Physics of the Interstellar and Intergalactic Medium
|
|
- Mary Shepherd
- 5 years ago
- Views:
Transcription
1 PYA0 Sior Sophistr Physics of th Itrstllar ad Itrgalactic Mdium Lctur 7: II gios Dr Graham M. arpr School of Physics, TCD
2 Follow-up radig for this ad t lctur Chaptr 5: Dyso ad Williams (lss dtaild) Chaptr 5: Spitzr (ovrlaps matrial hr) Chaptr 7: Tils (ovrlaps matrial hr) Chaptr 5: Drai (graduat lvl)
3 7. Photoioizatio gios II rgios ad platary bula II rgios physical procsss Siz of II rgio Ioizatio balac withi bula ow sharp is th dg? Effct of havy lmts Stratificatio of bula Tmpratur adio missio Fr-fr combiatio lis Pulsar disprsio masurs Uiformity of ISM ad bula Iitial pasio phas
4 II gios Trac th spiral arms - foud i/ar star formig rgios
5 Youg stars photoioizig thir viros S-55 (radius.7 pc) Courtsy of th UK Schmidt Tlscop (copyright i which is owd by th Particl Physics ad Astroomy sarch Coucil of th UK ad th Aglo-Australia Tlscop oard) ad th Southr Sky Survy as cratd by th SuprCOSMOS masurig machi. 5
6 Stllar ursry: ioiz whol rgios Multipl hot youg stars ca photoioiz th iitial molcular cloud, ad thir II rgios mrg ad joi up clarig larg volums 6
7 Physical procsss - ydrog ioizatio Photoioizatio rat 0 J d h cm Cas radiativ rcombiatio cof. at.60 0 T T cm s 0.75 s
8
9 Lyma cotiuum photos Cout th total th umbr of photoioizig photos N Lyc 0 L h d L, N ar th stllar lumiosity ad umbr of photoioizig photos Will d th ma itsity J ν to calculat th iozatio rat AND th hatig rat. First writ th lumiosity i trms of surfac flu L F T I T Isotropic missio Spcific Itsity of star is just th Plack fuctio (i blackbody appro.)
10 Th ma itsity J Dfiitio of ma itsity, ad approimatio for II rgios W(z) is th radiatio dilutio factor: sky fractio of solid agl subtdd by star * L z W T z W T d I J J J d I d I d I J star Diff star star star Ω (solid agl) Star poit i bula
11 Ioizatio alac alac btw photoioizatio ad rcombiatio i bula I Dfiitios 0 I 0 Diff J J d T h J d h I dsity of utral hydrog atoms, p ( p = II ) dsity of lctros ad protos, rspctivly total umbr of utral ad ioizd hydrog: p + I J* ma itsity from hot star J diff diffus ma itsity from bula α A, α radiativ rcombibatio cofficit (cm s - ) σ photoioizatio cross-sctio (cm ) p p T A O-th-spot approimatio
12 Strömgr radius of a II rgio Cosidr uiform II rgio hydrog is prdomiatly ioizd with a ioizatio fractio = [= fully ioizd, =0 utral] s Lyc N,, wh p p I II p Lyc s N alac total # ioizatios with ffctiv umbr of rcombiatios givs (gt) Strömgr s radius, sttig = (ioizd) Strömgr,., 99, ApJ, 89, 56
13 Typical Ioizatio alac Eampl: Adoptig typical dsity = 000 cm -, O star: r 0. 5pc 0 r F Lyc photos cm - s - With typical cross-sctio ad rcombiatio rats 0 Assumptio that hydrog is mostly ioizd is good (dpds o gas dsity)
14 Strömgr radius of a II rgio Lyma cotiuum lumiosity of O, stars: O: N(LyC) = 0 50 phot s - T = 60,000 K O5: N(LyC) = 0 9 phot s - T = 6,000 K O7: N(LyC) = phot s - T = 5,000 K O9: N(LyC) = 0 8 phot s - T =,000 K 0: N(LyC) = phot s - T = 0,000 K : N(LyC) = phot s - T = 0,000 K Thortical valus N(LyC) ucrtai NLTE/LTE, li blaktig Eampl: Adoptig typical dsity = 000 cm -, O5 star: S ~ 0 8 cm ~ pc Mass of II rgio M II S m N Lyc m **Lowr dsitis mor mass**
15 ow sharp is th dg? Ma fr path of ioizig photo L I cosidr =0.5 th L pc ΔL << S a vry sharp dg. ydari-malayri t al. (00, A&A, 7, 95)
16 Ioizatio balac (i mor dtail) p p p 0 0 * Lyc p I N d h L W T d h L W Writ ma itsity i trms of stllar lumiosity Lyc T N * p Attuatio by utral hydrog
17 Ioizatio balac Substitutig i th ioizatio balac quatio bcoms Lyc Lyc N T T N * p p p z S S z Dfi a ormalizd radius
18 Ioizatio balac p z S d [ A] d dz [ ] S Dfi Strömgr optical dpth (utral hydrog) S S s 0 0 cm NLyc 9 50 phot. s A S z p d dz S
19 Ioizatio balac 5 Elimiat - by combiig [A] ad [] d dz p d z dz z p Sttig ~ i th abov w obtai th solutio, l z Diffrtiatig, th with quatio [] givs th utral fractio d dz S z z S
20 Oio layrs I ( 0 ) 50Å photoioizatio cross-sctio E.g., O9 star N( Lyc) = 0 8 phot s - N( Lyc) = 0 7 phot s - II Strömgr radius is 75% of th II Strömgr radius For O star ad Strömgr radii ar about th sam siz small + shll ar to th star Shlls isid II rgio for abudat mtals with similar ioizatio pottials C, N, O mor compl atomic physics ivolvd Dust prst i cloud will absorb photos Last ffcts rduc siz of II rgio
