Investigation phase in case of Bragg coupling
|
|
|
- Simon Emery Baker
- 5 years ago
- Views:
Transcription
1 Journl of Th-Qr Unversty No.3 Vol.4 December/008 Investgton phse n cse of Brgg couplng Hder K. Mouhmd Deprtment of Physcs, College of Scence, Th-Qr, Unv. Mouhmd H. Abdullh Deprtment of Physcs, College of Scence, Dyl, Unv. Sf F. Hssun Deprtment of Physcs, College of Educton, Almustnsyrh, Unv. Abstrct These results of nvestgton hve show hgher controllng possblty by lght wves dffrcton phses n cse Brgg couplng Dffrcton of sotropc, nsotropc ntercton whch tke plce smultneously. The occurrence source These dstncton cse of ntercton produced from ddtonl phse shft of lght pss through the ultrsonc wves meshes s dffrcton grtng,nd controllng by prmeters dul ntercton Through (Rmn-Nth) Prmeters. Ths evdent vrton n lght wves dffrcton phses ( 0,, ) whch rech to () wth wde rnge vlue of Rmn-Nth Prmeters (.95 > v, >.7 ) nd unppernce of jump n phse of dffrcted wve lght n ny order of dffrcton must be to tke n to consderton when the modern (Acousto-optcs) devces desgn. 48
2 Journl of Th-Qr Unversty No.3 Vol.4 December/008. Introducton The lser nventon hs led the development of cousto-optcs ntercton nd ts pplcton, mnly for grtng phse, deflecton, modulton nd sgnl processng. Techncl progresses n utlzton of effcent brefrngent crystls nd hgh frequency pezoelectrc trnsducer hve brought vluble beneft to cousto-optcs components mprovement[,,4]. In these types of nterctons cn show the lght dffrcton by ultrsound n crystls n usully s ccompned by chnge n optcl polrzton nd ntenstes, wth mportnt chnge n mtchng phse. All ths mportnt chnges cn be descrbe s sum of sngle collson, ech of whch nvolves the nnhlton of one ncdent photon t frequency (ω ) nd one phonon t frequency (Ω ) nd smultons creton of new (dffrcted) photon t frequency (ω d ) s. ω d = ω + Ω..() Whch propgtes long the drecton of scttered bem? The conservton of momentum requres tht the momentum ħ(k+k) of colldng prtcles be equl to the momentum ħk d of scttered photon,so tht. k d = k + K...() Therefore the dffrcted bem s shfted n frequency by n mount equl the sound frequency (Ω ) ths led ω d < ω. But were reversed the drecton of the sound bem, the sctterng process could be consdered s on n whch new photon (dffrcted photon ) nd new phonon re generted whle the ncdent photon s nnhlted. In ths cse, the conservton of energy from the two cse s [-5]. ω d = ω Ω..(3) Ths relton between the sgn of frequency chnge nd sound propgton drecton s consstent wth Doppler-shft. Ths phenomen whch occurs n sotropc nd nsotropc med smultneously lso n brefrngent crystls only or homogenous crystls [7,6]. The present nvestgton concentrtes on phses ddtonl n cse Brgg Couplng mtchng tht s tke plce durng so-clled mxed sotropc nsotropc dffrcton. As couplng ddtonl phses n up-down shfted regmes of ntercton, 48
3 Journl of Th-Qr Unversty No.3 Vol.4 December/008 n two orders dffrcton. Ths mter cqures the property of n optcl phse grtng for perod to the coustc wvelength.. Theory Prt Under The supposton of plne wves, the lght phse n ll dffrcton orders durng the ntercton of Brgg couplng phse ( ) n sotropc-nsotropc dffrcton whch occurs smultneously s ddtonl phse-shft.my be determne from system of coupled wves equton (s known) s functon of Rmn Nth prmeters ( v v nd v ) [,5 ]. l M P (4) Equton (4) show The Rmn-Nth prmeter s proportonl to the squre root of cousto optc fgure mert ( v M ). M 6 p n....(5) 3 V It s know tht ( M ) proportonl to the second power of effectve photoelstc constnt ( p or p ) provdng the sotropc or nsotropc cousto optc ntercton, M p nd ( ) M p [, 7]. ( ) Therefore the rto of Rmn-Nth prmeters durng the combned nterctons s equl The rto of effectve photoelstc constnts ( v effectve photoelstc constnts ( p, coeffcents of optcl ndctrx [3,6]. where v p p ).The vlues of p ) were found from the chnges of the The Brgg couplng phse n ddton to the ddtonl phses-shft (, ) (,) referrng to the sotropc nd nsotropc dffrcton respectvely. Correspondng system of couplng wves equton [].esly to obtn t where [ = tn - (y/x)] therefore the system of coupled wves Eg. Cn be wrtten s. 48
