The strong CP puzzle and axions

Size: px
Start display at page:

Download "The strong CP puzzle and axions"

Transcription

1 The strong CP puzzle nd xions 1 Seongte Prk Center for Axion nd Precision Physics(CAPP) Institute for Bsic Science, South Kore Workshop on The strong CP puzzle nd xions LPSC, Grenoble Frnce My. 14~16, 018

2 Outline

3 3 Center for Axion nd Precision Physics (CAPP) t Institute for Bsic Science (IBS) (Director: Ynnis Semertzidis) Web site: Locted t KAIST cmpus in Dejeon, South Kore We re working on: Axion-drk mtter serch Microwve resonnce cvity xion serch (Cryogenics, Electronics, Super conducting mgnet, SQUID, etc.) ARIADNE, GNOME Storge ring Proton/Deuteron EDM Polrimeter, Bem position monitoring (with mgnetic shielding), Bem dynmics, etc. Storge ring xion serch Muon g- experiment Fermi lb. muon g-, J-PARC Others (COMET, etc) Ptrs workshop, 016 (next week, 0~4, June)

4 EDM nd CP violtion 4 Motivtion Strong CP problem, QCD Mtter-ntimtter symmetry (Bryogenesis) Electric Dipole Moment -Q +Q r d Qr P, T violtion due to n EDM H B d E T ( B, chnge) : H B d E P( E chnge) : H B d E q q g, d m mc A nonzero prticle EDM violtes P, T, nd ssuming CPT conservtion, lso CP violtion.

5 Serching EDM 5 Current EDM bounds The first EDM experiment strted by Smith, Purcell nd Rmsey in 1951 SM predicts non-vnishing EDM (nd published in 1957) obtining d e < e.cm limit of d n < e cm. d n,p < e.cm Beyond current experiment limit SUSY prediction: 10-5 ~10-8 e cm (nedm limit) Neutron EDM bound: d n <.9x10-6 e.cm ( 06) Proton EDM bound: d p <7.9x10-5 e.cm ( 09, 199 Hg) Electron EDM bound: d e <8.7x10-9 e. cm ( 14,ThO) Trget sensitivity level in the storge pedm experiment High sttistics (10 11 protons/store) is chievble using storge ring Gol 10-9 e cm (sttisticl limit in bout one yer) e cm (with n upgrde) Physics rech >10 3 TeV

6 EDM nd spin precession/principle Spin dynmics (with EDM nd MDM) in mgnetic+electric field (T-BMT eqution ) 0 B E with, 1 1 g B c E c E B m e MDM in B-field MDM in induced B-field EDM term 6 ) / ( ), / ( mc e d m e g ( edm ) s dxe xb dt ds edm (for prticle t rest) (T-BMT eqution: for moving prticle)

7 Storge ring technique for EDM serch 7 g- precession in pure electric ring e m m p E c for the proton (= (3)) >0 m 0 t p GeV/c : mgic momentum Use frozen spin method (sttic EDM mesurement) Spin freezes to the momentum direction >0 prticles (p,e, etc.): use mgic momentum Pure electric ring CW/CCW bems (minimize systemtic error!) <0 (deuteron) : use E+B field spin precesses only on the verticl plne! e E EDM m c Storge ring EDM collbortion is trying to estblish the experiment t CERN EDM Kick-off meeting t CERN in Mr. 017 Second meeting t Juelich, Germny (Mr. 018)

8 Polrimeter nd symmetry 8 Use symmetricl proton scttering on Crbon trget Hdronic elstic scttering (spin-orbit interction) Asymmetricl proton hit distribution on the detector plne L/R (U/D) symmetry for verticl (horizontl) component of proton polriztion For spin 1/ prticle ( ) ( )[1 PA] P y y unpol y y L / R symmetry 1 L R A L R L R L R P A LR y y Incoming protons P y is clculted from the symmetry with known A y P y chnges in time due to the precession in E field. Simultion by Hoyong Jeong

9 Slow bem extrction to trget 9 COSY crbon tube trget COSY ring (Juelich, Germny) COSY EDDA detector FZJ, Juelich, Germny

10 Sttisticl error of mesured EDM d (sttisticl sensitivity) 10 L/R symmetry for verticl polriztion LR ( t ) L R ( t ) L R pa t t de t / P: degree of bem polriztion d : EDM, E: Electric field, t : mesurement time Sttisticl error for d d PAE N tot ft tot p where P is the degree of polriztion, A nlyzing power nd E is the electric field cusing the spin precession. If we use the prmeters P = 0.8, A = 0.6, E = 10.5 MV/m, N tot = prticles/storge, n effective detection efficiency of f = 0.011, totl running time T tot = 10 7 s/yer, nd spin coherence time of p = 10 3 s, the resulting sttisticl error is ~ e.cm per yer.

11 Spin precession rte 11 *From pedm proposl In pedm experiment, spin processes on the verticl plne. The storge time will be 1000 s. EDM signl of ~3 rd/1000s Projected systemtic error << 1 ppm Need long spin coherence time Alredy chieved >1000 s SCT (COSY)

12 Sttisticl errors nd figure of merit 1 L/R symmetry LR L R p y Ay L R The uncertinty in the symmetry is given by p y LR y A 1 N A 0 y The denomintor is clled the Figure Of Merit. FOM A N 0 : differentil cross section Optimum ngle (FOM) rnge: 5~0 deg. pedm polrimeter (from pedm proposl)

13 AxionEDM serch 13

14 About xion induced oscillting EDM 14 Drk mtter xion bckground field is oscillting = 0 cos( t) m c /, m : xion mss The oscillting xion field is coupled with Photon P B VCQ sig g m 0 gluons, fermions, nucleon, etc. Oscillting EDM ( t ) 0 cos( mt ) dt () d cos( mt ) d n f L ecm cos( m t)[ ecm] x Generic feture Peter W. Grhm nd Surjeet Rjendrn. Phys. Rev. D, 84, , (011) Phys. Rev. D, 88, 03503, (013)

15 Axion coupled EDM mesurement using storge ring method 15 sredm (CAPP) Peter W. Grhm, Surjeet Rjendrn, Phys. Rev. D 84, (011). Experiments on xion serch() Our proposl: Scn frequency rnge 10-9 Hz~10 8 Hz using storge ring technique. xion prmeter spce:10 13 GeV f GeV