21
Session : Plasmas in Equilibrium
Sssio : Plasmas i Equilibrium Ioizatio ad Coductio i a High-prssur Plasma A ormal gas at T < 3000 K is a good lctrical isulator, bcaus thr ar almost o fr lctros i it. For prssurs > 0.1 atm, collisio amog
More informationEE 232 Lightwave Devices Lecture 3: Basic Semiconductor Physics and Optical Processes. Optical Properties of Semiconductors
3 Lightwav Dvics Lctur 3: Basic Smicoductor Physics ad Optical Procsss Istructor: Mig C. Wu Uivrsity of Califoria, Brly lctrical girig ad Computr Scics Dpt. 3 Lctur 3- Optical Proprtis of Smicoductors
More informationLecture contents. Density of states Distribution function Statistic of carriers. Intrinsic Extrinsic with no compensation Compensation
Ltur otts Dsity of stats Distributio futio Statisti of arrirs Itrisi trisi with o ompsatio ompsatio S 68 Ltur #7 Dsity of stats Problm: alulat umbr of stats pr uit rgy pr uit volum V() Larg 3D bo (L is
More informationz 1+ 3 z = Π n =1 z f() z = n e - z = ( 1-z) e z e n z z 1- n = ( 1-z/2) 1+ 2n z e 2n e n -1 ( 1-z )/2 e 2n-1 1-2n -1 1 () z
Sris Expasio of Rciprocal of Gamma Fuctio. Fuctios with Itgrs as Roots Fuctio f with gativ itgrs as roots ca b dscribd as follows. f() Howvr, this ifiit product divrgs. That is, such a fuctio caot xist
More informationcoulombs or esu charge. It s mass is about 1/1837 times the mass of hydrogen atom. Thus mass of electron is
1 ATOMIC STRUCTURE Fudamtal Particls: Mai Fudamtal Particl : (a) Elctro: It is a fudamtal particl of a atom which carris a uit gativ charg. It was discovrd by J.J. Thomso (1897) from th studis carrid out
More informationReview Exercises. 1. Evaluate using the definition of the definite integral as a Riemann Sum. Does the answer represent an area? 2
MATHEMATIS --RE Itgral alculus Marti Huard Witr 9 Rviw Erciss. Evaluat usig th dfiitio of th dfiit itgral as a Rima Sum. Dos th aswr rprst a ara? a ( d b ( d c ( ( d d ( d. Fid f ( usig th Fudamtal Thorm
More informationOption 3. b) xe dx = and therefore the series is convergent. 12 a) Divergent b) Convergent Proof 15 For. p = 1 1so the series diverges.
Optio Chaptr Ercis. Covrgs to Covrgs to Covrgs to Divrgs Covrgs to Covrgs to Divrgs 8 Divrgs Covrgs to Covrgs to Divrgs Covrgs to Covrgs to Covrgs to Covrgs to 8 Proof Covrgs to π l 8 l a b Divrgt π Divrgt
More informationProbability & Statistics,
Probability & Statistics, BITS Pilai K K Birla Goa Campus Dr. Jajati Kshari Sahoo Dpartmt of Mathmatics BITS Pilai, K K Birla Goa Campus Poisso Distributio Poisso Distributio: A radom variabl X is said
More informationEmission and Absorption
Stllar Atmosphrs: Emissio ad Absorptio Emissio ad Absorptio Stllar Atmosphrs: Emissio ad Absorptio Chmical compositio Stllar atmosphr mixtur, composd of may chmical lmts, prst as atoms, ios, or molculs
More informationLECTURE 13 Filling the bands. Occupancy of Available Energy Levels
LUR 3 illig th bads Occupacy o Availabl rgy Lvls W hav dtrmid ad a dsity o stats. W also d a way o dtrmiig i a stat is illd or ot at a giv tmpratur. h distributio o th rgis o a larg umbr o particls ad
More informationThey must have different numbers of electrons orbiting their nuclei. They must have the same number of neutrons in their nuclei.
37 1 How may utros ar i a uclus of th uclid l? 20 37 54 2 crtai lmt has svral isotops. Which statmt about ths isotops is corrct? Thy must hav diffrt umbrs of lctros orbitig thir ucli. Thy must hav th sam
More informationTime : 1 hr. Test Paper 08 Date 04/01/15 Batch - R Marks : 120
Tim : hr. Tst Papr 8 D 4//5 Bch - R Marks : SINGLE CORRECT CHOICE TYPE [4, ]. If th compl umbr z sisfis th coditio z 3, th th last valu of z is qual to : z (A) 5/3 (B) 8/3 (C) /3 (D) o of ths 5 4. Th itgral,
More informationHow many neutrino species?
ow may utrio scis? Two mthods for dtrmii it lium abudac i uivrs At a collidr umbr of utrio scis Exasio of th uivrs is ovrd by th Fridma quatio R R 8G tot Kc R Whr: :ubblcostat G :Gravitatioal costat 6.