4 48 Journl of Th-Qr Unversty No.3 Vol.4 December/008 tn tn 4 tn 0 Sn Sn Cos Remrkble the relton between Rmn-Nth prmeters present, the rto v v s evluted on the bsc of the used brefrngent crystls, whch dependent on the type of coustc mode nd on the chosen crystl cut. 3.Results nd Dssecton From Eg. (6), clculton the chnges of phses couplng, re presented n two fgures ( nd ) s functon of Rmn- Nth prmeter v (expressed n untes of ). The fgures shows the grph of the phses ( 0,, ) of zeroth nd sotropc, nsotropc dffrcton orders respectvely, where The zeroth phses 0 s represented by squre curve whle the nsotropc dffrcton phse s represented by sold nd the sotropc dffrcton phse s represented by dshed curve. Here observed mportnt dfference between ll the fgures from where the stremlned t ll curves to reches mxmum vlue for chnge n phse, versus vlue of v whch n rnge (.7-.95)..... (6)
5 Journl of Th-Qr Unversty No.3 Vol.4 December/008 Moreover, more mportnt observton the cutoff product of phses (, ) up to vlue ( v = 0.5 ) occurs only wth rto v v = tht mens tht the cousto-optcs ntercton wll vnsh t lower vlues of Rmn- Nth prmeter v. On the other hnd, from fgure () the chnge n phse of zeroth order rech to vlue ( ) s the stremlned unform progressve wthout jump to ( ) drectly, s well know the Brgg trdtonl condton. It s evdent tht durng Brgg sctterng pper to us the vlue of nsotropc - sotropc phse, they re meetng n hgh vlues t Rmn- Nth prmeter v. All ths dfferences s result of n ncrese of the rto of the Rmn-Nth prmeters v v from ( to 4). Remrkble the pek phses re obtned t hgh vlue of the Rmn-Nth prmeters. Fgs. (),() shows tht the vlues of prmeters v nd v t mxmum phses ( 0,, ) re lwys observed n rnge (.95 > v, >.7 ). 6. Concluson The study shows tht n cse of Brgg couplng n nsotropc sotropc of cousto-optcs ntercton the chnge of lght phse s tke plce wth the two nterctons smultneously. The ddtonl phse s consstent wth Doppler-shft, n ddton the mgntude of the chnge phse depended on the rto of Rmn- Nth prmeters effectve photoelstc constnts ( v v whch depended on coustc power P nd The rto of p, p ).Tht chnges gven possblty controlled phse of lght wve n sotropc or nsotropc dffrcton smultneously, wth wde rnge vlue. 44
6 Journl of Th-Qr Unversty No.3 Vol.4 December/ () For the rto 3.5 (b) For the rto Fg.() Phse chngng for combned processes. 48
7 Journl of Th-Qr Unversty No.3 Vol.4 December/008 89
8 Journl of Th-Qr Unversty No.3 Vol.4 December/008 REFERENCES [] Yrv A nd Yeh P, 984, Optcl Wves n Crystls, Wley, New York. [] Hssen J.A. 99 "Addtonl phse shft effect n cousto- optcl ntercton", Ph.D thess, College of Physcs, Moscow Stte, Unv. [3] Blkshy V., Hssn J.A. 993 "Polrzton effect n cousto-optcs ntercton" Optcl Eng., Vol.3, No.4, U.S.A. [4] Voloshnov V nd Tchernytn A, 000 "Smultneous up-shfted nd down-shfted Brgg dffrcton n brefrngent med" Journl of Optcs A: Pure nd Appled Optcs, Vol., No. 5. [5] Blkshy V. I., Nknorv E. A. nd prygn V. N., 983 Phse relton n Brgg dffrcton, Moscow Unv. Phys. Bull, Vol. 4,No. 6. [6] Bzhcnov V.Yu.,Vsnctsov M.V. Soskn M.S. 984 Optcl nsotropy of volume phse grtngs " Opt. Commun,Vol.50, No. 6. [7] Ptrov V.V., Lpn S.A. 003" Hgh Frequency n Brgg Cell Acousto-Optcs" September, Srtov Stte Unversty, Srtov Russ. 89
Effects of polarization on the reflected wave
Lecture Notes. L Ros PPLIED OPTICS Effects of polrzton on the reflected wve Ref: The Feynmn Lectures on Physcs, Vol-I, Secton 33-6 Plne of ncdence Z Plne of nterfce Fg. 1 Y Y r 1 Glss r 1 Glss Fg. Reflecton
Electrochemical Thermodynamics. Interfaces and Energy Conversion
CHE465/865, 2006-3, Lecture 6, 18 th Sep., 2006 Electrochemcl Thermodynmcs Interfces nd Energy Converson Where does the energy contrbuton F zϕ dn come from? Frst lw of thermodynmcs (conservton of energy):