16 Spin trcking for AxionEDM serch 16 B c E c E c E g B g B g s m e dt ds c E c E B m e dt d ) ( 1 1 ) ( 1 1 mc e s mc e d m ge m s ge 4 / ) / (, /4 ) / ( ( edm ) s dxe xb dt ds In prticle t rest 0 () cos( ) ()4 () dt d t dt mc t e In storge ring

17 EDM precession t resonnce condition 17 E * s EDM prec : d()>0 d()<0 EDM prec : s ds dt EDM e mc s E * dt () d cos( t ) dt ()4mc () t e 0

18 Resonnce of Axion induced oscillting EDM with g- precession in storge ring 18 c E B m e 1 1 B c E m e d * *, d d d E E E c B dt Benefit from strong effective E field! Deuteron, d 0 =10-7 e.cm -3x10-7 rd/s

19 Sttic EDM nd oscillting EDM experiments 19 Sttic EDM mesurement Use frozen spin (FS) method Spin precesses only on the verticl plne No precession on the ring plne edm e E mc Axion-EDM mesurement uses non-zero g- precession Resonnce method Spin precession on the ring plne Benefit from lrger effective E-field ( ) More sensitive Also uses FS method for low frequency serch (<mhz) edm d d E * *, E E c B dt s s=1/ for protons, 1 for deuterons

20 Estimtion of the sensitivity 0 f xion =10 5 Hz Error for the EDM d s d E * edm From symmetry simultion Simulted L/R symmetry with liner fit L R symmetry P A / LR y y L R L R

21 Determintion of storge ring prmeters 1 Pure mgnetic ring for deuteron, =-0.14 Ring bending rdius r=10m d PAE N tot ft tot p E+B ring Pure B field ring Use E+B combined ring to improve the sensitivity

22 Sensitivity clcultion results for Deuteron Sensitivity(e.cm), 8x10 7 s mesurement B (T) P (GeV/c) f g- (Hz) Er (V/m) E* (V/m) SCT=10 3 s SCT=10 4 s SCT=10 5 s Ring Q=3E6 Q=1E10 Q=3E6 Q=1E10 Q=3E6 Q=1E E E E E E E E E-3 9.9E E+0 8.8E E E E E E E E E E E E E E E E E E E E E E E E-31 1.E E-3 E/B ring E E E E E E-30.9E E E-3 A= E E E E E E-30.7E E E-3 r=10 m E E E E-30 7.E E-30.3E E-30 5.E E E E E-30 6.E E-30.0E E E E E E E E E E E E E E E E E E E E E E E+06.01E E E-31.5E E-3.5E E E E E E E E E E-3 A= E E E E-3 4.4E-30.5E-3 4.4E-30.4E-3 r=10 m E * : effective electric field, SCT: spin coherence time, Q:xion qulity fctor, A: nlyzing power of the polrimeter, r: ring rdius

23 Sensitivity clcultion results for Proton 3 Sensitivity(e.cm), 8x10 7 s mesurement B (T) P (GeV/c) f g- (Hz) Er (V/m) E* (V/m) SCT=10 3 s SCT=10 4 s SCT=10 5 s Q=3E6 Q=1E10 Q=3E6 Q=1E10 Q=3E6 Q=1E E E E E E E E E E E+0-8.0E E E E E E-31.E E E E E E E E E E E E E E+06.E E E E E E-31 E/B ring E E E E E E E E E-31 A= E E E E E E E E-30.0E-31 r=5 m E E E+06 1.E-9 1.1E-30 1.E-9 4.8E-31 1.E-9.3E E E E E-9 1.7E E-9 5.3E E-9.9E E+05-1.E E E-9 1.7E E-9 5.4E E-9 3.4E E E E+06.1E-9 1.7E-30.1E-9 5.5E-31.1E-9 3.8E E E E-9 3.6E E-9 1.9E E-9.4E-31 A= E E+09.3E-9 3.9E-3 3.4E-9 5.8E-3 3.4E-9 5.8E-3 r=10 m E * : effective electric field, SCT: spin coherence time, Q:xion qulity fctor, A: nlyzing power of the polrimeter, r: ring rdius

24 Axion phse effect 4 dt () d cos( t ) x =0 mens d is prllel to s, positive nd mx. 0 x EDM depends on the initil xion phse ( x ). However ctul EDM cn be obtined from the mesurement of two orthogonl initil spin settings. EDM EDM, S1 EDM, S Axion phse is not n experimentlly controllble prmeter

25 Low frequency (<mhz) mesurement with FS conditions 5 Exmple: with d 0 =10-7 e.cm FS condition Prticl Deuteron Momentum GeV/c B-field T E-field E+06 V/m E* E+07 V/m AP=0.36, SCT=10 4 s f xion =10-6 Hz No extr mesurement is required for the xion serch in this frequency region (<mhz). One cn do the sttic EDM experiment with frozen spin conditions nd do the nlysis for xion signl serch fterwrds. Sensitivity =4.x10-31 e.cm for 4 yers of mesurement ( 8x10 7 s)

26 Experiment limit 6 locl DM 0.3 GeV / cm 3 nedm: Ultr-cold neutron trp experiment

27 Summry nd pln 7 Sttic EDM serch using the storge ring with frozen spin method (cpedm collbortion), ~10-9 e.cm We propose using the storge ring EDM method to mesure the xion induced oscillting EDM t the resonnce conditions between the xion frequency nd g- precession frequency (> mhz). Bellow mhz region cn be serched using frozen spin condition. The resulting sensitivity reches up to ~10-3 e.cm for n oscillting EDM which hve never been implemented so fr. A wide rnge of frequency (10-9 Hz~10 8 Hz) of xion drk mtter cn be tested using both deuterons nd protons in the sme storge ring. One experiment two physics mesurements (EDM+Axion) Plns: Prepring proposl for the mesurement t COSY (Juelich, Germny) This work cn be found in the rxiv:

28 Center for Axion nd Precision Physics (, KAIST) 8 We re working on: Axion serch Proton/Deuteron EDM Muon g- experiment Etc. Locted t KAIST cmpus in Dejeon, South Kore Thnk you!