More informationSolid State Device Fundamentals
8 Biasd - Juctio Solid Stat Dvic Fudamtals 8. Biasd - Juctio ENS 345 Lctur Cours by Aladr M. Zaitsv aladr.zaitsv@csi.cuy.du Tl: 718 98 81 4N101b Dartmt of Egirig Scic ad Physics Biasig uiolar smicoductor
More informationDigital Signal Processing, Fall 2006
Digital Sigal Procssig, Fall 6 Lctur 9: Th Discrt Fourir Trasfor Zhg-Hua Ta Dpartt of Elctroic Systs Aalborg Uivrsity, Dar zt@o.aau.d Digital Sigal Procssig, I, Zhg-Hua Ta, 6 Cours at a glac MM Discrt-ti
More informationGalaxy Photometry. Recalling the relationship between flux and luminosity, Flux = brightness becomes
Galaxy Photomty Fo galaxis, w masu a sufac flux, that is, th couts i ach pixl. Though calibatio, this is covtd to flux dsity i Jaskys ( Jy -6 W/m/Hz). Fo a galaxy at som distac, d, a pixl of sid D subtds
More informationPhysics 2D Lecture Slides Lecture 14: Feb 3 rd 2004
Bria Wcht, th TA is back! Pl. giv all rgrad rqusts to him Quiz 4 is This Friday Physics D Lctur Slids Lctur 14: Fb 3 rd 004 Vivk Sharma UCSD Physics Whr ar th lctros isid th atom? Early Thought: Plum puddig
More informationChapter (8) Estimation and Confedence Intervals Examples
Chaptr (8) Estimatio ad Cofdc Itrvals Exampls Typs of stimatio: i. Poit stimatio: Exampl (1): Cosidr th sampl obsrvatios, 17,3,5,1,18,6,16,10 8 X i i1 17 3 5 118 6 16 10 116 X 14.5 8 8 8 14.5 is a poit
More information1985 AP Calculus BC: Section I
985 AP Calculus BC: Sctio I 9 Miuts No Calculator Nots: () I this amiatio, l dots th atural logarithm of (that is, logarithm to th bas ). () Ulss othrwis spcifid, th domai of a fuctio f is assumd to b
More informationOutline. Ionizing Radiation. Introduction. Ionizing radiation
Outli Ioizig Radiatio Chaptr F.A. Attix, Itroductio to Radiological Physics ad Radiatio Dosimtry Radiological physics ad radiatio dosimtry Typs ad sourcs of ioizig radiatio Dscriptio of ioizig radiatio
More informationStatistics 3858 : Likelihood Ratio for Exponential Distribution
Statistics 3858 : Liklihood Ratio for Expotial Distributio I ths two xampl th rjctio rjctio rgio is of th form {x : 2 log (Λ(x)) > c} for a appropriat costat c. For a siz α tst, usig Thorm 9.5A w obtai
More information5.1 The Nuclear Atom
Sav My Exams! Th Hom of Rvisio For mor awsom GSE ad lvl rsourcs, visit us at www.savmyxams.co.uk/ 5.1 Th Nuclar tom Qustio Papr Lvl IGSE Subjct Physics (0625) Exam oard Topic Sub Topic ooklt ambridg Itratioal
More informationBlackbody Radiation. All bodies at a temperature T emit and absorb thermal electromagnetic radiation. How is blackbody radiation absorbed and emitted?
All bodis at a tmpratur T mit ad absorb thrmal lctromagtic radiatio Blackbody radiatio I thrmal quilibrium, th powr mittd quals th powr absorbd How is blackbody radiatio absorbd ad mittd? 1 2 A blackbody
More informationWashington State University
he 3 Ktics ad Ractor Dsig Sprg, 00 Washgto Stat Uivrsity Dpartmt of hmical Egrg Richard L. Zollars Exam # You will hav o hour (60 muts) to complt this xam which cosists of four (4) problms. You may us
More informationQuantum Mechanics & Spectroscopy Prof. Jason Goodpaster. Problem Set #2 ANSWER KEY (5 questions, 10 points)
Chm 5 Problm St # ANSWER KEY 5 qustios, poits Qutum Mchics & Spctroscopy Prof. Jso Goodpstr Du ridy, b. 6 S th lst pgs for possibly usful costts, qutios d itgrls. Ths will lso b icludd o our futur ms..
More informationAPPENDIX: STATISTICAL TOOLS
I. Nots o radom samplig Why do you d to sampl radomly? APPENDI: STATISTICAL TOOLS I ordr to masur som valu o a populatio of orgaisms, you usually caot masur all orgaisms, so you sampl a subst of th populatio.