Jens Siebel (University of Applied Sciences Kaiserslautern) An Interactive Introduction to Complex Numbers
Jens Sebel (Unversty of Appled Scences Kserslutern) An Interctve Introducton to Complex Numbers 1. Introducton We know tht some polynoml equtons do not hve ny solutons on R/. Exmple 1.1: Solve x + 1= for
DCDM BUSINESS SCHOOL NUMERICAL METHODS (COS 233-8) Solutions to Assignment 3. x f(x)
DCDM BUSINESS SCHOOL NUMEICAL METHODS (COS -8) Solutons to Assgnment Queston Consder the followng dt: 5 f() 8 7 5 () Set up dfference tble through fourth dfferences. (b) Wht s the mnmum degree tht n nterpoltng
Many-Body Calculations of the Isotope Shift
Mny-Body Clcultons of the Isotope Shft W. R. Johnson Mrch 11, 1 1 Introducton Atomc energy levels re commonly evluted ssumng tht the nucler mss s nfnte. In ths report, we consder correctons to tomc levels
Rank One Update And the Google Matrix by Al Bernstein Signal Science, LLC
Introducton Rnk One Updte And the Google Mtrx y Al Bernsten Sgnl Scence, LLC www.sgnlscence.net here re two dfferent wys to perform mtrx multplctons. he frst uses dot product formulton nd the second uses
The Schur-Cohn Algorithm
Modelng, Estmton nd Otml Flterng n Sgnl Processng Mohmed Njm Coyrght 8, ISTE Ltd. Aendx F The Schur-Cohn Algorthm In ths endx, our m s to resent the Schur-Cohn lgorthm [] whch s often used s crteron for
4. Eccentric axial loading, cross-section core
. Eccentrc xl lodng, cross-secton core Introducton We re strtng to consder more generl cse when the xl force nd bxl bendng ct smultneousl n the cross-secton of the br. B vrtue of Snt-Vennt s prncple we
Quiz: Experimental Physics Lab-I
Mxmum Mrks: 18 Totl tme llowed: 35 mn Quz: Expermentl Physcs Lb-I Nme: Roll no: Attempt ll questons. 1. In n experment, bll of mss 100 g s dropped from heght of 65 cm nto the snd contner, the mpct s clled
Solution of Tutorial 5 Drive dynamics & control
ELEC463 Unversty of New South Wles School of Electrcl Engneerng & elecommunctons ELEC463 Electrc Drve Systems Queston Motor Soluton of utorl 5 Drve dynmcs & control 500 rev/mn = 5.3 rd/s 750 rted 4.3 Nm
UNIVERSITY OF IOANNINA DEPARTMENT OF ECONOMICS. M.Sc. in Economics MICROECONOMIC THEORY I. Problem Set II
Mcroeconomc Theory I UNIVERSITY OF IOANNINA DEPARTMENT OF ECONOMICS MSc n Economcs MICROECONOMIC THEORY I Techng: A Lptns (Note: The number of ndctes exercse s dffculty level) ()True or flse? If V( y )
Principle Component Analysis
Prncple Component Anlyss Jng Go SUNY Bufflo Why Dmensonlty Reducton? We hve too mny dmensons o reson bout or obtn nsghts from o vsulze oo much nose n the dt Need to reduce them to smller set of fctors
ψ ij has the eigenvalue
Moller Plesset Perturbton Theory In Moller-Plesset (MP) perturbton theory one tes the unperturbed Hmltonn for n tom or molecule s the sum of the one prtcle Foc opertors H F() where the egenfunctons of
Demand. Demand and Comparative Statics. Graphically. Marshallian Demand. ECON 370: Microeconomic Theory Summer 2004 Rice University Stanley Gilbert
Demnd Demnd nd Comrtve Sttcs ECON 370: Mcroeconomc Theory Summer 004 Rce Unversty Stnley Glbert Usng the tools we hve develoed u to ths ont, we cn now determne demnd for n ndvdul consumer We seek demnd
Before we can begin Ch. 3 on Radicals, we need to be familiar with perfect squares, cubes, etc. Try and do as many as you can without a calculator!!!
Nme: Algebr II Honors Pre-Chpter Homework Before we cn begin Ch on Rdicls, we need to be fmilir with perfect squres, cubes, etc Try nd do s mny s you cn without clcultor!!! n The nth root of n n Be ble
Two Coefficients of the Dyson Product
Two Coeffcents of the Dyson Product rxv:07.460v mth.co 7 Nov 007 Lun Lv, Guoce Xn, nd Yue Zhou 3,,3 Center for Combntorcs, LPMC TJKLC Nnk Unversty, Tnjn 30007, P.R. Chn lvlun@cfc.nnk.edu.cn gn@nnk.edu.cn
THE COMBINED SHEPARD ABEL GONCHAROV UNIVARIATE OPERATOR
