11th IUVSTA School on Lasers in Materials Science - SLIMS 8-15 July 2012, Isola di San Servolo, Venice, Italy

Size: px
Start display at page:

Download "11th IUVSTA School on Lasers in Materials Science - SLIMS 8-15 July 2012, Isola di San Servolo, Venice, Italy"

Transcription

1 11h IUVSA School o Lasrs i Marials Scic - SLIMS 8-15 July 01, Isola di Sa Srvolo, Vic, Ialy

2

3

4 Isiu of hrmophysics, Sibria Brach of RAS Mai rsarch dircios: Ha- ad mass-rasfr i o- ad wo-phas sysms ad i h sysms wih phas rasiios; Hydrodyamic isabiliis ad urbulc; Wav dyamics i liquid ad gas flows; Low-mpraur plasmas; hrmodyamic propris of mar; Lasr ablaio.

5 Diamod Jubil of UK govrig by h Qu lizabh II 100-yar Mmorial of iaic Diamod Jubil of h Uivrsiy of Souhampo Olympic ad Paralympic Gams 01 i Lodo

6

7 Mchaisms of mar xciaios ad ablaio wih ulrashor lasr pulss Svral xampls of coiuum modlig i applicaio o lasr ablaio Volum modificaio of raspar marials Cocludig rmarks

8 arg Lasr Scals of lasr-affcd rgios: - spo siz ~10 μm 1 mm; - dph ~10 m - fw μm dpdig o lasr focusig ad absorpio propris of a irradiad marial Coiuum: Dsiy, hrmal capaciy, hrmal coduciviy, viscosiy, mchaical propris Youg modulus, plasic yild, sil srgh, c. Msoscopic: Combis faurs of macroscopic ad aomisic approachs Soham al. APA 69, S Aomisic: Iraomic poial of iracio

9 Coiuum shll modl i applicaio o aoubs Yakobso al. Phys.Rv.L. 76, Axial comprssio Bdig orsio

10 Hydrodyamic modlig: Similariy bw spac ad laboraory asrophysics Sakagami & Nishihara, Phys.Fluids B, Hachisu al., Asrophys. J. 368, L From: Physiciss jok i Russia, Mulipl diios sic 1966.

11 Sl, λ = 780 m, lf: τ = 00 fs, F 0 = 0.5 J/cm ; righ: τ = 3.3 s, F 0 = 4. J/cm. From: Chichkov al. Appl. Phys. A 63, Sapphir, λ = 800 m, τ = 00 fs, F 0 = 4 J/cm ; gl lf ad srog ablaio phass. From: Soia al. Nucl. Isr. Mh. B ,

12 ypical xprimal sup o sudy lasr ablaio of solids I. lcroic xciaio Mals: - absorpio of lasr ligh by fr lcros Dilcrics ad smicoducors: - - g - graio of fr lcros by phoo-ioizaio; All marials: - lcro phoomissio fr lcros absorb lasr radiaio - + k I k av + - impac ioizaio I

13 . lcro-phoo couplig Ulrafas mlig oly smicoducors a 400 fs afr h ds plasma xciaio A. Rouss al. Naur 410, hrmal mlig picoscod im scal

14 Dilcrics Smicoducors rappig wih dfc formaio + + Phoo-rcombiaio Augr rcombiaio x g asir xciaio by x pulss Fusd silica, 800 m g = 9 V x = 5. V

15 Lasr M arg 1 Haig, mlig, 3 hrmal vaporizaio 4 phas xplosio Lcur by Profssor Miollo Rcoil prssur Hydrodyamic isabiliis

16 lcro-laic hrmalizaio im ~ ps Nar-hrshold flucs: 1 Spallaio Coulomb xplosio Lcur by Profssor Zhigili

17 wo-mpraur modl Kagaov al. Sov. Phys. JP 4, Aisimov al. Sov. Phys. JP 39, r l l, xp 1 0 l l l l l l g z K z C z I R g z K z C Lcur by Profssor Miollo

18 hory of lasiciy Yakobso al. Phys.Rv.L. 76, Coiuum shll modl orsio Axial comprssio Bdig Hydrodyamics Colombir al. Phys.Rv.B 74, Povarisy al. Appl. Surf. Sci. 53,

19 xprimal vidc for C i sapphir R. Soia, al. Phys. Rv. B 6, fs, l 800 m O + O + Normalizd vlociy disribuios for O + op riagls ad O + closd diamods: Momum scalig Ios ar mid ad acclrad by h lcric fild. ma his lads o h momum scalig mv

20 Ra quaio coiuiy MPI Lasr puls Phoomissio Poisso quaio absorpio ad rflcio dyamics fr-lcro absorpio lcric fild carrir drif ad diffusio Drud formalism avalach Ra quaio coiuiy Objcs for modlig: Au, Si, Al O 3 Rgims: = fs, l = 800 m

21 i j L S x J j j j j,, 1 D j = k B j / x i 0 j j j j j D J * i cr g Coiuiy quaio: Poisso quaio: Complx dilcric fucio:

22 ., 4, 3,, l l l l g C k K k C x g x J C Si: wo-mpraur modl:., 1/,, 0 ab 1 x P C x I x I I i g i a a g g g f

23 ,,, ab ph 6 6 x I x a h I x I x i a a Al O 3 :,,,, ab 1 x I x a x I h h x I x a a Si: Auaio of h lasr bam:

24 Mals Au: s k A I R k h F h k c J xp Smicoducors Si: P fr P Au Au P Si P Au s k A I R k h F h k l l c J xp Dilcrics Al O 3 : / xp l x I I P h a a N.M. Bulgakova al. Phys. Rv. B 69, ; Appl. Phys. A 81, W. Mari al. J. Appl. Phys. 103, Phoomissio:

25 i - [10 1 cm -3 ] = 100 fs 3 Al O 3 l = 800 m 1 Silico x 30 0 Gold x 100-0,1 0,0 0,1 0, 0,3 im [ps] Lasr fluc slighly abov h hrshold of io obsrvaio i plums: 4, 0.8, ad 1. J/cm for Al O 3, Si, ad Au, rspcivly

26 lcric fild [10 10 V/m] w = 0 / W a = 0 V a / 0 - Al O 3-4 h x0 a 3k 0 0 l Criical lcric fild For sapphir: h V/m Numbr of mid lcros: Al O Si Au ,1 0,0 0,1 0, 0,3 0,4 0,5 im [ps] Maximums of h lcric fild: Al O V/m; Si V/m; Au V/m

27 A.Wck al. Appl.Phys. A 90, Sailss sl

28 K K A.Y. Vorobyv, C. Guo: Appl. Phys. L. 86, Op. xprss 14, ,0 0,8 0,6 P 1-am air Vacuum 1.08-am N 0,4 1,0 0,8 0,6 0,4 0, 0,0 P N Ar H 0, Lasr fluc [J/cm ] 0, 0,0 Ablaio hrshold 0,01 0, Lasr fluc [J/cm ] Dpdc o ioizaio poial of h ambi gas

