < x = i/n for
Lecture 4: Piecewise Cubic Interpolation
Lecture notes on Vrtonl nd Approxmte Methods n Appled Mthemtcs - A Perce UBC Lecture 4: Pecewse Cubc Interpolton Compled 6 August 7 In ths lecture we consder pecewse cubc nterpolton n whch cubc polynoml
Numerical Integration
Numericl Integrtion Wouter J. Den Hn London School of Economics c 2011 by Wouter J. Den Hn June 3, 2011 Qudrture techniques I = f (x)dx n n w i f (x i ) = w i f i i=1 i=1 Nodes: x i Weights: w i Qudrture
Module 3 LOSSY IMAGE COMPRESSION SYSTEMS. Version 2 ECE IIT, Kharagpur
Module 3 LOSSY IMAGE COMPRESSION SYSTEMS Verson ECE IIT, Kharagpur Lesson 6 Theory of Quantzaton Verson ECE IIT, Kharagpur Instructonal Objectves At the end of ths lesson, the students should be able to:
PES 1120 Spring 2014, Spendier Lecture 6/Page 1
PES 110 Sprng 014, Spender Lecture 6/Page 1 Lecture today: Chapter 1) Electrc feld due to charge dstrbutons -> charged rod -> charged rng We ntroduced the electrc feld, E. I defned t as an nvsble aura
7.2 Volume. A cross section is the shape we get when cutting straight through an object.
7. Volume Let s revew the volume of smple sold, cylnder frst. Cylnder s volume=se re heght. As llustrted n Fgure (). Fgure ( nd (c) re specl cylnders. Fgure () s rght crculr cylnder. Fgure (c) s ox. A
Chemical Reaction Engineering
Lecture 20 hemcl Recton Engneerng (RE) s the feld tht studes the rtes nd mechnsms of chemcl rectons nd the desgn of the rectors n whch they tke plce. Lst Lecture Energy Blnce Fundmentls F E F E + Q! 0
International Journal of Pure and Applied Sciences and Technology
Int. J. Pure Appl. Sc. Technol., () (), pp. 44-49 Interntonl Journl of Pure nd Appled Scences nd Technolog ISSN 9-67 Avlle onlne t www.jopst.n Reserch Pper Numercl Soluton for Non-Lner Fredholm Integrl
Chapter 5. , r = r 1 r 2 (1) µ = m 1 m 2. r, r 2 = R µ m 2. R(m 1 + m 2 ) + m 2 r = r 1. m 2. r = r 1. R + µ m 1
Tor Kjellsson Stockholm University Chpter 5 5. Strting with the following informtion: R = m r + m r m + m, r = r r we wnt to derive: µ = m m m + m r = R + µ m r, r = R µ m r 3 = µ m R + r, = µ m R r. 4
Physics 121 Sample Common Exam 1 NOTE: ANSWERS ARE ON PAGE 8. Instructions:
Physics 121 Smple Common Exm 1 NOTE: ANSWERS ARE ON PAGE 8 Nme (Print): 4 Digit ID: Section: Instructions: Answer ll questions. uestions 1 through 16 re multiple choice questions worth 5 points ech. You
Chapter Newton-Raphson Method of Solving a Nonlinear Equation
Chpter 0.04 Newton-Rphson Method o Solvng Nonlner Equton Ater redng ths chpter, you should be ble to:. derve the Newton-Rphson method ormul,. develop the lgorthm o the Newton-Rphson method,. use the Newton-Rphson
University of Washington Department of Chemistry Chemistry 453 Winter Quarter 2010 Homework Assignment 4; Due at 5p.m. on 2/01/10
University of Wshington Deprtment of Chemistry Chemistry 45 Winter Qurter Homework Assignment 4; Due t 5p.m. on // We lerned tht the Hmiltonin for the quntized hrmonic oscilltor is ˆ d κ H. You cn obtin
Research Article On the Upper Bounds of Eigenvalues for a Class of Systems of Ordinary Differential Equations with Higher Order
Hndw Publshng Corporton Interntonl Journl of Dfferentl Equtons Volume 0, Artcle ID 7703, pges do:055/0/7703 Reserch Artcle On the Upper Bounds of Egenvlues for Clss of Systems of Ordnry Dfferentl Equtons
