Multi-Ion Space Plasma Research: Two highlights

Size: px
Start display at page:

Download "Multi-Ion Space Plasma Research: Two highlights"

Transcription

1 Multi-Io Sac Plasma Rsarch: Two highlights I. Plasma structurs ad boudaris i solar wid itractio with o-magtizd bodis II. Origi of cohrt larg-amlitud was i multi-io sac lasmas K. Saur * Max-Plack-Istitut für Aroomi, KatlburgLidau, Grmay * i clos cooratio with E. Dubii (MPA) ad artly with A. Liato ad J. McKzi Multi-Io Sac Plasma Rsarch: I. Plasma structurs ad boudaris i solar wid itractio with o-magtizd bodis MARS Comt Hal-o 1

2 Multi-Io Sac Plasma Rsarch: I. Plasma structurs ad boudaris i solar wid itractio with o-magtizd bodis Itroductio:...History of Mars Plasma Rsarch Two-fluid modl of itractio Numrical rsults Th MP at Mars - a w ty of lasma boudary Imlicatios to ROSETTA, MARS-EXPRESS ad CASSINI Io acoustic was i a Ar-H lasma Thory: Frid t al., 1971; Exrimt: Tra ad Coqurad, 1976 Lft: xrimtal wa attr for diffrt coctratio α. Th itrfrc attr for α 30% is du to th sur-ositio of th two wa mods. Right: has locity of th two io-acoustic mods rsus th coctratio α 2

3 Dust-acoustic was i a Q machi (arka t al., 1996) Dust-acoustic was (Rao, Shukla ad Yu ;1990): h k( T Ti) ( m d d 2 Z ) Diffrtial stramig btw rotos ad α-articls i th solar wid Hlios: Marsch t al., 1982 Ulysss: Nugbaur t al., 1994, 1996 Wid: Stibrg t al., 1996 V α - α Tmoral ariatio of α for o wk of Ulysss data (Nugbaur t al., 1996). 3

4 Solar wid itractio with Mars, Vus ad comts Comt Su hoto ioisatio Solar wid aramtrs: 500 km/s 5 cm -3 5 T T 10 V Mars surroudd by a iooshr Dyamic solar wid ad comt obsratio by Lasco o SOHO 4

5 Th comtary lasma boudaris Hally: Q s -1 IC SW roto caity S: ow Shock MP: Magtic Pil-u oudary IP: Iooaus comtoshath magtic il-u rgio magtic caity Plasma boudaris at comts ad Mars Hally S MP S MP IP IP MARS km km 0 5

6 Scitific ascts of solar wid - Mars itractio Study of fudamtal rocsss of lasma-lasma itractio which ar rlat for may othr situatios: comts, moos (Tita), astroids, Pluto, dust rigs, tc. Mars dhydratio: loss of watr by solar wid - atmoshr coulig; 1-10 m of surfac watr i 4.5 billio yars. Sac wathr: gratio of high rgtic articls, scially by CMEs (o shildig by a itrisic magtic fild). Solar wid scagig of th martia atmoshr > dhydratio Mars Exrss: ASPERA-3 will do global imagig ad i-situ masurmts of: Iflow solar wid Solar wid Outflow latary wid usig Ergtic utral atom camras ad lasma (iolctro) sctromtrs Platary wid 100 to/day 6

7 Scitific ascts of solar wid - Mars itractio Study of fudamtal rocsss of lasma-lasma itractio which ar rlat for may othr situatios: comts, moos (Tita), astroids, Pluto, dust, tc. Mars dhydratio: loss of watr by solar wid - atmoshr coulig; 1-10 m of surfac watr i 4.5 billio yars. Sac wathr: flux of high rgtic articls, scially by CMEs (o shildig by a itrisic magtic fild). History of Mars Plasma Rsarch S MP Our rst iw IP MARS km 0 7

8 Mars-2 obsratios i 1972 (Dolgio ad Grigauz, 1972) S MP Th saccraft crossd th bow shock (S) ad th obstacl boudary (magtoaus MP) Mars-2 obsratios i 1972 (Dolgio ad Grigauz, 1972) [T). S S MP I [A] Variatio of th magtic fild ad th lctro currt I at crossig th bow shock (S) ad th obstacl boudary (magtoaus MP) 8

9 Obstacl boudary i classical MHD modls Th solar wid dyamic rssur is balacd by iooshric thrmal rssur: ρ 2 k T (Iooaus) For T 1 V, a dsity of 10 4 cm -3 is rquird. Th iooshr of Mars is ot ds ough to rach such a dsity at about 500 km whr th obstacl boudary is obsrd. Thrfor, th obsrd boudary is ot a Iooaus. itrisic magtic rssur: ρ 2 2 /2µ 0 (Magtoaus) From th obsrd locatio of th obstacl boudary i a subsolar hight of about 500 km a magtic momt of Mars of about M T m 3 was stimatd. History of th Mars magtic momt From ositio ad sha of th obstacl boudary (MP) a magtic momt of M T m 3 was stimatd. Phobos-2 MGS 9

10 Th Phobos-2 missio i 1989 Th saccraft aroachd Mars dow to about 850 km durig 4 llitical orbits, arly o moth i a circular orbit, aroachd th Phobos moo u to 200 km. It was quid with imortat istrumts for lasma rsarch: magtomtr (MAGMA, FGMM), lctro ad io sctromtrs (ASPERA, TAUS), soudrs for low- ad high- frqucy lasma was Obsratio of th Io Comositio oudary (IC) by Phobos-2 S IC Sigaturs of th IC: - SW roto dsity dcrass - lctro dsity sharly icrass which -bcaus of charg utrality - mas a abrut icras of th latary io dsity: Protos ar rlacd by hay ios. 10