29 D C B A Q Q Q Q V / xp Ar a B B I m hk Q i B C k m Q 9/ 10 K 9 4 K / i D Q, 0 i i B Q d k d 3 / 1/ i i B i k M Q, B Q d k d * 1 1 Q k Q I Q Q Q D B C Ar B i k Q z s c s A k Q z s c s A a k A AJ Q, c z J z z c z z s / 1 R c z s r r F L L L / / xp 0 0 0

30 P r Ar div V 0 V V V p div ˆ U div VU pdivv div V, m, x, m,m = 1 3, m m z 100% ioizaio i h focal spo r = 50 μm ad z = 100 μm J J g z

31 = s F 0 = 4 J/cm, 65 fs Log focus = s = 650 s igh focusig = 4.7 s

32 N.M. Bulgakova al. SPI Proc. 7005, 70050C 008

33 = 0 + I Criical powr for slf-focusig P cr = 3. GW for air P cr =.8 MW i fusd silica

34 Volum aograigs M. Brsa, P.G. Kazasky OP.L., 35,

35

36 M. Brsa al. Appl. Phys. L. 98, Howvr, h misry of aograigs says ucovrd

37 Coursy of Pr G. Kazasky, Uivrsiy of Souhampo Puls rgy 39 μj/cm raslaio spd 50 μm/s Rpiio ra 100 khz Puls rgy 43 μj/cm raslaio spd 10 μm/s

38 I av I r xcio rappig Muliphoo ioizaio Avalach ioizaio R-xciaio

39 Kldysh paramr: m / 0.5 ff g L raio of im cssary o a lcro o ul hrough h poial barrir o h priod of h lasr fild A > 1 muliphoo ioizaio domias; a < 1 ulig domias. 1 a I W/cm I c 0 / a I W/cm 10 8 V/cm Isiy clampig upo volum modificaio a h lvl W/cm

40 " 1 PI g c R R W i d R f f ik ik r r r k i z I. No-liar Schrödigr quaio NLS r l a g r PI m m W / coupld wih h ra quaio for fr carrirs NLS is obaid from h Maxwll quaios i assumpio of bam propagaio

41 II. Maxwll quaios quaio for h lcric fild accouig fr carrir graio ad associad procsss 1 1 D 4 8 a PI 0 * c c c mc 0 * i D j ro H W 1 /4 c D Pm Pl Pl 1 fr fr R d m 4 0 coupld wih hydrodyamic modl for fr carrirs jv WPI W r v v i v m c

42 im scal: lasr puls propagaio hrough a glass sampl svral ps; NA = 0.45 J. Appl. Phys., 101, Phys. Rv. B, 77, Appl. Phys. L., 94, Oly a small par of h puls fro is fficily absorbd wihi h bam focus rgio. h rs pars of h bam flow ovr h grad lcro plasma wih rahr small absorpio.

43 i:sappir; bam rgy is.5 μj, bam wais 0.8 μm, puls duraio 80 fs, NA = 0.7

44 bam rgy is 1 μj, wais 1 μm, puls duraio 150 fs

45 Absorpio of h lasr rgy by lcros Graio of hrmolasic wavs lcro-laic hrmalizaio Formaio of sp mpraur gradis I. NLS or Maxwll quaios Ha coducio coolig of h lasr-affcd rgio II. Modls of hrmolasoplasics Spaial disribuio of absorbd rgy mpraur map

46 Froz js ad bubbl bls Impac of polarizaio o rgy dlivry io modificaio rgio Impac of lasr puls il o wavguid wriig Formaio ad moio of micro/aovoids i glass Naograigs i glass

47 Iracio of ulrashor lasr pulss wih marials is a fasciaig phomo ha is rich i physical co ad ops w uprcdd opporuiis for chological applicaios. I rquirs cosolidaig kowldg of opics, solid sa physics ad chmisry, plasma physics, hrmodyamics, hory of lasiciy ad plasiciy. hr's Ply of Room a h Boom, Richard P. Fyma

48 I hop you do o fl lik his poor sud udr iformaio bombardm Physics lsso by Srgi Korsu

49 Isad your criical viw is vry wlcom! All hs is ouragous li! hy los powr a hbar i h Schrödigr quaio ad drw lcros isad of muos i air showr! From a Ir forum of Russia suds By Sa Carroll

50 Isiu of hrmophysics SB RAS Dr. Alxadr Bulgakov Dr. Igor Burakov Dr. Yuri Shukhov Suds: Olga Bulgakova Ao vushko Srgy Sariski Maxim Shugav Lv Zakharov Prof. Pr Kazasky Opolcroics Rsarch Cr, Uivrsiy of Souhampo, UK Dr. Vladimir Zhukov Isiu of Compuaioal chologis SB RAS, Novosibirsk, Russia Dr. Yuri Mshchryakov Isiu of Hydrodyamics SB RAS, Novosibirsk, Russia Prof. laor Campbll diburgh Uivrsiy, UK Dr. Arkadi Rosfld Max-Bor-Isiu, Brli, Grmay Dr. Razva Soia Uivrsi Ja Mo, 4000 Sai i, Frac Dr. Aaoli Vorobyv Dr. Chuly Guo Rochsr Uivrsiy, USA

Fourier Series: main points

Fourier Series: main points BIOEN 3 Lcur 6 Fourir rasforms Novmbr 9, Fourir Sris: mai pois Ifii sum of sis, cosis, or boh + a a cos( + b si( All frqucis ar igr mulipls of a fudamal frqucy, o F.S. ca rprs ay priodic fucio ha w ca

More information

Part B: Transform Methods. Professor E. Ambikairajah UNSW, Australia

Part B: Transform Methods. Professor E. Ambikairajah UNSW, Australia Par B: rasform Mhods Profssor E. Ambikairaah UNSW, Ausralia Chapr : Fourir Rprsaio of Sigal. Fourir Sris. Fourir rasform.3 Ivrs Fourir rasform.4 Propris.4. Frqucy Shif.4. im Shif.4.3 Scalig.4.4 Diffriaio

More information

Mathematical Preliminaries for Transforms, Subbands, and Wavelets

Mathematical Preliminaries for Transforms, Subbands, and Wavelets Mahmaical Prlimiaris for rasforms, Subbads, ad Wavls C.M. Liu Prcpual Sigal Procssig Lab Collg of Compur Scic Naioal Chiao-ug Uivrsiy hp://www.csi.cu.du.w/~cmliu/courss/comprssio/ Offic: EC538 (03)5731877

More information

H is equal to the surface current J S

H is equal to the surface current J S Chapr 6 Rflcion and Transmission of Wavs 6.1 Boundary Condiions A h boundary of wo diffrn mdium, lcromagnic fild hav o saisfy physical condiion, which is drmind by Maxwll s quaion. This is h boundary condiion

More information

Analysis of TE (Transverse Electric) Modes of Symmetric Slab Waveguide

Analysis of TE (Transverse Electric) Modes of Symmetric Slab Waveguide Adv. Sudis Thor. Phs., Vol. 6,, o. 7, 33-336 Aalsis of T (Trasvrs lcric Mods of Smmric Slab Wavguid arr Rama SPCTC (Spcrum Tcholog Rsarch Group Dparm of lcrical, lcroic ad Ssms girig Naioal Uivrsi of Malasia

More information

Lecture 12: Introduction to nonlinear optics II.

