Fluid-Solid Coupling Analysis of Deep Foundation Pit s Seepage Under Non-Saturated Conditions
|
|
|
- Agatha Skinner
- 6 years ago
- Views:
Transcription
1 Physicl nd Nmeicl Simlion of Geoechnicl Engineeing 1s Isse, Sep Flid-Solid Copling Anlysis of Deep Fondion Pi s Seepge Unde Non-Sed Condiions CHENG Wei, HE Xing School of Civil Engineeing nd Achiece, Whn Polyechnic Univesi P.R. Chin, chengwei2359@163.com ABSTRACT: The phenomenon which mico-esin seepge effecs on fondion Pi wih infll is ypiclly non-sed seepge pocess. Howeve, ndegond we seepge nd infll infilion ding he deep fondion pi s excvion nd sppo exe significn impc pon he sbiliy of engineeing iself. The hos hve given some conemeses fe modeling nd clcling of his phenomenon nd mke n explnion of poblems which confoned ding deep fondion pi s excvion nd sppo by elevn heoies. Conclde he flow ph nd velociy ond fondion pi hogh clclion nde non-sed condiions. Then i combined he pedicions nd pcicl pplicions, poposed coespondingly poecive meses. EYWORDS: Flid-solid copling, Deep fondion pi s seepge, Non-sed condiions 1 INTRODUCTION Since he elsic modls of sof gond is smll nd he inensiy of he soil iself elively low, i will be esily led o fondion pi s globl insbiliy ding is excvion nd sppo pocess. Ye ding he excvion in domesic cosl es, disposl of ndegond we nd wepoof o diphgm eining wlls emins o be impoved. Piclly infll nd is infilion ding excvion nd sppo of fondion pi. I will significnly decese he she sengh of ock nd soil, nd hen effec on he sbiliy of engineeing iself. And he effec h seepge nd defomion hve on he boom of he fondion pi will cse he boom of fondion pi swell o piping eosion [1], nd heen o he sbiliy of fondion pi. Fondion pi wih diffeen geologicl condiions hve ge diffeence of pemebiliy nd bondy condiions, hs he poe pesse of fondion pi nd effecive sess wih he cion of is poe pesse is diffeen. The inflencing fcos of fondion pi e vie sch s design deph of diphgm eining wlls nd block bo ndegond we ding he excvion nd sppo of fondion pi is vey impon. Fondion pi s excvion is menwhile sess elese pocess. Excve fondion pi fom geologicl blnce plin will chnge he sess sce of ond envionmen. In ode o void he dve effecs o he sonding podcion nd conscion fe long peiod of fondion pi s excvion, i s necessy o obseve nd expeimen of he seepge field nd sess field in ime, nd seek o is chnge lw. Becse of he ndegond we seepge effec, hee will be defomion ond fondion pi. I is sefl o conol nd melioe he poo se of fondion pi h mke flid-solid nlysis o he seepge nd sess defomion ond fondion pi. Nowdys, he min isses of domesic deep fondion pi focs on: (1 Dynmic pocess of sess elese; (2 The defomion fo seepge, pecipiion sbiliy of fondion pi. (3 Soil liqefcion fo dynmic lod, nd he neven sedimenion nde effec of lye seepge. The nlysis on he seepge field nd sess field which mico-esin seepge effecs on fondion Pi wih infll nde non-sed condiions is bsed on he nlyic clclion of coelion model. 2 THEORY ANALYZE 2.1 The mechnism of gondwe migion s impc on he sbiliy nd defomion of fondion pi Beween wo impemeble lyes, s soon s he fondion pi ws excved, confined we hve we hed. The gondwe ss o mige nde he poe pesse effec. This effec mde hydlic pesse gdlly senghen long wih he incese of fondion pi deph diecly. The we hed ws loss s well. Since he poe we pesse is lowe hn sedy we pesse in cein e o of he fondion pi, he siion in he boom of fondion pi is evese. And his csed he gondwe seepge ino he inside of he fondion pi. A he sme ime, hee will be n opposie end of we pesse nd flow wy of ndegond we beween wo sides of he wll. This will be mde n indced cse o nsble fondion h is excvion. Combined wih he flow chceisics of ndegond we, if he fondion loced in ive o lck whee conin bndn we, he flow size will be scen, nd hee shold be some ppopie emegency meses. Moeove, wih diffeen ein, he chceisic nd sengh of soil ms be diffeen, nd he impession h we seepge o he fondion sble shold be nde he pemise h doing seils of cogen nd deil expeimen peviosly. While he bsic pinciple is simil, e de o he ndegond we flow fo we hed diffeence, nd hen cse he dynmic excvion poblems of deep fondion pi. Becse of imely spplemen infll, he ndegond we level is no deemined. Wih diffeen infll inensi he qniy of ndegond we flo nge will ST. PLUM-BLOSSOM PRESS PTY LTD