11 Obsratio of th MP/IC i larg distacs by Phobos-2 (1989) ( km) Jum of th magtic fild: MP Chag of io comositio: - SW rotos outsid - latary ios (oxyg) isid S MP IC MP rotos oxyg ios S Obsratio of th MP/IC i larg distacs by Phobos-2 ( km) Jum of th magtic fild: MP Chag of io comositio: - SW rotos outsid - latary ios (oxyg) isid 11

12 Phobos-2 obsratios of th Io Comositio oudary Io Comositio oudary (IC) Dubii t al., 1996 IC UT (h) Mars Global Suryor - its cotributio to Mars lasma rsarch S MGS orbit Most imortat: MGS wt dow to Mars u to about 150 km. Th saccraft carris a magtomtr ad a lctro sctromtr. It crossd th iooaus ad from th masurd magtic fild a momt of M T m 3 was dtrmid. This alu is mor tha o ordr of magitud wakr tha stimatd bfor. 12

13 Th Magtic Pil-u oudary at Mars ad comt Hally IP IP Mars Mazll t al., 2001 magtic caity Comt Hally Nubaur t al., 1986 First attmts to fid th IC i two-io fluid simulatios S IC IP 1D two-io fluid simulatios with latral ffcts h x (R M ) 13

14 First attmts to fid th IC i two-io fluid simulatios 1990 ASTRACT....This boudary is itrrtd as a multi-io cotact discotiuity whr th rotos ar dflctd by th Lortz forc arisig from th rlati motio btw both io fluids. Th magtic fild trats th IC... Aals Gohysica, 1990, 8, (10), Idicatio of thr lasma boudaris from th Phobos-2 obsratios; 1D bi-io fluid simulatios with latral ffcts (aftr MGS) Furthr sts i two-io fluid simulatios First thortical idc of a Io Comositio oudary (IC) i 2D simulatios of solar wid massloadig. (Th rotooaus - a io comositio boudary i th magtoshath of comts, Vus ad Mars; Saur t al., GRL) Imrod 2D two-io fluid modl (iclusio of thrmal ffcts) showig th Magtic Pil-u oudary (MP) at th sam locatio as th IC. (Th atur of th Martia obstacl boudary; Saur ad Dubii, Ad. Sac Rs.) Joit Phobos - MGS ISSI workshos: Mars book (Kluwr) Sac Scic Riw will b ublishd i srig of

15 Thortical mthods for dscribig multi-io lasmas Liar thory: Disrsio of LF multi-io was (fluid ad kitic modls) Statioary oliar was: Oscillitos - a w ty of solitary structur, origi of cohrt was Numrical simulatios: (1) 1D ad 2D bi-io fluid simulatios (2) 1D ad 2D bi-io hybrid cod simulatios Th two-io fluid Hall-MHD modl Protos () ad hay ios (h) ar cosidrd as sarat fluids which ar could by lctromagtic forcs Elctros ar mass lss Charg utrality: h No collisios Th systm of basic quatios cosists of - 2 cotiuity quatios - 2 momtum quatios - Faraday s law - Ergy quatio for lctros 15

16 Solar wid flow though a hay-io cloud, siml modl of lctrostatic itractio solar wid o magtic fild Situatio at t0: hay-io cloud cold ios, warm lctros: ( x) 0 t x 2 ( x) ( x ) E t x m h ( h hx) 0 t x 2 h ( h hx) ( h hx) E t x m 1 E - x h m 0 P ( x P )( γ - 1)P x 0. t x x x x h x ( x h hx )/ Solar wid flow though a hay-io cloud, siml modl of lctrostatic itractio Th itractio strogly dds o th Mach umbr of th icomig lasma flow 16

17 Solar wid flow though a hay-io cloud: siml modl of lctrostatic itractio Sursoic flow: M s 2.0 Solar wid flow though a hay-io cloud: siml modl of lctrostatic itractio Subsoic flow: M s 0.5 Th flow is acclratd withi th cloud: Laal ozzl ffct 17

18 Solar wid flow though a hay-io cloud: hybrid cod simulatios Sur- Sub- Alfic flow: M A Th flow is acclratd withi th cloud. Motschma, Saur ad Roatsch, 1992 Fluid dscritio i th mass-lss lctro aroximatio ( t ) ( P m ) m ( E x) Amr s law is usd to limiat E x µ 0 j x aroximatio of mass-lss lctros: m 0 j - h h Elctro-roto lasma - µ 0 1 x Two-io lasma h 1 - µ 0 x charg utrality: charg utrality: h 18

19 19 µ µ ) 2 (P ) P m ( ) m ( t - I µ µ h h ) 2 (P ) ( ) P m ( ) m ( t - I x charg utrality: h Equatio of motio i siglad two-io fluid dscritio Two-io lasma Sigl-io (roto) lasma gyro-radius ffcts Faraday s law: two-io lasma charg utrality: h Magtic fild quatio x E x 1-0 h µ 0 t x E sigl-io lasma ( ) 0 1 t 0 h h µ x x 0 t 0 µ x x x µ 1-0 Hall trm Hall trm