Lecture 12: Introduction to nonlinear optics II. Lcur : Iroduco o olar opcs II r Kužl ropagao of srog opc sgals propr olar ffcs Scod ordr ffcs! Thr-wav mxg has machg codo! Scod harmoc grao! Sum frqucy grao! aramrc grao Thrd ordr ffcs! Four-wav mxg! Opcal

More information

Lecture 1: Photoconductors and p-i-n Photodiodes

Lecture 1: Photoconductors and p-i-n Photodiodes Lcur 1: Poocoucors a p-i- Pooios Isrucor: Mig C. Wu Uivrsiy of Califoria, Brkly Elcrical Egirig a Compur Scics Dp. 1 Prof. Mig Wu Poocors Covrs lig o lcric sigals Mai yps of poocors Poocoucors P-i- pooios

More information

Modeling of the CML FD noise-to-jitter conversion as an LPTV process

Modeling of the CML FD noise-to-jitter conversion as an LPTV process Modlig of h CML FD ois-o-ir covrsio as a LPV procss Marko Alksic. Rvisio hisory Vrsio Da Comms. //4 Firs vrsio mrgd wo docums. Cyclosaioary Nois ad Applicaio o CML Frqucy Dividr Jir/Phas Nois Aalysis fil

More information

Numerical Simulation for the 2-D Heat Equation with Derivative Boundary Conditions

Numerical Simulation for the 2-D Heat Equation with Derivative Boundary Conditions IOSR Joural of Applid Chmisr IOSR-JAC -ISSN: 78-576.Volum 9 Issu 8 Vr. I Aug. 6 PP 4-8 www.iosrjourals.org Numrical Simulaio for h - Ha Equaio wih rivaiv Boudar Codiios Ima. I. Gorial parm of Mahmaics

More information

Poisson Arrival Process

Poisson Arrival Process Poisso Arrival Procss Arrivals occur i) i a mmylss mar ii) [ o arrival durig Δ ] = λδ + ( Δ ) P o [ o arrival durig Δ ] = λδ + ( Δ ) P o P j arrivals durig Δ = o Δ f j = 2,3, o Δ whr lim =. Δ Δ C C 2 C

More information

Poisson Arrival Process

Poisson Arrival Process 1 Poisso Arrival Procss Arrivals occur i) i a mmorylss mar ii) [ o arrival durig Δ ] = λδ + ( Δ ) P o [ o arrival durig Δ ] = 1 λδ + ( Δ ) P o P j arrivals durig Δ = o Δ for j = 2,3, ( ) o Δ whr lim =

More information

Arturo R. Samana* in collaboration with Carlos Bertulani*, & FranjoKrmpotic(UNLP-Argentina) *Department of Physics Texas A&M University -Commerce 07/

Arturo R. Samana* in collaboration with Carlos Bertulani*, & FranjoKrmpotic(UNLP-Argentina) *Department of Physics Texas A&M University -Commerce 07/ Comparison of RPA-lik modls in Nurino-Nuclus Nuclus Procsss Aruro R. Samana* in collaboraion wih Carlos Brulani* & FranjoKrmpoicUNLP-Argnina *Dparmn of Physics Txas A&M Univrsiy -Commrc 07/ 0/008 Aomic

More information

EE415/515 Fundamentals of Semiconductor Devices Fall 2012

EE415/515 Fundamentals of Semiconductor Devices Fall 2012 3 EE4555 Fudmls of Smicoducor vics Fll cur 8: PN ucio iod hr 8 Forwrd & rvrs bis Moriy crrir diffusio Brrir lowrd blcd by iffusio rducd iffusio icrsd mioriy crrir drif rif hcd 3 EE 4555. E. Morris 3 3

More information

A L A BA M A L A W R E V IE W

A L A BA M A L A W R E V IE W A L A BA M A L A W R E V IE W Volume 52 Fall 2000 Number 1 B E F O R E D I S A B I L I T Y C I V I L R I G HT S : C I V I L W A R P E N S I O N S A N D TH E P O L I T I C S O F D I S A B I L I T Y I N

More information

Adomian Decomposition Method for Dispersion. Phenomena Arising in Longitudinal Dispersion of. Miscible Fluid Flow through Porous Media

Adomian Decomposition Method for Dispersion. Phenomena Arising in Longitudinal Dispersion of. Miscible Fluid Flow through Porous Media dv. Thor. ppl. Mch. Vol. 3 o. 5 - domia Dcomposiio Mhod for Disprsio Phoma risig i ogiudial Disprsio of Miscibl Fluid Flow hrough Porous Mdia Ramakaa Mhr ad M.N. Mha Dparm of Mahmaics S.V. Naioal Isiu

More information

Phys463.nb Conductivity. Another equivalent definition of the Fermi velocity is

Phys463.nb Conductivity. Another equivalent definition of the Fermi velocity is 39 Anohr quival dfiniion of h Fri vlociy is pf vf (6.4) If h rgy is a quadraic funcion of k H k L, hs wo dfiniions ar idical. If is NOT a quadraic funcion of k (which could happ as will b discussd in h

More information

EEE 303: Signals and Linear Systems

EEE 303: Signals and Linear Systems 33: Sigls d Lir Sysms Orhogoliy bw wo sigls L us pproim fucio f () by fucio () ovr irvl : f ( ) = c( ); h rror i pproimio is, () = f() c () h rgy of rror sigl ovr h irvl [, ] is, { }{ } = f () c () d =

More information

Mixing time with Coupling

Mixing time with Coupling Mixig im wih Couplig Jihui Li Mig Zhg Saisics Dparm May 7 Goal Iroducio o boudig h mixig im for MCMC wih couplig ad pah couplig Prsig a simpl xampl o illusra h basic ida Noaio M is a Markov chai o fii

More information

14th Annual i-pcgrid Workshop. Xinzhou Dong. Professor Dept of Electrical Engineering Tsinghua University

14th Annual i-pcgrid Workshop. Xinzhou Dong. Professor Dept of Electrical Engineering Tsinghua University 14h Aual i-pcgrid Workshop Xizhou Dog Profssor Dp of Elcrical Egirig Tsighua Uivrsiy Cos 1. Iroducio 2. Graio ad faur of Faul grad Travllig Wavs FTW 3. Travllig wavs basd procio for EHV/UHV lis 4. Faul

More information

Linear Systems Analysis in the Time Domain

Linear Systems Analysis in the Time Domain Liar Sysms Aalysis i h Tim Domai Firs Ordr Sysms di vl = L, vr = Ri, d di L + Ri = () d R x= i, x& = x+ ( ) L L X() s I() s = = = U() s E() s Ls+ R R L s + R u () = () =, i() = L i () = R R Firs Ordr Sysms

More information

Let s express the absorption of radiation by dipoles as a dipole correlation function.