Electric Dipole Moments of Charged Particles

Electric Dipole Moments of Charged Particles 1 / 18 Electric Dipole Moments of Charged Particles Activities at COSY/Forschungszentrum Jülich - Plans for a new Storage Ring at CERN J. Pretz RWTH Aachen & FZ Jülich CERN, Physics Beyond Colliders, November

More information

Axion dark matter search using the storage ring EDM method

Axion dark matter search using the storage ring EDM method Axion dark matter search using the storage ring EDM method Seung Pyo Chang, a,b Selcuk Haciomeroglu, a On Kim, a,b Soohyung Lee, a Seongtae Park, a Yannis K. Semertzidis a,b a Center for Axion and Precision

More information

J. Ruz, J. K. Vogel, M. J. Pivovaroff, G. Brown, D. Smith, H. Hudson, B. Grefenstette, L. Glesener and H. Iain

J. Ruz, J. K. Vogel, M. J. Pivovaroff, G. Brown, D. Smith, H. Hudson, B. Grefenstette, L. Glesener and H. Iain J. Ruz, J. K. Vogel, M. J. Pivovroff, G. Brown, D. Smith, H. Hudson, B. Grefenstette, L. Glesener nd H. Iin August 10 th 2017 Columbus, OH LLNL-PRES-736641 This work ws performed under the uspices of the

More information

Transverse spin asymmetries at low momentum transfer at STAR

Transverse spin asymmetries at low momentum transfer at STAR Trnsverse spin symmetries t low momentum trnsfer t STAR Dmitry Svirid (ITEP) for the STAR Collbortion EDS Blois 2011 14th Workshop on Elstic nd Diffrctive Scttering, Qui Nhon, Vietnm, December 15-21, 2011

More information

Challenges for EDM Storage Ring

Challenges for EDM Storage Ring + - Challenges for EDM Storage Ring Mei Bai IKP-4, Forschungszentrum, Juelich M. Bai KFB workshop, Feb. 16-17, 2017, https://indico.cern.ch/event/581462/timetable/#all Outline Introduction Challenges o

More information

Nuclear Time-Reversal Violation and Atomic Electric Dipole Moments

Nuclear Time-Reversal Violation and Atomic Electric Dipole Moments 225 R Nucler Time-Reversl Violtion nd Atomic Electric Dipole Moments J. Engel University of North Crolin October 10, 2005 Outline T Symmetry EDM s 199 Hg 225 R 1 T Symmetry T is Different Observed T Violtion

More information

Challenges in optics requirement and control of Storage Rings for Precision Measurement of EDM

Challenges in optics requirement and control of Storage Rings for Precision Measurement of EDM Mitglied der Helmholtz-Gemeinschaft Challenges in optics requirement and control of Storage Rings for Precision Measurement of EDM February 6, 2015 Andreas Lehrach RWTH Aachen University & Forschungszentrum

More information

Storage Ring Based EDM Search Achievements and Goals

Storage Ring Based EDM Search Achievements and Goals Mitglied der Helmholtz-Gemeinschaft Storage Ring Based EDM Search Achievements and Goals October 20, 2014 Andreas Lehrach RWTH Aachen University & Forschungszentrum Jülich on behalf of the JEDI collaboration

More information

Nuclear Reactions. Shape, interaction, and excitation structures of nuclei scattering expt. cf. Experiment by Rutherford (α scatt.

Nuclear Reactions. Shape, interaction, and excitation structures of nuclei scattering expt. cf. Experiment by Rutherford (α scatt. Nucler Rections Shpe, interction, nd excittion structures of nuclei scttering expt. cf. Experiment by Rutherford (α sctt.) scttered prticles detector solid ngle projectile trget trnsmitted prticles http://www.th.phys.titech.c.jp/~muto/lectures/qmii11/qmii11_chp21.pdf

More information

Measurement of Electric Dipole Moments of Charged Particles in Storage Rings

Measurement of Electric Dipole Moments of Charged Particles in Storage Rings 1 / 52 Measurement of Electric Dipole Moments of Charged Particles in Storage Rings J. Pretz RWTH Aachen/ FZ Jülich on behalf of the JEDI collaboration NUPECC workshop, Jülich, March 2013 2 / 52 Outline

More information

Beam and Spin Dynamics for Charged Particle EDM Searches in Storage Rings

Beam and Spin Dynamics for Charged Particle EDM Searches in Storage Rings Mitglied der Helmholtz-Gemeinschaft Beam and Spin Dynamics for Charged Particle EDM Searches in Storage Rings September 11, 2015 Andreas Lehrach RWTH Aachen University & Forschungszentrum Jülich on behalf

More information

Spin-tracking studies for EDM search in storage rings

Spin-tracking studies for EDM search in storage rings Università degli Studi di Ferrara Dottorato in Fisica - XXVI ciclo Ferrara, 13 Dicembre 2013 Spin-tracking studies for EDM search in storage rings Tutor: Prof. Paolo Lenisa External Tutor: PD Dr. Andreas

More information

+ x 2 dω 2 = c 2 dt 2 +a(t) [ 2 dr 2 + S 1 κx 2 /R0

+ x 2 dω 2 = c 2 dt 2 +a(t) [ 2 dr 2 + S 1 κx 2 /R0 Notes for Cosmology course, fll 2005 Cosmic Dynmics Prelude [ ds 2 = c 2 dt 2 +(t) 2 dx 2 ] + x 2 dω 2 = c 2 dt 2 +(t) [ 2 dr 2 + S 1 κx 2 /R0 2 κ (r) 2 dω 2] nd x = S κ (r) = r, R 0 sin(r/r 0 ), R 0 sinh(r/r

More information

Week 10: Line Integrals

Week 10: Line Integrals Week 10: Line Integrls Introduction In this finl week we return to prmetrised curves nd consider integrtion long such curves. We lredy sw this in Week 2 when we integrted long curve to find its length.