20 20 0 ) ( t Cotiuity ad momtum quatios of rotos ad hais ( h, h ) Faraday s law. 0-1)P ( ) P ( P t γ Elctro rgy quatio h, with µ µ h h ) 2 (P ) ( m ) m P ( ) ( t - I x 1 / µ 0 h h x Th two-io Hall-MHD quatios ( ) 0 1 t 0 h h µ x x 2D hybrid simulatio of solar wid - comt itractio solar wid magtic fild hay io sourc: wakly outgassig comt (Wirta at 3 AU) Liato ad Saur, 1997 E

21 Comariso btw two-io fluid ad hybrid cod simulatios Itractio of th solar wid with a wak comt (Wirta at 3 AU) 3D hybrid cod simulatios Two-io fluid simulatios magtic fild solar wid hay io sourc M A 10, Q h s-1 agdoat ad Motschma, Saur t al., Plasma structurs for thr mass-loadig rgims hay-io dsity wak comt: Q<10 26 s -1 roto dsity icrasd. rat: Q s -1 comt lik G-S: Q s -1 Formatio of a roto caity Saur ad Dubii,

22 Two-fluid modlig of solar wid itractio with th Martia xoshric lasma A roto caity is formd. At th boudary saratig solar wid rotos from xoshric oxyg ios (IC Io Comositio oudary) th magtic fild ils u (MP) Saur ad Dubii, 1999 Comariso btw Phobos-2 obsratios ad two-fluid modlig (llitical orbit) Phobos-2 obsratios 2-fluid modlig S IC S IC 22

23 Comariso btw Phobos-2 obsratios ad two-fluid modlig (circular orbit) Phobos-2 obsratios S S IC 2-fluid modlig S IC S IC Hybrid simulatios: Formatio of a roto caity roto caity magtic fild IC solar wid hay io sourc Liato ad Saur,

24 3D hybrid simulatios of SW itractio with umagtizd lats Platary ios ar distributd or a shr, o iooshric rofils: Shimazu, 2001 rotos oxyg Imortat rsults: (1) Formatio of a IC (2) Multil shockstructur (3) Plasma acclratio at th flaks 3D hybrid simulatios of solar wid - Mars itractio (ößwttr, agdoat, Motschma - TU rauschwig K. Saur - MPA; 2004) S IC IC MP roto caity Mai sigaturs of itractio ar s. Locatio of S ad MP/IC ar i good agrmt with th obsratios. 24

25 Th Io Comositio oudary (IC) - a w ty of lasma boudary Shock > s soic oit < s soic oit < s hay-io lasma IC IC A shock is formd if th sursoic flow gos through th soic oit : s A IC is formd if th subsoic two-io flow bcoms acclratd ad gos through th gralizd soic oit : s (, h, h,β,...) Formatio of a roto caity i a subsoic flow hay-io cloud: h roto flow (M s 0.4) roto caity Saur t al.,

26 Plasma acclratio at th flaks of a imtrabl hay-io cloud hay-io cloud roto flow (M s 0.4) Th subsoic lasma flow (M s 0.4) is acclratd ad dflctd by th hay-io cloud i rgios whr its dsity is about Two-fluid modlig of SWhay io sourc itractio: 0 M s 4 solar wid Formatio of a roto caity hay-io sourc: qq m x(-r 2 /L 2 ) h h 26

27 Obsratio of shar boudaris i dusty lasmas udr micro-graity (Aarato t al., 2002) Argo lasma dust articls d3,4 µm dust articls d6,8 µm Obsratio of shar boudaris i dusty lasmas udr micro-graity dust oid Argo lasma Small articls Larg articls Itrfacs Tsytoich t al., x(mm)

28 Summary ad coclusio Th multi-fluid modl is abl to dscrib sstial lmts of solar wid itractio with o-magtizd bodis. Th trasitio from ry asymmtric lasma structurs at wak comts to th magtoshr of Mars with thr wll dlod lasma boudaris (S, IC/MP, IP) has b show. Th Io Comositio oudary (IC/MP) at comts ad Mars is a w ty of lasma boudary which is formd i mass-loadd lasmas. It rsults from th momtum coulig btw th two lasma oulatios at th gralizd soic oits. Summary ad coclusio Th rsults ha imlicatios to futur sac missios: ROSETTA I-situ masurmts ar a (wak) comt at ~ 3AU. MARS/VENUS EXPRESS Plasma ad utral gas masurmts with ASPERA-3. CASSINI Nw rsults about solar wid -Tita itractio. i Colombo Mrcury with its sodium atmoshr is a itrstig multi-io objct. 28

29 Summary ad coclusio Th work was do i th rojct Mars, Komt, kli Körr ~25 ublicatios i low costs: EU r aum...(cotacts to ISSI, CNRS, JPL) 29

Session : Plasmas in Equilibrium

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 information

How many neutrino species?

How 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 information

They must have different numbers of electrons orbiting their nuclei. They must have the same number of neutrons in their nuclei.

They 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 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

(Reference: sections in Silberberg 5 th ed.)

(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 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

The situation, approximately 14 billion years before right now: BANG

The situation, approximately 14 billion years before right now: BANG Th situatio, aroximatly 14 billio yars bfor right ow: BANG Th, shortly thraftr: = lctro = roto = utro = atilctro = atiroto = atiutro Th, th uivrs xadd ad coold: Th, Tru Lov! Each articl fids its soul mat.