More informationChapter 2 Infinite Series Page 1 of 11. Chapter 2 : Infinite Series
Chatr Ifiit Sris Pag of Sctio F Itgral Tst Chatr : Ifiit Sris By th d of this sctio you will b abl to valuat imror itgrals tst a sris for covrgc by alyig th itgral tst aly th itgral tst to rov th -sris
More informationPURE MATHEMATICS A-LEVEL PAPER 1
-AL P MATH PAPER HONG KONG EXAMINATIONS AUTHORITY HONG KONG ADVANCED LEVEL EXAMINATION PURE MATHEMATICS A-LEVEL PAPER 8 am am ( hours) This papr must b aswrd i Eglish This papr cosists of Sctio A ad Sctio
More informationMONTGOMERY COLLEGE Department of Mathematics Rockville Campus. 6x dx a. b. cos 2x dx ( ) 7. arctan x dx e. cos 2x dx. 2 cos3x dx
MONTGOMERY COLLEGE Dpartmt of Mathmatics Rockvill Campus MATH 8 - REVIEW PROBLEMS. Stat whthr ach of th followig ca b itgratd by partial fractios (PF), itgratio by parts (PI), u-substitutio (U), or o of
More information(Reference: sections in Silberberg 5 th ed.)
ALE. Atomic Structur Nam HEM K. Marr Tam No. Sctio What is a atom? What is th structur of a atom? Th Modl th structur of a atom (Rfrc: sctios.4 -. i Silbrbrg 5 th d.) Th subatomic articls that chmists
More informationLecture contents. Transport, scattering Generation/recombination. E c. E t. E v. NNSE508 / NENG452 Lecture #13. Band-to-band recombination
Lctur cotts Trasort, scattrig Gratio/rcobiatio E E c E t E v Bad-to-bad rcobiatio Tra-assistd (SRH) rcobiatio ad gratio Augr rcobiatio Elctro trasort: Gral cosidratios How fr carrirs ract o xtral lctric
More informationThe Death of Stars - II.
Th Dath of Stars - II. Larning Objctivs! How can w us H-R diagrams to masur th ag of star clustrs (and hnc th ag of our Univrs)?! Why do high and low mass stars volv diffrntly? How ar havy lmnts such as
More information10. Joint Moments and Joint Characteristic Functions
0 Joit Momts ad Joit Charactristic Fctios Followig sctio 6 i this sctio w shall itrodc varios paramtrs to compactly rprst th iformatio cotaid i th joit pdf of two rvs Giv two rvs ad ad a fctio g x y dfi
More informationHadamard Exponential Hankel Matrix, Its Eigenvalues and Some Norms
Math Sci Ltt Vol No 8-87 (0) adamard Exotial al Matrix, Its Eigvalus ad Som Norms İ ad M bula Mathmatical Scics Lttrs Itratioal Joural @ 0 NSP Natural Scics Publishig Cor Dartmt of Mathmatics, aculty of
More informationH2 Mathematics Arithmetic & Geometric Series ( )
H Mathmatics Arithmtic & Gomtric Sris (08 09) Basic Mastry Qustios Arithmtic Progrssio ad Sris. Th rth trm of a squc is 4r 7. (i) Stat th first four trms ad th 0th trm. (ii) Show that th squc is a arithmtic
More informationTerahertz band-gap in InAs/GaSb type II superlattices
Trart Scic ad Tcology, ISSN 1941-7411 Vol.1, No 4, Dcmbr 008 Trart bad-gap i IAs/GaSb typ II suprlattics L.L. Li 1, W. Xu 1, 3, Z. Zg 1, ad Y.L. Si 1 Ky Laboratory of Matrials Pysics, Istitut of Solid
More information3.1 Atomic Structure and The Periodic Table
Sav My Exams! Th Hom of Rvisio For mor awsom GSE ad lvl rsourcs, visit us at www.savmyxams.co.uk/ 3. tomic Structur ad Th Priodic Tabl Qustio Par Lvl IGSE Subjct hmistry (060) Exam oard ambridg Itratioal
More informationECE 340 Lecture 38 : MOS Capacitor I Class Outline:
ECE 34 Lctur 38 : MOS Capacitor I Class Outli: Idal MOS Capacitor higs you should ow wh you lav Ky Qustios What ar th diffrt ias rgios i MOS capacitors? What do th lctric fild ad lctrostatic pottial loo
More informationBlackbody Radiation. All bodies at a temperature T emit and absorb thermal electromagnetic radiation. How is blackbody radiation absorbed and emitted?
