DECAMETER RADIO EMISSION OF THE SUN: RECENT OBSERVATIONS

Size: px
Start display at page:

Download "DECAMETER RADIO EMISSION OF THE SUN: RECENT OBSERVATIONS"

Transcription

1 DECAMETER RADIO EMISSION OF THE SUN: RECENT OBSERVATIONS V. N. Melnik *,H.O.Rucker, A. A. Konovlenko, V. V. Dorovskyy, E. P. Abrnin, nd A. Leccheux Abstrct We present n overview of the recent results in solr observtions obtined t decmeter rdio wves using the rdio telescope UTR-2. Due to up-to-dte recording fcilities some newly discovered phenomen in the frequency rnge - 30 MHz re given: fst type III bursts, fine time structures in norml type III bursts, solr S-bursts, type IV bursts with zebr-like fine structures, third hrmonic in type II bursts nd bursts in bsorption of different time scle. Newly discovered properties of well known bursts such s type III bursts, type IIIb bursts, type II bursts nd drift pirs were obtined too. Introduction The use of the new spectrometer (continuous bndwidth of 2 MHz, high frequency nd time resolution of 2 khz nd ms respectively) on the rdio telescope UTR-2 (Ukrinin T-shped Rdio telescope - second modifiction) (frequency bnd 30 MHz, bemwidth nd sensitivity 5 Jy) llows us to strongly extend the fesibility of the studies of the solr decmeter rdio emission. In 0 the first decmeter type II burst ws recorded. The drift rte of decmeter type II bursts rnge from 30 khz/s to 70 khz/s. The usul type II bursts re found to hve fine structures in the form of short (durtions bout of s) components with drift rte MHz/s. Type II bursts with herringbone structures with wve-like bckground were observed too. For the first time fine time structures in usul type III bursts were observed. They consist of sub-bursts hving drift rtes tht cn be lrger or smller thn tht of the prent type III bursts. Decmeter S-bursts were lso observed. Observtionl chrcteristics of drift pirs t 8 30 MHz were nlyzed too. * Institute of Rdio Astronomy, Ukrinin Acdemy of Sciences, Chervonoprporn 4, 602, Khrkiv, Ukrine Spce Reserch Institute, Austrin Acdemy of Sciences, Schmiedlstrsse 6, A-8042 Grz, Austri LESIA, Observtoire de Pris, UMR CNRS 89, 9295 Meudon, Frnce 343

2 344 V. N. Melnik et l. 8 July 02 Flux in SFU 00 0 :44: :44: :44:30 :44:40 :44:50 Flux, W/(m Hz) b July 02 Frequency.2 MHz :44: :44: :44:30 :44:40 :44:50 :45:00 Figure : ) Type III-like burst (:44:30) during type III bursts storm; b) time profiles of type III-like burst nd usul type III bursts. 7 August 02 Flux in SFU -7 7 August 02 Frequency 2.50 MHz 00 0 Flux, W/(m Hz) :05:00 :05:50 :06:40 :07:30-2 b :05: :05:40 :06:00 :06: :06:40 Figure 2: ) Powerful type III burst during storm of type III bursts; b) time profile of powerful type III burst. In this pper we briefly present some recent results (fter PRE VI) obtined in the study of spordic rdio solr emissions. During this time fst type III burst (type III-like bursts), decmeter type IV bursts nd their fine structures in form of fiber bursts nd zebrptterns were reveled. Fine frequency structures of type IIIb bursts were considered. Decmeter spikes nd S-bursts s well s powerful type III bursts were nlyzed too. 2 Type III-like Bursts In the frequency bnd 30MHzweobservedforthefirsttimefsttypeIII-likebursts [Melnik et l., 08] (Fig. ). More thn 00 such bursts were recorded in the yers Their drift rtes ( 30 MHz/s) were sometimes higher thn those of the usul type III bursts (2 4 MHz/s) in the decmeter rnge. These bursts lst 2s nd re shorter thn usul type III bursts (Fig.b). Type III-like bursts re wek bursts, in most cses their flux density is not exceeding 0 sfu. Their interesting property is relted to the fct tht they re observed in dys when the ssocited ctive region is ner the centrl meridin. Therefore the beming of the rdio emission of type III-like bursts is bout -30. Their usul high frequency drift rte cn be relted to the group velocity of electromgnetic wves ner the emission source tht is similr to the speed of

3 Decmeter Rdio Emission of the Sun: Recent Observtions My 0 Flux in SFU ::00 09::05 09:: 09:: 09:: Figure 3: Type IIIb burst followed by type III burst. 8 July 04 Flux in SFU June 04 Flux in SFU 0 09:35:00 09:35: 09:35:40 09:36:00 09:36: b :45:50 :46:40 :47:30 Figure 4: ) Hrmonic pir of U-, J- bursts; b) splitting U-, J- bursts. fst electrons (see pper by Rutkevych nd Melnik []). 3 Powerful Type III Bursts We nlyzed the chrcteristics of powerful type III bursts with flux density > 9 W/m 2 Hz (Fig. 2) [Melnik et l., b]. The min feture of these bursts is the liner dependence of the drift rte in respect to the frequency. This mens tht in the rdio source region of the coron the plsm density n trend is exponentil (n(r) exp( r/), where is constnt). Another property of these bursts is tht their durtion decreses not so fst s /f, it grees with the reltionship 60f 2/3. 4 Decmeter Type IIIb Bursts The drift rte of these bursts is similr to the one of the usul type III bursts however their durtion is 3-4 times shorter. Type IIIb bursts show fine frequency structure similr to chins of strie. The frequency bndwidth of strie is khz [Melnik et

4 346 V. N. Melnik et l. 29 June 03 Flux in SFU :05:50 09:06:40 09:07:30 09:08: Figure 5: Dog-leg type III burst (9:06:). 3 July 04 Flux in SFU 0 08::00 08:53: 09::40 :00:00 :33: Figure 6: Decmeter type IV burst. l., ], their durtion nd therefore the durtion of type IIIb bursts is bout.2 s (Fig. 3). According to some ides these bursts cn be ssocited with electron bems which propgte through density fluctutions in coron. 5 Inverted Decmeter U- nd J-bursts During yers we observed in the frequency rnge 30 MHz more thn 50 inverted U- nd J- bursts [Dorovskyy et l., ] (Fig. 4). Tht confirms the evidence of mgnetic loops up to 2-3 solr rdii in the coron. Hrmonic pirs were seen not only in usul U- nd J- bursts but lso in Jb-bursts. There were some cses of splitting U- nd J- bursts (Fig. 4b) tht indicte rdio emission generted in rcdes of mgnetic loops of different sizes.