More information

State space systems analysis (continued) Stability. A. Definitions A system is said to be Asymptotically Stable (AS) when it satisfies

State space systems analysis (continued) Stability. A. Definitions A system is said to be Asymptotically Stable (AS) when it satisfies Stte spce systems nlysis (continued) Stbility A. Definitions A system is sid to be Asymptoticlly Stble (AS) when it stisfies ut () = 0, t > 0 lim xt () 0. t A system is AS if nd only if the impulse response

More information

Beam and Spin Dynamics for Charged Particle EDM Searches in Storage Rings

Beam and Spin Dynamics for Charged Particle EDM Searches in Storage Rings Mitglied der Helmholtz-Gemeinschaft Beam and Spin Dynamics for Charged Particle EDM Searches in Storage Rings September 11, 2015 Andreas Lehrach RWTH Aachen University & Forschungszentrum Jülich on behalf

More information

Development of Closed Orbit Diagnostics toward EDM Measurements at COSY in Jülich

Development of Closed Orbit Diagnostics toward EDM Measurements at COSY in Jülich Development of Closed Orbit Diagnostics toward EDM Measurements at COSY in Jülich March 17, 2016 Fabian Hinder 1, 2 for the JEDI collaboration DPG Frühjahrstagung Darmstadt 1 Institut für Kernphysik IV,

More information

) (m + M B. )]c 2 (2.1) (T + T A ) (2.2) 2π 2 dn. = de

) (m + M B. )]c 2 (2.1) (T + T A ) (2.2) 2π 2 dn. = de References --.54 Neutron Interctions nd Applictions (Spring 003) Lecture (/11/03) Neutron Rection Systemtics -- Energy Vritions of Cross Sections, Nucler Dt Enrico Fermi, Nucler Physics, Lecture Notes

More information

Particle Lifetime. Subatomic Physics: Particle Physics Lecture 3. Measuring Decays, Scatterings and Collisions. N(t) = N 0 exp( t/τ) = N 0 exp( Γt/)

Particle Lifetime. Subatomic Physics: Particle Physics Lecture 3. Measuring Decays, Scatterings and Collisions. N(t) = N 0 exp( t/τ) = N 0 exp( Γt/) Sutomic Physics: Prticle Physics Lecture 3 Mesuring Decys, Sctterings n Collisions Prticle lifetime n with Prticle ecy moes Prticle ecy kinemtics Scttering cross sections Collision centre of mss energy

More information

Physics 202, Lecture 14

Physics 202, Lecture 14 Physics 202, Lecture 14 Tody s Topics Sources of the Mgnetic Field (Ch. 28) Biot-Svrt Lw Ampere s Lw Mgnetism in Mtter Mxwell s Equtions Homework #7: due Tues 3/11 t 11 PM (4th problem optionl) Mgnetic

More information

Searching EDMs in Storage Rings - Challenges, Status and Computational Needs -

Searching EDMs in Storage Rings - Challenges, Status and Computational Needs - Mitglied der Helmholtz-Gemeinschaft Searching EDMs in Storage Rings - Challenges, Status and Computational Needs - October 15, 2015 Andreas Lehrach RWTH Aachen University & Forschungszentrum Jülich on

More information

Forces from Strings Under Tension A string under tension medites force: the mgnitude of the force from section of string is the tension T nd the direc

Forces from Strings Under Tension A string under tension medites force: the mgnitude of the force from section of string is the tension T nd the direc Physics 170 Summry of Results from Lecture Kinemticl Vribles The position vector ~r(t) cn be resolved into its Crtesin components: ~r(t) =x(t)^i + y(t)^j + z(t)^k. Rtes of Chnge Velocity ~v(t) = d~r(t)=

More information

PHY4605 Introduction to Quantum Mechanics II Spring 2005 Final exam SOLUTIONS April 22, 2005

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

More information

EDM measurements with storage rings

EDM measurements with storage rings EDM measurements with storage rings Gerco Onderwater VSI, University of Groningen the Netherlands Solvay Workshop 'Beyond the Standard model with Neutrinos and Nuclear Physics' 2017 Outline Motivation

More information

Outline. I. The Why and What of Inflation II. Gauge fields and inflation, generic setup III. Models within Isotropic BG

Outline. I. The Why and What of Inflation II. Gauge fields and inflation, generic setup III. Models within Isotropic BG Outline I. The Why nd Wht of Infltion II. Guge fields nd infltion, generic setup III. Models within Isotropic BG Guge-fltion model Chromo-nturl model IV. Model within Anisotropic BG Infltion with nisotropic

More information

99/105 Comparison of OrcaFlex with standard theoretical results

99/105 Comparison of OrcaFlex with standard theoretical results 99/105 Comprison of OrcFlex ith stndrd theoreticl results 1. Introduction A number of stndrd theoreticl results from literture cn be modelled in OrcFlex. Such cses re, by virtue of being theoreticlly solvble,

More information

Motion of Electrons in Electric and Magnetic Fields & Measurement of the Charge to Mass Ratio of Electrons

Motion of Electrons in Electric and Magnetic Fields & Measurement of the Charge to Mass Ratio of Electrons n eperiment of the Electron topic Motion of Electrons in Electric nd Mgnetic Fields & Mesurement of the Chrge to Mss Rtio of Electrons Instructor: 梁生 Office: 7-318 Emil: shling@bjtu.edu.cn Purposes 1.

More information

DECAMETER RADIO EMISSION OF THE SUN: RECENT OBSERVATIONS

DECAMETER RADIO EMISSION OF THE SUN: RECENT OBSERVATIONS DECAMETER RADIO EMISSION OF THE SUN: RECENT OBSERVATIONS V. N. Melnik *,H.O.Rucker, A. A. Konovlenko, V. V. Dorovskyy, E. P. Abrnin, nd A. Leccheux Abstrct We present n overview of the recent results in

More information

Introduction: Measurements in Particle Physics

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

More information

Physics 121 Sample Common Exam 1 NOTE: ANSWERS ARE ON PAGE 8. Instructions:

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

More information

JURONG JUNIOR COLLEGE

JURONG JUNIOR COLLEGE JURONG JUNIOR COLLEGE 2010 JC1 H1 8866 hysics utoril : Dynmics Lerning Outcomes Sub-topic utoril Questions Newton's lws of motion 1 1 st Lw, b, e f 2 nd Lw, including drwing FBDs nd solving problems by

More information

1 Bending of a beam with a rectangular section

1 Bending of a beam with a rectangular section 1 Bending of bem with rectngulr section x3 Episseur b M x 2 x x 1 2h M Figure 1 : Geometry of the bem nd pplied lod The bem in figure 1 hs rectngur section (thickness 2h, width b. The pplied lod is pure

More information

(Lifetime and) Dipole Moments

(Lifetime and) Dipole Moments Precision Measurements with the Muon: (Lifetime and) Dipole Moments B.L. Roberts Department of Physics Boston University roberts @bu.edu http://physics.bu.edu/roberts.html B. Lee Roberts, APPEAL07, CAST,

More information

Spin Tracking For Polarized Beam Experiments At The JüLich Cooler Synchrotron COSY (Juelich Electric Dipole Moment Invesigations JEDI)