2 Flid-Solid Copling Anlysis of Deep Fondion Pi s Seepge Unde Non-Sed Condiions DOI: /J. PNSGE be diffeen. And he cicmsnce h ne ive o lke e, ms be consideed independenly. When i ins cein ime fe he fondion pi hve been excve, hee will be ge impession on he ineged sppo of he fondion. I is pone o piping if we didn hve einfoce inefce h iniil sess elese o some coespondingly dinge emen of i, menwhile, conside he le of sess ding his non-sed pocess, nd he chnge of ndegond we seepge nd poe pesse h esls fom i, hee will be cein defomion long wih i in significn e. And in he pocess of ining, hee will be hin of emin infll nd seepge we in he fondion pi, nd i is he mico-esin. The seepge pocess nde fondion pi is compliced nde he mico-esin effec. 2.2 Relevn heoies of non-sed soil The elionship beween soil scion nd is sion. Becse of ock nd soil is poos medi, he ol poe pesse ms be lowe hn zeo nde non-sed condiion, nd he negive vle of he ol poe pesse eflec he soil scion. The sion of soil minins in nge fo he effec esls fom soil scion. Assignion he bsopion nd dehydion cve peviosl nd he le lw beween hese wo. The inside seepge of non-sed soil obey Dcy s lw, he solid nd liqid copling by sin nd poe pesse. The copled mhemicl eqions of sed-nsed seepge of ock nd soil e s follow fe efeenced by mliphse seepge heoy of poos medi [2,3,4] : ij, j ( Sp ij j fi 0 (1 S (2 F vk, k cp 0 ij is vlid sess; ij is konecke consn; p is poe pesse; f i is volme foce; S is he sion; ( snds fo he kk is volme sin; j deivion of he x coodine; ( snds fo he deivion of ime ; clcle eqion of c is s follow: c ns ds k dp F v k is Dcy s velociy; nd he (3 And c is soge consn; n is poosiy; modls; s is he fncion of poe pesse p ; k is blk The sengh heoy nd efeence compe eqions of non-sed soil e s follows: In 1959, Bishop poposed he sengh eqion of non-sed soil o single sess se vibles [5] : c [( ( ]n (4 In he eqion, is she sengh; c snds fo vlid cohesion; snds fo vlid inenl ficion ngle; w is poe i pesse; nd w is poe we pesse; ( w is soil scion; is consn beween 0 nd 1. b Obeg nd Sllfos poposed he she sengh foecs eqion of non-sed soil s follows [6] : c ( n ( ( S n (5 And S is he sion in his eqion Consideed non-sed condiion, he clcle eqion of pemebiliy long wih poe pesse chnge is s follows [7] : * (6 ( S s ( S S (1 S 3 3 s D seepge eqions [8] Sedy seepge eqion 1 2 p 1 F w 3/ 2 H H ( ( y Q 0 x x y y (7 x (8 Q is we flow Tnsien seepge eqion H H H ( k x ( k y c (9 x x y y x, y e pemebiliy in x nd y diecions, ni is m / s,h is ol we hed, H( x, Bondy condiions 1 We hed bondy H( x, C H0( x, (10 H ( x, is given we hed bond wih =0, 0 iniil we hed is H 0 ( x, y. 2 We flow bondy H k C q( h, x, n (11 3 SEEPAGE-STRESS ANALYSIS OF DEEP FOUNDATION PIT UNDER INFLUENCE OF MICRO-ARTESIAN 3.1 Rinfll infilion bondy condiions Mein nd Lson [9] sing infll inensiy q, he soil llowble infilion cpciy f, nd he pemebiliy P when soil is sed. When i mee he condiion: f P q s s, ll of he infll is infilion ino soil nd he cpciy is decese long wih he deph incese. 44
3 Physicl nd Nmeicl Simlion of Geoechnicl Engineeing 1s Isse, Sep Modeling nd clcling This exmple is sing 2-D finie elemen mehod o do he nmeicl clclion of fondion pi. All monio e is he seepge nge, o he flow egion of he gondwe. The boom, lef, nd igh bondy nd diphgm eining wlls bondies hve consin. Consideed he pemebiliy of soil is chnged long wih he chnge of sion, we defined se of d bsed on he following wo eqions: S s (12 c [ ( b ( ] ( Sn Si Si [ ( b ( (13 c ], s is pemebiliy when soil sed. e gs pesse nd we pesse in soil, nd, b, c,, b, c e meil coefficiens, S i is esidl sion. Sn is mximm sion. The beh of fondion pi is 3m, deph 20.32m, heigh 52.46m,sing whole beh 200m, heefoe cn conside lge nge, nd fe excvion, he diphgm eining wlls deph is 25m, hickness 0.1m, elsic modls 10.8 MP, Poisson s io 0.3, cohesion c 16P, ficion ngle 30 degee. Model in mesh s follow: Afe pmee seing, he clclion esls e s follows: Fige.1 Simplified digm of model Veicl effecive sess disibion: Fige.2 Disibion of poe pesse Hoizonl nd veicl displcemen: Fige.3 Disibion of veicl effec 45
4 Flid-Solid Copling Anlysis of Deep Fondion Pi s Seepge Unde Non-Sed Condiions DOI: /J. PNSGE Fige.4 Hoizonl displcemen Displcemen veco gph: Fige.5 Veicl displcemen Fige.6 Velociy of flow veco gph 4.1 Anlysis he nmeicl simlion of he flid-solid pocess In fige 1 nd 2, he displcemen in he boom nd ne e of he pi is compively lge, nd hydlic gdien in he boom of pi is vey lge, he soil ond he pi s o swell nd is inensify is edce fo he gviy nd sic we pesse effec. Fom he veco gph, we cn see he discepncy of velociy beween inside nd oside fondion pi e clely. As he min dinge oienion, he we pesse nd velociy of flow inside he pi is lge hn oside ny moe, menwhile, inside he pi, hee is pwd seepge. The effecive sess decese gdll nd in cein siion, i will evolve o piping Anlysis of fondion ebond nd sonding sfce sbsidence Ovell, since he feqenly flow of ndegond we, hee fomed lge e of displcemen nd defomion, nd ed snds fo posiive displcemen, ble