REVUE D ANALYSE NUMÉRIQUE ET DE THÉORIE DE L APPROXIMATION Tome 32, N o 1, 2003, pp 11 20 THE COMBINED SHEPARD ABEL GONCHAROV UNIVARIATE OPERATOR TEODORA CĂTINAŞ Abstrct We extend the Sheprd opertor by
Chemical Reaction Engineering
Lecture 20 hemcl Recton Engneerng (RE) s the feld tht studes the rtes nd mechnsms of chemcl rectons nd the desgn of the rectors n whch they tke plce. Lst Lecture Energy Blnce Fundmentls F 0 E 0 F E Q W
Lecture 4: Piecewise Cubic Interpolation
Lecture notes on Vrtonl nd Approxmte Methods n Appled Mthemtcs - A Perce UBC Lecture 4: Pecewse Cubc Interpolton Compled 6 August 7 In ths lecture we consder pecewse cubc nterpolton n whch cubc polynoml
Chemical Reaction Engineering
Lecture 20 hemcl Recton Engneerng (RE) s the feld tht studes the rtes nd mechnsms of chemcl rectons nd the desgn of the rectors n whch they tke plce. Lst Lecture Energy Blnce Fundmentls F E F E + Q! 0
ESCI 342 Atmospheric Dynamics I Lesson 1 Vectors and Vector Calculus
ESI 34 tmospherc Dnmcs I Lesson 1 Vectors nd Vector lculus Reference: Schum s Outlne Seres: Mthemtcl Hndbook of Formuls nd Tbles Suggested Redng: Mrtn Secton 1 OORDINTE SYSTEMS n orthonorml coordnte sstem
The Study of Lawson Criterion in Fusion Systems for the
Interntonl Archve of Appled Scences nd Technology Int. Arch. App. Sc. Technol; Vol 6 [] Mrch : -6 Socety of ducton, Ind [ISO9: 8 ertfed Orgnzton] www.soeg.co/st.html OD: IAASA IAAST OLI ISS - 6 PRIT ISS
Inelastic electron tunneling through a vibrational modulated barrier in STM
Romnn Reports n Physcs, olume 55, Numer 4, P. 47 58, 3 Inelstc electron tunnelng through vrtonl modulted rrer n SM P. udu culty of Physcs, Unversty of uchrest, PO ox MG, Mgurele, Romn strct: Usng mny ody
GAUSS ELIMINATION. Consider the following system of algebraic linear equations
Numercl Anlyss for Engneers Germn Jordnn Unversty GAUSS ELIMINATION Consder the followng system of lgebrc lner equtons To solve the bove system usng clsscl methods, equton () s subtrcted from equton ()
Katholieke Universiteit Leuven Department of Computer Science
Updte Rules for Weghted Non-negtve FH*G Fctorzton Peter Peers Phlp Dutré Report CW 440, Aprl 006 Ktholeke Unverstet Leuven Deprtment of Computer Scence Celestjnenln 00A B-3001 Heverlee (Belgum) Updte Rules
Chapter Newton-Raphson Method of Solving a Nonlinear Equation
Chpter.4 Newton-Rphson Method of Solvng Nonlner Equton After redng ths chpter, you should be ble to:. derve the Newton-Rphson method formul,. develop the lgorthm of the Newton-Rphson method,. use the Newton-Rphson
SYMMETRY CONCEPT APPLIED IN MOLECULAR SPECTROSCOPY
SYMMETRY CONCEPT APPLED N MOLECULAR SPECTROSCOPY 1 D.O. DOROHO, C.E. HRETCANU, 3 M.C. CRASMAREANU 1 Fculty of Physcs, Al.. Cuz Unversty, ş, Romn Food Engneerng Fculty, Ştefn cel Mre Unversty, Sucev, Romn
The Number of Rows which Equal Certain Row
Interntonl Journl of Algebr, Vol 5, 011, no 30, 1481-1488 he Number of Rows whch Equl Certn Row Ahmd Hbl Deprtment of mthemtcs Fcult of Scences Dmscus unverst Dmscus, Sr hblhmd1@gmlcom Abstrct Let be X
Point Lattices: Bravais Lattices
Physics for Solid Stte Applictions Februry 18, 2004 Lecture 7: Periodic Structures (cont.) Outline Review 2D & 3D Periodic Crystl Structures: Mthemtics X-Ry Diffrction: Observing Reciprocl Spce Point Lttices:
CENTROID (AĞIRLIK MERKEZİ )
CENTOD (ĞLK MEKEZİ ) centrod s geometrcl concept rsng from prllel forces. Tus, onl prllel forces possess centrod. Centrod s tougt of s te pont were te wole wegt of pscl od or sstem of prtcles s lumped.
Physics 121 Sample Common Exam 2 Rev2 NOTE: ANSWERS ARE ON PAGE 7. Instructions:
Physcs 121 Smple Common Exm 2 Rev2 NOTE: ANSWERS ARE ON PAGE 7 Nme (Prnt): 4 Dgt ID: Secton: Instructons: Answer ll 27 multple choce questons. You my need to do some clculton. Answer ech queston on the
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,
Remember: Project Proposals are due April 11.
