FIRST ORDER REVERSAL CURVES AND HYSTERESIS LOOPS OF FERROELECTRIC FILMS DESCRIBED BY PHENOMENOLOGICAL MODELS
|
|
- Reynard Wilson
- 5 years ago
- Views:
Transcription
1 Jounl of Optoelectonics d Advced Mteils Vol. 6, No. 3, Septeme 2004, p FIRST ORDER REVERSAL CURVES AND HYSTERESIS LOOPS OF FERROELECTRIC FILMS DESCRIBED BY PHENOMENOLOGICAL MODELS M. Feciou-Moiu *, D. Ricinschi, P. Postolche, C. E. Ciomg, A. Stcu, L. Mitoseiu,c Dept. of Electicity, Al. I. Cuz Univesity, Isi , Romi Gdute School of Eng. Science, Osk Univesity, Toyonk, Osk , Jp c Dept. of Chem. of Pocess Eng. DICheP, Univesity of Geno, I-16129, Itly The incesing pts of the non-symmetic P(E) hysteesis loops of PZT feoelectic films (Fist Ode Revesl Cuves - FORC), wee used in ode to clculte the FORC distiution in which seption of the evesile d ievesile contiutions to the poliztion ws otined. The ole of the fequency of the pplied field on the switching popeties of the feoelectic films wee lyzed y this method. A phenomenologicl model ws used to descie the P(E) hysteesis loops. Using the model pmetes detemined fom the fit of P(E) mjo loops, mino loops d the FORCs wee simulted, t vious fequencies d mplitudes of the pplied field. The clculted FORC digm ws comped with the expeimentl one d the limits of the model wee discussed. (Received Apil 19, 2004; ccepted June 22, 2004) Keywods: Feoelectic switching, Fist ode evesl cuves, Phenomenologicl model 1. Intoduction The method of investigtion of hysteetic systems y mes of Fist Ode Revesl Cuves (FORC) digms initilly poposed fo geologicl feomgnetic systems d ltely fo ecoding medi, spin glsses d feofluids [1-3] ws ecently pplied fo feoelectic films [4-5]. The method involves the mesuement of mino hysteesis loops otined y cycling the smple etween stution d vile evesl field. Being sensitive to vious pmetes, including chcteistics of the feoelectic system ut lso chcteistics of the field histoy d chcteistics, the expeimentl FORC digms contin ich infomtion. In ode to disclose the infomtion contined in these digms, modelling tools e used d the ole of the model pmetes on the FORC digms e septely investigted [6-8]. Vious techniques hve een employed fo desciing the hysteetic ehviou of feoelectics [9-11]. Among them, the semimcoscopic theoies comining the phenomenologicl ppoch with enegy eltions give esonle esults d hve smll nume of effective model pmetes. The phenomenologicl ppoch initilly poposed fo soft mgnetic mteils y Jiles d Atheton [12] ws successfully pplied fo desciing the hysteesis loops of PMN feoelectic elxos [13]. In this ppe, the expeimentl FORC digms otined fo P(Z,Ti)O 3 (PZT) thin films e comped with the ones simulted on the sis of the phenomenologicl model of Jiles-Atheton, with the ppoximtion of Dee [14]. An intepettion of the mechisms involved in the oseved pttens is poposed. 2. Expeiment d definition of the FORC digms P(Z,Ti)O 3 (PZT) films otined y Rf - sputteing technique hving Pt electodes wee used fo expeiments [15]. Single pulse hysteesis mesuements in 500Hz tigul signl with * Coesponding utho: mfeciou@stone.phys.uic.o
2 1060 M. Feciou Moiu, D. Ricinschi, P. Postolche, C. E. Ciomg, A. Stcu, L. Mitoseiu 10V mximum mplitude hve een pefomed using FCE feoelectic teste (Toyotechnic) ccoding to the sequence: (i) stution unde positive field E Est =400kV/cm; (ii) mping the field down to evesl vlue E, when the poliztion follows the descending ch of the Mjo Hysteesis Loop (MHL); (iii) incesing the field ck to the positive stution, when the poliztion is function of oth the ctul field E d of the evesl field E [4-5]. The FORC fmily stting on the descending MHL ch is denoted s p (E,E), similly, the FORCs + pforc (E,E) c e otined using the scending ch of the MHL [4]. The FORC digm epesents contou plot of the FORC distiution, defined s the mixed second deivtive of poliztion with espect to E d E [2]: 2 FORC [ χ (E,E)] 1 pforc (E,E) 1 ρ ( E,E) = = FORC, (1) 2 E E 2 E in which χ E, E) e the diffeentil susceptiilities mesued long the FORCs. The FORC ( ( E, E distiution ρ ) desciing the vition of poliztion with espect to chges in oth the evesl field E d the ctul electic field E d it ws detemined using the numeicl method poposed in [2]. By chging the coodintes of the FORC distiution fom (E,E) to {E c =(E-E )/2, E i =(E+E )/2}, whee E c d E i ply the ole of locl coecive d intection field espectively, ρ E,E ) ecomes identicl with the Peisch distiution [16] fo systems stisfying the clssicl ( c i Peisch model conditions [17]. The expeimentl FORC digms otined fo PZT film t the fequencies f = 5 Hz d f = 500 Hz e pesented in Fig. 1 (-). They clely show evesile d ievesile components