5 Decmeter Rdio Emission of the Sun: Recent Observtions 347 July 05 Flux in SFU :36:40 08:40:00 08:43: 08:46:40 08:50:00 08:53: Figure 7: Fiber bursts in emission nd bsorption. July 04 Flux in SFU 08:3: 08:3:40 08:32:00 08:32: 08:32:40 08:33:00 0 Flux, W/(m Hz) b2-9 - July 04 Frequency.45 MHz 08:3:50 08:32:00 08:32: 08:32: 08:32:30 08:32:40 Figure 8: ) Group of zebr pttern stripes; b) equidistnt stripes in zebr structure. 6 Dog-leg Type III Bursts Sometimes we observed strnge type III bursts which present discontinuity in drift rtes nd in durtion t some frequency (Fig. 5) [Dorovskyy et l., c]. There were more thn 0 of such dog-leg type III bursts during yers The jump points re distributed in the rnge 3 2 MHz with mximum t bout 6 MHz. The vlues of the sudden chnge of the frequency drift rte t the jump point my rech lso the fctor. We think tht the cuse of such unusul type III bursts is due to coronl plsm inhomogeneity in density, temperture or both of them. 7 Type IV Bursts During yers in the frequency rnge 30 MHz we recorded bout 40 type IV bursts [Melnik, et l., 08b]. The sequence of events which ccompnies type IV bursts is the following: group of powerful type III bursts, phse of bsorptions or lrge-scle burst in bsorption, type II burst nd finlly type IV burst (Fig. 6). The type II burst cn precede the type IV event or cn be simultneous with it. The durtion of type IV bursts

6 348 V. N. Melnik et l. vries from - 2 up to 6-7 hours. All the observed decmeter type IV events show fine structures in form of fiber bursts in emission nd bsorption [Konovlenko et l., 07; Melnik et l., b] with positive nd negtive drift rte (Fig. 7). Fiber drift rtes nd their durtions re close to those of usul type III bursts. In one cse we recorded fine structures in form of zebr pttern (Fig. 8) which ws repeted some times during the whole type IV burst. Ech such group consisted of sequence of equidistnt (up to 40) stripes (Fig 8b) [Melnik et l., 08b]. The time intervl between neighboring stripes ws 2.5 s (Fig. 8b). Type II bursts ssocited with type IV bursts show two or sometimes even three hrmonics (Fig. 9) [Melnik et l., 08b]. 8 Decmeter Spikes Decmeter spikes re short durtion bursts (life time bout s) with bndwidth khz [Melnik et l., d] with flux density up to 0 sfu. Spikes re plced choticlly on the dynmic spectrum (Fig. ). We believe tht they re generted by fst electron smll density bems nd tht their source hs not lrge sptil size. The spike durtion is defined by prticle collision time [Melnik et l., d]. This llows to estimte the temperture of the coronl plsm t frequencies 30 MHz. We found [Melnik et l., d], using dt from July 27 to August 2, 02, tht t height 3R s the plsm temperture ws bout 6 K. Moreover it is possible to find the ngle into which fst electrons propgte long open mgnetic field lines. In most cses this ngle is not lrger thn [Melnik et l., d]. 9 S-bursts S-bursts (Fig. b) re the shortest decmeter bursts, their durtion is only s [Melnik et l., c]. They, s type III bursts, drift from high to lower frequency, but their drift rte is 3-4 time smller thn those of usul type III bursts. Most S-bursts hve flux density smller thn 0 sfu. Another interesting property of these bursts is the liner increse of their bndwidth with frequency. It is possible to explin the properties of these bursts nd to find the mgnetic field nd the prmeters of the bckground Lngmuir turbulence in their source in the frme of the genertion model bsed on colescence of Lngmuir wves with fst mgnetosonic wves [Melnik et l., c]. During the pssge of n ctive region on the solr disk in July, 02 the estimted mgnetic field ws 2 G. Conclusion Our observtions of the solr rdio emission in the decmeter rnge during the period 0-06 gve us some importnt results. First of ll it is to mention type IV bursts which were ssocited with CMEs (Coronl Mss Ejection). The obtined dt fill the gp existing between meter nd hectometer rdio emission of the CMEs. The study of these bursts should be helpful in understnding the CME properties nd the peculirities

7 Decmeter Rdio Emission of the Sun: Recent Observtions June 04 Flux in SFU :46:40 07:55:00 08:03: 08::40 Figure 9: Type II bursts with three hrmonics ssocited with type IV burst. 8 August 02 Flux in SFU 0 30 My 0 Flux in SFU 0 09:50: 09:50:40 09:5: 09:5:40 09:52:00 b :4: :4: :4:30 :4:40 :4:50 Figure : ) Decmeter spikes choticlly locted on the dynmic spectrum; b) storm of S- bursts. of the interction of CMEs with the coronl plsm. The nlysis of properties of decmeter spikes, type III-like bursts nd S-bursts showed tht they cn be used s dignostic instrument for obtining some chrcteristics of the coronl plsm (density, temperture, mgnetic field, bckground Lngmuir turbulence) t height 3R s nd some prmeters pertinent to ccelerted electrons (velocity, density, size, etc). Our observtions show tht the fst electron bems responsible for type III bursts cn sometimes hve complex nture tht is mnifested in type III bursts with fine time structure. Moreover we obtined tht the durtion of usul decmeter type III bursts defines the spce size of the relted electrons but not the collision time. There re lso some chrcteristics of spordic decmeter rdio emissions such s fine structures in type II bursts, existence of the third hrmonic in type II bursts, burst in bsorption of different time scle, zebr structures in type IV, fiber bursts with positive frequency drift rtes etc, which wit for interprettion nd understnding. We re sure tht the recent nd future observtions with the UTR-2 (in the frequency rnge 30 MHz) nd the GURT (Gint Ukrinin Rdio Telescope in construction ner Khrkiv) (in the frequency rnge 70 MHz) will bring new findings in the field of solr rdio emission.