Least squares. Václav Hlaváč. Czech Technical University in Prague
Lest squres Václv Hlváč Czech echncl Unversty n Prgue hlvc@fel.cvut.cz http://cmp.felk.cvut.cz/~hlvc Courtesy: Fred Pghn nd J.P. Lews, SIGGRAPH 2007 Course; Outlne 2 Lner regresson Geometry of lest-squres
ψ ij has the eigenvalue
Moller Plesset Perturbton Theory In Moller-Plesset (MP) perturbton theory one tes the unperturbed Hmltonn for n tom or molecule s the sum of the one prtcle Foc opertors H F() where the egenfunctons of
d-mixing Ratios Calculations Using CST, a 2 -Ratio and LSF
JOURNA OF COEGE OFEDUCATION NO.. d-mxng Rtos Clcultons Usng CST, -Rto nd SF Methods or g-trnstons n 6 Fe Isotope By Pro. Khld S. Ibrhem Asst. Pro. Imn T. Al-Alwy Ahmed Mus Shweh Al-Mustnsryh Unversty -College
SOLUTIONS FOR ANALYSIS QUALIFYING EXAM, FALL (1 + µ(f n )) f(x) =. But we don t need the exact bound.) Set
SOLUTIONS FOR ANALYSIS QUALIFYING EXAM, FALL 28 Nottion: N {, 2, 3,...}. (Tht is, N.. Let (X, M be mesurble spce with σ-finite positive mesure µ. Prove tht there is finite positive mesure ν on (X, M such
Ionization fronts in HII regions
Ionzaton fronts n HII regons Intal expanson of HII onzaton front s supersonc, creatng a shock front. Statonary frame: front advances nto neutral materal In frame where shock front s statonary, neutral
Prof. Anchordoqui. Problems set # 4 Physics 169 March 3, 2015
Prof. Anchordoui Problems set # 4 Physics 169 Mrch 3, 15 1. (i) Eight eul chrges re locted t corners of cube of side s, s shown in Fig. 1. Find electric potentil t one corner, tking zero potentil to be
Solution of Tutorial 5 Drive dynamics & control
ELEC463 Unversty of New South Wles School of Electrcl Engneerng & elecommunctons ELEC463 Electrc Drve Systems Queston Motor Soluton of utorl 5 Drve dynmcs & control 500 rev/mn = 5.3 rd/s 750 rted 4.3 Nm
Quantifying Uncertainty
Partcle Flters Quantfyng Uncertanty Sa Ravela M. I. T Last Updated: Sprng 2013 1 Quantfyng Uncertanty Partcle Flters Partcle Flters Appled to Sequental flterng problems Can also be appled to smoothng problems
Cramer-Rao Lower Bound for a Nonlinear Filtering Problem with Multiplicative Measurement Errors and Forcing Noise
Preprnts of the 9th World Congress he Interntonl Federton of Automtc Control Crmer-Ro Lower Bound for Nonlner Flterng Problem wth Multplctve Mesurement Errors Forcng Nose Stepnov О.А. Vslyev V.А. Concern
Chemical Reaction Engineering
Lecture 20 hemcl Recton Engneerng (RE) s the feld tht studes the rtes nd mechnsms of chemcl rectons nd the desgn of the rectors n whch they tke plce. Lst Lecture Energy Blnce Fundmentls F 0 E 0 F E Q W
Physics Graduate Prelim exam
Physics Grdute Prelim exm Fll 2008 Instructions: This exm hs 3 sections: Mechnics, EM nd Quntum. There re 3 problems in ech section You re required to solve 2 from ech section. Show ll work. This exm is
PHY4605 Introduction to Quantum Mechanics II Spring 2005 Final exam SOLUTIONS April 22, 2005
. Short Answer. PHY4605 Introduction to Quntum Mechnics II Spring 005 Finl exm SOLUTIONS April, 005 () Write the expression ψ ψ = s n explicit integrl eqution in three dimensions, ssuming tht ψ represents
Rate of Absorption and Stimulated Emission
MIT Department of Chemstry 5.74, Sprng 005: Introductory Quantum Mechancs II Instructor: Professor Andre Tokmakoff p. 81 Rate of Absorpton and Stmulated Emsson The rate of absorpton nduced by the feld