with mximum t E M =-0.3E mx, E M =0.1E mx which hs the meing of the fields fo the highest nume of switchle units cusing the min contiution to the poliztion. An symmety of the of the ievesile FORC long E M =0.2E mx ws explined s due to selfpolizing effect in the film [4-5]. A highe speding d diffusion of the ievesile pt of the FORC distiution is found fo highe fequency togethe with incesing of the evesile component. The position of the mximum of the ievesile pt is slightly shifted towds highe fields fo f = 500 Hz. In the pesent ppe, the est fit pmetes of the phenomenologicl model Jiles-Atheton [12], with the ppoximtion of Dee wee used fo simulting the FORC poliztion d FORC digms t the two fequencies. Nomlized E /E mx 2E-8 1.9E-8 1.6E-8 1.3E-8 9.7E-9 6.8E-9 3.9E-9 Nomlized E /E mx 1.4E-8 1.3E-8 1.1E-8 8.7E-9 6.5E-9 4.4E-9 2.3E-9 1.3E-1-2E-9-9.3E-10-2E-9 - Fig. 1. Expeimentl FORC digms of PZT films t fequencies: () 5 Hz d () 500 Hz. 3. Theoy In the Jiles-Atheton ppoch [12] the P(E) hysteesis loops ws modeled in two steps [12]. Fistly, the idel hysteetic poliztion is clculted y consideing clssicl Boltzmn sttistics fo the poility of dipoles to occupy specific enegy sttes. The hysteetic effect is lte
3 Fist ode evesl cuves d hysteesis loops of feoelectic films 1061 dded y consideing the devitions fom the hysteetic stte due to the estiction of domin wll movement y pinning sites in the feoelectic. In the pesence of scling poliztion P 1, the ssumption tht dipoles c oient in y diection yields the Lgevin fomul: P E e = P1 + PS coth (2) Ee whee P S is the stution poliztion, is constt d E e is the effective field consideed s: E e ( E E ) + ( P ) = α (3) 0 P 0 in which αp qutifies the field contiutions due to the intedomin coupling d stess effects d (E 0, P 0 ) e the is field d espective poliztion consideed to ccount fo the symmeties of the hysteesis loops. The hysteesis cuve P(E) is otined y including the evesile P ev d ievesile poliztion P iev esulting fom the tsltion d ending of domin wlls pinned t the inclusions of mteil: iev de = P ~ δ iev (4) kδ α P ( P P ) iev whee, within the ppoximtion poposed y Dee [14]: { de > 0 d P > P } o { de < 0 d P P } ~ 1, < δ = (5) 0, othewise. The pmete k qutifies the vege enegy equied to eoient the domins d it is ssimptoticlly ppoximted y the coecive field in the soft mteils. In ou simultions, k pmete ws chosen s Gussi function of the vlues of the electic field. The totl poliztion is thus: P P ev + P iev =, in which: P c( P P ) ev = (6) iev The finl eqution of Jiles-Atheton model used y us in ou simultion ws: de ~ = δ δk ( 1 c)( P P) + c ( 1 c) α( P P) de (7) whee = 1 on the scendent d = -1 on the descendt ch of the hysteesis loop. 4. Results d discussion The expeimentl MHL loops of PZT films t the two fequencies hve een fistly fitted with the pesent model. A good fit ws otined fo f=500hz (Fig. 2 ) d esonle one fo f=5hz (Fig. 2 ), due to the spce chge effects lteing the switching poliztion d mifesting in the mesued P(E) loops minly t low-fequency.
4 1062 M. Feciou Moiu, D. Ricinschi, P. Postolche, C. E. Ciomg, A. Stcu, L. Mitoseiu - - simulted dt expeimentl dt Electic Field (kv/cm) simulted dt expeimentl dt Electic Field (kv/cm) - - Electic Field (kv/cm) c Electic Field (kv/cm) d Fig. 2. Expeimentl, est-fit MHL t () 5 Hz d () 500 Hz fequency of electic field d computed FORCs on the sis of phenomenologicl model t: (c) 5 Hz d (d) 500 Hz. Using the est fit vlues detemined fom the MHL, the FORCs wee simulted (Fig. 2 c, d). The computed FORC digms (Fig. 3, ). show simil ehviou with the expeimentl ones: evesile component with mximum t E=0 d ievesile pt locted t the sme field vlues s the expeimentl ones. The model is lso le to descie the symmety of the FORC digms long the E xis which peviously ws consideed s coming fom the pefeentil poliztion of the switching units locted t the ottom electode film intefce which c esily switch in one diection, ut they need highe d distiuted fields fo switching in the opposite one [4]. This effect, ecently found in ulk mteils d descied within Ldu models seems to e moe elted to intinsic chcteistics of the switchle system th to intefce effect [18]. The model is lso le to descie the effect of incesing fequency on the FORCs cusing shift of the mximum towds highe fields d speding of the distiution. Due to the fct tht the switchle dipoles e not le to follow the fst vition of the pplied fields t highe fequency, ppent highe coecivity is found in the simulted FORCs, like in the expeimentl digms (Fig. 1 ) Nomlized E /E mx Nomlized E /E mx Fig. 3. FORC digms computed on the sis of the phenomenologicl model t () 5 Hz d () 500 Hz.