8 350 V. N. Melnik et l. References Dorovskyy, V. V., V. N. Melnik, A. A. Konovlenko, H. O. Rucker, E. P. Abrnin, nd A. Leccheux, Solr U- nd J- rdio bursts t the decmeter wves, ASTRO- PHYSICS AND COSMOLOGY AFTER GAMOW, Proc. 4th Gmow Interntionl Conf. AIP Conference Proceedings, 6, ,. Dorovskyy, V. V., V. N. Melnik, A. A. Konovlenko, H. O. Rucker, E. P. Abrnin, nd A. Leccheux, Unusul Type III Bursts t the Decmetre Wvelengths, in Plnetry Rdio Emissions VII, edited by H. O. Rucker, W. S. Kurth, P. Lourn, nd G. Fischer, Austrin Acdemy of Sciences Press, Vienn, this issue, ,. Konovlenko, A. A., A. A. Stnislvsky, E. P. Abrnin, V. V. Dorovskyy, V. N. Melnik, M. L. Kiser, A. Leccheux, nd H. O. Rucker, Absorption in Burst Emission, Solr Phys., 5, 345, 07. Melnik,V.N.,A.A.Konovlenko,H.O.Rucker,B.P.Rutkevych,V.V.Dorovskyy, E.P.Abrnin, A. I. Brzhenko, A. A. Stnislvskyy, nd A. Leccheux, Decmeter Type III-like bursts, Solr Phys., 0, 33, 08. Melnik, V. N., H. O. Rucker, A. A. Konovlenko, V. V. Dorovskyy, E. P. Abrnin, A. I. Brzhenko, B. Thidé, A.A. Stnislvskyy, Solr Type IV Bursts t Frequencies -30 MHz, in Solr Physics Reserch Trends, edited by P. Wng, Nov Science Publishers, New York, 7 3, 08b. Melnik, V. N., H. O. Rucker, A. A. Konovlenko, N. V. Shevchuk, E. P. Abrnin, V. V. Dorovskyy, nd A. Leccheux, Type IIIb bursts nd their fine structure in frequency bnd 8-30 MHz, ASTROPHYSICS AND COSMOLOGY AFTER GAMOW, Proc. 4th Gmow Interntionl Conf. AIP Conference Proceedings, 6, ,. Melnik, V. N., A. A. Konovlenko, A. I. Brzhenko, H. O. Rucker, V. V. Dorovskyy, E. P. Abrnin, A. Leccheux, nd A. S. Lonsky, Bursts in emission nd bsorption s fine structure of Type IV bursts, ASTROPHYSICS AND COSMOLOGY AFTER GAMOW, Proc. 4th Gmow Interntionl Conf. AIP Conference Proceedings, 6, , b. Melnik, V. N., A. A. Konovlenko, H. O. Rucker, V. V. Dorovskyy, E. P. Abrnin, A. Leccheux, nd A. S. Lonsky, Solr S-bursts t Frequencies of -30 MHz, Solr Phys., 4, 3 7, c. Melnik, V. N., A. A. Konovlenko, H. O. Rucker, A. I. Boiko, V. V. Dorovskyy, E. P. Abrnin, nd A. Leccheux, Observtions of powerful type III bursts in the frequency rnge 30 MHz, Solr Phys., 9, 335,. Melnik, V. N., N. V. Shevchuk, H. O. Rucker, A. A. Konovlenko, E. P. Abrnin, V. V. Dorovskyy, A. Leccheux, Properties of decmeter spikes, Plnetry Rdio Emissions VII, edited by H.Ø. Rucker, W. S. Kurth, P. Lourn, nd G. Fischer, Austrin Acdemy of Sciences Press, Vienn, this issue, , b. Rutkevych, B. P., nd V. N. Melnik, Numericl Simultion of Propgtion of Type III Electrons Emission, Plnetry Rdio Emissions VII, this issue, ,.

1 Which of the following summarises the change in wave characteristics on going from infra-red to ultraviolet in the electromagnetic spectrum?

1 Which of the following summarises the change in wave characteristics on going from infra-red to ultraviolet in the electromagnetic spectrum? Which of the following summrises the chnge in wve chrcteristics on going from infr-red to ultrviolet in the electromgnetic spectrum? frequency speed (in vcuum) decreses decreses decreses remins constnt

More information

New Expansion and Infinite Series

New Expansion and Infinite Series Interntionl Mthemticl Forum, Vol. 9, 204, no. 22, 06-073 HIKARI Ltd, www.m-hikri.com http://dx.doi.org/0.2988/imf.204.4502 New Expnsion nd Infinite Series Diyun Zhng College of Computer Nnjing University

More information

CHM Physical Chemistry I Chapter 1 - Supplementary Material

CHM Physical Chemistry I Chapter 1 - Supplementary Material CHM 3410 - Physicl Chemistry I Chpter 1 - Supplementry Mteril For review of some bsic concepts in mth, see Atkins "Mthemticl Bckground 1 (pp 59-6), nd "Mthemticl Bckground " (pp 109-111). 1. Derivtion

More information

25 Which of the following summarises the change in wave characteristics on going from infra-red to ultraviolet in the electromagnetic spectrum?

25 Which of the following summarises the change in wave characteristics on going from infra-red to ultraviolet in the electromagnetic spectrum? PhysicsndMthsTutor.com 25 Which of the following summrises the chnge in wve chrcteristics on going from infr-red to ultrviolet in the electromgnetic spectrum? 972//M/J/2 frequency speed (in vcuum) decreses

More information

A027 Uncertainties in Local Anisotropy Estimation from Multi-offset VSP Data

A027 Uncertainties in Local Anisotropy Estimation from Multi-offset VSP Data A07 Uncertinties in Locl Anisotropy Estimtion from Multi-offset VSP Dt M. Asghrzdeh* (Curtin University), A. Bon (Curtin University), R. Pevzner (Curtin University), M. Urosevic (Curtin University) & B.