Bonformtcs ecture Notes Announcements Remember: Project Proposls re due Aprl. Clss 22 Aprl 4, 2002 A. Hdden Mrov Models. Defntons Emple - Consder the emple we tled bout n clss lst tme wth the cons. However,
Chapter Newton-Raphson Method of Solving a Nonlinear Equation
Chpter 0.04 Newton-Rphson Method o Solvng Nonlner Equton Ater redng ths chpter, you should be ble to:. derve the Newton-Rphson method ormul,. develop the lgorthm o the Newton-Rphson method,. use the Newton-Rphson
Torsion, Thermal Effects and Indeterminacy
ENDS Note Set 7 F007bn orson, herml Effects nd Indetermncy Deformton n orsonlly Loded Members Ax-symmetrc cross sectons subjected to xl moment or torque wll remn plne nd undstorted. At secton, nternl torque
Characteristics of Fiber Suspension Flow in a Turbulent Boundary Layer
Chrcterstcs of Fber Suspenson Flow n Turbulent Boundry Lyer Jnzhong Ln, Suhu Shen, Xoke Ku Deprtment of Mechncs Hngzhou, Zheng CHINA Correspondence to: Jnzhong Ln eml: meczln@publc.zu.edu.cn ABSTRACT The
Variable time amplitude amplification and quantum algorithms for linear algebra. Andris Ambainis University of Latvia
Vrble tme mpltude mplfcton nd quntum lgorthms for lner lgebr Andrs Ambns Unversty of Ltv Tlk outlne. ew verson of mpltude mplfcton;. Quntum lgorthm for testng f A s sngulr; 3. Quntum lgorthm for solvng
6. Chemical Potential and the Grand Partition Function
6. Chemcl Potentl nd the Grnd Prtton Functon ome Mth Fcts (see ppendx E for detls) If F() s n nlytc functon of stte vrles nd such tht df d pd then t follows: F F p lso snce F p F we cn conclude: p In other
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
International Journal of Pure and Applied Sciences and Technology
Int. J. Pure Appl. Sc. Technol., () (), pp. 44-49 Interntonl Journl of Pure nd Appled Scences nd Technolog ISSN 9-67 Avlle onlne t www.jopst.n Reserch Pper Numercl Soluton for Non-Lner Fredholm Integrl
Lesson 1: Quadratic Equations
Lesson 1: Qudrtic Equtions Qudrtic Eqution: The qudrtic eqution in form is. In this section, we will review 4 methods of qudrtic equtions, nd when it is most to use ech method. 1. 3.. 4. Method 1: Fctoring
Fundamental Theorem of Calculus
Fundmentl Theorem of Clculus Recll tht if f is nonnegtive nd continuous on [, ], then the re under its grph etween nd is the definite integrl A= f() d Now, for in the intervl [, ], let A() e the re under
13 Design of Revetments, Seawalls and Bulkheads Forces & Earth Pressures
13 Desgn of Revetments, Sewlls nd Bulkheds Forces & Erth ressures Ref: Shore rotecton Mnul, USACE, 1984 EM 1110--1614, Desgn of Revetments, Sewlls nd Bulkheds, USACE, 1995 Brekwters, Jettes, Bulkheds nd
Definition of Tracking
Trckng Defnton of Trckng Trckng: Generte some conclusons bout the moton of the scene, objects, or the cmer, gven sequence of mges. Knowng ths moton, predct where thngs re gong to project n the net mge,
LOCAL FRACTIONAL LAPLACE SERIES EXPANSION METHOD FOR DIFFUSION EQUATION ARISING IN FRACTAL HEAT TRANSFER
Yn, S.-P.: Locl Frctonl Lplce Seres Expnson Method for Dffuson THERMAL SCIENCE, Yer 25, Vol. 9, Suppl., pp. S3-S35 S3 LOCAL FRACTIONAL LAPLACE SERIES EXPANSION METHOD FOR DIFFUSION EQUATION ARISING IN
Applied Statistics Qualifier Examination
Appled Sttstcs Qulfer Exmnton Qul_june_8 Fll 8 Instructons: () The exmnton contns 4 Questons. You re to nswer 3 out of 4 of them. () You my use ny books nd clss notes tht you mght fnd helpful n solvng
Electrical double layer: revisit based on boundary conditions
Electrcal double layer: revst based on boundary condtons Jong U. Km Department of Electrcal and Computer Engneerng, Texas A&M Unversty College Staton, TX 77843-318, USA Abstract The electrcal double layer
Solubilities and Thermodynamic Properties of SO 2 in Ionic
Solubltes nd Therodync Propertes of SO n Ionc Lquds Men Jn, Yucu Hou, b Weze Wu, *, Shuhng Ren nd Shdong Tn, L Xo, nd Zhgng Le Stte Key Lbortory of Checl Resource Engneerng, Beng Unversty of Checl Technology,
Department of Electrical and Computer Engineering, Cornell University. ECE 4070: Physics of Semiconductors and Nanostructures.