5 Fist ode evesl cuves d hysteesis loops of feoelectic films Conclusions The expeimentl FORC distiution otined fo PZT films t diffeent fequencies wee comped with ones computed on the sis of phenomenologicl model. The Jiles-Atheton theoy in the vesion poposed y De ws used fo the fitting of the MHL. Using the est vlues fits, the FORCs wee simulted. The computed FORC digms show simil ehvio with the expeimentl ones. The model is le to descie coectly the evesile d ievesile components on the P(E) loops, the symmety of the FORC digms long the E xis d the effect of incesing fequency on the FORC digms. Refeences [1] I. Myegoyz, Mthemticl Models of Hysteesis, Spinge, New Yok, [2] C. R. Pike, A. P. Roets, K. L. Veosu, J. Appl. Phys. 85, 6640 (1999); Geophys. J. Int. 145, 721 (2001). [3] H. G. Ktzge, F. Pzmdi, C. R. Pike, K. Liu, R. T. Sclett, K. L. Veosu, G. T. Zimyi, Phys. Rev. Lett. 89, (2002). [4] A. Stcu, D. Ricinschi, L. Mitoseiu, P. Postolche, M. Okuym, Appl. Phys. Lett. 83, 3767 (2003). [5] D. Ricinschi, A. Stcu, L. Mitoseiu, P. Postolche d M. Okuym, J. Optoelecton. Adv. Mte. (to e pulished). [6] C. R. Pike, A. P. Roets, M. J. Dekkes, K. L. Veosu, Phys. Eth d Plety Inteios 126, 11 (2001). [7] A. Stcu, C. Pike, L. Stoleiu, P. Postolche, D. Cimpoesu, J. Appl. Phys. 93, 6620 (2003) [8] C. Enchescu, PhD Thesis, Univ. of Vesilles, Fce, (2003). [9] I. W. Chen, Y. Wg, Feoelectics 206, 245 (1998). [10] W. Chen, C. S. Lynch, J. Int. Mte. Systems d Stuctues 9, 427 (1998). [11] P. Ge, M. Joueh, Pecision Eng. 17, 211 (1995). [12] D. C. Jiles, D. L. Atheton, J. Mgn. Mgn. Mte. 61, 48 (1986). [13] R. C. Smith, C. L. Hom, SPIE Vol. 3667, Newpot Bech, CA, Mch 1-4, 150 (1999). [14] J. H. B.Dee, IEEE Ts. Mgn. 30, 5 (1994). [15] D. Ricinschi, M. Okuym, Appl. Phys. Lett. 81, 4040 (2002); Integ. Feoel. 50, 149 (2002). [16] F. Peisch, Z. Phys. 94, 277 (1935). [17] A. Stcu, C. Pike, L. Stoleiu, P. Postolche, D. Cimpoesu, J. Appl. Phys. 93, 6620 (2003) [18] D. Ricinschi, L. Mitoseiu, A. Stcu, P. Postolche, M. Okuym, The 16 th Intentionl Symposium of Integ. Feoel. ISIF 2004, 5-8 Ap. 2004, Koe.
3.1 Magnetic Fields. Oersted and Ampere
3.1 Mgnetic Fields Oested nd Ampee The definition of mgnetic induction, B Fields of smll loop (dipole) Mgnetic fields in mtte: ) feomgnetism ) mgnetiztion, (M ) c) mgnetic susceptiility, m d) mgnetic field,
More informationFourier-Bessel Expansions with Arbitrary Radial Boundaries
Applied Mthemtics,,, - doi:./m.. Pulished Online My (http://www.scirp.og/jounl/m) Astct Fouie-Bessel Expnsions with Aity Rdil Boundies Muhmmd A. Mushef P. O. Box, Jeddh, Sudi Ai E-mil: mmushef@yhoo.co.uk
More information( ) D x ( s) if r s (3) ( ) (6) ( r) = d dr D x
SIO 22B, Rudnick dpted fom Dvis III. Single vile sttistics The next few lectues e intended s eview of fundmentl sttistics. The gol is to hve us ll speking the sme lnguge s we move to moe dvnced topics.
More informationDiscrete Model Parametrization
Poceedings of Intentionl cientific Confeence of FME ession 4: Automtion Contol nd Applied Infomtics Ppe 9 Discete Model Pmetition NOKIEVIČ, Pet Doc,Ing,Cc Deptment of Contol ystems nd Instumenttion, Fculty
More informationPhysics 505 Fall 2005 Midterm Solutions. This midterm is a two hour open book, open notes exam. Do all three problems.
Physics 55 Fll 5 Midtem Solutions This midtem is two hou open ook, open notes exm. Do ll thee polems. [35 pts] 1. A ectngul ox hs sides of lengths, nd c z x c [1] ) Fo the Diichlet polem in the inteio
More informationAvailable online at ScienceDirect. Procedia Engineering 91 (2014 ) 32 36
Aville online t wwwsciencediectcom ScienceDiect Pocedi Engineeing 91 (014 ) 3 36 XXIII R-S-P semin Theoeticl Foundtion of Civil Engineeing (3RSP) (TFoCE 014) Stess Stte of Rdil Inhomogeneous Semi Sphee
More informationOn the Eötvös effect
On the Eötvös effect Mugu B. Răuţ The im of this ppe is to popose new theoy bout the Eötvös effect. We develop mthemticl model which loud us bette undestnding of this effect. Fom the eqution of motion
More informationSchool of Electrical and Computer Engineering, Cornell University. ECE 303: Electromagnetic Fields and Waves. Fall 2007
School of Electicl nd Compute Engineeing, Conell Univesity ECE 303: Electomgnetic Fields nd Wves Fll 007 Homewok 3 Due on Sep. 14, 007 by 5:00 PM Reding Assignments: i) Review the lectue notes. ii) Relevnt
More informationU>, and is negative. Electric Potential Energy
Electic Potentil Enegy Think of gvittionl potentil enegy. When the lock is moved veticlly up ginst gvity, the gvittionl foce does negtive wok (you do positive wok), nd the potentil enegy (U) inceses. When
More informationStudy of Electromagnetic Wave Propagation in Periodic Dielectric Structure; MathCAD Analysis
Communictions in Applied Sciences ISSN -737 Volume Nume 3-9 Stud of lectomgnetic Wve Popgtion in Peiodic Dielectic Stuctue; MthCAD Anlsis Ugwu mmnuel.i Ieogu C. nd chi M.I Deptment of Industil phsics oni
More informationQualitative Analysis for Solutions of a Class of. Nonlinear Ordinary Differential Equations
Adv. Theo. Appl. Mech., Vol. 7, 2014, no. 1, 1-7 HIKARI Ltd, www.m-hiki.com http://dx.doi.og/10.12988/tm.2014.458 Qulittive Anlysis fo Solutions of Clss of Nonline Odiny Diffeentil Equtions Juxin Li *,
More informationChapter 7. Kleene s Theorem. 7.1 Kleene s Theorem. The following theorem is the most important and fundamental result in the theory of FA s:
Chpte 7 Kleene s Theoem 7.1 Kleene s Theoem The following theoem is the most impotnt nd fundmentl esult in the theoy of FA s: Theoem 6 Any lnguge tht cn e defined y eithe egul expession, o finite utomt,