Chapter Newton-Raphson Method of Solving a Nonlinear Equation
Chpter.4 Newton-Rphson Method of Solvng Nonlner Equton After redng ths chpter, you should be ble to:. derve the Newton-Rphson method formul,. develop the lgorthm of the Newton-Rphson method,. use the Newton-Rphson
Baryonic Spectral Functions at Finite Temperature
Baryonic Spectral Functions at Finite Temperature Masayuki Asakawa Department of Physics, Osaka University July 2008 @ XQCD 2008 QCD Phase Diagram T LHC 160-190 MeV 100MeV ~ 10 12 K RHIC crossover CEP(critical
Recent developments in the nonelastic reaction code BRIEFF deuteron induced reaction and emission
Recent developments n the nonelastc reacton code BRIEFF deuteron nduced reacton and emsson H. Duarte CEA/DAM/DIF helder.duarte@cea.fr EFNUDAT Pars, France 25-27 May 20 H. Duarte EFNUDAT, May 20 LCP producton
The History and Lessons of the Hagedorn Model
The History and Lessons of the Hagedorn Model K.A.Bugaev Bogolyubov ITP, Kiev, Ukraine in collaboration with J.B.Ellio", L.W. Phair and L.G.More"o 1 Outline: What T do we see in A+A and elementary particle
. You need to do this for each force. Let s suppose that there are N forces, with components ( N) ( N) ( N) = i j k
EN3: Introducton to Engneerng and Statcs Dvson of Engneerng Brown Unversty 3. Resultant of systems of forces Machnes and structures are usually subected to lots of forces. When we analyze force systems
Math 426: Probability Final Exam Practice
Mth 46: Probbility Finl Exm Prctice. Computtionl problems 4. Let T k (n) denote the number of prtitions of the set {,..., n} into k nonempty subsets, where k n. Argue tht T k (n) kt k (n ) + T k (n ) by
Fundamentals of Analytical Chemistry
Homework Fundmentls of nlyticl hemistry hpter 9 0, 1, 5, 7, 9 cids, Bses, nd hpter 9(b) Definitions cid Releses H ions in wter (rrhenius) Proton donor (Bronsted( Lowry) Electron-pir cceptor (Lewis) hrcteristic
Substitution Matrices and Alignment Statistics. Substitution Matrices
Susttuton Mtrces nd Algnment Sttstcs BMI/CS 776 www.ostt.wsc.edu/~crven/776.html Mrk Crven crven@ostt.wsc.edu Ferur 2002 Susttuton Mtrces two oulr sets of mtrces for roten seuences PAM mtrces [Dhoff et
4 The dynamical FRW universe
4 The dynmicl FRW universe 4.1 The Einstein equtions Einstein s equtions G µν = T µν (7) relte the expnsion rte (t) to energy distribution in the universe. On the left hnd side is the Einstein tensor which
F(T) Dark Energy Model and SNe Data
Avlble onlne t www.worldscentfcnews.com WSN (5) -6 EISSN 39-9 F() Drk Energy Model nd SNe Dt S. Dvood Sdtn, Amn Anvr b Deprtment of Physcs, Fculty of Bsc Scences, Unversty of Neyshbur, P. O. Box 9387333,
PH12b 2010 Solutions HW#3
PH 00 Solutions HW#3. The Hmiltonin of this two level system is where E g < E e The experimentlist sis is H E g jgi hgj + E e jei hej j+i p (jgi + jei) j i p (jgi jei) ) At t 0 the stte is j (0)i j+i,
The Periodically Forced Harmonic Oscillator
The Periodiclly Forced Hrmonic Oscilltor S. F. Ellermeyer Kennesw Stte University July 15, 003 Abstrct We study the differentil eqution dt + pdy + qy = A cos (t θ) dt which models periodiclly forced hrmonic
- 5 - TEST 2. This test is on the final sections of this session's syllabus and. should be attempted by all students.