Spin Tracking For Polarized Beam Experiments At The JüLich Cooler Synchrotron COSY (Juelich Electric Dipole Moment Invesigations JEDI) Mitglied der Helmholtz-Gemeinschaft Spin Tracking For Polarized Beam Experiments At The JüLich Cooler Synchrotron COSY (Juelich Electric Dipole Moment Invesigations JEDI) December 17, 2011 Bernd Lorentz

More information

Charged Particle Electric Dipole Moment Searches in Storage Rings

Charged Particle Electric Dipole Moment Searches in Storage Rings Charged Particle Electric Dipole Moment Searches in Storage Rings RWTH Aachen University, Forschungszentrum Jülich & JARA - FAME E-mail: pretz@physik.rwth-aachen.de The Electric Dipole Moment (EDM) is

More information

Intro to Nuclear and Particle Physics (5110)

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

More information

Section 14.3 Arc Length and Curvature

Section 14.3 Arc Length and Curvature Section 4.3 Arc Length nd Curvture Clculus on Curves in Spce In this section, we ly the foundtions for describing the movement of n object in spce.. Vector Function Bsics In Clc, formul for rc length in

More information

EDM of the muon, deuteron, and proton in storage rings

EDM of the muon, deuteron, and proton in storage rings EDM of the muon, deuteron, and proton in storage rings William Morse BNL W.Morse - BNL 1 Storage Ring EDM Collaboration Aristotle University of Thessaloniki, Thessaloniki/Greece (3) 21 Institutions 80

More information

Search for charged particle Electric Dipole Moments in storage rings

Search for charged particle Electric Dipole Moments in storage rings Mitglied der Helmholtz-Gemeinschaft Yur Senichev Search for charged particle Electric Dipole Moments in storage rings on behalf of Collaboration JülichElectricDipole moment Investigation 8. November 06

More information

4 The dynamical FRW universe

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

More information

( dg. ) 2 dt. + dt. dt j + dh. + dt. r(t) dt. Comparing this equation with the one listed above for the length of see that

( dg. ) 2 dt. + dt. dt j + dh. + dt. r(t) dt. Comparing this equation with the one listed above for the length of see that Arc Length of Curves in Three Dimensionl Spce If the vector function r(t) f(t) i + g(t) j + h(t) k trces out the curve C s t vries, we cn mesure distnces long C using formul nerly identicl to one tht we

More information

Nuclear Reactions. Shape, interaction, and excitation structures of nuclei scattering expt. cf. Experiment by Rutherford (a scatt.

Nuclear Reactions. Shape, interaction, and excitation structures of nuclei scattering expt. cf. Experiment by Rutherford (a scatt. Nucler Rections Shpe, interction, nd excittion structures of nuclei scttering expt. cf. Experiment by Rutherford ( sctt.) scttered prticles detector solid ngle projectile trget trnsmitted prticles http://www.th.phys.titech.c.jp/~muto/lectures/qmii11/qmii11_chp21.pdf

More information

Name Solutions to Test 3 November 8, 2017

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

More information

(See Notes on Spontaneous Emission)

(See Notes on Spontaneous Emission) ECE 240 for Cvity from ECE 240 (See Notes on ) Quntum Rdition in ECE 240 Lsers - Fll 2017 Lecture 11 1 Free Spce ECE 240 for Cvity from Quntum Rdition in The electromgnetic mode density in free spce is

More information

The IBS/CAPP research plan

The IBS/CAPP research plan The IBS/CAPP research plan YkS, March 018 The axion is a consequence of the most elegant solution, suggested by Alberto Peccei and Helen Quinn in the 1970 s, to the strong CP problem, i.e., why the experimental

More information

7.6 The Use of Definite Integrals in Physics and Engineering

7.6 The Use of Definite Integrals in Physics and Engineering Arknss Tech University MATH 94: Clculus II Dr. Mrcel B. Finn 7.6 The Use of Definite Integrls in Physics nd Engineering It hs been shown how clculus cn be pplied to find solutions to geometric problems

More information

Summary of equations chapters 7. To make current flow you have to push on the charges. For most materials:

Summary of equations chapters 7. To make current flow you have to push on the charges. For most materials: Summry of equtions chpters 7. To mke current flow you hve to push on the chrges. For most mterils: J E E [] The resistivity is prmeter tht vries more thn 4 orders of mgnitude between silver (.6E-8 Ohm.m)

More information

High-Energy Axion Detection: Probing hadronic axions with the CAST calorimeter

High-Energy Axion Detection: Probing hadronic axions with the CAST calorimeter High-Energy Axion Detection: Probing hdronic xions with the CAST clorimeter I. Origin of hdronic xion models nd constrints II. Axion emission by nucler de-excittion III. The CAST γ-clorimeter & results

More information

1.2. Linear Variable Coefficient Equations. y + b "! = a y + b " Remark: The case b = 0 and a non-constant can be solved with the same idea as above.

1.2. Linear Variable Coefficient Equations. y + b ! = a y + b  Remark: The case b = 0 and a non-constant can be solved with the same idea as above. 1 12 Liner Vrible Coefficient Equtions Section Objective(s): Review: Constnt Coefficient Equtions Solving Vrible Coefficient Equtions The Integrting Fctor Method The Bernoulli Eqution 121 Review: Constnt

More information

ragsdale (zdr82) HW2 ditmire (58335) 1

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

More information

Point Lattices: Bravais Lattices

Point Lattices: Bravais Lattices Physics for Solid Stte Applictions Februry 18, 2004 Lecture 7: Periodic Structures (cont.) Outline Review 2D & 3D Periodic Crystl Structures: Mthemtics X-Ry Diffrction: Observing Reciprocl Spce Point Lttices:

More information

Phys 7221, Fall 2006: Homework # 6

Phys 7221, Fall 2006: Homework # 6 Phys 7221, Fll 2006: Homework # 6 Gbriel González October 29, 2006 Problem 3-7 In the lbortory system, the scttering ngle of the incident prticle is ϑ, nd tht of the initilly sttionry trget prticle, which

More information

Introduction to ISAR imaging systems. Elaborazione Sistemi Radar delle immagini radar

Introduction to ISAR imaging systems. Elaborazione Sistemi Radar delle immagini radar Introduction to ISAR imging systems SAR_RANGE 1 Rdr imging systems More in generl rdr imges re obtined by exploiting the reltive motion between the rdr ntenn nd the scene to be imged. SAR: KNOWN reltive

More information

Storage ring Electric Dipole Moment experiment for the proton Yannis K. Semertzidis, BNL