All bodis at a tmpratur T mit ad absorb thrmal lctromagtic radiatio Blackbody radiatio I thrmal quilibrium, th powr mittd quals th powr absorbd How is blackbody radiatio absorbd ad mittd? 1 2 A blackbody
More informationChapter 8: Electron Configurations and Periodicity
Elctron Spin & th Pauli Exclusion Principl Chaptr 8: Elctron Configurations and Priodicity 3 quantum numbrs (n, l, ml) dfin th nrgy, siz, shap, and spatial orintation of ach atomic orbital. To xplain how
More informationln x = n e = 20 (nearest integer)
H JC Prlim Solutios 6 a + b y a + b / / dy a b 3/ d dy a b at, d Giv quatio of ormal at is y dy ad y wh. d a b () (,) is o th curv a+ b () y.9958 Qustio Solvig () ad (), w hav a, b. Qustio d.77 d d d.77
More informationHow many neutrons does this aluminium atom contain? A 13 B 14 C 27 D 40
alumiium atom has a uclo umbr of 7 ad a roto umbr of 3. How may utros dos this alumiium atom cotai? 3 4 7 40 atom of lmt Q cotais 9 lctros, 9 rotos ad 0 utros. What is Q? calcium otassium strotium yttrium
More informationPartition Functions and Ideal Gases
Partitio Fuctios ad Idal Gass PFIG- You v lard about partitio fuctios ad som uss ow w ll xplor tm i mor dpt usig idal moatomic diatomic ad polyatomic gass! for w start rmmbr: Q( N ( N! N Wat ar N ad? W
More informationOrdinary Differential Equations
Ordiary Diffrtial Equatio Aftr radig thi chaptr, you hould b abl to:. dfi a ordiary diffrtial quatio,. diffrtiat btw a ordiary ad partial diffrtial quatio, ad. Solv liar ordiary diffrtial quatio with fid
More informationUNIT 2: MATHEMATICAL ENVIRONMENT
UNIT : MATHEMATICAL ENVIRONMENT. Itroductio This uit itroducs som basic mathmatical cocpts ad rlats thm to th otatio usd i th cours. Wh ou hav workd through this uit ou should: apprciat that a mathmatical
More informationBipolar Junction Transistors
ipolar Juctio Trasistors ipolar juctio trasistors (JT) ar activ 3-trmial dvics with aras of applicatios: amplifirs, switch tc. high-powr circuits high-spd logic circuits for high-spd computrs. JT structur:
More informationChapter Taylor Theorem Revisited
Captr 0.07 Taylor Torm Rvisitd Atr radig tis captr, you sould b abl to. udrstad t basics o Taylor s torm,. writ trascdtal ad trigoomtric uctios as Taylor s polyomial,. us Taylor s torm to id t valus o
More information07 - SEQUENCES AND SERIES Page 1 ( Answers at he end of all questions ) b, z = n
07 - SEQUENCES AND SERIES Pag ( Aswrs at h d of all qustios ) ( ) If = a, y = b, z = c, whr a, b, c ar i A.P. ad = 0 = 0 = 0 l a l
More informationIdeal crystal : Regulary ordered point masses connected via harmonic springs
Statistical thrmodyamics of crystals Mooatomic crystal Idal crystal : Rgulary ordrd poit masss coctd via harmoic sprigs Itratomic itractios Rprstd by th lattic forc-costat quivalt atom positios miima o
More informationmacro Road map to this lecture Objectives Aggregate Supply and the Phillips Curve Three models of aggregate supply W = ω P The sticky-wage model
Road map to this lctur macro Aggrgat Supply ad th Phillips Curv W rlax th assumptio that th aggrgat supply curv is vrtical A vrsio of th aggrgat supply i trms of iflatio (rathr tha th pric lvl is calld
More informationEffect of Electric Fields on Electron Thermal Transport in Laser-Produced Plasmas
FFC OF LCRIC FILDS ON LCRON HRMAL RANSPOR IN LASR-PRODUCD PLASMAS ffct of lctric Filds o lctro hrmal rasport i Lasr-Producd Plasmas Itroductio hrmal trasport plays a importat rol i dirct-dri irtial cofimt
More informationMILLIKAN OIL DROP EXPERIMENT
11 Oct 18 Millika.1 MILLIKAN OIL DROP EXPERIMENT This xprimt is dsigd to show th quatizatio of lctric charg ad allow dtrmiatio of th lmtary charg,. As i Millika s origial xprimt, oil drops ar sprayd ito
More informationWorksheet: Taylor Series, Lagrange Error Bound ilearnmath.net
Taylor s Thorm & Lagrag Error Bouds Actual Error This is th ral amout o rror, ot th rror boud (worst cas scario). It is th dirc btw th actual () ad th polyomial. Stps:. Plug -valu ito () to gt a valu.
More informationFigure 2-18 Thevenin Equivalent Circuit of a Noisy Resistor
.8 NOISE.8. Th Nyquist Nois Thorm W ow wat to tur our atttio to ois. W will start with th basic dfiitio of ois as usd i radar thory ad th discuss ois figur. Th typ of ois of itrst i radar thory is trmd
More information2.29 Numerical Fluid Mechanics Spring 2015 Lecture 12
REVIEW Lctur 11: Numrical Fluid Mchaics Sprig 2015 Lctur 12 Fiit Diffrcs basd Polyomial approximatios Obtai polyomial (i gral u-qually spacd), th diffrtiat as dd Nwto s itrpolatig polyomial formulas Triagular
More informationDynamic Contraction of the Positive Column of a Self- Sustained Glow Discharge in Nitrogen/Air Flow. M.N. Shneider 1
1 Dyamic Cotractio of th Positiv Colum of a Slf- Sustaid Glow Discharg i Nitrog/Air Flow M.N. Shidr 1 I collaboratio with M.S. Mokrov 2 ad G.M. Milikh 3 (1 Pricto Uivrsity (2 Istitut of Problm i Mchaics,
More informationThe Death of Stars - I.