More informationSchool of Electrical and Computer Engineering, Cornell University. ECE 303: Electromagnetic Fields and Waves. Fall 2007
School of Electicl nd Compute Engineeing, Conell Univesity ECE 303: Electomgnetic Fields nd Wves Fll 007 Homewok 4 Due on Sep. 1, 007 by 5:00 PM Reding Assignments: i) Review the lectue notes. ii) Relevnt
More information10 Statistical Distributions Solutions
Communictions Engineeing MSc - Peliminy Reding 1 Sttisticl Distiutions Solutions 1) Pove tht the vince of unifom distiution with minimum vlue nd mximum vlue ( is ) 1. The vince is the men of the sques
More informationImportant design issues and engineering applications of SDOF system Frequency response Functions
Impotnt design issues nd engineeing pplictions of SDOF system Fequency esponse Functions The following desciptions show typicl questions elted to the design nd dynmic pefomnce of second-ode mechnicl system
More informationIntegrals and Polygamma Representations for Binomial Sums
3 47 6 3 Jounl of Intege Sequences, Vol. 3 (, Aticle..8 Integls nd Polygmm Repesenttions fo Binomil Sums Anthony Sofo School of Engineeing nd Science Victoi Univesity PO Box 448 Melboune City, VIC 8 Austli
More informationInfluence of Hydraulic Hysteresis on Effective Stress in Unsaturated Clay
Intentionl Jounl of Envionmentl nd Eth Sciences 1:1 21 Influence of Hydulic Hysteesis on Effective Stess in Unstuted Cly Anuchit Uchipicht Abstct A compehensive pogm of lbotoy testing on compcted kolin
More informationMichael Rotkowitz 1,2
Novembe 23, 2006 edited Line Contolles e Unifomly Optiml fo the Witsenhusen Counteexmple Michel Rotkowitz 1,2 IEEE Confeence on Decision nd Contol, 2006 Abstct In 1968, Witsenhusen intoduced his celebted
More informationPhysics 604 Problem Set 1 Due Sept 16, 2010
Physics 64 Polem et 1 Due ept 16 1 1) ) Inside good conducto the electic field is eo (electons in the conducto ecuse they e fee to move move in wy to cncel ny electic field impessed on the conducto inside
More informationPreviously. Extensions to backstepping controller designs. Tracking using backstepping Suppose we consider the general system
436-459 Advnced contol nd utomtion Extensions to bckstepping contolle designs Tcking Obseves (nonline dmping) Peviously Lst lectue we looked t designing nonline contolles using the bckstepping technique
More information4.2 Boussinesq s Theory. Contents
00477 Pvement Stuctue 4. Stesses in Flexible vement Contents 4. Intoductions to concet of stess nd stin in continuum mechnics 4. Boussinesq s Theoy 4. Bumiste s Theoy 4.4 Thee Lye System Weekset Sung Chte
More informationElastic limit angular speed of solid and annular disks under thermomechanical
MultiCft Intentionl Jounl of Engineeing, Science nd Technology Vol. 8, No., 016, pp. 30-45 INTERNATIONAL JOURNAL OF ENGINEERING, SCIENCE AND TECHNOLOGY www.ijest-ng.com www.jol.info/index.php/ijest 016
More informationFriedmannien equations
..6 Fiedmnnien equtions FLRW metic is : ds c The metic intevl is: dt ( t) d ( ) hee f ( ) is function which detemines globl geometic l popety of D spce. f d sin d One cn put it in the Einstein equtions
More informationElectronic Supplementary Material
Electonic Supplementy Mteil On the coevolution of socil esponsiveness nd behvioul consistency Mx Wolf, G Snde vn Doon & Fnz J Weissing Poc R Soc B 78, 440-448; 0 Bsic set-up of the model Conside the model
More informationdx was area under f ( x ) if ( ) 0
13. Line Integls Line integls e simil to single integl, f ( x) dx ws e unde f ( x ) if ( ) 0 Insted of integting ove n intevl [, ] (, ) f xy ds f x., we integte ove cuve, (in the xy-plne). **Figue - get
More informationFI 2201 Electromagnetism
FI 1 Electomgnetism Alexnde A. Isknd, Ph.D. Physics of Mgnetism nd Photonics Resech Goup Electosttics ELECTRIC PTENTIALS 1 Recll tht we e inteested to clculte the electic field of some chge distiution.
More informationRELATIVE KINEMATICS. q 2 R 12. u 1 O 2 S 2 S 1. r 1 O 1. Figure 1
RELAIVE KINEMAICS he equtions of motion fo point P will be nlyzed in two diffeent efeence systems. One efeence system is inetil, fixed to the gound, the second system is moving in the physicl spce nd the
More informationMATHEMATICS IV 2 MARKS. 5 2 = e 3, 4
MATHEMATICS IV MARKS. If + + 6 + c epesents cicle with dius 6, find the vlue of c. R 9 f c ; g, f 6 9 c 6 c c. Find the eccenticit of the hpeol Eqution of the hpeol Hee, nd + e + e 5 e 5 e. Find the distnce
More informationAlgebra Based Physics. Gravitational Force. PSI Honors universal gravitation presentation Update Fall 2016.notebookNovember 10, 2016
Newton's Lw of Univesl Gvittion Gvittionl Foce lick on the topic to go to tht section Gvittionl Field lgeb sed Physics Newton's Lw of Univesl Gvittion Sufce Gvity Gvittionl Field in Spce Keple's Thid Lw
More informationSolution of fuzzy multi-objective nonlinear programming problem using interval arithmetic based alpha-cut
Intentionl Jounl of Sttistics nd Applied Mthemtics 016; 1(3): 1-5 ISSN: 456-145 Mths 016; 1(3): 1-5 016 Stts & Mths www.mthsounl.com Received: 05-07-016 Accepted: 06-08-016 C Lognthn Dept of Mthemtics
More informationReview of Mathematical Concepts
ENEE 322: Signls nd Systems view of Mthemticl Concepts This hndout contins ief eview of mthemticl concepts which e vitlly impotnt to ENEE 322: Signls nd Systems. Since this mteil is coveed in vious couses
More informationThis immediately suggests an inverse-square law for a "piece" of current along the line.