More information

The Properties of Stars

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

More information

A Brief Review on Akkar, Sandikkaya and Bommer (ASB13) GMPE

A Brief Review on Akkar, Sandikkaya and Bommer (ASB13) GMPE Southwestern U.S. Ground Motion Chrcteriztion Senior Seismic Hzrd Anlysis Committee Level 3 Workshop #2 October 22-24, 2013 A Brief Review on Akkr, Sndikky nd Bommer (ASB13 GMPE Sinn Akkr Deprtment of

More information

Driving Cycle Construction of City Road for Hybrid Bus Based on Markov Process Deng Pan1, a, Fengchun Sun1,b*, Hongwen He1, c, Jiankun Peng1, d

Driving Cycle Construction of City Road for Hybrid Bus Based on Markov Process Deng Pan1, a, Fengchun Sun1,b*, Hongwen He1, c, Jiankun Peng1, d Interntionl Industril Informtics nd Computer Engineering Conference (IIICEC 15) Driving Cycle Construction of City Rod for Hybrid Bus Bsed on Mrkov Process Deng Pn1,, Fengchun Sun1,b*, Hongwen He1, c,

More information

1.1. Linear Constant Coefficient Equations. Remark: A differential equation is an equation

1.1. Linear Constant Coefficient Equations. Remark: A differential equation is an equation 1 1.1. Liner Constnt Coefficient Equtions Section Objective(s): Overview of Differentil Equtions. Liner Differentil Equtions. Solving Liner Differentil Equtions. The Initil Vlue Problem. 1.1.1. Overview

More information

THE INTERVAL LATTICE BOLTZMANN METHOD FOR TRANSIENT HEAT TRANSFER IN A SILICON THIN FILM

THE INTERVAL LATTICE BOLTZMANN METHOD FOR TRANSIENT HEAT TRANSFER IN A SILICON THIN FILM ROMAI J., v.9, no.2(2013), 173 179 THE INTERVAL LATTICE BOLTZMANN METHOD FOR TRANSIENT HEAT TRANSFER IN A SILICON THIN FILM Alicj Piseck-Belkhyt, Ann Korczk Institute of Computtionl Mechnics nd Engineering,

More information

4- Cosmology - II. introduc)on to Astrophysics, C. Bertulani, Texas A&M-Commerce 1

4- Cosmology - II. introduc)on to Astrophysics, C. Bertulani, Texas A&M-Commerce 1 4- Cosmology - II introduc)on to Astrophysics, C. Bertulni, Texs A&M-Commerce 1 4.1 - Solutions of Friedmnn Eqution As shown in Lecture 3, Friedmnn eqution is given by! H 2 = # " & % 2 = 8πG 3 ρ k 2 +

More information

(See Notes on Spontaneous Emission)

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

More information

Vorticity. curvature: shear: fluid elements moving in a straight line but at different speeds. t 1 t 2. ATM60, Shu-Hua Chen

Vorticity. curvature: shear: fluid elements moving in a straight line but at different speeds. t 1 t 2. ATM60, Shu-Hua Chen Vorticity We hve previously discussed the ngulr velocity s mesure of rottion of body. This is suitble quntity for body tht retins its shpe but fluid cn distort nd we must consider two components to rottion:

More information

Factors affecting the phonation threshold pressure and frequency

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

More information

Kepler's Three LAWS. Universal Gravitation Chapter 12. Heliocentric Model. Geocentric Model. Other Models. Johannes Kepler

Kepler's Three LAWS. Universal Gravitation Chapter 12. Heliocentric Model. Geocentric Model. Other Models. Johannes Kepler Universl Grvittion Chpter 1 Johnnes Kepler Johnnes Kepler ws Germn mthemticin, stronomer nd strologer, nd key figure in the 17th century Scientific revolution. He is best known for his lws of plnetry motion,

More information

Predict Global Earth Temperature using Linier Regression

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

More information

Fully Kinetic Simulations of Ion Beam Neutralization

Fully Kinetic Simulations of Ion Beam Neutralization Fully Kinetic Simultions of Ion Bem Neutrliztion Joseph Wng University of Southern Cliforni Hideyuki Usui Kyoto University E-mil: josephjw@usc.edu; usui@rish.kyoto-u.c.jp 1. Introduction Ion em emission/neutrliztion

More information

Physics 201 Lab 3: Measurement of Earth s local gravitational field I Data Acquisition and Preliminary Analysis Dr. Timothy C. Black Summer I, 2018

Physics 201 Lab 3: Measurement of Earth s local gravitational field I Data Acquisition and Preliminary Analysis Dr. Timothy C. Black Summer I, 2018 Physics 201 Lb 3: Mesurement of Erth s locl grvittionl field I Dt Acquisition nd Preliminry Anlysis Dr. Timothy C. Blck Summer I, 2018 Theoreticl Discussion Grvity is one of the four known fundmentl forces.

More information

Vector potential quantization and the photon wave-particle representation

Vector potential quantization and the photon wave-particle representation Vector potentil quntiztion nd the photon wve-prticle representtion Constntin Meis, Pierre-Richrd Dhoo To cite this version: Constntin Meis, Pierre-Richrd Dhoo. Vector potentil quntiztion nd the photon

More information

The heat budget of the atmosphere and the greenhouse effect

The heat budget of the atmosphere and the greenhouse effect The het budget of the tmosphere nd the greenhouse effect 1. Solr rdition 1.1 Solr constnt The rdition coming from the sun is clled solr rdition (shortwve rdition). Most of the solr rdition is visible light

More information

5.7 Improper Integrals

5.7 Improper Integrals 458 pplictions of definite integrls 5.7 Improper Integrls In Section 5.4, we computed the work required to lift pylod of mss m from the surfce of moon of mss nd rdius R to height H bove the surfce of the

More information

Math 8 Winter 2015 Applications of Integration

Math 8 Winter 2015 Applications of Integration Mth 8 Winter 205 Applictions of Integrtion Here re few importnt pplictions of integrtion. The pplictions you my see on n exm in this course include only the Net Chnge Theorem (which is relly just the Fundmentl

More information

P 3 (x) = f(0) + f (0)x + f (0) 2. x 2 + f (0) . In the problem set, you are asked to show, in general, the n th order term is a n = f (n) (0)

P 3 (x) = f(0) + f (0)x + f (0) 2. x 2 + f (0) . In the problem set, you are asked to show, in general, the n th order term is a n = f (n) (0) 1 Tylor polynomils In Section 3.5, we discussed how to pproximte function f(x) round point in terms of its first derivtive f (x) evluted t, tht is using the liner pproximtion f() + f ()(x ). We clled this

More information

Measuring Electron Work Function in Metal

Measuring Electron Work Function in Metal n experiment of the Electron topic Mesuring Electron Work Function in Metl Instructor: 梁生 Office: 7-318 Emil: shling@bjtu.edu.cn Purposes 1. To understnd the concept of electron work function in metl nd