Th Dath of Stars - I. Larning Objctivs! B abl to sktch th H-R diagram and includ stars by siz, sctral ty, liftim, color, mass, magnitud, tmratur and luminosity, rlativ to our Sun! Comar Rd Dwarfs to our
More informationDiscrete Fourier Transform (DFT)
Discrt Fourir Trasorm DFT Major: All Egirig Majors Authors: Duc guy http://umricalmthods.g.us.du umrical Mthods or STEM udrgraduats 8/3/29 http://umricalmthods.g.us.du Discrt Fourir Trasorm Rcalld th xpotial
More informationTaylor and Maclaurin Series
Taylor ad Maclauri Sris Taylor ad Maclauri Sris Thory sctio which dals with th followig topics: - Th Sigma otatio for summatio. - Dfiitio of Taylor sris. - Commo Maclauri sris. - Taylor sris ad Itrval
More informationLecture #2: Wave Nature of the Electron and the Internal Structure of an Atom
5.61 Fall 013 Lctur # pag 1 Lctur #: Wav Natur of t Elctro ad t Itral Structur of a Atom Last tim: Surpris Ligt as particl 1. Potolctric ffct, spcially KE vs. ν. Ligt as packts of rgy, calld potos, E =
More informationCDS 101: Lecture 5.1 Reachability and State Space Feedback
CDS, Lctur 5. CDS : Lctur 5. Rachability ad Stat Spac Fdback Richard M. Murray 7 Octobr 3 Goals: Di rachability o a cotrol systm Giv tsts or rachability o liar systms ad apply to ampls Dscrib th dsig o
More informationA Review of Complex Arithmetic
/0/005 Rviw of omplx Arithmti.do /9 A Rviw of omplx Arithmti A omplx valu has both a ral ad imagiary ompot: { } ad Im{ } a R b so that w a xprss this omplx valu as: whr. a + b Just as a ral valu a b xprssd
More informationph People Grade Level: basic Duration: minutes Setting: classroom or field site
ph Popl Adaptd from: Whr Ar th Frogs? in Projct WET: Curriculum & Activity Guid. Bozman: Th Watrcours and th Council for Environmntal Education, 1995. ph Grad Lvl: basic Duration: 10 15 minuts Stting:
More informationCh. 24 Molecular Reaction Dynamics 1. Collision Theory
Ch. 4 Molcular Raction Dynamics 1. Collision Thory Lctur 16. Diffusion-Controlld Raction 3. Th Matrial Balanc Equation 4. Transition Stat Thory: Th Eyring Equation 5. Transition Stat Thory: Thrmodynamic
More informationTechnical Support Document Bias of the Minimum Statistic
Tchical Support Documt Bias o th Miimum Stattic Itroductio Th papr pla how to driv th bias o th miimum stattic i a radom sampl o siz rom dtributios with a shit paramtr (also kow as thrshold paramtr. Ths
More informationIntroduction to Quantum Information Processing. Overview. A classical randomised algorithm. q 3,3 00 0,0. p 0,0. Lecture 10.
Itroductio to Quatum Iformatio Procssig Lctur Michl Mosca Ovrviw! Classical Radomizd vs. Quatum Computig! Dutsch-Jozsa ad Brsti- Vazirai algorithms! Th quatum Fourir trasform ad phas stimatio A classical
More informationDiscrete Fourier Transform. Nuno Vasconcelos UCSD
Discrt Fourir Trasform uo Vascoclos UCSD Liar Shift Ivariat (LSI) systms o of th most importat cocpts i liar systms thory is that of a LSI systm Dfiitio: a systm T that maps [ ito y[ is LSI if ad oly if
More informationHigh Energy Physics. Lecture 5 The Passage of Particles through Matter
High Enrgy Physics Lctur 5 Th Passag of Particls through Mattr 1 Introduction In prvious lcturs w hav sn xampls of tracks lft by chargd particls in passing through mattr. Such tracks provid som of th most
More informationToday s topic 2 = Setting up the Hydrogen Atom problem. Schematic of Hydrogen Atom
Today s topic Sttig up th Hydog Ato pobl Hydog ato pobl & Agula Motu Objctiv: to solv Schödig quatio. st Stp: to dfi th pottial fuctio Schatic of Hydog Ato Coulob s aw - Z 4ε 4ε fo H ato Nuclus Z What
More informationDTFT Properties. Example - Determine the DTFT Y ( e ) of n. Let. We can therefore write. From Table 3.1, the DTFT of x[n] is given by 1
DTFT Proprtis Exampl - Dtrmi th DTFT Y of y α µ, α < Lt x α µ, α < W ca thrfor writ y x x From Tabl 3., th DTFT of x is giv by ω X ω α ω Copyright, S. K. Mitra Copyright, S. K. Mitra DTFT Proprtis DTFT
More informationOn the approximation of the constant of Napier
Stud. Uiv. Babş-Bolyai Math. 560, No., 609 64 O th approximatio of th costat of Napir Adri Vrscu Abstract. Startig from som oldr idas of [] ad [6], w show w facts cocrig th approximatio of th costat of
More informationCorrelation in tree The (ferromagnetic) Ising model
5/3/00 :\ jh\slf\nots.oc\7 Chaptr 7 Blf propagato corrlato tr Corrlato tr Th (frromagtc) Isg mol Th Isg mol s a graphcal mol or par ws raom Markov fl cosstg of a urct graph wth varabls assocat wth th vrtcs.