Electomgnetic Theoy (EMT) Pof Rui, UNC Asheville, doctophys on YouTube Chpte T Notes The iot-svt Lw T nvese-sque Lw fo Mgnetism Compe the mgnitude of the electic field t distnce wy fom n infinite line
More information(A) 6.32 (B) 9.49 (C) (D) (E) 18.97
Univesity of Bhin Physics 10 Finl Exm Key Fll 004 Deptment of Physics 13/1/005 8:30 10:30 e =1.610 19 C, m e =9.1110 31 Kg, m p =1.6710 7 Kg k=910 9 Nm /C, ε 0 =8.8410 1 C /Nm, µ 0 =4π10 7 T.m/A Pt : 10
More informationELECTRO - MAGNETIC INDUCTION
NTRODUCTON LCTRO - MAGNTC NDUCTON Whenee mgnetic flu linked with cicuit chnges, n e.m.f. is induced in the cicuit. f the cicuit is closed, cuent is lso induced in it. The e.m.f. nd cuent poduced lsts s
More information10 m, so the distance from the Sun to the Moon during a solar eclipse is. The mass of the Sun, Earth, and Moon are = =
Chpte 1 nivesl Gvittion 11 *P1. () The un-th distnce is 1.4 nd the th-moon 8 distnce is.84, so the distnce fom the un to the Moon duing sol eclipse is 11 8 11 1.4.84 = 1.4 The mss of the un, th, nd Moon
More informationExperimental Verification of Variable-Frequency Rocking Bearings for Near-fault Seismic Isolation
Expeimentl Veiiction o Vile-Fequency Rocking Beings o Ne-ult Seismic Isoltion Lyn-Ywn Lu Deptment o Constuction Engineeing Ntionl Kohsiung Fist Univesity o Science nd Technology, Kohsiung, Tiwn Tzu-Ying
More informationLecture 11: Potential Gradient and Capacitor Review:
Lectue 11: Potentil Gdient nd Cpcito Review: Two wys to find t ny point in spce: Sum o Integte ove chges: q 1 1 q 2 2 3 P i 1 q i i dq q 3 P 1 dq xmple of integting ove distiution: line of chge ing of
More information9.4 The response of equilibrium to temperature (continued)
9.4 The esponse of equilibium to tempetue (continued) In the lst lectue, we studied how the chemicl equilibium esponds to the vition of pessue nd tempetue. At the end, we deived the vn t off eqution: d
More informationRadial geodesics in Schwarzschild spacetime
Rdil geodesics in Schwzschild spcetime Spheiclly symmetic solutions to the Einstein eqution tke the fom ds dt d dθ sin θdϕ whee is constnt. We lso hve the connection components, which now tke the fom using
More informationSuggested t-z and q-z functions for load-movement responsef
40 Rtio (Exponent = 0.5 80 % Fnction (.5 times 0 Hypeolic ( = 0 % SHAFT SHEAR (% of lt 00 80 60 ULT Zhng = 0.0083 / = 50 % Exponentil (e = 0.45 80 % (stin-softening 40 0 0 0 5 0 5 0 5 RELATIVE MOVEMENT
More informationMicro-scale adhesive contact of a spherical rigid punch on a. piezoelectric half-space
http://www.ppe.edu.cn Mico-scle dhesive contct of spheicl igid punch on piezoelectic hlf-spce Z.R. Chen, S.W. Yu * Deptment of Engineeing Mechnics, Tsinghu Univesity, Beijing 84, P.R. Chin Abstct The mico-scle
More informationSPA7010U/SPA7010P: THE GALAXY. Solutions for Coursework 1. Questions distributed on: 25 January 2018.
SPA7U/SPA7P: THE GALAXY Solutions fo Cousewok Questions distibuted on: 25 Jnuy 28. Solution. Assessed question] We e told tht this is fint glxy, so essentilly we hve to ty to clssify it bsed on its spectl
More informationOptimization. x = 22 corresponds to local maximum by second derivative test
Optimiztion Lectue 17 discussed the exteme vlues of functions. This lectue will pply the lesson fom Lectue 17 to wod poblems. In this section, it is impotnt to emembe we e in Clculus I nd e deling one-vible
More informationInvestigations of Boundary Treatments in Incompressible Smoothed Particle Hydrodynamics for Fluid-Structural Interactions
Recent Reseches in Mechnics Investigtions of Boundy Tetments in Incompessile Smoothed Pticle Hydodynmics fo Fluid-Stuctul Intections Fnfn Sun, Mingyi Tn, nd Jing T Xing Astct Two oundy tetment methods
More informationChapter 21: Electric Charge and Electric Field
Chpte 1: Electic Chge nd Electic Field Electic Chge Ancient Gees ~ 600 BC Sttic electicit: electic chge vi fiction (see lso fig 1.1) (Attempted) pith bll demonsttion: inds of popeties objects with sme
More informationπ,π is the angle FROM a! TO b
Mth 151: 1.2 The Dot Poduct We hve scled vectos (o, multiplied vectos y el nume clled scl) nd dded vectos (in ectngul component fom). Cn we multiply vectos togethe? The nswe is YES! In fct, thee e two
More informationElectric Potential. and Equipotentials