Deprtment of Electricl nd Computer Engineering, Cornell University ECE 4070: Physics of Semiconductors nd Nnostructures Spring 2014 Exm 2 ` April 17, 2014 INSTRUCTIONS: Every problem must be done in the
Acoustooptic Cell Array (AOCA) System for DWDM Application in Optical Communication
596 Acoustooptc Cell Arry (AOCA) System for DWDM Applcto Optcl Commucto ml S. Rwt*, Mocef. Tyh, Sumth R. Ktkur d Vdy Nll Deprtmet of Electrcl Egeerg Uversty of Nevd, Reo, NV 89557, U.S.A. Tel: -775-78-57;
Bridging the gap: GCSE AS Level
Bridging the gp: GCSE AS Level CONTENTS Chpter Removing rckets pge Chpter Liner equtions Chpter Simultneous equtions 8 Chpter Fctors 0 Chpter Chnge the suject of the formul Chpter 6 Solving qudrtic equtions
NUMERICAL MODELLING OF A CILIUM USING AN INTEGRAL EQUATION
NUEICAL ODELLING OF A CILIU USING AN INTEGAL EQUATION IHAI EBICAN, DANIEL IOAN Key words: Cl, Numercl nlyss, Electromgnetc feld, gnetton. The pper presents fst nd ccurte method to model the mgnetc behvour
Two ways of understanding electronic structure in solids:
Bnd structure from the top down Two wys of understndng electronc structure n solds: Top-down - strt from free electron gs nd mpose correctons for ctully hvng on cores nd crystl lttce: nerly-free electron
An Ising model on 2-D image
School o Coputer Scence Approte Inerence: Loopy Bele Propgton nd vrnts Prolstc Grphcl Models 0-708 Lecture 4, ov 7, 007 Receptor A Knse C Gene G Receptor B Knse D Knse E 3 4 5 TF F 6 Gene H 7 8 Hetunndn
Chapter 1: Logarithmic functions and indices
Chpter : Logrithmic functions nd indices. You cn simplify epressions y using rules of indices m n m n m n m n ( m ) n mn m m m m n m m n Emple Simplify these epressions: 5 r r c 4 4 d 6 5 e ( ) f ( ) 4
Convergence of Fourier Series and Fejer s Theorem. Lee Ricketson
Convergence of Fourier Series nd Fejer s Theorem Lee Ricketson My, 006 Abstrct This pper will ddress the Fourier Series of functions with rbitrry period. We will derive forms of the Dirichlet nd Fejer
COMPOSITE BEAM WITH WEAK SHEAR CONNECTION SUBJECTED TO THERMAL LOAD
COMPOSITE BEAM WITH WEAK SHEAR CONNECTION SUBJECTED TO THERMAL LOAD Ákos Jósef Lengyel, István Ecsed Assstant Lecturer, Professor of Mechancs, Insttute of Appled Mechancs, Unversty of Mskolc, Mskolc-Egyetemváros,
Research Article On the Upper Bounds of Eigenvalues for a Class of Systems of Ordinary Differential Equations with Higher Order
Hndw Publshng Corporton Interntonl Journl of Dfferentl Equtons Volume 0, Artcle ID 7703, pges do:055/0/7703 Reserch Artcle On the Upper Bounds of Egenvlues for Clss of Systems of Ordnry Dfferentl Equtons
Copyright 2017 by Taylor Enterprises, Inc., All Rights Reserved. Adjusted Control Limits for P Charts. Dr. Wayne A. Taylor
Taylor Enterprses, Inc. Control Lmts for P Charts Copyrght 2017 by Taylor Enterprses, Inc., All Rghts Reserved. Control Lmts for P Charts Dr. Wayne A. Taylor Abstract: P charts are used for count data
6 Roots of Equations: Open Methods
HK Km Slghtly modfed 3//9, /8/6 Frstly wrtten t Mrch 5 6 Roots of Equtons: Open Methods Smple Fed-Pont Iterton Newton-Rphson Secnt Methods MATLAB Functon: fzero Polynomls Cse Study: Ppe Frcton Brcketng
Engineering Tensors. Friday November 16, h30 -Muddy Charles. A BEH430 review session by Thomas Gervais.
ngneerng Tensors References: BH4 reew sesson b Thoms Gers tgers@mt.ed Long, RR, Mechncs of Solds nd lds, Prentce-Hll, 96, pp - Deen, WD, nlss of trnsport phenomen, Oford, 998, p. 55-56 Goodbod, M, Crtesn
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
Calculus 2: Integration. Differentiation. Integration
Clculus 2: Integrtion The reverse process to differentition is known s integrtion. Differentition f() f () Integrtion As it is the opposite of finding the derivtive, the function obtined b integrtion is
? plate in A G in
Proble (0 ponts): The plstc block shon s bonded to rgd support nd to vertcl plte to hch 0 kp lod P s ppled. Knong tht for the plstc used G = 50 ks, deterne the deflecton of the plte. Gven: G 50 ks, P 0
References: 1. Introduction to Solid State Physics, Kittel 2. Solid State Physics, Ashcroft and Mermin
Lecture 12 Bn Gp Toy: 1. Seres solutons to the cosne potentl Hmltonn. 2. Dervton of the bngrms the grphcl representton of sngle electron solutons 3. Anlytcl expresson for bngps Questons you shoul be ble
Math 1431 Section M TH 4:00 PM 6:00 PM Susan Wheeler Office Hours: Wed 6:00 7:00 PM Online ***NOTE LABS ARE MON AND WED