Storage ring Electric Dipole Moment experiment for the proton Yannis K. Semertzidis, BNL Lattice Computations BNL, 16 May 2012 Storage ring Electric Dipole Moment experiment for the proton Yannis K. Semertzidis, BNL Goal: 10-29 e cm; Probe New Physics ~10 3 TeV Systematics best in an all-electric

More information

arxiv:gr-qc/ v1 14 Mar 2000

arxiv:gr-qc/ v1 14 Mar 2000 The binry blck-hole dynmics t the third post-newtonin order in the orbitl motion Piotr Jrnowski Institute of Theoreticl Physics, University of Bi lystok, Lipow 1, 15-2 Bi lystok, Polnd Gerhrd Schäfer Theoretisch-Physiklisches

More information

ME 141. Lecture 10: Kinetics of particles: Newton s 2 nd Law

ME 141. Lecture 10: Kinetics of particles: Newton s 2 nd Law ME 141 Engineering Mechnics Lecture 10: Kinetics of prticles: Newton s nd Lw Ahmd Shhedi Shkil Lecturer, Dept. of Mechnicl Engg, BUET E-mil: sshkil@me.buet.c.bd, shkil6791@gmil.com Website: techer.buet.c.bd/sshkil

More information

References and Resources:

References and Resources: Surfce nd Interfce Science Physics 627; Chemistry 542 Lectures 4 Feb 3, 2013 Determining Surfce Structure Diffrction methods: LEED; RHEED Rel Spce: STEM References nd Resources: Woodruff nd Delchr (2 nd

More information

Purpose of the experiment

Purpose of the experiment Newton s Lws II PES 6 Advnced Physics Lb I Purpose of the experiment Exmine two cses using Newton s Lws. Sttic ( = 0) Dynmic ( 0) fyi fyi Did you know tht the longest recorded flight of chicken is thirteen

More information

It may be that the next exciting thing to come along will be the discovery of a neutron or atomic or electron electric dipole moment.

It may be that the next exciting thing to come along will be the discovery of a neutron or atomic or electron electric dipole moment. It may be that the next exciting thing to come along will be the discovery of a neutron or atomic or electron electric dipole moment. These electric dipole moments... seem to me to offer one of the most

More information

Classical Mechanics. From Molecular to Con/nuum Physics I WS 11/12 Emiliano Ippoli/ October, 2011

Classical Mechanics. From Molecular to Con/nuum Physics I WS 11/12 Emiliano Ippoli/ October, 2011 Clssicl Mechnics From Moleculr to Con/nuum Physics I WS 11/12 Emilino Ippoli/ October, 2011 Wednesdy, October 12, 2011 Review Mthemtics... Physics Bsic thermodynmics Temperture, idel gs, kinetic gs theory,

More information

The Wave Equation I. MA 436 Kurt Bryan

The Wave Equation I. MA 436 Kurt Bryan 1 Introduction The Wve Eqution I MA 436 Kurt Bryn Consider string stretching long the x xis, of indeterminte (or even infinite!) length. We wnt to derive n eqution which models the motion of the string

More information

Development of a Rogowski coil Beam Position Monitor for Electric Dipole Moment measurements at storage rings

Development of a Rogowski coil Beam Position Monitor for Electric Dipole Moment measurements at storage rings Development of a Rogowski coil Beam Position Monitor for Electric Dipole Moment measurements at storage rings PHD defense talk Physics Institute III B Nuclear Physics Institute (IKP-II) Fabian Trinkel

More information

Properties of Integrals, Indefinite Integrals. Goals: Definition of the Definite Integral Integral Calculations using Antiderivatives

Properties of Integrals, Indefinite Integrals. Goals: Definition of the Definite Integral Integral Calculations using Antiderivatives Block #6: Properties of Integrls, Indefinite Integrls Gols: Definition of the Definite Integrl Integrl Clcultions using Antiderivtives Properties of Integrls The Indefinite Integrl 1 Riemnn Sums - 1 Riemnn

More information

PhysicsAndMathsTutor.com

PhysicsAndMathsTutor.com 1. A uniform circulr disc hs mss m, centre O nd rdius. It is free to rotte bout fixed smooth horizontl xis L which lies in the sme plne s the disc nd which is tngentil to the disc t the point A. The disc

More information

DARK MATTER AND THE UNIVERSE. Answer question ONE (Compulsory) and TWO other questions.

DARK MATTER AND THE UNIVERSE. Answer question ONE (Compulsory) and TWO other questions. Dt Provided: A formul sheet nd tble of physicl constnts is ttched to this pper. Picture of glxy cluster Abell 2218 required for question 4(c) is ttched. DEPARTMENT OF PHYSICS AND ASTRONOMY Autumn Semester

More information

CBE 291b - Computation And Optimization For Engineers

CBE 291b - Computation And Optimization For Engineers The University of Western Ontrio Fculty of Engineering Science Deprtment of Chemicl nd Biochemicl Engineering CBE 9b - Computtion And Optimiztion For Engineers Mtlb Project Introduction Prof. A. Jutn Jn

More information

Factors affecting the phonation threshold pressure and frequency

Factors affecting the phonation threshold pressure and frequency 3SC Fctors ffecting the phontion threshold pressure nd frequency Zhoyn Zhng School of Medicine, University of Cliforni Los Angeles, CA, USA My, 9 57 th ASA Meeting, Portlnd, Oregon Acknowledgment: Reserch

More information

Multiple Integrals. Review of Single Integrals. Planar Area. Volume of Solid of Revolution

Multiple Integrals. Review of Single Integrals. Planar Area. Volume of Solid of Revolution Multiple Integrls eview of Single Integrls eding Trim 7.1 eview Appliction of Integrls: Are 7. eview Appliction of Integrls: Volumes 7.3 eview Appliction of Integrls: Lengths of Curves Assignment web pge

More information

INSTRUMENTS USED FOR MEASURINNG THE MAGNETIC PROPERTIES OF ONE KILOGRAM MASS STANDARD IN CENTER FOR MEASUREMENT STANDARDS (CMS)

INSTRUMENTS USED FOR MEASURINNG THE MAGNETIC PROPERTIES OF ONE KILOGRAM MASS STANDARD IN CENTER FOR MEASUREMENT STANDARDS (CMS) INSTRUMENTS USED OR MEASURINNG THE MAGNETIC PROPERTIES O ONE KILOGRAM MASS STANDARD IN CENTER OR MEASUREMENT STANDARDS (CMS) Sheu-shi Pn, H. C. Lu nd C. S. Chng Center for Mesurement Stndrds, Industril