Electic Potentil nd Euipotentils U Electicl Potentil Review: W wok done y foce in going fom to long pth. l d E dl F W dl F θ Δ l d E W U U U Δ Δ l d E W U U U U potentil enegy electic potentil Potentil
More informationFluids & Bernoulli s Equation. Group Problems 9
Goup Poblems 9 Fluids & Benoulli s Eqution Nme This is moe tutoil-like thn poblem nd leds you though conceptul development of Benoulli s eqution using the ides of Newton s 2 nd lw nd enegy. You e going
More informationWeek 8. Topic 2 Properties of Logarithms
Week 8 Topic 2 Popeties of Logithms 1 Week 8 Topic 2 Popeties of Logithms Intoduction Since the esult of ithm is n eponent, we hve mny popeties of ithms tht e elted to the popeties of eponents. They e
More informationTwo dimensional polar coordinate system in airy stress functions
I J C T A, 9(9), 6, pp. 433-44 Intentionl Science Pess Two dimensionl pol coodinte system in iy stess functions S. Senthil nd P. Sek ABSTRACT Stisfy the given equtions, boundy conditions nd bihmonic eqution.in
More informationSAR FOCUSING: SCALED INVERSE FOURIER TRANSFORMATION
Univesität Siegen Poject Secto - Optiml Signl Pocessing - Senso Dt Fusion, Remote Sensing - SAR ZESS SAR FOCUSING: SCALED INVERSE FOURIER TRANSFORMATION AND CHIRP SCALING O. Loeld, A. Hein Univesity o
More informationigid nd non-leky two-comptment building. Yu et l [8] developed non-line govening equtions by consideing the effect of bckgound lekge. Howeve, thee e n
The Seventh Intentionl Colloquium on Bluff Body Aeodynmics nd Applictions (BBAA7) Shnghi, Chin; Septembe -, Coupled vibtion between wind-induced intenl pessues nd lge spn oof fo two-comptment building
More informationRELATIONSHIP BETWEEN DESIGN RESPONSE SPECTRA FOR RARE AND FREQUENT EARTHQUAKE LEVELS
th Wold Confeence on Ethquke Engineeing ncouve, B.C., Cnd ugust -6, 00 Ppe No. 9 ELIONHIP BEWEEN EIGN EPONE PEC O E N EQUEN EHQUKE LEEL Yingmin LI Cheng HI Ming LI Ling HN UMMY It is known tht uilding
More informationComparative Studies of Law of Gravity and General Relativity. No.1 of Comparative Physics Series Papers
Comptive Studies of Lw of Gvity nd Genel Reltivity No. of Comptive hysics Seies pes Fu Yuhu (CNOOC Resech Institute, E-mil:fuyh945@sin.com) Abstct: As No. of comptive physics seies ppes, this ppe discusses
More informationSection 35 SHM and Circular Motion
Section 35 SHM nd Cicul Motion Phsics 204A Clss Notes Wht do objects do? nd Wh do the do it? Objects sometimes oscillte in simple hmonic motion. In the lst section we looed t mss ibting t the end of sping.
More informationPhysics 11b Lecture #11
Physics 11b Lectue #11 Mgnetic Fields Souces of the Mgnetic Field S&J Chpte 9, 3 Wht We Did Lst Time Mgnetic fields e simil to electic fields Only diffeence: no single mgnetic pole Loentz foce Moving chge
More informationProf. Dr. Yong-Su Na (32-206, Tel )
Fusion Recto Technology I (459.76, 3 Cedits) Pof. D. Yong-Su N (3-6, Tel. 88-74) Contents Week 1. Mgnetic Confinement Week -3. Fusion Recto Enegetics Week 4. sic Tokmk Plsm Pmetes Week 5. Plsm Heting nd
More informationExperimental evaluation of the process of decohesion of adhesive joints with polymer films
olimey, No. 11-12, 2, p. 82 Expeimentl evlution of the pocess of decohesion of dhesive oints with polyme films M. Zenkiewicz nd J. Dzwonkowski Tnsltion submitted by J.E. Bke Selected fom Intentionl olyme
More informationOptimized Second-Order Dynamical Systems and Their RLC Circuit Models with PWL Controlled Sources
ADIOENGINEEING VO. NO. SEPTEMBE Optimized Second-Ode Dynmicl Systems nd Thei icit Models with PW ontolled Soces Jiří POSPÍŠI Zdeně KOKA Stnislv HANUS Jiří PETŽEA Jomí BZOBOHATÝ Dept. of dio Electonics
More informationAnswers to test yourself questions
Answes to test youself questions opic Descibing fields Gm Gm Gm Gm he net field t is: g ( d / ) ( 4d / ) d d Gm Gm Gm Gm Gm Gm b he net potentil t is: V d / 4d / d 4d d d V e 4 7 9 49 J kg 7 7 Gm d b E
More informationChapter 25: Current, Resistance and Electromotive Force. ~10-4 m/s Typical speeds ~ 10 6 m/s
Chpte 5: Cuent, esistnce nd lectomotive Foce Chge cie motion in conducto in two pts Constnt Acceletion F m q ndomizing Collisions (momentum, enegy) >esulting Motion http://phys3p.sl.psu.edu/phys_nim/m/ndom_wlk.vi
More informationCh 26 - Capacitance! What s Next! Review! Lab this week!