e snds fo compehensive defomion egion in ems of ndegond we flow effec. When i effec fo peiod of ime, he sess concene in downside inefce of he wll, inside of he fondion hee e plif defomion. The clcle esl evel h he ebond flo of fondion pi elively lge, nd i deemined minly by poosiy of soil nd he elionship beween gondwe level nd he wll deph. The finie elemen nlysis of his pocess will be discoveed h he chceisic nd sion of soil will be chnge gdlly long wih he infilion degee of infll. And i will ke gdlly diffeence of ndegond we infile fee, hen he following chnge of poosiy nd pemebiliy of soil. I cn lso pedic he elive chnge end gph hoogh he clcling de h he sess nd sin chnge of fondion elemen nd node, o he vlid sess ph of node. Combine hese de, we conclded h he sess nd sin of elemen will be chnge when we give diffeen infll inensiy nd ende ime, nd he esl si o he infll infilion conclsion The finie elemen nlysis of soil sess nd sin chnge: In ems of he nlysis of de h node o elemen displcemen inenl soil, we cn conclded sess ph of evey node nd ol sin end. We cn lso obseve he ol sin in diffeen sion nd poe pesse, nd he poenil egion of iniil descion nd dvese geologicl phenomen, o see he impession e inegiy. Finie elemen mehod will be ccely clcled he de of sess nd sin of evey node nd elemen, hen doing sess nd defomion nlysis wih hese esls. Wih he sess ph h he mehod hd been clcled, we cn foecs he sin of soil nde cein foce cicmsnce. And hen foecs he genel end of soil 46
5 Physicl nd Nmeicl Simlion of Geoechnicl Engineeing 1s Isse, Sep sin. The ls pojec we ms ccomplish is h esonble pojecion he migh phenomen ding fondion pi excvion in cein cicmsnce. 4.2 Poposl o he deep fondion pi s excvion nd sppo Ge imponce shold be ched o he chnge of he gondwe seepge nd we shold void he iny seson nd mke good sppo when excve fondion pi. Mke pedicion bo seepge popey in cein peiod befoe excvion, nd seek o he bes sppo wy of his ime. Simill mke discssion bo he benefi wy o excvion in diffeen locion When he qife hickness is compively lge nd he sme s pemebili he convenionl mehod is combine sing diphgm eining wlls nd going cin, b ely sed veicl bck cove. And he going cin is good wy o block he gondwe nde he boom of fondion pi The deph h diphgm eining wlls ino ock lye shold be enogh, howeve, fo economic consideion, how o deemine he bes deph shold be bsed on echnology nd he pemebiliy of envionmen h fondion pi loce. In he boom of he fondion pi, inensiy is no necessy b we ms ense h he wepoof biliy of diphgm eining wlls is sfficien. Menwhile, we shold conside he envionmen popey ond fondion pi when i dinge. This wok shold be bsed on he mple envionmenl invesigion in ll, nd hen mke ionl disibion. 5 CONCLUSION The poblem h gondwe seepge ding he excvion nd sppo of fondion pi coninosly he key isse of fondion pi excvion. Bsed on he bndn invesigion of ond envionmen, we cn pedic he seepge field of gondwe nd is chnge lw befoe conscion hogh nmeicl clclion. I will povide vlble efeence meil o deemine he excvion mehod in ime, o choose he ionl pogm conside economicl fcos. Deep fondion pi s excvion in iny seson will fom diffeenly seepge siion. Unde we seepge effec, hee will be compise displcemen nd sedimenion in lge field, nd edce he fondion pi s sbiliy. We give he ionl nswe bo hese qesions. (1 The soil sengh is significnly elevn o is poe pesse nd pemebiliy nde he infll infilion non-sed condiion. I is benefi fo fondion pi s devise of sppo pogm nd conscion h combine wih infll siion nd foecs he dynmic chnge of ndegond we. (2 Use he pcicl compe eqion of soil nde non-sed condiion enble s mke deil nlysis of he dynmic chnge ph of sess nd sin ding infll nd filion pocess. Howeve, i need fhe esech in hese isses: Sbiliy of he fondion pi nde diffeen infll inensiy nd sbiliy in diffeen kinds of lye nd soil popeies which his ppe didn clcle. REFERENCES [1]. C.Yn, X.S.Li ec. The FEM Anlysis of deep fondion pi s sbiliy nde inflence of mico-esin, Sie Invesigion Science nd Technolog 2006, 2: 3~7 (in Chinese [2]. S. E. Cho, S. R. Lee. Insbiliy of nsed soil slopes de o infilion [J]. Compes nd Geo-echnics, 2001 (28: [3]. Fedlnd, D. G. nd H. Rhdjo. Soil mechnics fo nsed soils Ameicn Sociey of Civil Enginees, [4]. WANG Zhi-cheng, WANG Peng nd ec. Nmeicl Simlion of Unsed Soil Slope Sbiliy Copling nde Rinfll [J]. Sbgde Engineeing, 2010 (2: (In Chinese [5]. Bishop A.W. The pinciple of effecive sess[m]. Teknisk Ukebld. 1959, 106 (39: [6]. Fedlnd D.G. nd Anqing Xing. Eqions fo he soil-we chceisic cve [J]. Cndin Geoechnicl Joml. 1994, 31: [7]. A. T A Glek in/les-sqes finie elemen fomlion fo consolidion [J]. Inenionl Jonl Fo Nmeicl Mehods In Engineeing, 2001 (52: [8]. ong Xingyn. Advnced Mechnics of Flids in Poos Medi. Hefei: Univesiy of Science nd Technology of Chin Pess, 1999: 52~56 (in Chinese [9]. R.G., Mein nd C.L., Lson. Modeling infilion ding sedy in. We Resoce, Res.vol.9 NO.2 384~394, Apil