- 5 - TEST 2 This test is on the finl sections of this session's syllbus nd should be ttempted by ll students. Anything written here will not be mrked. - 6 - QUESTION 1 [Mrks 22] A thin non-conducting
Quantum Physics I (8.04) Spring 2016 Assignment 8
Quntum Physics I (8.04) Spring 206 Assignment 8 MIT Physics Deprtment Due Fridy, April 22, 206 April 3, 206 2:00 noon Problem Set 8 Reding: Griffiths, pges 73-76, 8-82 (on scttering sttes). Ohnin, Chpter
CHAPTER - 7. Firefly Algorithm based Strategic Bidding to Maximize Profit of IPPs in Competitive Electricity Market
CHAPTER - 7 Frefly Algorthm sed Strtegc Bddng to Mxmze Proft of IPPs n Compettve Electrcty Mrket 7. Introducton The renovton of electrc power systems plys mjor role on economc nd relle operton of power
consider in the case of 1) internal resonance ω 2ω and 2) external resonance Ω ω and small damping
consder n the cse o nternl resonnce nd externl resonnce Ω nd smll dmpng recll rom "Two_Degs_Frdm_.ppt" tht θ + μ θ + θ = θφ + cos Ω t + τ where = k α α nd φ + μ φ + φ = θ + cos Ω t where = α τ s constnt
CSC 411 / CSC D11 / CSC C11
18 Boostng s a general strategy for learnng classfers by combnng smpler ones. The dea of boostng s to take a weak classfer that s, any classfer that wll do at least slghtly better than chance and use t
FUNDAMENTALS ON ALGEBRA MATRICES AND DETERMINANTS
Dol Bgyoko (0 FUNDAMENTALS ON ALGEBRA MATRICES AND DETERMINANTS Introducton Expressons of the form P(x o + x + x + + n x n re clled polynomls The coeffcents o,, n re ndependent of x nd the exponents 0,,,
Lecture 3: Shannon s Theorem
CSE 533: Error-Correctng Codes (Autumn 006 Lecture 3: Shannon s Theorem October 9, 006 Lecturer: Venkatesan Guruswam Scrbe: Wdad Machmouch 1 Communcaton Model The communcaton model we are usng conssts
Introduction: Measurements in Particle Physics
Sutomic Physics: Prticle Physics Lecture 2: Prcticl Prticle Physics 3rd Novemer 2009 Wht cn we mesure t the LHC, nd how do we interpret tht in term of fundmentl prticles nd interctions? Prticle Properties
Effects of polarization on the reflected wave
Lecture Notes. L Ros PPLIED OPTICS Effects of polrzton on the reflected wve Ref: The Feynmn Lectures on Physcs, Vol-I, Secton 33-6 Plne of ncdence Z Plne of nterfce Fg. 1 Y Y r 1 Glss r 1 Glss Fg. Reflecton
COMPLEX NUMBERS INDEX
COMPLEX NUMBERS INDEX. The hstory of the complex numers;. The mgnry unt I ;. The Algerc form;. The Guss plne; 5. The trgonometrc form;. The exponentl form; 7. The pplctons of the complex numers. School
Math 8 Winter 2015 Applications of Integration
Mth 8 Winter 205 Applictions of Integrtion Here re few importnt pplictions of integrtion. The pplictions you my see on n exm in this course include only the Net Chnge Theorem (which is relly just the Fundmentl
Math 497C Sep 17, Curves and Surfaces Fall 2004, PSU
Mth 497C Sep 17, 004 1 Curves nd Surfces Fll 004, PSU Lecture Notes 3 1.8 The generl defnton of curvture; Fox-Mlnor s Theorem Let α: [, b] R n be curve nd P = {t 0,...,t n } be prtton of [, b], then the
ragsdale (zdr82) HW2 ditmire (58335) 1
rgsdle (zdr82) HW2 ditmire (58335) This print-out should hve 22 questions. Multiple-choice questions my continue on the next column or pge find ll choices before nswering. 00 0.0 points A chrge of 8. µc
QUANTUM CHEMISTRY. Hückel Molecular orbital Theory Application PART I PAPER:2, PHYSICAL CHEMISTRY-I
Subject PHYSICAL Pper No nd Title TOPIC Sub-Topic (if ny) Module No., PHYSICAL -II QUANTUM Hückel Moleculr orbitl Theory CHE_P_M3 PAPER:, PHYSICAL -I MODULE: 3, Hückel Moleculr orbitl Theory TABLE OF CONTENTS.