Let s express the absorption of radiation by dipoles as a dipole correlation function. MIT Deparme of Chemisry 5.74, Sprig 004: Iroducory Quaum Mechaics II Isrucor: Prof. Adrei Tokmakoff p. 81 Time-Correlaio Fucio Descripio of Absorpio Lieshape Le s express he absorpio of radiaio by dipoles

More information

1973 AP Calculus BC: Section I

1973 AP Calculus BC: Section I 97 AP Calculus BC: Scio I 9 Mius No Calculaor No: I his amiaio, l dos h aural logarihm of (ha is, logarihm o h bas ).. If f ( ) =, h f ( ) = ( ). ( ) + d = 7 6. If f( ) = +, h h s of valus for which f

More information

P a g e 5 1 of R e p o r t P B 4 / 0 9

P a g e 5 1 of R e p o r t P B 4 / 0 9 P a g e 5 1 of R e p o r t P B 4 / 0 9 J A R T a l s o c o n c l u d e d t h a t a l t h o u g h t h e i n t e n t o f N e l s o n s r e h a b i l i t a t i o n p l a n i s t o e n h a n c e c o n n e

More information

10. If p and q are the lengths of the perpendiculars from the origin on the tangent and the normal to the curve

10. If p and q are the lengths of the perpendiculars from the origin on the tangent and the normal to the curve 0. If p and q ar h lnghs of h prpndiculars from h origin on h angn and h normal o h curv + Mahmaics y = a, hn 4p + q = a a (C) a (D) 5a 6. Wha is h diffrnial quaion of h family of circls having hir cnrs

More information

An Indian Journal FULL PAPER. Trade Science Inc. A stage-structured model of a single-species with density-dependent and birth pulses ABSTRACT

An Indian Journal FULL PAPER. Trade Science Inc. A stage-structured model of a single-species with density-dependent and birth pulses ABSTRACT [Typ x] [Typ x] [Typ x] ISSN : 974-7435 Volum 1 Issu 24 BioTchnology 214 An Indian Journal FULL PAPE BTAIJ, 1(24), 214 [15197-1521] A sag-srucurd modl of a singl-spcis wih dnsiy-dpndn and birh pulss LI

More information

Response of LTI Systems to Complex Exponentials

Response of LTI Systems to Complex Exponentials 3 Fourir sris coiuous-im Rspos of LI Sysms o Complx Expoials Ouli Cosidr a LI sysm wih h ui impuls rspos Suppos h ipu sigal is a complx xpoial s x s is a complx umbr, xz zis a complx umbr h or h h w will

More information

Some Applications of the Poisson Process

Some Applications of the Poisson Process Applid Maaics, 24, 5, 3-37 Publishd Oli Novbr 24 i SciRs. hp://www.scirp.org/oural/a hp://dx.doi.org/.4236/a.24.59288 So Applicaios of Poisso Procss Kug-Ku s Dpar of Maaics, Ka Uivrsiy, Uio, USA Eail:

More information

EE Control Systems LECTURE 11

EE Control Systems LECTURE 11 Up: Moy, Ocor 5, 7 EE 434 - Corol Sy LECTUE Copyrigh FL Lwi 999 All righ rrv POLE PLACEMET A STEA-STATE EO Uig fc, o c ov h clo-loop pol o h h y prforc iprov O c lo lc uil copor o oi goo y- rcig y uyig

More information

Almost power law : Tempered power-law models (T-FADE)

Almost power law : Tempered power-law models (T-FADE) Almos powr law : Tmprd powr-law modls T-FADE Yong Zhang Dsr Rsarch Insiu Novmbr 4, 29 Acknowldgmns Boris Baumr Mark Mrschar Donald Rvs Oulin Par Spac T-FADE modl. Inroducion 2. Numrical soluion 3. Momn

More information

UNIT #5 EXPONENTIAL AND LOGARITHMIC FUNCTIONS

UNIT #5 EXPONENTIAL AND LOGARITHMIC FUNCTIONS Answr Ky Nam: Da: UNIT # EXPONENTIAL AND LOGARITHMIC FUNCTIONS Par I Qusions. Th prssion is quivaln o () () 6 6 6. Th ponnial funcion y 6 could rwrin as y () y y 6 () y y (). Th prssion a is quivaln o

More information

In-fiber acousto-optic interaction

In-fiber acousto-optic interaction I-fib acouo-opic iacio Migul V. Adé Laboaoio d Fiba Ópica d la Uividad d Valcia Dpaamo d Fíica Aplicada ICMUV migul.ad@uv. Gal objciv Fabicaio of all-fib dyamic dvic bad o h i-fib acouo-opic iacio A adad

More information

EE 232 Lightwave Devices Lecture 3: Basic Semiconductor Physics and Optical Processes. Optical Properties of Semiconductors

EE 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 information

From Fourier Series towards Fourier Transform

From Fourier Series towards Fourier Transform From Fourir Sris owards Fourir rasform D D d D, d wh lim Dparm of Elcrical ad Compur Eiri D, d wh lim L s Cosidr a fucio G d W ca xprss D i rms of Gw D G Dparm of Elcrical ad Compur Eiri D G G 3 Dparm

More information

Continous system: differential equations

Continous system: differential equations /6/008 Coious sysm: diffrial quaios Drmiisic modls drivaivs isad of (+)-( r( compar ( + ) R( + r ( (0) ( R ( 0 ) ( Dcid wha hav a ffc o h sysm Drmi whhr h paramrs ar posiiv or gaiv, i.. giv growh or rducio

More information

Web-appendix 1: macro to calculate the range of ( ρ, for which R is positive definite

Web-appendix 1: macro to calculate the range of ( ρ, for which R is positive definite Wb-basd Supplmary Marials for Sampl siz cosidraios for GEE aalyss of hr-lvl clusr radomizd rials by Sv Trsra, Big Lu, oh S. Prissr, Tho va Achrbrg, ad Gorg F. Borm Wb-appdix : macro o calcula h rag of

More information

Solid State Device Fundamentals

Solid 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 information

Effects of ion motion on linear Landau damping

Effects of ion motion on linear Landau damping Effcs of ion moion on linar Landau damping Hui Xu 1**, Zhng-Ming Shng 2,3,4, Xiang-Mu Kong 1, Fu-Fang Su 1 1 Shandong Provincial Ky Laboraory of Lasr Polarizaion and Informaion Tchnology, Dparmn of Physics,

More information

Intrinsic formulation for elastic line deformed on a surface by an external field in the pseudo-galilean space 3. Nevin Gürbüz

Intrinsic formulation for elastic line deformed on a surface by an external field in the pseudo-galilean space 3. Nevin Gürbüz risic formuaio for asic i form o a surfac by a xra fi i h psuo-aia spac Nvi ürbüz Eskişhir Osmaazi Uivrsiy Mahmaics a Compur Scics Dparm urbuz@ouur Absrac: his papr w riv irisic formuaio for asic i form

More information

Control Systems. Transient and Steady State Response.

Control Systems. Transient and Steady State Response. Corol Sym Trai a Say Sa Ro chibum@oulch.ac.kr Ouli Tim Domai Aalyi orr ym Ui ro Ui ram ro Ui imul ro Chibum L -Soulch Corol Sym Tim Domai Aalyi Afr h mahmaical mol of h ym i obai, aalyi of ym rformac i.