Compressive modulus of adhesive bonded rubber block
Songklnkin J. Sci. Tecnol. 0 (, -5, M. - Ap. 008 p://www.sjs.ps.c. Oiginl Aicle Compessive modls of desive bonded bbe block Coeny Decwykl nd Wiiy Tongng * Depmen of Mecnicl Engineeing, Fcly of Engineeing,
EFFECT OF TEMPERATURE ON NON-LINEAR DYNAMICAL PROPERTY OF STUFFER BOX CRIMPING AND BUBBLE ELECTROSPINNING
Hng, J.-X., e l.: Effec of empee on Nonline ynmicl Popey... HERM SCIENCE: Ye, Vol. 8, No. 3, pp. 9-53 9 Open fom EFFEC OF EMPERURE ON NON-INER YNMIC PROPERY OF SUFFER BOX CRIMPING N BUBBE EECROSPINNING
Physics 201, Lecture 5
Phsics 1 Lecue 5 Tod s Topics n Moion in D (Chp 4.1-4.3): n D Kinemicl Quniies (sec. 4.1) n D Kinemics wih Consn Acceleion (sec. 4.) n D Pojecile (Sec 4.3) n Epeced fom Peiew: n Displcemen eloci cceleion
() t. () t r () t or v. ( t) () () ( ) = ( ) or ( ) () () () t or dv () () Section 10.4 Motion in Space: Velocity and Acceleration
Secion 1.4 Moion in Spce: Velociy nd Acceleion We e going o dive lile deepe ino somehing we ve ledy inoduced, nmely () nd (). Discuss wih you neighbo he elionships beween posiion, velociy nd cceleion you
ME 141. Engineering Mechanics
ME 141 Engineeing Mechnics Lecue 13: Kinemics of igid bodies hmd Shhedi Shkil Lecue, ep. of Mechnicl Engg, UET E-mil: sshkil@me.bue.c.bd, shkil6791@gmil.com Websie: eche.bue.c.bd/sshkil Couesy: Veco Mechnics
Solvability of nonlinear Klein-Gordon equation by Laplace Decomposition Method
Vol. 84 pp. 37-4 Jly 5 DOI:.5897/JMCSR4.57 icle Nbe: 63F95459 ISSN 6-973 Copyigh 5 hos ein he copyigh of his icle hp://www.cdeicjonls.og/jmcsr ficn Jonl of Mheics nd Cope Science Resech Fll Lengh Resech
Reinforcement learning
CS 75 Mchine Lening Lecue b einfocemen lening Milos Huskech milos@cs.pi.edu 539 Senno Sque einfocemen lening We wn o len conol policy: : X A We see emples of bu oupus e no given Insed of we ge feedbck
Suggested 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
Circuits 24/08/2010. Question. Question. Practice Questions QV CV. Review Formula s RC R R R V IR ... Charging P IV I R ... E Pt.
4/08/00 eview Fomul s icuis cice s BL B A B I I I I E...... s n n hging Q Q 0 e... n... Q Q n 0 e Q I I0e Dischging Q U Q A wie mde of bss nd nohe wie mde of silve hve he sme lengh, bu he dimee of he bss
Motion on a Curve and Curvature
Moion on Cue nd Cuue his uni is bsed on Secions 9. & 9.3, Chpe 9. All ssigned edings nd execises e fom he exbook Objecies: Mke cein h you cn define, nd use in conex, he ems, conceps nd fomuls lised below:
Technical Vibration - text 2 - forced vibration, rotational vibration
Technicl Viion - e - foced viion, oionl viion 4. oced viion, viion unde he consn eenl foce The viion unde he eenl foce. eenl The quesion is if he eenl foce e is consn o vying. If vying, wh is he foce funcion.
LECTURE 5. is defined by the position vectors r, 1. and. The displacement vector (from P 1 to P 2 ) is defined through r and 1.
LECTURE 5 ] DESCRIPTION OF PARTICLE MOTION IN SPACE -The displcemen, veloci nd cceleion in -D moion evel hei veco nue (diecion) houh he cuion h one mus p o hei sin. Thei full veco menin ppes when he picle
v T Pressure Extra Molecular Stresses Constitutive equations for Stress v t Observation: the stress tensor is symmetric
Momenum Blnce (coninued Momenum Blnce (coninued Now, wh o do wih Π? Pessue is p of i. bck o ou quesion, Now, wh o do wih? Π Pessue is p of i. Thee e ohe, nonisoopic sesses Pessue E Molecul Sesses definiion:
Science Advertisement Intergovernmental Panel on Climate Change: The Physical Science Basis 2/3/2007 Physics 253
Science Adeisemen Inegoenmenl Pnel on Clime Chnge: The Phsicl Science Bsis hp://www.ipcc.ch/spmfeb7.pdf /3/7 Phsics 53 hp://www.fonews.com/pojecs/pdf/spmfeb7.pdf /3/7 Phsics 53 3 Sus: Uni, Chpe 3 Vecos
Chapter Finite Difference Method for Ordinary Differential Equations
Chape 8.7 Finie Diffeence Mehod fo Odinay Diffeenial Eqaions Afe eading his chape, yo shold be able o. Undesand wha he finie diffeence mehod is and how o se i o solve poblems. Wha is he finie diffeence
f(x) dx with An integral having either an infinite limit of integration or an unbounded integrand is called improper. Here are two examples dx x x 2
Impope Inegls To his poin we hve only consideed inegls f() wih he is of inegion nd b finie nd he inegnd f() bounded (nd in fc coninuous ecep possibly fo finiely mny jump disconinuiies) An inegl hving eihe
Ch.4 Motion in 2D. Ch.4 Motion in 2D