Mth 43 Section 4839 M TH 4: PM 6: PM Susn Wheeler swheeler@mth.uh.edu Office Hours: Wed 6: 7: PM Online ***NOTE LABS ARE MON AND WED t :3 PM to 3: pm ONLINE Approimting the re under curve given the type
COMPLEX NUMBER & QUADRATIC EQUATION
MCQ COMPLEX NUMBER & QUADRATIC EQUATION Syllus : Comple numers s ordered prs of rels, Representton of comple numers n the form + nd ther representton n plne, Argnd dgrm, lger of comple numers, modulus
INTRODUCTION TO COMPLEX NUMBERS
INTRODUCTION TO COMPLEX NUMBERS The numers -4, -3, -, -1, 0, 1,, 3, 4 represent the negtve nd postve rel numers termed ntegers. As one frst lerns n mddle school they cn e thought of s unt dstnce spced
Haddow s Experiment:
schemtc drwng of Hddow's expermentl set-up movng pston non-contctng moton sensor bems of sprng steel poston vres to djust frequences blocks of sold steel shker Hddow s Experment: terr frm Theoretcl nd
( ) 2. ( ) is the Fourier transform of! ( x). ( ) ( ) ( ) = Ae i kx"#t ( ) = 1 2" ( )"( x,t) PC 3101 Quantum Mechanics Section 1
1. 1D Schrödinger Eqution G chpters 3-4. 1.1 the Free Prticle V 0 "( x,t) i = 2 t 2m x,t = Ae i kxt "( x,t) x 2 where = k 2 2m. Normliztion must hppen: 2 x,t = 1 Here, however: " A 2 dx " " As this integrl
QUB XRD Course. The crystalline state. The Crystalline State
QUB XRD Course Introduction to Crystllogrphy 1 The crystlline stte Mtter Gseous Stte Solid stte Liquid Stte Amorphous (disordered) Crystlline (ordered) 2 The Crystlline Stte A crystl is constructed by
Lesson 2. Thermomechanical Measurements for Energy Systems (MENR) Measurements for Mechanical Systems and Production (MMER)
Lesson 2 Thermomechncl Mesurements for Energy Systems (MEN) Mesurements for Mechncl Systems nd Producton (MME) 1 A.Y. 2015-16 Zccr (no ) Del Prete A U The property A s clled: «mesurnd» the reference property
PHYS Summer Professor Caillault Homework Solutions. Chapter 2
PHYS 1111 - Summer 2007 - Professor Cillult Homework Solutions Chpter 2 5. Picture the Problem: The runner moves long the ovl trck. Strtegy: The distnce is the totl length of trvel, nd the displcement
A Family of Multivariate Abel Series Distributions. of Order k
Appled Mthemtcl Scences, Vol. 2, 2008, no. 45, 2239-2246 A Fmly of Multvrte Abel Seres Dstrbutons of Order k Rupk Gupt & Kshore K. Ds 2 Fculty of Scence & Technology, The Icf Unversty, Agrtl, Trpur, Ind
HW3, Math 307. CSUF. Spring 2007.
HW, Mth 7. CSUF. Spring 7. Nsser M. Abbsi Spring 7 Compiled on November 5, 8 t 8:8m public Contents Section.6, problem Section.6, problem Section.6, problem 5 Section.6, problem 7 6 5 Section.6, problem
EXTINCTION COEFFICIENT USED AS PARAMETER IN GAMMA-RAY DOSIMETRY
EXTINCTION COEFFICIENT USE AS PARAMETER IN GAMMA-RAY OSIMETRY C. POSTOLACHE Hor Hulue Ntonl Insttute for Nucler Physcs nd Engneerng, P.O. Box MG-6, RO-07715 Buchrest-Mgurele, Romn E-ml: crstp@npne.ro Receved
SUMMER KNOWHOW STUDY AND LEARNING CENTRE
SUMMER KNOWHOW STUDY AND LEARNING CENTRE Indices & Logrithms 2 Contents Indices.2 Frctionl Indices.4 Logrithms 6 Exponentil equtions. Simplifying Surds 13 Opertions on Surds..16 Scientific Nottion..18
Lecture 36. Finite Element Methods
CE 60: Numercl Methods Lecture 36 Fnte Element Methods Course Coordntor: Dr. Suresh A. Krth, Assocte Professor, Deprtment of Cvl Engneerng, IIT Guwht. In the lst clss, we dscussed on the ppromte methods
Linear Inequalities: Each of the following carries five marks each: 1. Solve the system of equations graphically.
Liner Inequlities: Ech of the following crries five mrks ech:. Solve the system of equtions grphiclly. x + 2y 8, 2x + y 8, x 0, y 0 Solution: Considerx + 2y 8.. () Drw the grph for x + 2y = 8 by line.it
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
ARITHMETIC OPERATIONS. The real numbers have the following properties: a b c ab ac
REVIEW OF ALGEBRA Here we review the bsic rules nd procedures of lgebr tht you need to know in order to be successful in clculus. ARITHMETIC OPERATIONS The rel numbers hve the following properties: b b
consider in the case of 1) internal resonance ω 2ω and 2) external resonance Ω ω and small damping
consder n the cse o nternl resonnce nd externl resonnce Ω nd smll dmpng recll rom "Two_Degs_Frdm_.ppt" tht θ + μ θ + θ = θφ + cos Ω t + τ where = k α α nd φ + μ φ + φ = θ + cos Ω t where = α τ s constnt
Kai Sun. University of Michigan, Ann Arbor
Ki Sun University of Michign, Ann Arbor How to see toms in solid? For conductors, we cn utilize scnning tunneling microscope (STM) to see toms (Nobel Prize in Physics in 1986) Limittions: (1) conductors