More informationCDS 101: Lecture 5.1 Reachability and State Space Feedback
CDS, Lctur 5. CDS : Lctur 5. Rachability ad Stat Spac Fdback Richard M. Murray ad Hido Mabuchi 5 Octobr 4 Goals: Di rachability o a cotrol systm Giv tsts or rachability o liar systms ad apply to ampls
More informationThe real E-k diagram of Si is more complicated (indirect semiconductor). The bottom of E C and top of E V appear for different values of k.
Modr Smcoductor Dvcs for Itgratd rcuts haptr. lctros ad Hols Smcoductors or a bad ctrd at k=0, th -k rlatoshp ar th mmum s usually parabolc: m = k * m* d / dk d / dk gatv gatv ffctv mass Wdr small d /
More informationPHYS-3301 Lecture 7. CHAPTER 4 Structure of the Atom. Rutherford Scattering. Sep. 18, 2018
CHAPTER 4 Structure of the Atom PHYS-3301 Lecture 7 4.1 The Atomic Models of Thomso ad Rutherford 4.2 Rutherford Scatterig 4.3 The Classic Atomic Model 4.4 The Bohr Model of the Hydroge Atom 4.5 Successes
More informationChapter 11.00C Physical Problem for Fast Fourier Transform Civil Engineering
haptr. Physical Problm for Fast Fourir Trasform ivil Egirig Itroductio I this chaptr, applicatios of FFT algorithms [-5] for solvig ral-lif problms such as computig th dyamical (displacmt rspos [6-7] of
More informationA Simple Proof that e is Irrational
Two of th most bautiful ad sigificat umbrs i mathmatics ar π ad. π (approximatly qual to 3.459) rprsts th ratio of th circumfrc of a circl to its diamtr. (approximatly qual to.788) is th bas of th atural
More informationAIT. Blackbody Radiation IAAT
3 1 Blackbody Radiatio Itroductio 3 2 First radiatio process to look at: radiatio i thermal equilibrium with itself: blackbody radiatio Assumptios: 1. Photos are Bosos, i.e., more tha oe photo per phase
More informationChapter Five. More Dimensions. is simply the set of all ordered n-tuples of real numbers x = ( x 1
Chatr Fiv Mor Dimsios 51 Th Sac R W ar ow rard to mov o to sacs of dimsio gratr tha thr Ths sacs ar a straightforward gralizatio of our Euclida sac of thr dimsios Lt b a ositiv itgr Th -dimsioal Euclida
More informationLecture contents. Semiconductor statistics. NNSE508 / NENG452 Lecture #12
Ltur otts Sioutor statistis S58 / G45 Ltur # illig th pty bas: Distributio futio ltro otratio at th rgy (Dsity of stats) (istributio futio): ( ) ( ) f ( ) Pauli lusio Priipl: o two ltros (frios) a hav
More informationProperties and types of water. Properties of water
PART 3 Proprtis and typs of watr Proprtis of watr Chmical form: H 2 O Physical stats: gas (vapor) liquid (watr) solid (ic, snow) Molcular structur: On oxygn atom and two hydrogn atoms ar arrangd as in
More informationLight-induced atomic transitions
Light-iducd atomic trasitios Prturbativ calculatio of th probability of quatum trasitios I th absc of itractios with thir surroudigs, isolatd systms rst i th lowst-rgy igstat of th Hamiltoia. Itractios
More informationONLINE SUPPLEMENT Optimal Markdown Pricing and Inventory Allocation for Retail Chains with Inventory Dependent Demand
Submittd to Maufacturig & Srvic Opratios Maagmt mauscript MSOM 5-4R2 ONLINE SUPPLEMENT Optimal Markdow Pricig ad Ivtory Allocatio for Rtail Chais with Ivtory Dpdt Dmad Stph A Smith Dpartmt of Opratios
More informationLecture Outline. Skin Depth Power Flow 8/7/2018. EE 4347 Applied Electromagnetics. Topic 3e
8/7/018 Cours Instructor Dr. Raymond C. Rumpf Offic: A 337 Phon: (915) 747 6958 E Mail: rcrumpf@utp.du EE 4347 Applid Elctromagntics Topic 3 Skin Dpth & Powr Flow Skin Dpth Ths & Powr nots Flow may contain
More information8(4 m0) ( θ ) ( ) Solutions for HW 8. Chapter 25. Conceptual Questions
Solutios for HW 8 Captr 5 Cocptual Qustios 5.. θ dcrass. As t crystal is coprssd, t spacig d btw t plas of atos dcrass. For t first ordr diffractio =. T Bragg coditio is = d so as d dcrass, ust icras for
More information+ x. x 2x. 12. dx. 24. dx + 1)
INTEGRATION of FUNCTION of ONE VARIABLE INDEFINITE INTEGRAL Fidig th idfiit itgrals Rductio to basic itgrals, usig th rul f ( ) f ( ) d =... ( ). ( )d. d. d ( ). d. d. d 7. d 8. d 9. d. d. d. d 9. d 9.