Moion in plne, such s in he sceen, is clled 2-dimensionl (2D) moion. 1. Posiion, displcemen nd eloci ecos If he picle s posiion is ( 1, 1 ) 1, nd ( 2, 2 ) 2, he posiions ecos e 1 = 1 1 2 = 2 2 Aege eloci
Ans: In the rectangular loop with the assigned direction for i2: di L dt , (1) where (2) a) At t = 0, i1(t) = I1U(t) is applied and (1) becomes
omewok # P7-3 ecngul loop of widh w nd heigh h is siued ne ve long wie cing cuen i s in Fig 7- ssume i o e ecngul pulse s shown in Fig 7- Find he induced cuen i in he ecngul loop whose self-inducnce is
Answers 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
Some algorthim for solving system of linear volterra integral equation of second kind by using MATLAB 7 ALAN JALAL ABD ALKADER
. Soe lgoi o solving syse o line vole inegl eqion o second ind by sing MATLAB 7 ALAN JALAL ABD ALKADER College o Edcion / Al- Msnsiiy Univesiy Depen o Meics تقديم البحث :-//7 قبول النشر:- //. Absc ( /
D zone schemes
Ch. 5. Enegy Bnds in Cysls 5.. -D zone schemes Fee elecons E k m h Fee elecons in cysl sinα P + cosα cosk α cos α cos k cos( k + π n α k + πn mv ob P 0 h cos α cos k n α k + π m h k E Enegy is peiodic
Available online at Pelagia Research Library. Advances in Applied Science Research, 2011, 2 (3):
Avilble online www.pelgireserchlibrry.com Pelgi Reserch Librry Advnces in Applied Science Reserch 0 (): 5-65 ISSN: 0976-860 CODEN (USA): AASRFC A Mhemicl Model of For Species Syn-Ecosymbiosis Comprising
Available online Journal of Scientific and Engineering Research, 2018, 5(10): Research Article
vilble online www.jse.com Jounl of Scienific n Engineeing Resech, 8, 5():5-58 Resech icle ISSN: 94-6 CODEN(US): JSERBR Soluion of he Poblem of Sess-Sin Se of Physiclly Non-Line Heeiily Plsic Infinie Ple
4.8 Improper Integrals
4.8 Improper Inegrls Well you ve mde i hrough ll he inegrion echniques. Congrs! Unforunely for us, we sill need o cover one more inegrl. They re clled Improper Inegrls. A his poin, we ve only del wih inegrls
PHYSICS 102. Intro PHYSICS-ELECTROMAGNETISM
PHYS 0 Suen Nme: Suen Numbe: FAUTY OF SIENE Viul Miem EXAMINATION PHYSIS 0 Ino PHYSIS-EETROMAGNETISM Emines: D. Yoichi Miyh INSTRUTIONS: Aemp ll 4 quesions. All quesions hve equl weighs 0 poins ech. Answes
ENGR 1990 Engineering Mathematics The Integral of a Function as a Function
ENGR 1990 Engineering Mhemics The Inegrl of Funcion s Funcion Previously, we lerned how o esime he inegrl of funcion f( ) over some inervl y dding he res of finie se of rpezoids h represen he re under
Previously. 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
U>, 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
Contraction Mapping Principle Approach to Differential Equations
epl Journl of Science echnology 0 (009) 49-53 Conrcion pping Principle pproch o Differenil Equions Bishnu P. Dhungn Deprmen of hemics, hendr Rn Cmpus ribhuvn Universiy, Khmu epl bsrc Using n eension of
Rotations.
oons j.lbb@phscs.o.c.uk To s summ Fmes of efeence Invnce une nsfomons oon of wve funcon: -funcons Eule s ngles Emple: e e - - Angul momenum s oon geneo Genec nslons n Noehe s heoem Fmes of efeence Conse
AP Calculus AB Exam Review Sheet B - Session 1
AP Clcls AB Em Review Sheet B - Session Nme: AP 998 # Let e the nction given y e.. Find lim nd lim.. Find the solte minimm vle o. Jstiy tht yo nswe is n solte minimm. c. Wht is the nge o? d. Conside the
Interaction of Lamb Waves with Geometric Discontinuities: An Analytical Approach Compared with FEM
Ineacion of Lamb Waves ih Geomeic Disconiniies: An Analyical Appoach Compaed ih FEM Banibaa Podda a) and Vico Gigii a) a) Depamen of Mechanical Engineeing, Univesiy of Soh Caolina, USA Absac. The non-descive
Average & instantaneous velocity and acceleration Motion with constant acceleration
Physics 7: Lecure Reminders Discussion nd Lb secions sr meeing ne week Fill ou Pink dd/drop form if you need o swich o differen secion h is FULL. Do i TODAY. Homework Ch. : 5, 7,, 3,, nd 6 Ch.: 6,, 3 Submission
MEEN 617 Handout #11 MODAL ANALYSIS OF MDOF Systems with VISCOUS DAMPING
MEEN 67 Handou # MODAL ANALYSIS OF MDOF Sysems wih VISCOS DAMPING ^ Symmeic Moion of a n-dof linea sysem is descibed by he second ode diffeenial equaions M+C+K=F whee () and F () ae n ows vecos of displacemens
15/03/1439. Lecture 4: Linear Time Invariant (LTI) systems
Lecre 4: Liner Time Invrin LTI sysems 2. Liner sysems, Convolion 3 lecres: Implse response, inp signls s coninm of implses. Convolion, discree-ime nd coninos-ime. LTI sysems nd convolion Specific objecives
1. Find a basis for the row space of each of the following matrices. Your basis should consist of rows of the original matrix.