More information

Module 6: LINEAR TRANSFORMATIONS

Module 6: LINEAR TRANSFORMATIONS Module 6: LINEAR TRANSFORMATIONS. Trnsformtions nd mtrices Trnsformtions re generliztions of functions. A vector x in some set S n is mpped into m nother vector y T( x). A trnsformtion is liner if, for

More information

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

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

More information

Consequently, the temperature must be the same at each point in the cross section at x. Let:

Consequently, the temperature must be the same at each point in the cross section at x. Let: HW 2 Comments: L1-3. Derive the het eqution for n inhomogeneous rod where the therml coefficients used in the derivtion of the het eqution for homogeneous rod now become functions of position x in the

More information

Simulation of Eclipsing Binary Star Systems. Abstract

Simulation of Eclipsing Binary Star Systems. Abstract Simultion of Eclipsing Binry Str Systems Boris Yim 1, Kenny Chn 1, Rphel Hui 1 Wh Yn College Kowloon Diocesn Boys School Abstrct This report briefly introduces the informtion on eclipsing binry str systems.

More information

Entropy ISSN

Entropy ISSN Entropy 006, 8[], 50-6 50 Entropy ISSN 099-4300 www.mdpi.org/entropy/ ENTROPY GENERATION IN PRESSURE GRADIENT ASSISTED COUETTE FLOW WITH DIFFERENT THERMAL BOUNDARY CONDITIONS Abdul Aziz Deprtment of Mechnicl

More information

Quantum Mechanics Qualifying Exam - August 2016 Notes and Instructions

Quantum Mechanics Qualifying Exam - August 2016 Notes and Instructions Quntum Mechnics Qulifying Exm - August 016 Notes nd Instructions There re 6 problems. Attempt them ll s prtil credit will be given. Write on only one side of the pper for your solutions. Write your lis

More information

1 The fundamental theorems of calculus.

1 The fundamental theorems of calculus. The fundmentl theorems of clculus. The fundmentl theorems of clculus. Evluting definite integrls. The indefinite integrl- new nme for nti-derivtive. Differentiting integrls. Theorem Suppose f is continuous

More information

R. I. Badran Solid State Physics

R. I. Badran Solid State Physics I Bdrn Solid Stte Physics Crystl vibrtions nd the clssicl theory: The ssmption will be mde to consider tht the men eqilibrim position of ech ion is t Brvis lttice site The ions oscillte bot this men position

More information

Tests for the Ratio of Two Poisson Rates

Tests for the Ratio of Two Poisson Rates Chpter 437 Tests for the Rtio of Two Poisson Rtes Introduction The Poisson probbility lw gives the probbility distribution of the number of events occurring in specified intervl of time or spce. The Poisson

More information

NUMERICAL SIMULATION OF FRONTAL MIXED CLOUD SYSTEMS AND CLOUD MICROSTRUCTURE EFFECT ON SATELLITE SIGNAL

NUMERICAL SIMULATION OF FRONTAL MIXED CLOUD SYSTEMS AND CLOUD MICROSTRUCTURE EFFECT ON SATELLITE SIGNAL NUMERICAL SIMULATION OF FRONTAL MIXED CLOUD SYSTEMS AND CLOUD MICROSTRUCTURE EFFECT ON SATELLITE SIGNAL V. Bkhnov, O. Kryvook, B. Dormn Ukrinin Hydrometeorologicl Reserch Institute, Avenue of Science 37,

More information

KINEMATICS OF RIGID BODIES

KINEMATICS OF RIGID BODIES KINEMTICS OF RIGID ODIES Introduction In rigid body kinemtics, e use the reltionships governing the displcement, velocity nd ccelertion, but must lso ccount for the rottionl motion of the body. Description

More information

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

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

More information

NATIONAL RADIO ASTRONOMY OBSERVATORY SOCORRO, NEW MEXICO. VLA Test Memorandum No. 117 POINTING RUN - FEBRUARY 15-16, E. Fomalont.

NATIONAL RADIO ASTRONOMY OBSERVATORY SOCORRO, NEW MEXICO. VLA Test Memorandum No. 117 POINTING RUN - FEBRUARY 15-16, E. Fomalont. NATIONAL RADIO ASTRONOMY OBSERVATORY SOCORRO, NEW MEXICO VLA Test Memorndum No. 117 POINTING RUN - FEBRUARY 15-16, 1977 E. Fomlont Februry 1977 Two twelve-hour periods of identicl pointing runs were mde

More information

AMPERE CONGRESS AMPERE on Magnetic Resonance and Related Phenomena. Under the auspices of The GROUPEMENT AMPERE

AMPERE CONGRESS AMPERE on Magnetic Resonance and Related Phenomena. Under the auspices of The GROUPEMENT AMPERE AMPERE 2000 th 30 CONGRESS AMPERE on Mgnetic Resonnce nd Relted Phenomen Lison, Portugl, 23-2 July 2000 Under the uspices of The GROUPEMENT AMPERE Edited y: A.F. MARTINS, A.G. FEIO nd J.G. MOURA Sponsoring

More information

Keywords Synthetic Aperture Radar (SAR); Range Doppler Algorithm (RDA); Range Cell Migration (RCM); remote sensing; Radarsat1 Y 0

Keywords Synthetic Aperture Radar (SAR); Range Doppler Algorithm (RDA); Range Cell Migration (RCM); remote sensing; Radarsat1 Y 0 Sedighe Mirbolouk * Deptment of Electricl Volume 3, Issue 5, My 013 ISSN: 77 18X Interntionl Journl of Advnced Reserch in Computer Science nd Softwre Reserch Pper Avilble online t: www.ijrcsse.com Synthetic

More information

SUPPLEMENTARY INFORMATION

SUPPLEMENTARY INFORMATION DOI:.38/NMAT343 Hybrid Elstic olids Yun Li, Ying Wu, Ping heng, Zho-Qing Zhng* Deprtment of Physics, Hong Kong University of cience nd Technology Cler Wter By, Kowloon, Hong Kong, Chin E-mil: phzzhng@ust.hk

More information

Lecture 20: Numerical Integration III

Lecture 20: Numerical Integration III cs4: introduction to numericl nlysis /8/0 Lecture 0: Numericl Integrtion III Instructor: Professor Amos Ron Scribes: Mrk Cowlishw, Yunpeng Li, Nthnel Fillmore For the lst few lectures we hve discussed