More information

MONTGOMERY 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 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

ECE 340 Lecture 38 : MOS Capacitor I Class Outline:

ECE 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 information

How many neutrons does this aluminium atom contain? A 13 B 14 C 27 D 40

How 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 information

Chapter 6. pn-junction diode: I-V characteristics

Chapter 6. pn-junction diode: I-V characteristics Chatr 6. -jucto dod: -V charactrstcs Tocs: stady stat rsos of th jucto dod udr ald d.c. voltag. ucto udr bas qualtatv dscusso dal dod quato Dvatos from th dal dod Charg-cotrol aroach Prof. Yo-S M Elctroc

More information

Lecture contents. Transport, scattering Generation/recombination. E c. E t. E v. NNSE508 / NENG452 Lecture #13. Band-to-band recombination

Lecture 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 information

coulombs or esu charge. It s mass is about 1/1837 times the mass of hydrogen atom. Thus mass of electron is

coulombs 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 information

3.1 Atomic Structure and The Periodic Table

3.1 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 information

H2 Mathematics Arithmetic & Geometric Series ( )

H2 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 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

Washington State University

Washington 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 information

Narayana IIT Academy

Narayana IIT Academy INDIA Sc: LT-IIT-SPARK Dat: 9--8 6_P Max.Mars: 86 KEY SHEET PHYSIS A 5 D 6 7 A,B 8 B,D 9 A,B A,,D A,B, A,B B, A,B 5 A 6 D 7 8 A HEMISTRY 9 A B D B B 5 A,B,,D 6 A,,D 7 B,,D 8 A,B,,D 9 A,B, A,B, A,B,,D A,B,

More information

Electronic Supplementary Information

Electronic Supplementary Information Elctroic Supplmtary Matrial (ESI) for Joural of Matrials Chmistry A. This joural is Th Royal Socity of Chmistry 2016 Elctroic Supplmtary Iformatio Photolctrochmical Watr Oxidatio usig a Bi 2 MoO 6 / MoO

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

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

Shocks waves and discontinuities.

Shocks waves and discontinuities. Shocks waes ad discotiuities Laurece Rezeau http://www.lpp.fr/?laurece-rezeau OUTLINE Obseratios of discotiuities Jump coditios at the boudary Differet kids of discotiuities What about the boudaries aroud

More information

Physics 2D Lecture Slides Lecture 14: Feb 3 rd 2004

Physics 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 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

Frequency Measurement in Noise

Frequency Measurement in Noise Frqucy Masurmt i ois Porat Sctio 6.5 /4 Frqucy Mas. i ois Problm Wat to o look at th ct o ois o usig th DFT to masur th rqucy o a siusoid. Cosidr sigl complx siusoid cas: j y +, ssum Complx Whit ois Gaussia,

More information

Electromagnetic radiation and steady states of hydrogen atom

Electromagnetic radiation and steady states of hydrogen atom Elctromagtic radiatio ad stady stats of hydrog atom Jiaomig Luo Egirig Rsarch Ctr i Biomatrials, Sichua Uivrsity, 9# Wagjiag Road, Chgdu, Chia, 610064 Abstract. Elctromagtic phoma i hydrog atom ar cotrolld

More information

ECE594I Notes set 6: Thermal Noise

ECE594I Notes set 6: Thermal Noise C594I ots, M. odwll, copyrightd C594I Nots st 6: Thrmal Nois Mark odwll Uivrsity of Califoria, ata Barbara rodwll@c.ucsb.du 805-893-344, 805-893-36 fax frcs ad Citatios: C594I ots, M. odwll, copyrightd

More information

Review Exercises. 1. Evaluate using the definition of the definite integral as a Riemann Sum. Does the answer represent an area? 2

Review 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 information

Physics of the Interstellar and Intergalactic Medium

Physics of the Interstellar and Intergalactic Medium PYA0 Sior Sophistr Physics of th Itrstllar ad Itrgalactic Mdium Lctur 7: II gios Dr Graham M. arpr School of Physics, TCD Follow-up radig for this ad t lctur Chaptr 5: Dyso ad Williams (lss dtaild) Chaptr

More information

Ion-acoustic waves in an inhomogeneous plasma with negative ions

Ion-acoustic waves in an inhomogeneous plasma with negative ions Joural of Kig Saud Uivrsity Scic (01) 4, 4 49 Kig Saud Uivrsity Joural of Kig Saud Uivrsity Scic www.su.du.sa www.scicdirct.com ORIGINAL ARTICLE Io-acoustic wavs i a ihomogous lasma with gativ ios A.E.

More information

Discrete Fourier Transform (DFT)

Discrete 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 information

5.1 The Nuclear Atom

5.1 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 information

Blackbody Radiation. All bodies at a temperature T emit and absorb thermal electromagnetic radiation. How is blackbody radiation absorbed and emitted?