Mh 7 Exm - Prcice Prolem Solions. Find sis for he row spce of ech of he following mrices. Yor sis shold consis of rows of he originl mrix. 4 () 7 7 8 () Since we wn sis for he row spce consising of rows
Faraday s Law. To be able to find. motional emf transformer and motional emf. Motional emf
Objecie F s w Tnsfome Moionl To be ble o fin nsfome. moionl nsfome n moionl. 331 1 331 Mwell s quion: ic Fiel D: Guss lw :KV : Guss lw H: Ampee s w Poin Fom Inegl Fom D D Q sufce loop H sufce H I enclose
Class 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:
Go over vector and vector algebra Displacement and position in 2-D Average and instantaneous velocity in 2-D Average and instantaneous acceleration
Mh Csquee Go oe eco nd eco lgeb Dsplcemen nd poson n -D Aege nd nsnneous eloc n -D Aege nd nsnneous cceleon n -D Poecle moon Unfom ccle moon Rele eloc* The componens e he legs of he gh ngle whose hpoenuse
_ J.. C C A 551NED. - n R ' ' t i :. t ; . b c c : : I I .., I AS IEC. r '2 5? 9
C C A 55NED n R 5 0 9 b c c \ { s AS EC 2 5? 9 Con 0 \ 0265 o + s ^! 4 y!! {! w Y n < R > s s = ~ C c [ + * c n j R c C / e A / = + j ) d /! Y 6 ] s v * ^ / ) v } > { ± n S = S w c s y c C { ~! > R = n
Classification of Equations Characteristics
Clssiiion o Eqions Cheisis Consie n elemen o li moing in wo imensionl spe enoe s poin P elow. The ph o P is inie he line. The posiion ile is s so h n inemenl isne long is s. Le he goening eqions e epesene
Motion. ( (3 dim) ( (1 dim) dt. Equations of Motion (Constant Acceleration) Newton s Law and Weight. Magnitude of the Frictional Force
Insucos: ield/mche PHYSICS DEPARTMENT PHY 48 Em Sepeme 6, 4 Nme pin, ls fis: Signue: On m hono, I he neihe gien no eceied unuhoied id on his eminion. YOUR TEST NUMBER IS THE 5-DIGIT NUMBER AT THE TOP O
Molecular Dynamics Simulations (Leach )
Molecul Dynmics Simulions Lech 7.-7.5 compue hemlly eged popeies by smpling epesenie phse-spce jecoy i numeicl soluion of he clssicl equions of moion fo sysem of N inecing picles he coupled e.o.m. e: d
Today - Lecture 13. Today s lecture continue with rotations, torque, Note that chapters 11, 12, 13 all involve rotations
Today - Lecue 13 Today s lecue coninue wih oaions, oque, Noe ha chapes 11, 1, 13 all inole oaions slide 1 eiew Roaions Chapes 11 & 1 Viewed fom aboe (+z) Roaional, o angula elociy, gies angenial elociy
Equations from The Four Principal Kinetic States of Material Bodies. Copyright 2005 Joseph A. Rybczyk
Equions fom he Fou Pinipl Kinei Ses of Meil Bodies Copyigh 005 Joseph A. Rybzyk Following is omplee lis of ll of he equions used in o deied in he Fou Pinipl Kinei Ses of Meil Bodies. Eh equion is idenified
Computer Propagation Analysis Tools
Compue Popagaion Analysis Tools. Compue Popagaion Analysis Tools Inoducion By now you ae pobably geing he idea ha pedicing eceived signal sengh is a eally impoan as in he design of a wieless communicaion
Week 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
ELASTIC AND PLASTIC BUCKLING OF SPHERICAL SHELLS UNDER VARIOUS LOADING CONDITIONS SHAHIN NAYYERI AMIRI
ELASTIC AND PLASTIC BUCKLING OF SPHERICAL SHELLS UNDER VARIOUS LOADING CONDITIONS by SHAHIN NAYYERI AMIRI B.Sc., Univesiy o Tbiz, M.Sc., Univesiy o Tbiz, M.Phil., Univesiy o Tbiz, 6 M.Sc., Knss Se Univesiy,
1. Kinematics of Particles
1. Kinemics o Picles 1.1 Inoducion o Dnmics Dnmics - Kinemics: he sud o he geome o moion; ele displcemen, eloci, cceleion, nd ime, wihou eeence o he cuse o he moion. - Kineics: he sud o he elion eising
9.4 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
Algebra 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
Low-complexity Algorithms for MIMO Multiplexing Systems
Low-complexiy Algoihms fo MIMO Muliplexing Sysems Ouline Inoducion QRD-M M algoihm Algoihm I: : o educe he numbe of suviving pahs. Algoihm II: : o educe he numbe of candidaes fo each ansmied signal. :
WORK POWER AND ENERGY Consevaive foce a) A foce is said o be consevaive if he wok done by i is independen of pah followed by he body b) Wok done by a consevaive foce fo a closed pah is zeo c) Wok done
(b) 10 yr. (b) 13 m. 1.6 m s, m s m s (c) 13.1 s. 32. (a) 20.0 s (b) No, the minimum distance to stop = 1.00 km. 1.
Answers o Een Numbered Problems Chper. () 7 m s, 6 m s (b) 8 5 yr 4.. m ih 6. () 5. m s (b).5 m s (c).5 m s (d) 3.33 m s (e) 8. ().3 min (b) 64 mi..3 h. ().3 s (b) 3 m 4..8 mi wes of he flgpole 6. (b)
Motion. Part 2: Constant Acceleration. Acceleration. October Lab Physics. Ms. Levine 1. Acceleration. Acceleration. Units for Acceleration.
Moion Accelerion Pr : Consn Accelerion Accelerion Accelerion Accelerion is he re of chnge of velociy. = v - vo = Δv Δ ccelerion = = v - vo chnge of velociy elpsed ime Accelerion is vecor, lhough in one-dimensionl
Homework 5 for BST 631: Statistical Theory I Solutions, 09/21/2006
Homewok 5 fo BST 63: Sisicl Theoy I Soluions, 9//6 Due Time: 5:PM Thusy, on 9/8/6. Polem ( oins). Book olem.8. Soluion: E = x f ( x) = ( x) f ( x) + ( x ) f ( x) = xf ( x) + xf ( x) + f ( x) f ( x) Accoing
RELATIVE 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
Combinatorial Approach to M/M/1 Queues. Using Hypergeometric Functions
Inenaional Mahemaical Foum, Vol 8, 03, no 0, 463-47 HIKARI Ld, wwwm-hikaicom Combinaoial Appoach o M/M/ Queues Using Hypegeomeic Funcions Jagdish Saan and Kamal Nain Depamen of Saisics, Univesiy of Delhi,
Sections 3.1 and 3.4 Exponential Functions (Growth and Decay)
Secions 3.1 and 3.4 Eponenial Funcions (Gowh and Decay) Chape 3. Secions 1 and 4 Page 1 of 5 Wha Would You Rahe Have... $1million, o double you money evey day fo 31 days saing wih 1cen? Day Cens Day Cens
0 for t < 0 1 for t > 0
8.0 Sep nd del funcions Auhor: Jeremy Orloff The uni Sep Funcion We define he uni sep funcion by u() = 0 for < 0 for > 0 I is clled he uni sep funcion becuse i kes uni sep = 0. I is someimes clled he Heviside
Picture Array Generation Based on Membrane Systems and 2D Context-Free Grammars
Jounl of Mhemics nd Infomics Vol. 7, 07, 7-44 ISSN: 49-06 (P), 49-0640 (online) Pulished Mch 07 www.esechmhsci.og DOI: hp://dx.doi.og/0.457/jmi.v75 Jounl of Picue y Geneion Bsed on Memne Sysems nd D Conex-Fee
The sphere of radius a has the geographical form. r (,)=(acoscos,acossin,asin) T =(p(u)cos v, p(u)sin v,q(u) ) T.