arxiv:hep-th/ v1 27 Jan 2003
KOBE-TH-- Stablty of Neutral Ferm Balls wth Mult-Flavor Fermons T.Yoshda Department of Physcs, Tokyo Unversty, Hongo 7--, Bunkyo-Ku, Tokyo -, Japan K.Ogure arxv:hep-th/6v 7 Jan Department of Physcs, Kobe
An Ising model on 2-D image
School o Coputer Scence Approte Inerence: Loopy Bele Propgton nd vrnts Prolstc Grphcl Models 0-708 Lecture 4, ov 7, 007 Receptor A Knse C Gene G Receptor B Knse D Knse E 3 4 5 TF F 6 Gene H 7 8 Hetunndn
Vectors and Tensors. R. Shankar Subramanian. R. Aris, Vectors, Tensors, and the Equations of Fluid Mechanics, Prentice Hall (1962).
005 Vectors nd Tensors R. Shnkr Subrmnn Good Sources R. rs, Vectors, Tensors, nd the Equtons of Flud Mechncs, Prentce Hll (96). nd ppendces n () R. B. Brd, W. E. Stewrt, nd E. N. Lghtfoot, Trnsport Phenomen,
Complex atoms and the Periodic System of the elements
Complex atoms and the Peodc System of the elements Non-cental foces due to electon epulson Cental feld appoxmaton electonc obtals lft degeneacy of l E n l = R( hc) ( n δ ) l Aufbau pncple Lectue Notes
Nonlocal Gravity and Structure in the Universe
Nonlocl rvity nd Structure in the Universe Sohyun Prk Penn Stte University Co-uthor: Scott Dodelson Bsed on PRD 87 (013) 04003, 109.0836, PRD 90 (014) 000000, 1310.439 August 5, 014 Chicgo, IL Cosmo 014
The Study of Lawson Criterion in Fusion Systems for the
Interntonl Archve of Appled Scences nd Technology Int. Arch. App. Sc. Technol; Vol 6 [] Mrch : -6 Socety of ducton, Ind [ISO9: 8 ertfed Orgnzton] www.soeg.co/st.html OD: IAASA IAAST OLI ISS - 6 PRIT ISS
Massachusetts Institute of Technology Department of Electrical Engineering and Computer Science Quantum Optical Communication
Msschusetts Institute of Technology Deprtment of Electricl Engineering nd Computer Science 6.453 Quntum Opticl Communiction Problem Set 6 Fll 2004 Issued: Wednesdy, October 13, 2004 Due: Wednesdy, October
Title: Radiative transitions and spectral broadening
Lecture 6 Ttle: Radatve transtons and spectral broadenng Objectves The spectral lnes emtted by atomc vapors at moderate temperature and pressure show the wavelength spread around the central frequency.
Chapter 9 Many Electron Atoms
Chem 356: Introductory Quntum Mechnics Chpter 9 Mny Electron Atoms... 11 MnyElectron Atoms... 11 A: HrtreeFock: Minimize the Energy of Single Slter Determinnt.... 16 HrtreeFock Itertion Scheme... 17 Chpter