More information

Note 6 Frequency Response

Note 6 Frequency Response No 6 Frqucy Rpo Dparm of Mchaical Egirig, Uivriy Of Sakachwa, 57 Campu Driv, Sakaoo, S S7N 59, Caada Dparm of Mchaical Egirig, Uivriy Of Sakachwa, 57 Campu Driv, Sakaoo, S S7N 59, Caada. alyical Exprio

More information

The Exile Began. Family Journal Page. God Called Jeremiah Jeremiah 1. Preschool. below. Tell. them too. Kids. Ke Passage: Ezekiel 37:27

The Exile Began. Family Journal Page. God Called Jeremiah Jeremiah 1. Preschool. below. Tell. them too. Kids. Ke Passage: Ezekiel 37:27 Faily Jo Pag Th Exil Bg io hy u c prof b jo ou Shar ab ou job ab ar h o ay u Yo ra u ar u r a i A h ) ar par ( grp hav h y y b jo i crib blo Tll ri ir r a r gro up Allo big u r a i Rvi h b of ha u ha a

More information

Chemistry 988 Part 1

Chemistry 988 Part 1 Chmisry 988 Par 1 Radiaion Dcion & Masurmn Dp. of Chmisry --- Michigan Sa Univ. aional Suprconducing Cycloron Lab DJMorrissy Spring/2oo9 Cours informaion can b found on h wbsi: hp://www.chmisry.msu.du/courss/cm988uclar/indx.hml

More information

OH BOY! Story. N a r r a t iv e a n d o bj e c t s th ea t e r Fo r a l l a g e s, fr o m th e a ge of 9

OH BOY! Story. N a r r a t iv e a n d o bj e c t s th ea t e r Fo r a l l a g e s, fr o m th e a ge of 9 OH BOY! O h Boy!, was or igin a lly cr eat ed in F r en ch an d was a m a jor s u cc ess on t h e Fr en ch st a ge f or young au di enc es. It h a s b een s een by ap pr ox i ma t ely 175,000 sp ect at

More information

P a g e 3 6 of R e p o r t P B 4 / 0 9

P a g e 3 6 of R e p o r t P B 4 / 0 9 P a g e 3 6 of R e p o r t P B 4 / 0 9 p r o t e c t h um a n h e a l t h a n d p r o p e r t y fr om t h e d a n g e rs i n h e r e n t i n m i n i n g o p e r a t i o n s s u c h a s a q u a r r y. J

More information

Review Topics from Chapter 3&4. Fourier Series Fourier Transform Linear Time Invariant (LTI) Systems Energy-Type Signals Power-Type Signals

Review Topics from Chapter 3&4. Fourier Series Fourier Transform Linear Time Invariant (LTI) Systems Energy-Type Signals Power-Type Signals Rviw opics from Chapr 3&4 Fourir Sris Fourir rasform Liar im Ivaria (LI) Sysms Ergy-yp Sigals Powr-yp Sigals Fourir Sris Rprsaio for Priodic Sigals Dfiiio: L h sigal () b a priodic sigal wih priod. ()

More information

Research and Development Work on Lithium-ion Batteries for Environmental Vehicles

Research and Development Work on Lithium-ion Batteries for Environmental Vehicles ISSN 3-6653 Th World Elcric Vhicl Aociaio Joural, Vol. 1, 7 Rarch ad Dvlopm Work o Lihium-io Bari for Eviromal Vhicl Oamu Shimamura*, Takaaki Ab*, Kyoichi Waaab*, Yauhiko Ohawa*, Hidaki Hori* Ir i lcric

More information

( A) ( B) ( C) ( D) ( E)

( A) ( B) ( C) ( D) ( E) d Smsr Fial Exam Worksh x 5x.( NC)If f ( ) d + 7, h 4 f ( ) d is 9x + x 5 6 ( B) ( C) 0 7 ( E) divrg +. (NC) Th ifii sris ak has h parial sum S ( ) for. k Wha is h sum of h sris a? ( B) 0 ( C) ( E) divrgs

More information

Coherence and interactions in diffusive systems. Lecture 4. Diffusion + e-e interations

Coherence and interactions in diffusive systems. Lecture 4. Diffusion + e-e interations Cohrnc and inracions in diffusiv sysms G. Monambaux cur 4 iffusion + - inraions nsiy of sas anomaly phasing du o lcron-lcron inracions - inracion andau Frmi liquid picur iffusion slows down lcrons ( )

More information

The Development of Suitable and Well-founded Numerical Methods to Solve Systems of Integro- Differential Equations,

The Development of Suitable and Well-founded Numerical Methods to Solve Systems of Integro- Differential Equations, Shiraz Uivrsiy of Tchology From h SlcdWorks of Habibolla Laifizadh Th Dvlopm of Suiabl ad Wll-foudd Numrical Mhods o Solv Sysms of Igro- Diffrial Equaios, Habibolla Laifizadh, Shiraz Uivrsiy of Tchology

More information

Spatial channeling of energy and momentum of energetic ions by destabilized Alfvén eigenmodes

Spatial channeling of energy and momentum of energetic ions by destabilized Alfvén eigenmodes Spatial channling of nrgy and momntum of nrgtic ions by dstabilizd Alfvén ignmods Ya.I. Kolsnichnko 1,V.V. Lutsnko 1, R.B. Whit, Yu.V. Yakovnko 1 1 Institut for Nuclar Rsarch, Kyiv, Ukrain Princton Plasma

More information

Coherence and interactions in diffusive systems. Cours 4. Diffusion + e-e interations

Coherence and interactions in diffusive systems. Cours 4. Diffusion + e-e interations Cohrnc and inracions in diffusiv sysms G. Monambaux Cours 4 iffusion + - inraions nsiy of sas anomaly phasing du o lcron-lcron inracions Why ar h flucuaions univrsal and wak localizaion is no? ΔG G cl

More information

S- AND P-POLARIZED REFLECTIVITIES OF EXPLOSIVELY DRIVEN STRONGLY NON-IDEAL XENON PLASMA

S- AND P-POLARIZED REFLECTIVITIES OF EXPLOSIVELY DRIVEN STRONGLY NON-IDEAL XENON PLASMA S- AND P-POLARIZED REFLECTIVITIES OF EXPLOSIVELY DRIVEN STRONGLY NON-IDEAL XENON PLASMA Zaporozhts Yu.B.*, Mitsv V.B., Gryazov V.K., Riholz H., Röpk G. 3, Fortov V.E. 4 Istitut of Problms of Chmical Physics

More information

Physics 160 Lecture 3. R. Johnson April 6, 2015

Physics 160 Lecture 3. R. Johnson April 6, 2015 Physics 6 Lcur 3 R. Johnson April 6, 5 RC Circui (Low-Pass Filr This is h sam RC circui w lookd a arlir h im doma, bu hr w ar rsd h frquncy rspons. So w pu a s wav sad of a sp funcion. whr R C RC Complx

More information

Modeling of Reductive Biodegradation of TCE to ETH. Adam Worsztynowicz, Dorota Rzychon, Sebastian Iwaszenko, Tomasz Siobowicz