Blackbody 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 information

MILLIKAN OIL DROP EXPERIMENT

MILLIKAN 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 information

Figure 2-18 Thevenin Equivalent Circuit of a Noisy Resistor

Figure 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 information

ln x = n e = 20 (nearest integer)

ln 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 information

1985 AP Calculus BC: Section I

1985 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 information

LECTURE 13 Filling the bands. Occupancy of Available Energy Levels

LECTURE 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 information

Worksheet: Taylor Series, Lagrange Error Bound ilearnmath.net

Worksheet: 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 information

Fermi Gas. separation

Fermi Gas. separation ri Gas Distiguishabl Idistiguishabl Classical dgrat dd o dsity. If th wavlgth siilar to th saratio tha dgrat ri gas articl h saratio largr traturs hav sallr wavlgth d tightr ackig for dgracy

More information

Concatenated Processes in Commercial Business and in Global Economy

Concatenated Processes in Commercial Business and in Global Economy ibusiss, 22, 4, 293-299 htt://d.doi.org/.4236/ib.22.4437 Publishd Oli Dcmbr 22 (htt://www.scirp.org/joural/ib) 293 Cocatatd Procsss i Commrcial Busiss ad i Global Ecoomy Gustav Cciasy, Ladislav Schwart

More information

Lecture #2: Wave Nature of the Electron and the Internal Structure of an Atom

Lecture #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 information

APPENDIX: STATISTICAL TOOLS

APPENDIX: 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 information

1 of 42. Abbreviated title: [SAP-SVT-Nmsm-g & 137] - Updated on 31 July, 09. Shankar V.Narayanan

1 of 42. Abbreviated title: [SAP-SVT-Nmsm-g & 137]  - Updated on 31 July, 09. Shankar V.Narayanan 1 of 4 ONE EQUATION ad FOUR Subatomic Particls ad thir FOUR Itractios icludig (g &17) factors with Spac Vortx Thory (A No matrial shll modl) (Part 1 of ) (Th cotts of this txt ar th sam as i Subatomic

More information

1 of 46. Abbreviated title: [SAP-SVT-Nmsm-g & 137] - Updated on 07 Oct, 09. Shankar V.Narayanan

1 of 46. Abbreviated title: [SAP-SVT-Nmsm-g & 137]  - Updated on 07 Oct, 09. Shankar V.Narayanan 1 of 46 Subatomic Particls ad thir FOUR Itractios icludig (g &17) (p&) factors with Spac Vortx Thory (A No matrial shll modl) (Part 1 of ) (Th cotts of this txt ar th sam as i ONE EQUATION ad FOUR Subatomic

More information

Available online at Energy Procedia 4 (2011) Energy Procedia 00 (2010) GHGT-10

Available online at   Energy Procedia 4 (2011) Energy Procedia 00 (2010) GHGT-10 Availabl oli at www.scicdirct.com Ergy Procdia 4 (01 170 177 Ergy Procdia 00 (010) 000 000 Ergy Procdia www.lsvir.com/locat/procdia www.lsvir.com/locat/xxx GHGT-10 Exprimtal Studis of CO ad CH 4 Diffusio

More information

THE WEAK INTERACTION. e - MISN by J. Christman. 1. Overview Assigned Readings... 1

THE WEAK INTERACTION. e - MISN by J. Christman. 1. Overview Assigned Readings... 1 MISN0281 THE WEAK INTERACTION by J. Christma THE WEAK INTERACTION 1. Ovrviw.................................................. 1 2. Assigd Radigs....................................... 1 s d d _ u d s d

More information

Equation Sheet Please tear off this page and keep it with you

Equation Sheet Please tear off this page and keep it with you ECE 30L, Exam Fall 05 Equatio Sht Plas tar off this ag ad k it with you Gral Smicoductor: 0 i ( EF EFi ) kt 0 i ( EFi EF ) kt Eg i N C NV kt 0 0 V IR L, D, τ, d d τ c g L D kt I J diff D D µ * m σ (µ +

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

Two-dimensional modeling RF glow discharge at low pressure

Two-dimensional modeling RF glow discharge at low pressure lhadj HABL, Byssaad KRALOUA, Ali HNNA Uivrsité ds Scics t d la Tchologi d'ora-mohamd Boudiaf, USTO-MB, FG-LMS, BP l M Naour, Ora, Algria doi:.99/8.7..8 Two-dimsioal modlig RF glow discharg at low prssur

More information

Bipolar Junction Transistors

Bipolar 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 information

Hybrid Intelligent Control of Ceramic Shuttle Kiln Firing Temperature

Hybrid Intelligent Control of Ceramic Shuttle Kiln Firing Temperature Itratioal Cofrc o Alid Mathmatics, Simulatio ad Modllig (AMSM 2016) Hybrid Itlligt Cotrol of Cramic Shuttl Kil Firig mratur Yoghog Zhu* ad Yifg Zhao School of Mchaical & Elctroic Egirig, Jigdzh Cramic

More information

Statistics 3858 : Likelihood Ratio for Exponential Distribution

Statistics 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 information

Elasto-Plastic Constitutive Model for Finite Element Simulation of structural Adhesives

Elasto-Plastic Constitutive Model for Finite Element Simulation of structural Adhesives Elasto-Plastic Costituti Modl for Fiit Elmt Simulatio of structural Adhsis Pirr Jousst (a), Mohamd Rachi (b) (a): Sia Tchology AG, 848 Zürich, Switzrlad (b): Uirsité d Tchologi d Comièg, Laboratoir Robral,

More information

Comparison of Simple Indicator Kriging, DMPE, Full MV Approach for Categorical Random Variable Simulation

Comparison of Simple Indicator Kriging, DMPE, Full MV Approach for Categorical Random Variable Simulation Papr 17, CCG Aual Rport 11, 29 ( 29) Compariso of Simpl Idicator rigig, DMPE, Full MV Approach for Catgorical Radom Variabl Simulatio Yupg Li ad Clayto V. Dutsch Ifrc of coditioal probabilitis at usampld