More information

Fig. 1. Open-Loop and Closed-Loop Systems with Plant Variations

Fig. 1. Open-Loop and Closed-Loop Systems with Plant Variations ME 3600 Control ystems Chrcteristics of Open-Loop nd Closed-Loop ystems Importnt Control ystem Chrcteristics o ensitivity of system response to prmetric vritions cn be reduced o rnsient nd stedy-stte responses

More information

Lecture XVII. Vector functions, vector and scalar fields Definition 1 A vector-valued function is a map associating vectors to real numbers, that is

Lecture XVII. Vector functions, vector and scalar fields Definition 1 A vector-valued function is a map associating vectors to real numbers, that is Lecture XVII Abstrct We introduce the concepts of vector functions, sclr nd vector fields nd stress their relevnce in pplied sciences. We study curves in three-dimensionl Eucliden spce nd introduce the

More information

Section 5.1 #7, 10, 16, 21, 25; Section 5.2 #8, 9, 15, 20, 27, 30; Section 5.3 #4, 6, 9, 13, 16, 28, 31; Section 5.4 #7, 18, 21, 23, 25, 29, 40

Section 5.1 #7, 10, 16, 21, 25; Section 5.2 #8, 9, 15, 20, 27, 30; Section 5.3 #4, 6, 9, 13, 16, 28, 31; Section 5.4 #7, 18, 21, 23, 25, 29, 40 Mth B Prof. Audrey Terrs HW # Solutions by Alex Eustis Due Tuesdy, Oct. 9 Section 5. #7,, 6,, 5; Section 5. #8, 9, 5,, 7, 3; Section 5.3 #4, 6, 9, 3, 6, 8, 3; Section 5.4 #7, 8,, 3, 5, 9, 4 5..7 Since

More information

7.2 The Definite Integral

7.2 The Definite Integral 7.2 The Definite Integrl the definite integrl In the previous section, it ws found tht if function f is continuous nd nonnegtive, then the re under the grph of f on [, b] is given by F (b) F (), where

More information

Basic model for traffic interweave

Basic model for traffic interweave Journl of Physics: Conference Series PAPER OPEN ACCESS Bsic model for trffic interweve To cite this rticle: Ding-wei Hung 25 J. Phys.: Conf. Ser. 633 227 Relted content - Bsic sciences gonize in Turkey!

More information

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

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

More information

Continuous Random Variables

Continuous Random Variables STAT/MATH 395 A - PROBABILITY II UW Winter Qurter 217 Néhémy Lim Continuous Rndom Vribles Nottion. The indictor function of set S is rel-vlued function defined by : { 1 if x S 1 S (x) if x S Suppose tht

More information

Abstract. Introduction

Abstract. Introduction Apprent chnge of position of light source reltive to detector/observer due to rottion nd ccelertion - new interprettion nd nlysis of Michelson-Morley nd gnc experiments Abstrct Henok Tdesse, Electricl

More information

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

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

More information

WMAP satellite. 16 Feb Feb Feb 2012

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

More information

13: Diffusion in 2 Energy Groups

13: Diffusion in 2 Energy Groups 3: Diffusion in Energy Groups B. Rouben McMster University Course EP 4D3/6D3 Nucler Rector Anlysis (Rector Physics) 5 Sept.-Dec. 5 September Contents We study the diffusion eqution in two energy groups

More information

Material Space Motion Time Phenomenon of Kinetic Energy and Inertia of Material Bodies

Material Space Motion Time Phenomenon of Kinetic Energy and Inertia of Material Bodies AASCIT Journl of Physics 15; 1(4): 9-96 Published online July, 15 (http://wwwscitorg/journl/physics) Mteril Spce Motion Time Phenomenon of Kinetic Energy nd Inerti of Mteril Bodies F F Mende B Verkin Institute

More information

1 The fundamental theorems of calculus.

1 The fundamental theorems of calculus. The fundmentl theorems of clculus. The fundmentl theorems of clculus. Evluting definite integrls. The indefinite integrl- new nme for nti-derivtive. Differentiting integrls. Tody we provide the connection

More information

Overview of Calculus I

Overview of Calculus I Overview of Clculus I Prof. Jim Swift Northern Arizon University There re three key concepts in clculus: The limit, the derivtive, nd the integrl. You need to understnd the definitions of these three things,

More information

CALCULATED POWDER X-RAY DIFFRACTION LINE PROFILES VIA ABSORPTION

CALCULATED POWDER X-RAY DIFFRACTION LINE PROFILES VIA ABSORPTION 16 17 CALCULATED POWDER X-RAY DFFRACTON LNE PROFLES VA ABSORPTON Keji Liu nd Heifen Chen School of Mteril Science nd Engineering, Shnghi nstitute of Technology, Shnghi, Chin 2233 ABSTRACT We hve clculted

More information

Non-Linear & Logistic Regression

Non-Linear & Logistic Regression Non-Liner & Logistic Regression If the sttistics re boring, then you've got the wrong numbers. Edwrd R. Tufte (Sttistics Professor, Yle University) Regression Anlyses When do we use these? PART 1: find

More information

AB Calculus Review Sheet

AB Calculus Review Sheet AB Clculus Review Sheet Legend: A Preclculus, B Limits, C Differentil Clculus, D Applictions of Differentil Clculus, E Integrl Clculus, F Applictions of Integrl Clculus, G Prticle Motion nd Rtes This is

More information

The Active Universe. 1 Active Motion

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

More information

( ) as a fraction. Determine location of the highest

( ) as a fraction. Determine location of the highest AB Clculus Exm Review Sheet - Solutions A. Preclculus Type prolems A1 A2 A3 A4 A5 A6 A7 This is wht you think of doing Find the zeros of f ( x). Set function equl to 0. Fctor or use qudrtic eqution if

More information

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

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

More information

Riemann Sums and Riemann Integrals

Riemann Sums and Riemann Integrals Riemnn Sums nd Riemnn Integrls Jmes K. Peterson Deprtment of Biologicl Sciences nd Deprtment of Mthemticl Sciences Clemson University August 26, 2013 Outline 1 Riemnn Sums 2 Riemnn Integrls 3 Properties

More information

Phys 7221, Fall 2006: Homework # 6

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

More information

Section 14.3 Arc Length and Curvature

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

More information

( ) where f ( x ) is a. AB Calculus Exam Review Sheet. A. Precalculus Type problems. Find the zeros of f ( x).