More information

Storage ring proton EDM experiment and systematic error studies

Storage ring proton EDM experiment and systematic error studies Storage ring proton EDM experiment and systematic error studies Physics of Fundamental Symmetries and Interactions PSI 2016 Selcuk Haciomeroglu On Behalf of the pedm Collaboration Center for Axion and

More information

WMAP satellite. 16 Feb Feb Feb 2012

WMAP satellite. 16 Feb Feb Feb 2012 16 Feb 2012 21 Feb 2012 23 Feb 2012 è Announcements è Problem 5 (Hrtle 18.3). Assume V * is nonreltivistic. The reltivistic cse requires more complicted functions. è Outline è WMAP stellite è Dipole nisotropy

More information

a < a+ x < a+2 x < < a+n x = b, n A i n f(x i ) x. i=1 i=1

a < a+ x < a+2 x < < a+n x = b, n A i n f(x i ) x. i=1 i=1 Mth 33 Volume Stewrt 5.2 Geometry of integrls. In this section, we will lern how to compute volumes using integrls defined by slice nlysis. First, we recll from Clculus I how to compute res. Given the

More information

13: Diffusion in 2 Energy Groups

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

More information

E S dition event Vector Mechanics for Engineers: Dynamics h Due, next Wednesday, 07/19/2006! 1-30

E S dition event Vector Mechanics for Engineers: Dynamics h Due, next Wednesday, 07/19/2006! 1-30 Vector Mechnics for Engineers: Dynmics nnouncement Reminders Wednesdy s clss will strt t 1:00PM. Summry of the chpter 11 ws posted on website nd ws sent you by emil. For the students, who needs hrdcopy,

More information

MAC-solutions of the nonexistent solutions of mathematical physics

MAC-solutions of the nonexistent solutions of mathematical physics Proceedings of the 4th WSEAS Interntionl Conference on Finite Differences - Finite Elements - Finite Volumes - Boundry Elements MAC-solutions of the nonexistent solutions of mthemticl physics IGO NEYGEBAUE

More information

Method of Localisation and Controlled Ejection of Swarms of Likely Charged Particles

Method of Localisation and Controlled Ejection of Swarms of Likely Charged Particles Method of Loclistion nd Controlled Ejection of Swrms of Likely Chrged Prticles I. N. Tukev July 3, 17 Astrct This work considers Coulom forces cting on chrged point prticle locted etween the two coxil,

More information

POLARIMETRY FOR A STORAGE-RING ELECTRIC-DIPOLE-MOMENT MEASUREMENT MARIA ŻUREK FOR THE JEDI COLLABORATION

POLARIMETRY FOR A STORAGE-RING ELECTRIC-DIPOLE-MOMENT MEASUREMENT MARIA ŻUREK FOR THE JEDI COLLABORATION POLARIMETRY FOR A STORAGE-RING ELECTRIC-DIPOLE-MOMENT MEASUREMENT 8 JUNE 2018 MARIA ŻUREK FOR THE JEDI COLLABORATION MOTIVATION Barion Asymmetry Problem Barion Asymmetry Observation Standard Cosmological

More information

MAT187H1F Lec0101 Burbulla

MAT187H1F Lec0101 Burbulla Chpter 6 Lecture Notes Review nd Two New Sections Sprint 17 Net Distnce nd Totl Distnce Trvelled Suppose s is the position of prticle t time t for t [, b]. Then v dt = s (t) dt = s(b) s(). s(b) s() is

More information

Dynamics and control of mechanical systems. Content

Dynamics and control of mechanical systems. Content Dynmics nd control of mechnicl systems Dte Dy 1 (01/08) Dy (03/08) Dy 3 (05/08) Dy 4 (07/08) Dy 5 (09/08) Dy 6 (11/08) Content Review of the bsics of mechnics. Kinemtics of rigid bodies plne motion of

More information

Spin Feedback System at COSY

Spin Feedback System at COSY Spin Feedback System at COSY 21.7.2016 Nils Hempelmann Outline Electric Dipole Moments Spin Manipulation Feedback System Validation Using Vertical Spin Build-Up Wien Filter Method 21.7.2016 Nils Hempelmann

More information

Multiple Integrals. Review of Single Integrals. Planar Area. Volume of Solid of Revolution

Multiple Integrals. Review of Single Integrals. Planar Area. Volume of Solid of Revolution Multiple Integrls eview of Single Integrls eding Trim 7.1 eview Appliction of Integrls: Are 7. eview Appliction of Integrls: olumes 7.3 eview Appliction of Integrls: Lengths of Curves Assignment web pge

More information

The Active Universe. 1 Active Motion

The Active Universe. 1 Active Motion The Active Universe Alexnder Glück, Helmuth Hüffel, Sš Ilijić, Gerld Kelnhofer Fculty of Physics, University of Vienn helmuth.hueffel@univie.c.t Deprtment of Physics, FER, University of Zgreb ss.ilijic@fer.hr

More information

Practice Problems Solution

Practice Problems Solution Prctice Problems Solution Problem Consier D Simple Hrmonic Oscilltor escribe by the Hmiltonin Ĥ ˆp m + mwˆx Recll the rte of chnge of the expecttion of quntum mechnicl opertor t A ī A, H] + h A t. Let

More information

Vadose Zone Hydrology

Vadose Zone Hydrology Objectives Vdose Zone Hydrology 1. Review bsic concepts nd terminology of soil physics. 2. Understnd the role of wter-tble dynmics in GW-SW interction. Drcy s lw is useful in region A. Some knowledge of

More information

Reinforcement learning II

Reinforcement learning II CS 1675 Introduction to Mchine Lerning Lecture 26 Reinforcement lerning II Milos Huskrecht milos@cs.pitt.edu 5329 Sennott Squre Reinforcement lerning Bsics: Input x Lerner Output Reinforcement r Critic

More information

Поиск электрических дипольных моментов частиц и ядер в накопительных кольцах

Поиск электрических дипольных моментов частиц и ядер в накопительных кольцах Поиск электрических дипольных моментов частиц и ядер в накопительных кольцах Alexander J. Silenko Research Institute for Nuclear Problems, BSU, Minsk, Belarus Joint Institute for Nuclear Research, Dubna,