Ch 26 - Cpcitnce! Wht s Next! Cpcitnce" One week unit tht hs oth theoeticl n pcticl pplictions! Cuent & Resistnce" Moving chges, finlly!! Diect Cuent Cicuits! Pcticl pplictions of ll the stuff tht we ve
More informationFreedericksz transition threshold in nematic liquid crystals filled with ferroelectric nanoparticles
Feedeicksz tnsition theshold in nemtic liquid cystls filled with feoelectic nnopticles.yu. Reshetnyk, S.M. Shelestiuk nd T.J. Sluckin b Physics Fculty, Kyiv Ntionl Ts Shevchenko Univesity Pospekt Glushkov,
More informationSolutions to Midterm Physics 201
Solutions to Midtem Physics. We cn conside this sitution s supeposition of unifomly chged sphee of chge density ρ nd dius R, nd second unifomly chged sphee of chge density ρ nd dius R t the position of
More informationChapter 6 Thermoelasticity
Chpte 6 Themoelsticity Intoduction When theml enegy is dded to n elstic mteil it expnds. Fo the simple unidimensionl cse of b of length L, initilly t unifom tempetue T 0 which is then heted to nonunifom
More informationPlane Wave Expansion Method (PWEM)
/15/18 Instucto D. Rymond Rumpf (915) 747 6958 cumpf@utep.edu EE 5337 Computtionl Electomgnetics Lectue #19 Plne Wve Expnsion Method (PWEM) Lectue 19 These notes my contin copyighted mteil obtined unde
More informationSupplementary Figure 1. Circular parallel lamellae grain size as a function of annealing time at 250 C. Error bars represent the 2σ uncertainty in
Supplementay Figue 1. Cicula paallel lamellae gain size as a function of annealing time at 50 C. Eo bas epesent the σ uncetainty in the measued adii based on image pixilation and analysis uncetainty contibutions
More informationside-chain polymeric crystal effets sont caract6ris6s par une valeur classique pulsed electrical field was used to study the characterised by a
J. Phys. II Fnce 2 (1992) 209-218 FEBRUARY 1992, PAGE 209 effect in isotopic phse of side-chin polymeic Ke cystl liquid L bit flingence induite p un chmp Iectique impulsionnel t6 utilis6e pou R4sum4. Ies
More informationElectricity & Magnetism Lecture 6: Electric Potential
Electicity & Mgnetism Lectue 6: Electic Potentil Tody s Concept: Electic Potenl (Defined in tems of Pth Integl of Electic Field) Electicity & Mgnesm Lectue 6, Slide Stuff you sked bout:! Explin moe why
More informationScientific Computing & Modelling NV, Vrije Universiteit, Theoretical Chemistry, De Boelelaan 1083, 1081 HV Amsterdam, The Netherlands c
Electonic Supplementy Mteil (ESI) fo Physicl Chemisty Chemicl Physics. This jounl is The Royl Society of Chemisty 2014 Suppoting Infomtion fo: Pedicting phosphoescent lifetimes nd zeo-field splitting of
More informationA COMPARISON OF MEMBRANE SHELL THEORIES OF HYBRID ANISOTROPIC MATERIALS ABSTRACT
A COMPARISON OF MEMBRANE SHELL THEORIES OF HYBRID ANISOTROPIC MATERIALS S. W. Chung* School of Achitectue Univesity of Uth Slt Lke City, Uth, USA S.G. Hong Deptment of Achitectue Seoul Ntionl Univesity
More informationTests for Correlation on Bivariate Non-Normal Data
Jounl of Moden Applied Sttisticl Methods Volume 0 Issue Aticle 9 --0 Tests fo Coeltion on Bivite Non-Noml Dt L. Bevesdof Noth Colin Stte Univesity, lounneb@gmil.com Ping S Univesity of Noth Floid, ps@unf.edu
More informationChapter 25: Current, Resistance and Electromotive Force. Charge carrier motion in a conductor in two parts
Chpte 5: Cuent, esistnce nd Electomotive Foce Chge cie motion in conducto in two pts Constnt Acceletion F m qe ndomizing Collisions (momentum, enegy) =>esulting Motion Avege motion = Dift elocity = v d
More informationAbout Some Inequalities for Isotonic Linear Functionals and Applications
Applied Mthemticl Sciences Vol. 8 04 no. 79 8909-899 HIKARI Ltd www.m-hiki.com http://dx.doi.og/0.988/ms.04.40858 Aout Some Inequlities fo Isotonic Line Functionls nd Applictions Loedn Ciudiu Deptment
More information1. The sphere P travels in a straight line with speed
1. The sphee P tels in stight line with speed = 10 m/s. Fo the instnt depicted, detemine the coesponding lues of,,,,, s mesued eltie to the fixed Oxy coodinte system. (/134) + 38.66 1.34 51.34 10sin 3.639
More informationITI Introduction to Computing II
ITI 1121. Intoduction to Computing II Mcel Tucotte School of Electicl Engineeing nd Compute Science Abstct dt type: Stck Stck-bsed lgoithms Vesion of Febuy 2, 2013 Abstct These lectue notes e ment to be
More informationTWO NEW D. MATTER PROFILES FOR MILKY WAY HALO GOT FROM ROTATION CURVE M. Abarca
TWO NW D. MATTR PROFILS FOR MILKY WAY HALO GOT FROM ROTATION CURV M. Ac TWO NW D.M. DNSITY PROFILS FOR MILKY WAY HALO GOT FROM ROTATION CURV Autho Mnuel Ac Henndez emil mche1@gmil.com 1. ASTRACT.... INTRODUCTION...
More information6. Gravitation. 6.1 Newton's law of Gravitation
Gvittion / 1 6.1 Newton's lw of Gvittion 6. Gvittion Newton's lw of gvittion sttes tht evey body in this univese ttcts evey othe body with foce, which is diectly popotionl to the poduct of thei msses nd
More informationDEPARTMENT OF CIVIL AND ENVIRONMENTAL ENGINEERING FLUID MECHANICS III Solutions to Problem Sheet 3
DEPATMENT OF CIVIL AND ENVIONMENTAL ENGINEEING FLID MECHANICS III Solutions to Poblem Sheet 3 1. An tmospheic vote is moelle s combintion of viscous coe otting s soli boy with ngul velocity Ω n n iottionl
More informationInternational Journal of Pure and Applied Sciences and Technology
Int. J. Pue l. Sci. Technol. () (0). -6 Intentionl Jounl of Pue nd lied Sciences nd Technology ISSN 9-607 vilble online t www.ijost.in Resech Pe Rdil Vibtions in Mico-Isotoic Mico-Elstic Hollow Shee R.