Modeling of Reductive Biodegradation of TCE to ETH. Adam Worsztynowicz, Dorota Rzychon, Sebastian Iwaszenko, Tomasz Siobowicz Modlig of Rduciv Biodgradaio of o ETH Adam Worszyowicz, Doroa Rzycho, Sbasia Iwaszo, Tomasz Siobowicz Isiu for Ecology of Idusrial Aras Kossuha S., Kaowic, Polad l. (+-) 5, fax: (+-) 5 7 7 -mail: iu@iu.aowic.pl

More information

Fourier Techniques Chapters 2 & 3, Part I

Fourier Techniques Chapters 2 & 3, Part I Fourir chiqus Chaprs & 3, Par I Dr. Yu Q. Shi Dp o Elcrical & Compur Egirig Nw Jrsy Isiu o chology Email: shi@i.du usd or h cours: , 4 h Ediio, Lahi ad Dog, Oord

More information

NEWBERRY FOREST MGT UNIT Stand Level Information Compartment: 10 Entry Year: 2001

NEWBERRY FOREST MGT UNIT Stand Level Information Compartment: 10 Entry Year: 2001 iz oy- kg vg. To. 1 M 6 M 10 11 100 60 oh hwoo uvg N o hul 0 Mix bg. woo, moly low quliy. Coif ompo houghou - WP/hmlok/pu/blm/. vy o whi pi o h ouh fig of. iffiul o. Th o hi i o PVT l wh h g o wll big

More information

8(4 m0) ( θ ) ( ) Solutions for HW 8. Chapter 25. Conceptual Questions

8(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

Software Development Cost Model based on NHPP Gompertz Distribution

Software Development Cost Model based on NHPP Gompertz Distribution Idia Joural of Scic ad Tchology, Vol 8(12), DOI: 10.17485/ijs/2015/v8i12/68332, Ju 2015 ISSN (Pri) : 0974-6846 ISSN (Oli) : 0974-5645 Sofwar Dvlopm Cos Modl basd o NHPP Gomprz Disribuio H-Chul Kim 1* ad

More information

Wave Equation (2 Week)

Wave Equation (2 Week) Rfrnc Wav quaion ( Wk 6.5 Tim-armonic filds 7. Ovrviw 7. Plan Wavs in Losslss Mdia 7.3 Plan Wavs in Loss Mdia 7.5 Flow of lcromagnic Powr and h Poning Vcor 7.6 Normal Incidnc of Plan Wavs a Plan Boundaris

More information

Economics 302 (Sec. 001) Intermediate Macroeconomic Theory and Policy (Spring 2011) 3/28/2012. UW Madison

Economics 302 (Sec. 001) Intermediate Macroeconomic Theory and Policy (Spring 2011) 3/28/2012. UW Madison Economics 302 (Sc. 001) Inrmdia Macroconomic Thory and Policy (Spring 2011) 3/28/2012 Insrucor: Prof. Mnzi Chinn Insrucor: Prof. Mnzi Chinn UW Madison 16 1 Consumpion Th Vry Forsighd dconsumr A vry forsighd

More information

4.1 The Uniform Distribution Def n: A c.r.v. X has a continuous uniform distribution on [a, b] when its pdf is = 1 a x b

4.1 The Uniform Distribution Def n: A c.r.v. X has a continuous uniform distribution on [a, b] when its pdf is = 1 a x b 4. Th Uniform Disribuion Df n: A c.r.v. has a coninuous uniform disribuion on [a, b] whn is pdf is f x a x b b a Also, b + a b a µ E and V Ex4. Suppos, h lvl of unblivabiliy a any poin in a Transformrs

More information

Charging of capacitor through inductor and resistor

Charging of capacitor through inductor and resistor cur 4&: R circui harging of capacior hrough inducor and rsisor us considr a capacior of capacianc is conncd o a D sourc of.m.f. E hrough a rsisr of rsisanc R, an inducor of inducanc and a y K in sris.

More information

CVFU. Model CVFU Contents. EBARA PRO Cast Vortex Sewage Pumps

CVFU. Model CVFU Contents. EBARA PRO Cast Vortex Sewage Pumps Modl Cos EBARA PRO Cas Vorx Swag Pumps... CVBU. CVCU. CVBU.7 CVCU.7.7 Scio Pag Spciicaios Slcio Car Prormac Curvs 7 Dimsios Scioal Viw QDC Iormaio Moor Daa moor lcrical spciicaios cabl daa wirig diagrams

More information

Lecture 4: Laplace Transforms

Lecture 4: Laplace Transforms Lur 4: Lapla Transforms Lapla and rlad ransformaions an b usd o solv diffrnial quaion and o rdu priodi nois in signals and imags. Basially, hy onvr h drivaiv opraions ino mulipliaion, diffrnial quaions

More information

Research Article Modelling of Rehydration of Freeze-dried Dumpling Wrapper

Research Article Modelling of Rehydration of Freeze-dried Dumpling Wrapper Rsarch Joural of Applid Scics, Egirig ad Tchology 1(5): 556-561, 16 DOI:1.196/rjas.1. 683 ISSN: 4-7459; -ISSN: 4-7467 16 axwll Sciific Publicaio Corp. Submid: Spmbr 1, 15 Accpd: Ocobr 3, 15 Publishd: arch

More information

, then the old equilibrium biomass was greater than the new B e. and we want to determine how long it takes for B(t) to reach the value B e.

, then the old equilibrium biomass was greater than the new B e. and we want to determine how long it takes for B(t) to reach the value B e. SURPLUS PRODUCTION (coiud) Trasiio o a Nw Equilibrium Th followig marials ar adapd from lchr (978), o h Rcommdd Radig lis caus () approachs h w quilibrium valu asympoically, i aks a ifii amou of im o acually

More information

COMBUSTION. TA : Donggi Lee ROOM: Building N7-2 #3315 TELEPHONE : 3754 Cellphone : PROF.

COMBUSTION. TA : Donggi Lee ROOM: Building N7-2 #3315 TELEPHONE : 3754 Cellphone : PROF. COMBUSIO ROF. SEUG WOOK BAEK DEARME OF AEROSACE EGIEERIG, KAIS, I KOREA ROOM: Buldng 7- #334 ELEHOE : 3714 Cellphone : 1-53 - 5934 swbaek@kast.a.kr http://proom.kast.a.kr A : Dongg Lee ROOM: Buldng 7-

More information

Lecture contents Macroscopic Electrodynamics Propagation of EM Waves in dielectrics and metals

Lecture contents Macroscopic Electrodynamics Propagation of EM Waves in dielectrics and metals Leure oes Marosopi lerodyamis Propagaio of M Waves i dieleris ad meals NNS 58 M Leure #4 Maxwell quaios Maxwell equaios desribig he ouplig of eleri ad magei fields D q ev B D J [SI] [CGS] D 4 B D 4 J B

More information

4. Which of the following organs develops first?

4. Which of the following organs develops first? Biology 4. Which of h following organs dvlops firs? (A) Livr (C) Kidny (B) Har (D) Noochord 12. During mbryonic priod, animals rpa mbryonic sags of hir ancsors. This law is calld (A) Flokin s law (B) Biognic

More information

Decline Curves. Exponential decline (constant fractional decline) Harmonic decline, and Hyperbolic decline.