( ) where f ( x ) is a. AB Calculus Exam Review Sheet. A. Precalculus Type problems. Find the zeros of f ( x). AB Clculus Exm Review Sheet A. Preclculus Type prolems A1 Find the zeros of f ( x). This is wht you think of doing A2 A3 Find the intersection of f ( x) nd g( x). Show tht f ( x) is even. A4 Show tht f

More information

Computational Fluid Dynamics. Lecture 6

Computational Fluid Dynamics. Lecture 6 omputtionl Fluid Dynmics Lecture 6 Spce differencing errors. ψ ψ + = 0 Seek trveling wve solutions. e ( t) ik k is wve number nd is frequency. =k is dispersion reltion. where is phse speed. =, true solution

More information

Section 6.1 INTRO to LAPLACE TRANSFORMS

Section 6.1 INTRO to LAPLACE TRANSFORMS Section 6. INTRO to LAPLACE TRANSFORMS Key terms: Improper Integrl; diverge, converge A A f(t)dt lim f(t)dt Piecewise Continuous Function; jump discontinuity Function of Exponentil Order Lplce Trnsform

More information

ADVANCEMENT OF THE CLOSELY COUPLED PROBES POTENTIAL DROP TECHNIQUE FOR NDE OF SURFACE CRACKS

ADVANCEMENT OF THE CLOSELY COUPLED PROBES POTENTIAL DROP TECHNIQUE FOR NDE OF SURFACE CRACKS ADVANCEMENT OF THE CLOSELY COUPLED PROBES POTENTIAL DROP TECHNIQUE FOR NDE OF SURFACE CRACKS F. Tkeo 1 nd M. Sk 1 Hchinohe Ntionl College of Technology, Hchinohe, Jpn; Tohoku University, Sendi, Jpn Abstrct:

More information

Space Charge Limited Currents Calculations in Coaxial Cylindrical Diodes Using Particle-in-Cell Simulations

Space Charge Limited Currents Calculations in Coaxial Cylindrical Diodes Using Particle-in-Cell Simulations The Open Plsm Physics Journl, 2009, 2, 63-69 63 Open Access Spce Chrge Limited Currents Clcultions in Coxil Cylindricl Diodes Using Prticle-in-Cell Simultions S. Mhlingm *, C. Nieter, J. Loverich, D. Smithe

More information

Chapter 9: Inferences based on Two samples: Confidence intervals and tests of hypotheses

Chapter 9: Inferences based on Two samples: Confidence intervals and tests of hypotheses Chpter 9: Inferences bsed on Two smples: Confidence intervls nd tests of hypotheses 9.1 The trget prmeter : difference between two popultion mens : difference between two popultion proportions : rtio of

More information

Riemann Sums and Riemann Integrals

Riemann Sums and Riemann Integrals Riemnn Sums nd Riemnn Integrls Jmes K. Peterson Deprtment of Biologicl Sciences nd Deprtment of Mthemticl Sciences Clemson University August 26, 203 Outline Riemnn Sums Riemnn Integrls Properties Abstrct

More information

Calculus of Variations

Calculus of Variations Clculus of Vritions Com S 477/577 Notes) Yn-Bin Ji Dec 4, 2017 1 Introduction A functionl ssigns rel number to ech function or curve) in some clss. One might sy tht functionl is function of nother function

More information

Math 360: A primitive integral and elementary functions

Math 360: A primitive integral and elementary functions Mth 360: A primitive integrl nd elementry functions D. DeTurck University of Pennsylvni October 16, 2017 D. DeTurck Mth 360 001 2017C: Integrl/functions 1 / 32 Setup for the integrl prtitions Definition:

More information

Topics Covered AP Calculus AB

Topics Covered AP Calculus AB Topics Covered AP Clculus AB ) Elementry Functions ) Properties of Functions i) A function f is defined s set of ll ordered pirs (, y), such tht for ech element, there corresponds ectly one element y.

More information

interatomic distance

interatomic distance Dissocition energy of Iodine molecule using constnt devition spectrometer Tbish Qureshi September 2003 Aim: To verify the Hrtmnn Dispersion Formul nd to determine the dissocition energy of I 2 molecule

More information

Math 32B Discussion Session Session 7 Notes August 28, 2018

Math 32B Discussion Session Session 7 Notes August 28, 2018 Mth 32B iscussion ession ession 7 Notes August 28, 28 In tody s discussion we ll tlk bout surfce integrls both of sclr functions nd of vector fields nd we ll try to relte these to the mny other integrls

More information

Energy Bands Energy Bands and Band Gap. Phys463.nb Phenomenon

Energy Bands Energy Bands and Band Gap. Phys463.nb Phenomenon Phys463.nb 49 7 Energy Bnds Ref: textbook, Chpter 7 Q: Why re there insultors nd conductors? Q: Wht will hppen when n electron moves in crystl? In the previous chpter, we discussed free electron gses,

More information

Interactive system for geomagnetic data analysis

Interactive system for geomagnetic data analysis Interctive system for geomgnetic dt nlysis Igor Solovev * Institute of Cosmophysicl Reserch nd Rdio Wve Propgtion FEB RAS, 684034 Kmchtk region, Elizovskiy district, Prtunk, Mirny str., 7, Russi Abstrct.