DYNAMIC PROPAGATION OF A WEAK-DISCONTINUOUS INTERFACE CRACK IN FUNCTIONALLY GRADED LAYERS UNDER ANTI-PLANE SHEAR
8 TH INTERNTIONL CONFERENCE ON COMPOSITE MTERILS DYNMIC PROPGTION OF WEK-DISCONTINUOUS INTERFCE CRCK IN FUNCTIONLLY GRDED LYERS UNDER NTI-PLNE SHER J.W. Sn *, Y.S. Lee, S.C. Km, I.H. Hwng 3 Subsystem Deprtment,
Computing a complete histogram of an image in Log(n) steps and minimum expected memory requirements using hypercubes
Computng complete hstogrm of n mge n Log(n) steps nd mnmum expected memory requrements usng hypercubes TAREK M. SOBH School of Engneerng, Unversty of Brdgeport, Connectcut, USA. Abstrct Ths work frst revews
INTRODUCTION TO LINEAR ALGEBRA
ME Applied Mthemtics for Mechnicl Engineers INTRODUCTION TO INEAR AGEBRA Mtrices nd Vectors Prof. Dr. Bülent E. Pltin Spring Sections & / ME Applied Mthemtics for Mechnicl Engineers INTRODUCTION TO INEAR
Dennis Bricker, 2001 Dept of Industrial Engineering The University of Iowa. MDP: Taxi page 1
Denns Brcker, 2001 Dept of Industrl Engneerng The Unversty of Iow MDP: Tx pge 1 A tx serves three djcent towns: A, B, nd C. Ech tme the tx dschrges pssenger, the drver must choose from three possble ctons:
A Theoretical Study on the Rank of the Integral Operators for Large- Scale Electrodynamic Analysis
Purdue Unversty Purdue e-pubs ECE Techncl Reports Electrcl nd Computer Engneerng -22-2 A Theoretcl Study on the Rnk of the Integrl Opertors for Lrge- Scle Electrodynmc Anlyss Wenwen Ch Purdue Unversty,
Jack Simons, Henry Eyring Scientist and Professor Chemistry Department University of Utah
1. Born-Oppenheimer pprox.- energy surfces 2. Men-field (Hrtree-Fock) theory- orbitls 3. Pros nd cons of HF- RHF, UHF 4. Beyond HF- why? 5. First, one usully does HF-how? 6. Bsis sets nd nottions 7. MPn,
Read section 3.3, 3.4 Announcements:
Dte: 3/1/13 Objective: SWBAT pply properties of exponentil functions nd will pply properties of rithms. Bell Ringer: 1. f x = 3x 6, find the inverse, f 1 x., Using your grphing clcultor, Grph 1. f x,f
4.4 Areas, Integrals and Antiderivatives
. res, integrls nd ntiderivtives 333. Ares, Integrls nd Antiderivtives This section explores properties of functions defined s res nd exmines some connections mong res, integrls nd ntiderivtives. In order
Physics 5153 Classical Mechanics. Principle of Virtual Work-1
P. Guterrez 1 Introducton Physcs 5153 Classcal Mechancs Prncple of Vrtual Work The frst varatonal prncple we encounter n mechancs s the prncple of vrtual work. It establshes the equlbrum condton of a mechancal
Linear and Nonlinear Optimization
Lner nd Nonlner Optmzton Ynyu Ye Deprtment of Mngement Scence nd Engneerng Stnford Unversty Stnford, CA 9430, U.S.A. http://www.stnford.edu/~yyye http://www.stnford.edu/clss/msnde/ Ynyu Ye, Stnford, MS&E
Lecture 5 Single factor design and analysis
Lectue 5 Sngle fcto desgn nd nlss Completel ndomzed desgn (CRD Completel ndomzed desgn In the desgn of expements, completel ndomzed desgns e fo studng the effects of one pm fcto wthout the need to tke
523 P a g e. is measured through p. should be slower for lesser values of p and faster for greater values of p. If we set p*
R. Smpth Kumr, R. Kruthk, R. Rdhkrshnn / Interntonl Journl of Engneerng Reserch nd Applctons (IJERA) ISSN: 48-96 www.jer.com Vol., Issue 4, July-August 0, pp.5-58 Constructon Of Mxed Smplng Plns Indexed
Identification of Robot Arm s Joints Time-Varying Stiffness Under Loads
TELKOMNIKA, Vol.10, No.8, December 2012, pp. 2081~2087 e-issn: 2087-278X ccredted by DGHE (DIKTI), Decree No: 51/Dkt/Kep/2010 2081 Identfcton of Robot Arm s Jonts Tme-Vryng Stffness Under Lods Ru Xu 1,
4 7x =250; 5 3x =500; Read section 3.3, 3.4 Announcements: Bell Ringer: Use your calculator to solve
Dte: 3/14/13 Objective: SWBAT pply properties of exponentil functions nd will pply properties of rithms. Bell Ringer: Use your clcultor to solve 4 7x =250; 5 3x =500; HW Requests: Properties of Log Equtions
Properties of the Riemann Integral
Properties of the Riemnn Integrl Jmes K. Peterson Deprtment of Biologicl Sciences nd Deprtment of Mthemticl Sciences Clemson University Februry 15, 2018 Outline 1 Some Infimum nd Supremum Properties 2
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
ACCESS TO SCIENCE, ENGINEERING AND AGRICULTURE: MATHEMATICS 1 MATH00030 SEMESTER /2019
ACCESS TO SCIENCE, ENGINEERING AND AGRICULTURE: MATHEMATICS MATH00030 SEMESTER 208/209 DR. ANTHONY BROWN 7.. Introduction to Integrtion. 7. Integrl Clculus As ws the cse with the chpter on differentil