Che 5. Dieeil Geome o Sces 5. Sce i meic om I 3D sce c be eeseed b. Elici om z =. Imlici om z = 3. Veco om = o moe geel =z deedig o wo mees. Emle. he shee o dis hs he geoghicl om =coscoscossisi Emle. he
Electric 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
2D Motion WS. A horizontally launched projectile s initial vertical velocity is zero. Solve the following problems with this information.
Nme D Moion WS The equions of moion h rele o projeciles were discussed in he Projecile Moion Anlsis Acii. ou found h projecile moes wih consn eloci in he horizonl direcion nd consn ccelerion in he ericl
DEPARTMENT 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
September 20 Homework Solutions
College of Engineering nd Compuer Science Mechnicl Engineering Deprmen Mechnicl Engineering A Seminr in Engineering Anlysis Fll 7 Number 66 Insrucor: Lrry Creo Sepember Homework Soluions Find he specrum
Read Range Analysis of Passive RFID Systems for Manufacturing Control Systems
Red Rnge Anlysis of Pssive RFID Sysems fo Mnufcuing Conol Sysems M. Keskilmmi, L. Sydänheimo, P. Slonen, M. Kivikoski leconics Tmpee Univesiy of Technology P.O. Box 69, FIN-3311 Tmpee FINLAND Absc: - An
Physic 231 Lecture 4. Mi it ftd l t. Main points of today s lecture: Example: addition of velocities Trajectories of objects in 2 = =
Mi i fd l Phsic 3 Lecure 4 Min poins of od s lecure: Emple: ddiion of elociies Trjecories of objecs in dimensions: dimensions: g 9.8m/s downwrds ( ) g o g g Emple: A foobll pler runs he pern gien in he
MATHEMATICAL FOUNDATIONS FOR APPROXIMATING PARTICLE BEHAVIOUR AT RADIUS OF THE PLANCK LENGTH
Fundamenal Jounal of Mahemaical Phsics Vol 3 Issue 013 Pages 55-6 Published online a hp://wwwfdincom/ MATHEMATICAL FOUNDATIONS FOR APPROXIMATING PARTICLE BEHAVIOUR AT RADIUS OF THE PLANCK LENGTH Univesias
Control Volume Derivation
School of eospace Engineeing Conol Volume -1 Copyigh 1 by Jey M. Seizman. ll ighs esee. Conol Volume Deiaion How o cone ou elaionships fo a close sysem (conol mass) o an open sysem (conol olume) Fo mass
Physics 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
General Non-Arbitrage Model. I. Partial Differential Equation for Pricing A. Traded Underlying Security
1 Geneal Non-Abiage Model I. Paial Diffeenial Equaion fo Picing A. aded Undelying Secuiy 1. Dynamics of he Asse Given by: a. ds = µ (S, )d + σ (S, )dz b. he asse can be eihe a sock, o a cuency, an index,
The order of reaction is defined as the number of atoms or molecules whose concentration change during the chemical reaction.
www.hechemisryguru.com Re Lw Expression Order of Recion The order of recion is defined s he number of oms or molecules whose concenrion chnge during he chemicl recion. Or The ol number of molecules or
Discrete 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
Fluids & 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
PHYS PRACTICE EXAM 2
PHYS 1800 PRACTICE EXAM Pa I Muliple Choice Quesions [ ps each] Diecions: Cicle he one alenaive ha bes complees he saemen o answes he quesion. Unless ohewise saed, assume ideal condiions (no ai esisance,
USING LOWER CLASS WEIGHTS TO CORRECT AND CHECK THE NONLINEARITY OF BALANCES
USING OWER CSS WEIGHTS TO CORRECT ND CHECK THE NONINERITY OF BNCES Tiohy Chnglin Wng, Qiho Yun, hu Reichuh Mele-Toledo Insuens Shnghi Co. d, Shnghi, P R Chin Mele-Toledo GH, Geifensee, Swizelnd BSTRCT
CSE590B Lecture 4 More about P 1
SE590 Lece 4 Moe abo P 1 Tansfoming Tansfomaions James. linn Jimlinn.om h://coses.cs.washingon.ed/coses/cse590b/13a/ Peviosly On SE590b Tansfomaions M M w w w w w The ncion w w w w w w 0 w w 0 w 0 w The
Orthotropic Materials
Kapiel 2 Ohoopic Maeials 2. Elasic Sain maix Elasic sains ae elaed o sesses by Hooke's law, as saed below. The sesssain elaionship is in each maeial poin fomulaed in he local caesian coodinae sysem. ε
f t f a f x dx By Lin McMullin f x dx= f b f a. 2
Accumulion: Thoughs On () By Lin McMullin f f f d = + The gols of he AP* Clculus progrm include he semen, Sudens should undersnd he definie inegrl s he ne ccumulion of chnge. 1 The Topicl Ouline includes
Available 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
Fourier-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
Mathematics 805 Final Examination Answers
. 5 poins Se he Weiersrss M-es. Mhemics 85 Finl Eminion Answers Answer: Suppose h A R, nd f n : A R. Suppose furher h f n M n for ll A, nd h Mn converges. Then f n converges uniformly on A.. 5 poins Se