More information

signal amplification; design of digital logic; memory circuits

signal amplification; design of digital logic; memory circuits hatr Th lctroc dvc that s caabl of currt ad voltag amlfcato, or ga, cojucto wth othr crcut lmts, s th trasstor, whch s a thr-trmal dvc. Th dvlomt of th slco trasstor by Bard, Bratta, ad chockly at Bll

More information

Ordinary Differential Equations

Ordinary 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 information

INTRODUCTION TO SAMPLING DISTRIBUTIONS

INTRODUCTION TO SAMPLING DISTRIBUTIONS http://wiki.stat.ucla.du/socr/id.php/socr_courss_2008_thomso_econ261 INTRODUCTION TO SAMPLING DISTRIBUTIONS By Grac Thomso INTRODUCTION TO SAMPLING DISTRIBUTIONS Itro to Samplig 2 I this chaptr w will

More information

Effect of Electric Fields on Electron Thermal Transport in Laser-Produced Plasmas

Effect 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 information

Chapter Five. More Dimensions. is simply the set of all ordered n-tuples of real numbers x = ( x 1

Chapter 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 information

Outline. Ionizing Radiation. Introduction. Ionizing radiation

Outline. 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 information

Reliability of time dependent stress-strength system for various distributions

Reliability of time dependent stress-strength system for various distributions IOS Joural of Mathmatcs (IOS-JM ISSN: 78-578. Volum 3, Issu 6 (Sp-Oct., PP -7 www.osrjourals.org lablty of tm dpdt strss-strgth systm for varous dstrbutos N.Swath, T.S.Uma Mahswar,, Dpartmt of Mathmatcs,

More information

Sec 2.3 Modeling with First Order Equations

Sec 2.3 Modeling with First Order Equations Sc.3 Modling with First Ordr Equations Mathmatical modls charactriz physical systms, oftn using diffrntial quations. Modl Construction: Translating physical situation into mathmatical trms. Clarly stat

More information

Eigenvalue Distributions of Quark Matrix at Finite Isospin Chemical Potential

Eigenvalue Distributions of Quark Matrix at Finite Isospin Chemical Potential Tim: Tusday, 5: Room: Chsapak A Eignvalu Distributions of Quark Matri at Finit Isospin Chmical Potntial Prsntr: Yuji Sasai Tsuyama National Collg of Tchnology Co-authors: Grnot Akmann, Atsushi Nakamura

More information

Chapter 11.00C Physical Problem for Fast Fourier Transform Civil Engineering

Chapter 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 information

THz intervalence band antipolaritons

THz intervalence band antipolaritons THz itrvalc bad atipolaritos FARAGAI, Iuwa A ad PEREIRA, Mauro Availabl from Shffild Hallam Uivrsity Rsarch Archiv (SHURA) at: http://shura.shu.ac.uk/8488/ This documt

More information

Chapter 2 Infinite Series Page 1 of 11. Chapter 2 : Infinite Series

Chapter 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 information

A Novel Approach to Recovering Depth from Defocus

A Novel Approach to Recovering Depth from Defocus Ssors & Trasducrs 03 by IFSA http://www.ssorsportal.com A Novl Approach to Rcovrig Dpth from Dfocus H Zhipa Liu Zhzhog Wu Qiufg ad Fu Lifag Collg of Egirig Northast Agricultural Uivrsity 50030 Harbi Chia

More information

Blackbody Radiation. All bodies at a temperature T emit and absorb thermal electromagnetic radiation. How is blackbody radiation absorbed and emitted?

Blackbody 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 information

How Fast a Hydrogen Atom can Move Before Its Proton and Electron Fly Apart?

How Fast a Hydrogen Atom can Move Before Its Proton and Electron Fly Apart? Optis ad Photois Joural,,, 36- doi:.36/opj..6 Publishd Oli Ju (http://www.sirp.org/joural/opj/) How Fast a Hydrog Atom a Mo Bfor Its Proto ad Eltro Fly Apart? Abstrat Wi-Xig Xu Nwth Moitorig I., Oshawa,

More information

Ordinary Differential Equations

Ordinary Differential Equations Basi Nomlatur MAE 0 all 005 Egirig Aalsis Ltur Nots o: Ordiar Diffrtial Equatios Author: Profssor Albrt Y. Tog Tpist: Sakurako Takahashi Cosidr a gral O. D. E. with t as th idpdt variabl, ad th dpdt variabl.

More information

The Relativistic Stern-Gerlach Force C. Tschalär 1. Introduction

The Relativistic Stern-Gerlach Force C. Tschalär 1. Introduction Th Rlativistic Strn-Grlach Forc C. Tschalär. Introduction For ovr a dcad, various formulations of th Strn-Grlach (SG) forc acting on a particl with spin moving at a rlativistic vlocity in an lctromagntic

More information

Topological Insulators in 2D and 3D

Topological Insulators in 2D and 3D Topological Isulators i D ad 3D 0. Elctric polarizatio, Chr Numbr, Itgr Quatum Hall Effct I. Graph - Halda modl - Tim rvrsal symmtry ad Kramrs thorm II. D quatum spi Hall isulator - Z topological ivariat

More information

NET/JRF, GATE, IIT JAM, JEST, TIFR

NET/JRF, GATE, IIT JAM, JEST, TIFR Istitut for NET/JRF, GATE, IIT JAM, JEST, TIFR ad GRE i PHYSICAL SCIENCES Mathmatical Physics JEST-6 Q. Giv th coditio φ, th solutio of th quatio ψ φ φ is giv by k. kφ kφ lφ kφ lφ (a) ψ (b) ψ kφ (c) ψ