More informationNS-IBTS indices calculation procedure
ICES Dt Cente DATRAS 1.1 NS-IBTS indices 2013 DATRAS Pocedue Document NS-IBTS indices clcultion pocedue Contents Genel... 2 I Rw ge dt CA -> Age-length key by RFA fo defined ge nge ALK... 4 II Rw length
More informationProf. Anchordoqui Problems set # 12 Physics 169 May 12, 2015
Pof. Anchodoqui Poblems set # 12 Physics 169 My 12, 2015 1. Two concentic conducting sphees of inne nd oute dii nd b, espectively, cy chges ±Q. The empty spce between the sphees is hlf-filled by hemispheicl
More informationElastic scattering of 4 He atoms at the surface of liquid helium
Indin Jounl of Pue & Applied Physics Vol. 48, Octobe, pp. 743-748 Elstic sctteing of 4 He toms t the sufce of liquid helium P K Toongey, K M Khnn, Y K Ayodo, W T Skw, F G Knyeki, R T Eki, R N Kimengichi
More informationGeneral Physics II. number of field lines/area. for whole surface: for continuous surface is a whole surface
Genel Physics II Chpte 3: Guss w We now wnt to quickly discuss one of the moe useful tools fo clculting the electic field, nmely Guss lw. In ode to undestnd Guss s lw, it seems we need to know the concept
More informationPX3008 Problem Sheet 1
PX38 Poblem Sheet 1 1) A sphee of dius (m) contins chge of unifom density ρ (Cm -3 ). Using Guss' theoem, obtin expessions fo the mgnitude of the electic field (t distnce fom the cente of the sphee) in
More informationUnit 6. Magnetic forces
Unit 6 Mgnetic foces 6.1 ntoduction. Mgnetic field 6. Mgnetic foces on moving electic chges 6. oce on conducto with cuent. 6.4 Action of unifom mgnetic field on flt cuent-cying loop. Mgnetic moment. Electic
More informationMultiple-input multiple-output (MIMO) communication systems. Advanced Modulation and Coding : MIMO Communication Systems 1
Multiple-input multiple-output (MIMO) communiction systems Advnced Modultion nd Coding : MIMO Communiction Systems System model # # #n #m eceive tnsmitte infobits infobits #N #N N tnsmit ntenns N (k) M
More informationCHAPTER 18: ELECTRIC CHARGE AND ELECTRIC FIELD
ollege Physics Student s Mnul hpte 8 HAPTR 8: LTRI HARG AD LTRI ILD 8. STATI LTRIITY AD HARG: OSRVATIO O HARG. ommon sttic electicity involves chges nging fom nnocoulombs to micocoulombs. () How mny electons
More informationOn Natural Partial Orders of IC-Abundant Semigroups
Intentionl Jounl of Mthemtics nd Computtionl Science Vol. No. 05 pp. 5-9 http://www.publicsciencefmewok.og/jounl/ijmcs On Ntul Ptil Odes of IC-Abundnt Semigoups Chunhu Li Bogen Xu School of Science Est
More informationCreep modeling in functionally graded rotating disc of variable thickness
Jounl of Mechnicl Science nd Technology 4 () () ~3 www.spingelink.com/content/738-494x DOI.7/s6--87- Ceep modeling in functionlly gded otting disc of vile thickness D. Deepk, V. K. Gupt,* nd A. K. Dhm
More informationMark Scheme (Results) January 2008
Mk Scheme (Results) Jnuy 00 GCE GCE Mthemtics (6679/0) Edecel Limited. Registeed in Englnd nd Wles No. 4496750 Registeed Office: One90 High Holbon, London WCV 7BH Jnuy 00 6679 Mechnics M Mk Scheme Question
More informationInternational Journal of Technical Research and Applications e-issn: , Special Issue 19 (June, 2015), PP.
Intentionl Jounl of Technicl Resech nd Applictions e-issn: 3-863,.ijt.com Specil Issue 9 (June, 5), PP. 39-46 HEAT AND MASS TRANSFER FOR SORET, DUFOUR S AND MAGNETCI EFFECTS IN TRANSIENT FLOW OF CONDUCTING
More informationWinter 2004 OSU Sources of Magnetic Fields 1 Chapter 32
Winte 4 OSU 1 Souces Of Mgnetic Fields We lened two wys to clculte Electic Field Coulomb's Foce de 4 E da 1 dq Q enc ˆ ute Foce Clcultion High symmety Wht e the nlogous equtions fo the Mgnetic Field? Winte
More informationClass Summary. be functions and f( D) , we define the composition of f with g, denoted g f by
Clss Summy.5 Eponentil Functions.6 Invese Functions nd Logithms A function f is ule tht ssigns to ech element D ectly one element, clled f( ), in. Fo emple : function not function Given functions f, g:
More informationDielectric elastomer cylindrical actuators: electromechanical modelling and experimental evaluation
Mteils Science nd Engineeing C 4 (004) 555 56 www.elsevie.com/locte/msec Dielectic elstome cylindicl ctutos: electomechnicl modelling nd expeimentl evlution Fedeico Cpi*, Dnilo De Rossi Intedeptmentl Resech
More informationPearson s Chi-Square Test Modifications for Comparison of Unweighted and Weighted Histograms and Two Weighted Histograms
Peason s Chi-Squae Test Modifications fo Compaison of Unweighted and Weighted Histogams and Two Weighted Histogams Univesity of Akueyi, Bogi, v/noduslód, IS-6 Akueyi, Iceland E-mail: nikolai@unak.is Two
More informationEfficiency of excitation of piezoceramic transducer at antiresonance frequency
fficiency of excittion of piezocemic tnsduce t ntiesonnce fequency Mezheitsky A.V. fficiency of excittion of piezocemic tnsduce t ntiesonnce fequency dpted fom I Tns. Ultson. Feoelect. Feq. Cont. vol.
More informationLecture 4. Beyond the Hückel π-electron theory. Charge density is an important parameter that is used widely to explain properties of molecules.
Lectue 4. Beyond the Hückel π-electon theoy 4. Chge densities nd bond odes Chge density is n impotnt pmete tht is used widely to explin popeties of molecules. An electon in n obitl ψ = c φ hs density distibution
More informationContinuous Charge Distributions
Continuous Chge Distibutions Review Wht if we hve distibution of chge? ˆ Q chge of distibution. Q dq element of chge. d contibution to due to dq. Cn wite dq = ρ dv; ρ is the chge density. = 1 4πε 0 qi
More information(a) Counter-Clockwise (b) Clockwise ()N (c) No rotation (d) Not enough information
m m m00 kg dult, m0 kg bby. he seesw stts fom est. Which diection will it ottes? ( Counte-Clockwise (b Clockwise ( (c o ottion ti (d ot enough infomtion Effect of Constnt et oque.3 A constnt non-zeo toque
More information