Decline Curves. Exponential decline (constant fractional decline) Harmonic decline, and Hyperbolic decline. Dlin Curvs Dlin Curvs ha lo flow ra vs. im ar h mos ommon ools for forasing roduion and monioring wll rforman in h fild. Ths urvs uikly show by grahi mans whih wlls or filds ar roduing as xd or undr roduing.

More information

Self-interaction mass formula that relates all leptons and quarks to the electron

Self-interaction mass formula that relates all leptons and quarks to the electron Slf-intraction mass formula that rlats all lptons and quarks to th lctron GERALD ROSEN (a) Dpartmnt of Physics, Drxl Univrsity Philadlphia, PA 19104, USA PACS. 12.15. Ff Quark and lpton modls spcific thoris

More information

1a.- Solution: 1a.- (5 points) Plot ONLY three full periods of the square wave MUST include the principal region.

1a.- Solution: 1a.- (5 points) Plot ONLY three full periods of the square wave MUST include the principal region. INEL495 SIGNALS AND SYSEMS FINAL EXAM: Ma 9, 8 Pro. Doigo Rodrígz SOLUIONS Probl O: Copl Epoial Forir Sri A priodi ri ar wav l ad a daal priod al o o od. i providd wi a a 5% d a.- 5 poi: Plo r ll priod

More information

x, x, e are not periodic. Properties of periodic function: 1. For any integer n,

x, x, e are not periodic. Properties of periodic function: 1. For any integer n, Chpr Fourir Sri, Igrl, d Tror. Fourir Sri A uio i lld priodi i hr i o poiiv ur p uh h p, p i lld priod o R i,, r priodi uio.,, r o priodi. Propri o priodi uio:. For y igr, p. I d g hv priod p, h h g lo

More information

On the Speed of Heat Wave. Mihály Makai

On the Speed of Heat Wave. Mihály Makai On h Spd of Ha Wa Mihály Maai maai@ra.bm.hu Conns Formulaion of h problm: infini spd? Local hrmal qulibrium (LTE hypohsis Balanc quaion Phnomnological balanc Spd of ha wa Applicaion in plasma ranspor 1.

More information

176 5 t h Fl oo r. 337 P o ly me r Ma te ri al s

176 5 t h Fl oo r. 337 P o ly me r Ma te ri al s A g la di ou s F. L. 462 E l ec tr on ic D ev el op me nt A i ng er A.W.S. 371 C. A. M. A l ex an de r 236 A d mi ni st ra ti on R. H. (M rs ) A n dr ew s P. V. 326 O p ti ca l Tr an sm is si on A p ps

More information

Pupil / Class Record We can assume a word has been learned when it has been either tested or used correctly at least three times.

Pupil / Class Record We can assume a word has been learned when it has been either tested or used correctly at least three times. 2 Pupi / Css Rr W ssum wr hs b r wh i hs b ihr s r us rry s hr ims. Nm: D Bu: fr i bus brhr u firs hf hp hm s uh i iv iv my my mr muh m w ih w Tik r pp push pu sh shu sisr s sm h h hir hr hs im k w vry

More information

Microscopic Flow Characteristics Time Headway - Distribution

Microscopic Flow Characteristics Time Headway - Distribution CE57: Traffic Flow Thory Spring 20 Wk 2 Modling Hadway Disribuion Microscopic Flow Characrisics Tim Hadway - Disribuion Tim Hadway Dfiniion Tim Hadway vrsus Gap Ahmd Abdl-Rahim Civil Enginring Dparmn,

More information

CATAVASII LA NAȘTEREA DOMNULUI DUMNEZEU ȘI MÂNTUITORULUI NOSTRU, IISUS HRISTOS. CÂNTAREA I-A. Ήχος Πα. to os se e e na aș te e e slă ă ă vi i i i i

CATAVASII LA NAȘTEREA DOMNULUI DUMNEZEU ȘI MÂNTUITORULUI NOSTRU, IISUS HRISTOS. CÂNTAREA I-A. Ήχος Πα. to os se e e na aș te e e slă ă ă vi i i i i CATAVASII LA NAȘTEREA DOMNULUI DUMNEZEU ȘI MÂNTUITORULUI NOSTRU, IISUS HRISTOS. CÂNTAREA I-A Ήχος α H ris to os s n ș t slă ă ă vi i i i i ți'l Hris to o os di in c ru u uri, în tâm pi i n ți i'l Hris

More information

Chp6. pn Junction Diode: I-V Characteristics I

Chp6. 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 information

, R we have. x x. ) 1 x. R and is a positive bounded. det. International Journal of Basic & Applied Sciences IJBAS-IJENS Vol:10 No:06 11

, R we have. x x. ) 1 x. R and is a positive bounded. det. International Journal of Basic & Applied Sciences IJBAS-IJENS Vol:10 No:06 11 raioal Joral of asic & ppli Scics JS-JENS Vol: No:6 So Dirichl ors a Pso Diffrial Opraors wih Coiioall Epoial Cov cio aa. M. Kail Dpar of Mahaics; acl of Scic; Ki laziz Uivrsi Jah Sai raia Eail: fkail@ka..sa

More information

Gavilan JCCD Trustee Areas Plan Adopted October 13, 2015

Gavilan JCCD Trustee Areas Plan Adopted October 13, 2015 S Jos Gvil JCCD Trust Ar Pl Aopt Octobr, 0 p Lrs Pl Aopt Oct, 0 Cit/Csus Dsigt Plc ighw US 0 Cit Arom ollistr igmr S Jos Trs Pios cr Ps 4 ut S Bito ut 0 0 ils Arom ollistr igmr Trs Pios 7 S Bito ut Lpoff

More information

Control System Engineering (EE301T) Assignment: 2

Control System Engineering (EE301T) Assignment: 2 Conrol Sysm Enginring (EE0T) Assignmn: PART-A (Tim Domain Analysis: Transin Rspons Analysis). Oain h rspons of a uniy fdack sysm whos opn-loop ransfr funcion is (s) s ( s 4) for a uni sp inpu and also

More information

Mixed Mode Oscillations as a Mechanism for Pseudo-Plateau Bursting

Mixed Mode Oscillations as a Mechanism for Pseudo-Plateau Bursting Mixd Mod Oscillatios as a Mchaism for Psudo-Platau Burstig Richard Brtram Dpartmt of Mathmatics Florida Stat Uivrsity Tallahass, FL Collaborators ad Support Thodor Vo Marti Wchslbrgr Joël Tabak Uivrsity

More information

EE 434 Lecture 22. Bipolar Device Models

EE 434 Lecture 22. Bipolar Device Models EE 434 Lcur 22 Bipolar Dvic Modls Quiz 14 Th collcor currn of a BJT was masurd o b 20mA and h bas currn masurd o b 0.1mA. Wha is h fficincy of injcion of lcrons coming from h mir o h collcor? 1 And h numbr

More information

Analysis of Non-Sinusoidal Waveforms Part 2 Laplace Transform

Analysis of Non-Sinusoidal Waveforms Part 2 Laplace Transform Aalyi o No-Siuoidal Wavorm Par Laplac raorm I h arlir cio, w lar ha h Fourir Sri may b wri i complx orm a ( ) C jω whr h Fourir coici C i giv by o o jωo C ( ) d o I h ymmrical orm, h Fourir ri i wri wih