More information

A Strain-based Non-linear Elastic Model for Geomaterials

A Strain-based Non-linear Elastic Model for Geomaterials A Strai-basd No-liar Elastic Modl for Gomatrials ANDREW HEATH Dpartmt of Architctur ad Civil Egirig Uivrsity of Bath Bath, BA2 7AY UNITED KINGDOM A.Hath@bath.ac.uk http://www.bath.ac.uk/ac Abstract: -

More information

Triple Play: From De Morgan to Stirling To Euler to Maclaurin to Stirling

Triple Play: From De Morgan to Stirling To Euler to Maclaurin to Stirling Tripl Play: From D Morga to Stirlig To Eulr to Maclauri to Stirlig Augustus D Morga (186-1871) was a sigificat Victoria Mathmaticia who mad cotributios to Mathmatics History, Mathmatical Rcratios, Mathmatical

More information

Joule-Lenz Energy of Quantum Electron Transitions Compared with the Electromagnetic Emission of Energy

Joule-Lenz Energy of Quantum Electron Transitions Compared with the Electromagnetic Emission of Energy Joural of Modr Physics, 06, 7, 440-448 Publishd Oli August 06 i SciRs http://wwwscirporg/joural/jmp http://dxdoiorg/0436/jmp0673 Joul-Lz Ergy of Quatum Elctro Trasitios Compard with th Elctromagtic Emissio

More information

Lecture 14. P-N Junction Diodes: Part 3 Quantitative Analysis (Math, math and more math) Reading: Pierret 6.1

Lecture 14. P-N Junction Diodes: Part 3 Quantitative Analysis (Math, math and more math) Reading: Pierret 6.1 Lctur 4 - ucto ods art 3 Quattatv alyss Math, math ad mor math Radg rrt 6. Gorga Tch ECE 3040 - r. la oolttl Quattatv - od Soluto ssumtos stady stat codtos o- dgrat dog 3 o- dmsoal aalyss 4 low- lvl jcto

More information

Investigation of defects formed by ion implantation of H2+ into silicon

Investigation of defects formed by ion implantation of H2+ into silicon Rochstr Istitut of chology RI Scholar Works hss hsis/dissrtatio Collctios 8-1-2009 Ivstigatio of dfcts formd by io imlatatio of H2+ ito silico Patrick Whitig Follow this ad additioal works at: htt://scholarworks.rit.du/thss

More information

Introduction to Condensed Matter Physics

Introduction to Condensed Matter Physics Introduction to Condnsd Mattr Physics pcific hat M.P. Vaughan Ovrviw Ovrviw of spcific hat Hat capacity Dulong-Ptit Law Einstin modl Dby modl h Hat Capacity Hat capacity h hat capacity of a systm hld at

More information

2.29 Numerical Fluid Mechanics Spring 2015 Lecture 12

2.29 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 information

Robust Tracking Control for Constrained Robots

Robust Tracking Control for Constrained Robots Aailabl oli at www.scicirct.com Procia Egirig 4 ( 9 97 Itratioal Symosium o Robotics a Itlligt Ssors (IRIS Robust rackig Cotrol for Costrai Robots Haifa Mhi, Olfa Boubakr* Natioal Istitut of Ali Scics

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

INSTABILITY DYNAMICS WITH ELECTRON CLOUD BUILDUP IN LONG BUNCHES

INSTABILITY DYNAMICS WITH ELECTRON CLOUD BUILDUP IN LONG BUNCHES J C NSTABLTY YNAMCS WTH ELECTRON CLOU BULUP N LONG BUNCHES M. Blaskiwicz, BNL 9B, Upto, NY 97-, USA Abstract For log buchs, trailig dg multi-pactig causs th lctro cloud dsity at th trailig dg of th buch

More information

Space-charge compensation for high-intensity linear and circular accelerators at Fermilab

Space-charge compensation for high-intensity linear and circular accelerators at Fermilab Saccharg comsatio for highitsity liar ad circular acclrators at Frmila Moss Chug*, Liol Prost, ad Vladimir Shiltsv Octor 1, 013 NAPAC 13, Pasada, CA May valual iuts from Qig Ji / Dav Grot (WARP simulatio),

More information

NEW VERSION OF SZEGED INDEX AND ITS COMPUTATION FOR SOME NANOTUBES

NEW VERSION OF SZEGED INDEX AND ITS COMPUTATION FOR SOME NANOTUBES Digst Joural of Naomatrials ad Biostructurs Vol 4, No, March 009, p 67-76 NEW VERSION OF SZEGED INDEX AND ITS COMPUTATION FOR SOME NANOTUBES A IRANMANESH a*, O KHORMALI b, I NAJAFI KHALILSARAEE c, B SOLEIMANI

More information

The Determination of the Bipolar Transistor Commutation Time Components by Using a Virtual Circuit

The Determination of the Bipolar Transistor Commutation Time Components by Using a Virtual Circuit h Dtrmiatio of th Bipolar rasistor ommutatio im ompots by Usig a Virtual ircuit Floara BAIU, Nicola POPOVIIU Hyprio Uivrsity of Bucharst, Faculty of Mathmatics-Iformatics 169, ălăraşilor Strt, Bucharst,

More information

Journal of Modern Applied Statistical Methods

Journal of Modern Applied Statistical Methods Joural of Modr Applid Statistical Mthods Volum Issu Articl 6 --03 O Som Proprtis of a Htrogous Trasfr Fuctio Ivolvig Symmtric Saturatd Liar (SATLINS) with Hyprbolic Tagt (TANH) Trasfr Fuctios Christophr

More information

Numerov-Cooley Method : 1-D Schr. Eq. Last time: Rydberg, Klein, Rees Method and Long-Range Model G(v), B(v) rotation-vibration constants.