More informationUniversity of Illinois at Chicago Department of Physics. Thermodynamics & Statistical Mechanics Qualifying Examination
Univrsity of Illinois at Chicago Dpartmnt of hysics hrmodynamics & tatistical Mchanics Qualifying Eamination January 9, 009 9.00 am 1:00 pm Full crdit can b achivd from compltly corrct answrs to 4 qustions.
More informationChp6. pn Junction Diode: I-V Characteristics I
147 C6. uctio Diod: I-V Caractristics I 6.1. THE IDEAL DIODE EQUATION 6.1.1. Qualitativ Drivatio 148 Figur rfrc: Smicoductor Dvic Fudamtals Robrt F. Pirrt, Addiso-Wsly Publicig Comay 149 Figur 6.1 juctio
More informationThe Analysis and Calculation of DC Earth Electrode Electric Field Coupling with Thermal based on Shell Theory
Prprits www.prprits.org O PEER-REVEWED Postd: 5 April 7 doi:.944/prprits74.9.v Articl h Aalysis ad alculatio of D Earth Elctrod Elctric Fild ouplig with hrmal basd o Shll hory Jigli Li, Liyig Guo, Pg Hu,
More informationτ(line) = 0.01 L, τ s n k h T l a t p O (cm -2 ) NH 2
Th Institut of Spac and Astronautical Scinc Rport SP No.14, Dcmbr 2000 Absorption Masurmnt of Hydrogn Molculs in th Early Univrs By Hiroshi Shibai Λ (Novmbr 1, 2000) Abstract: Th obsrvability of Hydrogn
More informationto the SCHRODINGER EQUATION The case of an electron propagating in a crystal lattice
Lctur Nots PH 411/511 ECE 598 A. La Rosa INTRODUCTION TO QUANTUM MECHANICS CHAPTER-9 From th HAMILTONIAN EQUATIONS to th SCHRODINGER EQUATION Th cas of a lctro propagatig i a crystal lattic 9.1 Hamiltoia
More information10. Excitons in Bulk and Two-dimensional Semiconductors
Excitos i Bulk ad Two-dimsioal Smicoductors Th Wair modl drivd i th prvious chaptr provids a simpl framwork for th iclusio of xcitos i th optical proprtis of smicoductors I this chaptr w will valuat th
More informationTitle: Vibrational structure of electronic transition
Titl: Vibrational structur of lctronic transition Pag- Th band spctrum sn in th Ultra-Violt (UV) and visibl (VIS) rgions of th lctromagntic spctrum can not intrprtd as vibrational and rotational spctrum
More information2018-JEE Entrance Examination - Advanced Paper-1
SLUTINS 8-JEE Etrac Eamiatio - Advacd Papr- PAT-I PHYSICS.(C) kr U ( r) du F kr dr L m v mk mv k k v m V V.(AC).(AC) F () t i () j a t i j m () t t v a dt i t t t j r vdt i j 6 t At t s r i j 6 F () i
More information4. Money cannot be neutral in the short-run the neutrality of money is exclusively a medium run phenomenon.
PART I TRUE/FALSE/UNCERTAIN (5 points ach) 1. Lik xpansionary montary policy, xpansionary fiscal policy rturns output in th mdium run to its natural lvl, and incrass prics. Thrfor, fiscal policy is also
More informationLinear Algebra Existence of the determinant. Expansion according to a row.
Lir Algbr 2270 1 Existc of th dtrmit. Expsio ccordig to row. W dfi th dtrmit for 1 1 mtrics s dt([]) = (1) It is sy chck tht it stisfis D1)-D3). For y othr w dfi th dtrmit s follows. Assumig th dtrmit
More informationScattering Parameters. Scattering Parameters
Motivatio cattrig Paramtrs Difficult to implmt op ad short circuit coditios i high frqucis masurmts du to parasitic s ad Cs Pottial stability problms for activ dvics wh masurd i oopratig coditios Difficult
More informationThe power of analytical spectroscopy
The power of aalytical spectroscopy Daiila et al. J. Rama Spectr. 33, 807 (00) Reflected light Red lake varish UV light Rama spectrum Lead white ciabar Caput mortuum Byzatie Ico (AD Our 534), Lady, Our
More informationChapter 3 Lecture 14 Longitudinal stick free static stability and control 3 Topics
Chaptr 3 Lctur 14 Longitudinal stick fr static stability and control 3 Topics 3.4.4 Rquirmnt for propr stick forc variation 3.4.5 Fl of th stability lvl by th pilot Exampl 3.3 3.5 Dtrmination of stick-fr
More informationSolid State Device Fundamentals
Solid State Device Fudametals ES 345 Lecture ourse by Alexader M. Zaitsev alexader.zaitsev@csi.cuy.edu Tel: 718 98 81 4101b ollege of State Islad / UY Dopig semicoductors Doped semicoductors are semicoductors,
More information