More information

Predict Global Earth Temperature using Linier Regression

Predict Global Earth Temperature using Linier Regression Predict Globl Erth Temperture using Linier Regression Edwin Swndi Sijbt (23516012) Progrm Studi Mgister Informtik Sekolh Teknik Elektro dn Informtik ITB Jl. Gnesh 10 Bndung 40132, Indonesi 23516012@std.stei.itb.c.id

More information

The Tiny Muon versus the Standard Model. Paul Debevec Physics 403 November 14 th, 2017

The Tiny Muon versus the Standard Model. Paul Debevec Physics 403 November 14 th, 2017 The Tiny Muon versus the Standard Model Paul Debevec Physics 403 November 14 th, 2017 BNL E821 Muon g-2 Collaboration Standard Model of Particle Physics Components of the Standard Model of Particle Physics

More information

Axions In QCD and Cosmology

Axions In QCD and Cosmology Axions In QCD nd Cosmology George K. Fnourkis Institute of Nucler Physics NCSR Demokritos Outline The U(1) A Problem of QCD The QCD Vcuum nd the Strong CP Problem A solution: U(1) PQ nd Axions Invisible

More information

The Properties of Stars

The Properties of Stars 10/11/010 The Properties of Strs sses Using Newton s Lw of Grvity to Determine the ss of Celestil ody ny two prticles in the universe ttrct ech other with force tht is directly proportionl to the product

More information

LECTURE 14. Dr. Teresa D. Golden University of North Texas Department of Chemistry

LECTURE 14. Dr. Teresa D. Golden University of North Texas Department of Chemistry LECTURE 14 Dr. Teres D. Golden University of North Texs Deprtment of Chemistry Quntittive Methods A. Quntittive Phse Anlysis Qulittive D phses by comprison with stndrd ptterns. Estimte of proportions of

More information

Electric Dipole Moment Searches using Storage Rings

Electric Dipole Moment Searches using Storage Rings Electric Dipole Moment Searches using Storage Rings Frank Rathmann (on behalf of the JEDI collaboration) Paul-Scherrer Institut, 06.12.2018 Electric Dipole Moment Searches using Storage Rings Frank Rathmann

More information

Simple Harmonic Motion I Sem

Simple Harmonic Motion I Sem Simple Hrmonic Motion I Sem Sllus: Differentil eqution of liner SHM. Energ of prticle, potentil energ nd kinetic energ (derivtion), Composition of two rectngulr SHM s hving sme periods, Lissjous figures.

More information

Magnetic forces on a moving charge. EE Lecture 26. Lorentz Force Law and forces on currents. Laws of magnetostatics

Magnetic forces on a moving charge. EE Lecture 26. Lorentz Force Law and forces on currents. Laws of magnetostatics Mgnetic forces on moving chrge o fr we ve studied electric forces between chrges t rest, nd the currents tht cn result in conducting medium 1. Mgnetic forces on chrge 2. Lws of mgnetosttics 3. Mgnetic

More information

19 th INTERNATIONAL CONGRESS ON ACOUSTICS MADRID, 2-7 SEPTEMBER 2007 A NON-CONTACT SYSTEM FOR TRANSPORTING OBJECTS USING ULTRASONIC LEVITATION

19 th INTERNATIONAL CONGRESS ON ACOUSTICS MADRID, 2-7 SEPTEMBER 2007 A NON-CONTACT SYSTEM FOR TRANSPORTING OBJECTS USING ULTRASONIC LEVITATION 19 th INTERNATIONAL CONGRESS ON ACOUSTICS MADRID, -7 SEPTEMBER 007 A NON-CONTACT SYSTEM FOR TRANSPORTING OBJECTS USING ULTRASONIC LEVITATION PACS: 3.5.Uv Gudr, Tdeusz 1 ; Perkowski, Dniel ; Opielinski,

More information

1. a) Describe the principle characteristics and uses of the following types of PV cell: Single Crystal Silicon Poly Crystal Silicon

1. a) Describe the principle characteristics and uses of the following types of PV cell: Single Crystal Silicon Poly Crystal Silicon 2001 1. ) Describe the principle chrcteristics nd uses of the following types of PV cell: Single Crystl Silicon Poly Crystl Silicon Amorphous Silicon CIS/CIGS Gllium Arsenide Multijunction (12 mrks) b)

More information

Definition of Continuity: The function f(x) is continuous at x = a if f(a) exists and lim

Definition of Continuity: The function f(x) is continuous at x = a if f(a) exists and lim Mth 9 Course Summry/Study Guide Fll, 2005 [1] Limits Definition of Limit: We sy tht L is the limit of f(x) s x pproches if f(x) gets closer nd closer to L s x gets closer nd closer to. We write lim f(x)

More information

JUST THE MATHS UNIT NUMBER INTEGRATION APPLICATIONS 8 (First moments of a volume) A.J.Hobson

JUST THE MATHS UNIT NUMBER INTEGRATION APPLICATIONS 8 (First moments of a volume) A.J.Hobson JUST THE MATHS UNIT NUMBER 3.8 INTEGRATIN APPLICATINS 8 (First moments of volume) b A.J.Hobson 3.8. Introduction 3.8. First moment of volume of revolution bout plne through the origin, perpendiculr to

More information

A. Limits - L Hopital s Rule. x c. x c. f x. g x. x c 0 6 = 1 6. D. -1 E. nonexistent. ln ( x 1 ) 1 x 2 1. ( x 2 1) 2. 2x x 1.

A. Limits - L Hopital s Rule. x c. x c. f x. g x. x c 0 6 = 1 6. D. -1 E. nonexistent. ln ( x 1 ) 1 x 2 1. ( x 2 1) 2. 2x x 1. A. Limits - L Hopitl s Rule Wht you re finding: L Hopitl s Rule is used to find limits of the form f ( ) lim where lim f or lim f limg. c g = c limg( ) = c = c = c How to find it: Try nd find limits by

More information

A REVIEW OF CALCULUS CONCEPTS FOR JDEP 384H. Thomas Shores Department of Mathematics University of Nebraska Spring 2007

A REVIEW OF CALCULUS CONCEPTS FOR JDEP 384H. Thomas Shores Department of Mathematics University of Nebraska Spring 2007 A REVIEW OF CALCULUS CONCEPTS FOR JDEP 384H Thoms Shores Deprtment of Mthemtics University of Nebrsk Spring 2007 Contents Rtes of Chnge nd Derivtives 1 Dierentils 4 Are nd Integrls 5 Multivrite Clculus

More information