Numerov-Cooley Method : 1-D Schr. Eq. Last time: Rydberg, Klein, Rees Method and Long-Range Model G(v), B(v) rotation-vibration constants. Numrov-Cooly Mthod : 1-D Schr. Eq. Last tim: Rydbrg, Kli, Rs Mthod ad Log-Rag Modl G(v), B(v) rotatio-vibratio costats 9-1 V J (x) pottial rgy curv x = R R Ev,J, v,j, all cocivabl xprimts wp( x, t) = ai

More information

TECHNO-ECONOMIC ANALYSIS OF A SOLAR AIR HEATER WITH DIMPLE SHAPED PROTRUSIONS ON THE SURFACE Hassan Bin Nasir 1, Abhishek Saxena 2, Nitin Agarwal 3 1,

TECHNO-ECONOMIC ANALYSIS OF A SOLAR AIR HEATER WITH DIMPLE SHAPED PROTRUSIONS ON THE SURFACE Hassan Bin Nasir 1, Abhishek Saxena 2, Nitin Agarwal 3 1, TEHNO-EONOMI ANAYSIS OF A SOAR AIR HEATER WITH DIME SHAED ROTRUSIONS ON THE SURFAE Hassa Bi Nasir 1, Abhishk Saxa 2, Niti Agarwal 3 1, Scholar (.G), Mchaical Egirig Dartmt, M.I.T., Moradabad, Idia 2, 3

More information

Chemical Physics II. More Stat. Thermo Kinetics Protein Folding...

Chemical Physics II. More Stat. Thermo Kinetics Protein Folding... Chmical Physics II Mor Stat. Thrmo Kintics Protin Folding... http://www.nmc.ctc.com/imags/projct/proj15thumb.jpg http://nuclarwaponarchiv.org/usa/tsts/ukgrabl2.jpg http://www.photolib.noaa.gov/corps/imags/big/corp1417.jpg

More information

Chapter 8: Electron Configurations and Periodicity

Chapter 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 information

Studies of Turbulence and Transport in Alcator C-Mod Ohmic Plasmas with Phase Contrast Imaging and Comparisons with GYRO*

Studies of Turbulence and Transport in Alcator C-Mod Ohmic Plasmas with Phase Contrast Imaging and Comparisons with GYRO* Studis of Turbulnc and Transport in Ohmic Plasmas with Phas Contrast Imaging and Comparisons with GYRO* L. Lin 1, M. Porkolab 1, E.M. Edlund 1, J.C. Rost 1, M. Grnwald 1, D.R. Mikklsn 2, N. Tsujii 1 1

More information

The pn junction: 2 Current vs Voltage (IV) characteristics

The pn junction: 2 Current vs Voltage (IV) characteristics Th pn junction: Currnt vs Voltag (V) charactristics Considr a pn junction in quilibrium with no applid xtrnal voltag: o th V E F E F V p-typ Dpltion rgion n-typ Elctron movmnt across th junction: 1. n

More information

PHASE EQUILIBRIUM AND KINETICS OF SALINE SOIL WATER FREEZING

PHASE EQUILIBRIUM AND KINETICS OF SALINE SOIL WATER FREEZING PHASE EQUILIBRIUM AND KINETICS OF SALINE SOIL WATER FREEZING S.E. Grchishchv, A.V. Pavlov, V.V. Poomarv Vavilov strt, 30/6, room 85, Earth Cryosphr Istitut; Russia, 117982 Moscow, -mail: cryodor@balashikha.x400.rosprit.ru

More information

Chapter (8) Estimation and Confedence Intervals Examples

Chapter (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 information

Thomas J. Osler. 1. INTRODUCTION. This paper gives another proof for the remarkable simple

Thomas J. Osler. 1. INTRODUCTION. This paper gives another proof for the remarkable simple 5/24/5 A PROOF OF THE CONTINUED FRACTION EXPANSION OF / Thomas J Oslr INTRODUCTION This ar givs aothr roof for th rmarkabl siml cotiud fractio = 3 5 / Hr is ay ositiv umbr W us th otatio x= [ a; a, a2,

More information

Low-energy QED tests (and what we can learn from them)

Low-energy QED tests (and what we can learn from them) Low-nrgy QED tsts (and what w can larn from thm) (0γ) 2γ (4γ) (1γ) 3γ (5γ) Indirct Sarchs for Nw Physics at th tim of LHC Flornc, March 2010 Andrzj Czarncki U. of Albrta & CERN Outlin Gyromagntic factors

More information

PURE MATHEMATICS A-LEVEL PAPER 1

PURE 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 information

Collisions between electrons and ions

Collisions between electrons and ions DRAFT 1 Collisions btwn lctrons and ions Flix I. Parra Rudolf Pirls Cntr for Thortical Physics, Unirsity of Oxford, Oxford OX1 NP, UK This rsion is of 8 May 217 1. Introduction Th Fokkr-Planck collision

More information