More information

Songklanakarin Journal of Science and Technology SJST R1 Thongchan. A Modified Hyperbolic Secant Distribution

Songklanakarin Journal of Science and Technology SJST R1 Thongchan. A Modified Hyperbolic Secant Distribution A Modified Hyperbolic Secnt Distribution Journl: Songklnkrin Journl of Science nd Technology Mnuscript ID SJST-0-0.R Mnuscript Type: Originl Article Dte Submitted by the Author: 0-Mr-0 Complete List of

More information

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

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

More information

Ordinary differential equations

Ordinary differential equations Ordinry differentil equtions Introduction to Synthetic Biology E Nvrro A Montgud P Fernndez de Cordob JF Urchueguí Overview Introduction-Modelling Bsic concepts to understnd n ODE. Description nd properties

More information

Vadose Zone Hydrology

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

More information

On the Linear Stability of Compound Capillary Jets

On the Linear Stability of Compound Capillary Jets ILASS Americs, th Annul Conference on Liquid Atomiztion nd Spry Systems, Chicgo, IL, My 7 On the Liner Stbility of Compound Cpillry Jets Mksud (Mx) Ismilov, Stephen D Heister School of Aeronutics nd Astronutics,

More information

STRUCTURAL AND MAGNETIC PROPERTIES OF Fe/Si x Fe 1! x MULTILAYERS

STRUCTURAL AND MAGNETIC PROPERTIES OF Fe/Si x Fe 1! x MULTILAYERS MOLECULAR PHYSICS REPORTS 0 (00) 8-86 STRUCTURAL AND MAGNETIC PROPERTIES OF Fe/ x Fe! x MULTILAYERS P. WANDZIUK, M. KOPCEWICZ, B. SZYMAŃSKI, AND T. LUCIŃSKI Institute of Moleculr Physics, Polish Acdemy

More information

8 Laplace s Method and Local Limit Theorems

8 Laplace s Method and Local Limit Theorems 8 Lplce s Method nd Locl Limit Theorems 8. Fourier Anlysis in Higher DImensions Most of the theorems of Fourier nlysis tht we hve proved hve nturl generliztions to higher dimensions, nd these cn be proved

More information

Higher Checklist (Unit 3) Higher Checklist (Unit 3) Vectors

Higher Checklist (Unit 3) Higher Checklist (Unit 3) Vectors Vectors Skill Achieved? Know tht sclr is quntity tht hs only size (no direction) Identify rel-life exmples of sclrs such s, temperture, mss, distnce, time, speed, energy nd electric chrge Know tht vector

More information

Conservation Law. Chapter Goal. 5.2 Theory

Conservation Law. Chapter Goal. 5.2 Theory Chpter 5 Conservtion Lw 5.1 Gol Our long term gol is to understnd how mny mthemticl models re derived. We study how certin quntity chnges with time in given region (sptil domin). We first derive the very

More information

Supporting Online Material for

Supporting Online Material for Correction: 1 December 007 www.sciencemg.org/cgi/content/full/318/5857/1750/dc1 Supporting Online Mteril for Mott Trnsition in VO Reveled by Infrred Spectroscopy nd Nno- Imging M. M. Qzilbsh,* M. Brehm,

More information

Supplementary Material for Wave-pinning and cell polarity from a bistable reaction-diffusion system

Supplementary Material for Wave-pinning and cell polarity from a bistable reaction-diffusion system Supplementry Mteril for Wve-pinning nd cell polrity from bistble rection-diffusion system Yoichiro Mori, Alendr Jilkine nd Leh Edelstein-Keshet Model Comprisons We concentrte here the three systems to

More information

Thermal Performance of Electrocaloric Refrigeration using Thermal Switches of Fluid Motion and Changing Contact Conductance

Thermal Performance of Electrocaloric Refrigeration using Thermal Switches of Fluid Motion and Changing Contact Conductance Americn Journl of Physics nd Applictions 2016; 4(5): 134-139 http://www.sciencepublishinggroup.com/j/jp doi:.11648/j.jp.20160405.12 ISSN: 2330-4286 (Print); ISSN: 2330-4308 (Online) Therml Performnce of

More information

A5682: Introduction to Cosmology Course Notes. 4. Cosmic Dynamics: The Friedmann Equation. = GM s

A5682: Introduction to Cosmology Course Notes. 4. Cosmic Dynamics: The Friedmann Equation. = GM s 4. Cosmic Dynmics: The Friedmnn Eqution Reding: Chpter 4 Newtonin Derivtion of the Friedmnn Eqution Consider n isolted sphere of rdius R s nd mss M s, in uniform, isotropic expnsion (Hubble flow). The

More information

Review of Probability Distributions. CS1538: Introduction to Simulations

Review of Probability Distributions. CS1538: Introduction to Simulations Review of Proility Distriutions CS1538: Introduction to Simultions Some Well-Known Proility Distriutions Bernoulli Binomil Geometric Negtive Binomil Poisson Uniform Exponentil Gmm Erlng Gussin/Norml Relevnce

More information

ELE B7 Power Systems Engineering. Power System Components Modeling

ELE B7 Power Systems Engineering. Power System Components Modeling Power Systems Engineering Power System Components Modeling Section III : Trnsformer Model Power Trnsformers- CONSTRUCTION Primry windings, connected to the lternting voltge source; Secondry windings, connected

More information

Monte Carlo method in solving numerical integration and differential equation

Monte Carlo method in solving numerical integration and differential equation Monte Crlo method in solving numericl integrtion nd differentil eqution Ye Jin Chemistry Deprtment Duke University yj66@duke.edu Abstrct: Monte Crlo method is commonly used in rel physics problem. The

More information

4 Results and Discussions

4 Results and Discussions 4 Results nd Discussions 4. Generl Considertion In this chpter, results will be presented nd discussed. Further, if possible, they will be compred with men-field results. As mentioned in previous chpters,

More information

Energy creation in a moving solenoid? Abstract

Energy creation in a moving solenoid? Abstract Energy cretion in moving solenoid? Nelson R. F. Brg nd Rnieri V. Nery Instituto de Físic, Universidde Federl do Rio de Jneiro, Cix Postl 68528, RJ 21941-972 Brzil Abstrct The electromgnetic energy U em

More information

du = C dy = 1 dy = dy W is invertible with inverse U, so that y = W(t) is exactly the same thing as t = U(y),

du = C dy = 1 dy = dy W is invertible with inverse U, so that y = W(t) is exactly the same thing as t = U(y), 29. Differentil equtions. The conceptul bsis of llometr Did it occur to ou in Lecture 3 wh Fiboncci would even cre how rpidl rbbit popultion grows? Mbe he wnted to et the rbbits. If so, then he would be

More information

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

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

More information

MAC-solutions of the nonexistent solutions of mathematical physics

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

More information

Vibrational Relaxation of HF (v=3) + CO

Vibrational Relaxation of HF (v=3) + CO Journl of the Koren Chemicl Society 26, Vol. 6, No. 6 Printed in the Republic of Kore http://dx.doi.org/.52/jkcs.26.6.6.462 Notes Vibrtionl Relxtion of HF (v3) + CO Chng Soon Lee Deprtment of Chemistry,

More information