More information

Poisson process Markov process

Poisson process Markov process E2200 Quuing hory and lraffic 2nd lcur oion proc Markov proc Vikoria Fodor KTH Laboraory for Communicaion nwork, School of Elcrical Enginring 1 Cour oulin Sochaic proc bhind quuing hory L2-L3 oion proc

More information

2.1. Differential Equations and Solutions #3, 4, 17, 20, 24, 35

2.1. Differential Equations and Solutions #3, 4, 17, 20, 24, 35 MATH 5 PS # Summr 00.. Diffrnial Equaions and Soluions PS.# Show ha ()C #, 4, 7, 0, 4, 5 ( / ) is a gnral soluion of h diffrnial quaion. Us a compur or calculaor o skch h soluions for h givn valus of h

More information

Department of Electronics & Telecommunication Engineering C.V.Raman College of Engineering

Department of Electronics & Telecommunication Engineering C.V.Raman College of Engineering Lcur No Lcur-6-9 Ar rdig his lsso, you will lr ou Fourir sris xpsio rigoomric d xpoil Propris o Fourir Sris Rspos o lir sysm Normlizd powr i Fourir xpsio Powr spcrl dsiy Ec o rsr ucio o PSD. FOURIER SERIES

More information

Superfluid Liquid Helium

Superfluid Liquid Helium Surfluid Liquid Hlium:Bo liquid ad urfluidity Ladau thory: two fluid modl Bo-iti Codatio ad urfluid ODLRO, otaou ymmtry brakig, macrocoic wafuctio Gro-Pitakii GP quatio Fyma ictur Rfrc: Thory of quatum

More information

UNSTEADY FLOW OF A FLUID PARTICLE SUSPENSION BETWEEN TWO PARALLEL PLATES SUDDENLY SET IN MOTION WITH SAME SPEED

UNSTEADY FLOW OF A FLUID PARTICLE SUSPENSION BETWEEN TWO PARALLEL PLATES SUDDENLY SET IN MOTION WITH SAME SPEED 006-0 Asian Rsarch Publishing work (ARP). All righs rsrvd. USTEADY FLOW OF A FLUID PARTICLE SUSPESIO BETWEE TWO PARALLEL PLATES SUDDELY SET I MOTIO WITH SAME SPEED M. suniha, B. Shankr and G. Shanha 3

More information

STK4080/9080 Survival and event history analysis

STK4080/9080 Survival and event history analysis STK48/98 Survival ad eve hisory aalysis Marigales i discree ime Cosider a sochasic process The process M is a marigale if Lecure 3: Marigales ad oher sochasic processes i discree ime (recap) where (formally

More information

Emigration The movement of individuals out of an area The population decreases

Emigration The movement of individuals out of an area The population decreases Nm Clss D C 5 Puls S 5 1 Hw Puls Gw (s 119 123) Ts s fs ss us sb ul. I ls sbs fs ff ul sz xls w xl w ls w. Css f Puls ( 119) 1. W fu m ss f ul?. G sbu. Gw b. Ds. A suu 2. W s ul s sbu? I s b b ul. 3. A

More information

Strictly as per the compliance and regulations of :

Strictly as per the compliance and regulations of : Global Joural of Scic Froir Rsarch Mahaics & Dcisio Scics Volu Issu Vrsio. Typ : Doubl lid Pr Rviwd Iraioal Rsarch Joural Publishr: Global Jourals Ic. US Oli ISSN: 9-66 & i ISSN: 975-5896 Oscillaory Fr

More information

2 Dirac delta function, modeling of impulse processes. 3 Sine integral function. Exponential integral function

2 Dirac delta function, modeling of impulse processes. 3 Sine integral function. Exponential integral function Chapr VII Spcial Fucios Ocobr 7, 7 479 CHAPTER VII SPECIAL FUNCTIONS Cos: Havisid sp fucio, filr fucio Dirac dla fucio, modlig of impuls procsss 3 Si igral fucio 4 Error fucio 5 Gamma fucio E Epoial igral

More information

) and furthermore all X. The definition of the term stationary requires that the distribution fulfills the condition:

) and furthermore all X. The definition of the term stationary requires that the distribution fulfills the condition: Assigm Thomas Aam, Spha Brumm, Haik Lor May 6 h, 3 8 h smsr, 357, 7544, 757 oblm For R b X a raom variabl havig ormal isribuio wih ma µ a variac σ (his is wri as ~ (,) X. by: R a. Is X ) a urhrmor all

More information

C(p, ) 13 N. Nuclear reactions generate energy create new isotopes and elements. Notation for stellar rates: p 12

C(p, ) 13 N. Nuclear reactions generate energy create new isotopes and elements. Notation for stellar rates: p 12 Iroducio o sellar reacio raes Nuclear reacios geerae eergy creae ew isoopes ad elemes Noaio for sellar raes: p C 3 N C(p,) 3 N The heavier arge ucleus (Lab: arge) he ligher icomig projecile (Lab: beam)

More information

5. An object moving along an x-coordinate axis with its scale measured in meters has a velocity of 6t

5. An object moving along an x-coordinate axis with its scale measured in meters has a velocity of 6t AP CALCULUS FINAL UNIT WORKSHEETS ACCELERATION, VELOCTIY AND POSITION In problms -, drmin h posiion funcion, (), from h givn informaion.. v (), () = 5. v ()5, () = b g. a (), v() =, () = -. a (), v() =

More information

Frequency Response. Lecture #12 Chapter 10. BME 310 Biomedical Computing - J.Schesser

Frequency Response. Lecture #12 Chapter 10. BME 310 Biomedical Computing - J.Schesser Frquncy Rspns Lcur # Chapr BME 3 Bimdical Cmpuing - J.Schssr 99 Idal Filrs W wan sudy Hω funcins which prvid frquncy slciviy such as: Lw Pass High Pass Band Pass Hwvr, w will lk a idal filring, ha is,

More information

CSE 245: Computer Aided Circuit Simulation and Verification

CSE 245: Computer Aided Circuit Simulation and Verification CSE 45: Compur Aidd Circui Simulaion and Vrificaion Fall 4, Sp 8 Lcur : Dynamic Linar Sysm Oulin Tim Domain Analysis Sa Equaions RLC Nwork Analysis by Taylor Expansion Impuls Rspons in im domain Frquncy

More information

ADORO TE DEVOTE (Godhead Here in Hiding) te, stus bat mas, la te. in so non mor Je nunc. la in. tis. ne, su a. tum. tas: tur: tas: or: ni, ne, o:

ADORO TE DEVOTE (Godhead Here in Hiding) te, stus bat mas, la te. in so non mor Je nunc. la in. tis. ne, su a. tum. tas: tur: tas: or: ni, ne, o: R TE EVTE (dhd H Hdg) L / Mld Kbrd gú s v l m sl c m qu gs v nns V n P P rs l mul m d lud 7 súb Fí cón ví f f dó, cru gs,, j l f c r s m l qum t pr qud ct, us: ns,,,, cs, cut r l sns m / m fí hó sn sí

More information