Friedmannien 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
Homework 3 MAE 118C Problems 2, 5, 7, 10, 14, 15, 18, 23, 30, 31 from Chapter 5, Lamarsh & Baratta. The flux for a point source is:
. Homewok 3 MAE 8C Poblems, 5, 7, 0, 4, 5, 8, 3, 30, 3 fom Chpte 5, msh & Btt Point souces emit nuetons/sec t points,,, n 3 fin the flux cuent hlf wy between one sie of the tingle (blck ot). The flux fo
Dynamically Equivalent Systems. Dynamically Equivalent Systems. Dynamically Equivalent Systems. ME 201 Mechanics of Machines
ME 0 Mechnics of Mchines 8//006 Dynmicy Equivent Systems Ex: Connecting od G Dynmicy Equivent Systems. If the mss of the connecting od m G m m B m m m. Moment out cente of gvity shoud e zeo m G m B Theefoe;
This 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
Radial 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
STUDY OF THE STRESS-STRENGTH RELIABILITY AMONG THE PARAMETERS OF GENERALIZED INVERSE WEIBULL DISTRIBUTION
Inenaional Jounal of Science, Technology & Managemen Volume No 04, Special Issue No. 0, Mach 205 ISSN (online): 2394-537 STUDY OF THE STRESS-STRENGTH RELIABILITY AMONG THE PARAMETERS OF GENERALIZED INVERSE
Physics 2A HW #3 Solutions
Chper 3 Focus on Conceps: 3, 4, 6, 9 Problems: 9, 9, 3, 41, 66, 7, 75, 77 Phsics A HW #3 Soluions Focus On Conceps 3-3 (c) The ccelerion due o grvi is he sme for boh blls, despie he fc h he hve differen
the king's singers And So It Goes the colour of song Words and Vusic by By Joel LEONARD Arranged by Bob Chilcott
085850 SATB div cppell US $25 So Goes Wods nd Vusic by By Joel Anged by Bob Chilco he king's singes L he colou of song A H EXCLUSVELY DSTRBUTED BY LEONARD (Fom The King's Singes 25h Annivesy Jubilee) So
ENGI 4430 Advanced Calculus for Engineering Faculty of Engineering and Applied Science Problem Set 9 Solutions [Theorems of Gauss and Stokes]
![ENGI 4430 Advanced Calculus for Engineering Faculty of Engineering and Applied Science Problem Set 9 Solutions [Theorems of Gauss and Stokes]](/thumbs/91/106162145.jpg "ENGI 4430 Advanced Calculus for Engineering Faculty of Engineering and Applied Science Problem Set 9 Solutions [Theorems of Gauss and Stokes]")
ENGI 44 Avance alculus fo Engineeing Faculy of Engineeing an Applie cience Poblem e 9 oluions [Theoems of Gauss an okes]. A fla aea A is boune by he iangle whose veices ae he poins P(,, ), Q(,, ) an R(,,
ME 3560 Fluid Mechanics
ME3560 Flid Mechanics Fall 08 ME 3560 Flid Mechanics Analsis of Flid Flo Analsis of Flid Flo ME3560 Flid Mechanics Fall 08 6. Flid Elemen Kinemaics In geneal a flid paicle can ndego anslaion, linea defomaion
ÖRNEK 1: THE LINEAR IMPULSE-MOMENTUM RELATION Calculate the linear momentum of a particle of mass m=10 kg which has a. kg m s
MÜHENDİSLİK MEKANİĞİ. HAFTA İMPULS- MMENTUM-ÇARPIŞMA Linea oenu of a paicle: The sybol L denoes he linea oenu and is defined as he ass ies he elociy of a paicle. L ÖRNEK : THE LINEAR IMPULSE-MMENTUM RELATIN
The shortest path between two truths in the real domain passes through the complex domain. J. Hadamard
Complex Analysis R.G. Halbud R.Halbud@ucl.ac.uk Depamen of Mahemaics Univesiy College London 202 The shoes pah beween wo uhs in he eal domain passes hough he complex domain. J. Hadamad Chape The fis fundamenal
School 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
Available online Journal of Scientific and Engineering Research, 2017, 4(2): Research Article
Avlble onlne www.jse.com Jonl of Scenfc nd Engneeng Resech, 7, 4():5- Resech Acle SSN: 394-63 CODEN(USA): JSERBR Exc Solons of Qselsc Poblems of Lne Theoy of Vscoelscy nd Nonlne Theoy Vscoelscy fo echnclly
Magnetostatics Bar Magnet. Magnetostatics Oersted s Experiment
Mgneosics Br Mgne As fr bck s 4500 yers go, he Chinese discovered h cerin ypes of iron ore could rc ech oher nd cerin mels. Iron filings "mp" of br mgne s field Crefully suspended slivers of his mel were
156 There are 9 books stacked on a shelf. The thickness of each book is either 1 inch or 2
156 Thee ae 9 books sacked on a shelf. The hickness of each book is eihe 1 inch o 2 F inches. The heigh of he sack of 9 books is 14 inches. Which sysem of equaions can be used o deemine x, he numbe of
Lecture 18: Kinetics of Phase Growth in a Two-component System: general kinetics analysis based on the dilute-solution approximation
Lecue 8: Kineics of Phase Gowh in a Two-componen Sysem: geneal kineics analysis based on he dilue-soluion appoximaion Today s opics: In he las Lecues, we leaned hee diffeen ways o descibe he diffusion