Design of elementary switches for high power with minimal moving mass

Size: px
Start display at page:

Download "Design of elementary switches for high power with minimal moving mass"

Transcription

1 Design of elementary swithes for high power with minimal moving mass alter Holaus ETH Zürih, High Voltage Laoratory Physistrasse 3, CH-89 Zurih Switzerlan ABSTRACT For the use in hyri systems an for synhronous urrent interruption, ultra-fast swithes with high withstan voltage an high ontinuous urrent are require, ut they on t nee failities for fore ar ooling. This paper presents esigns for linearly an rotationally operate opening an losing swithes with a repulsion rive, that feature opening veloities of several m/s, requiring a rive energy of less than J. Base on the efinition of an elementary swith, the main imensions of these swithes suh as require ontat gap, ontat ross setion an minimal moving mass are estimate. A generally appliale equation to alulate the resulting opening veloity is given. As a result, rotational operation shows muh higher opening veloity than linear operation for the same esign parameters with goo agreement to measure values. KEY ORDS: Fast Swithes, Minimal mass, Repulsion rive, System protetion. INTRODUCTION Eletromehanial swithgear suh as iruit reaers, relays an ontators are state of the art for swithing in low, meium an high voltage systems []. They are ale to ope with the swithing emans require y stanars an toay are eonomially most attrative. The main rawa of iruit reaers in high voltage systems is, that its swithing priniple oes not feature a (fault) urrent limiting funtionality for two reasons: The rive system is to slow to at within ms The ar voltage annot e raise up to many V within several milliseons. Both prolems oul e overome, if using powersemionutor swithing evies, suh as GTO s or IGBT s. However, these evies are eonomially unattrative, eause the interrupting power of a single semionutor element is aroun 3 orers of magnitue lower ompare to high voltage iruit reaers (HVCB) as shown in Fig.. Therefore, thousans of these elements have to e operate simultaneously to replae one HVCB. Semionutor elements an operate in the highest power ratings ( M) only at a very short interrupting time of... µs ue to the losses generate uring swithing. The highest power ratings of eletromehanial swithes (> G) are possile at interrupting times of ms, whih is too slow for effetive fault urrent limitation in 5/6 Hz systems. Interrupting power per element [M] Minimal require operating time for effetive urrent limiting an syhronous reaing in 5/6 Hz iruits Integrate gate turn off thyristor Hyri systems High Voltage Ciruit Breaers Low voltage magnet last reaer Range of semionutor Range of eletro- swithes mehanial swithes.... Interruption time [ms] Fig. : Overview on interrupting power an swithing time of single semionutor elements an eletromehanial swithes. Reently, several puliations have shown how to use simple ut very fast swithes in hyri onepts to ahieve fault urrent limitation at meium-voltage levels []-[4]. The presente hyri systems show an interrupting power up to several M an require a mehanial opening swith in the ontinuous urrent path that ommutates the still inreasing (fault) urrent on a parallel path within several µs. Therefore, this swith has not to e esigne as a iruit reaer ut rather as a fast ommutation element. The mentione appliation in a hyri system requires fast swithes ut no ar ooling failities. Another appliation with the very same eman is the well-nown synhronous urrent interruption, where the neessarily fast swith is triggere to open shortly prior to urrent zero in an a iruit. Therefore, the goal of this paper is to present an isuss useful esigns for ultra-fast high power swithes that are showing opening veloities of several m/s ut are not equippe with fore ar ooling failities.. ELEMENTARY SITCHES Given the omprehensive nowlege on the esign an physis of moern high power swithing evies, it is highly unliely that a feasile an eonomial esign for high power swithgear an e foun without onsiering a major hange in the swithing approah. Therefore, the iea of using elementary swithes as high power swithes is isusse in the present paper: This wor was supporte y ABB Switzerlan Lt.

2 hat is an elementary swith? The swithing tas in toay s high power swithgear is mehanially performe y a rive- an ontat system ut the swithing ar eletrially performs it. Aoring to Fig., the swithing ar exist for several ms in the swith an the swith itself has to extinguish the ar at a urrent zero rossing. Therefore, when using this well woring priniple, to ope with the swithing ar has a major impat on swithgear esign. The situation is ifferent, if presuming an ultra-fast opening swith for fast ommutation or for synhronous urrent interruption, where the swithing ar exists for a very short time perio (several µs) only. There is no nee to esign a fast swith so to ope with an enuring highurrent ar. A high power swith, whih oes not onsier a esign impat of the ar at all, is terme an elementary swith in the present wor. Therefore, an elementary swith is a theoretial entity, whih serves as a asis to erive the very limits of inertia an opening veloity of power swithes. Anyhow, it will e shown in hapter 3, that, with the use of a repulsion rive, implementations are possile, whih are losely mathing the elementary swith esign. The main goal of the elementary swith esign is high opening veloity. Hene, the aelerate mass ( inertia) is to e minimize an the operating mehanism has to e ept as simple as possile. Both is ahieve, if the moving ontat part is the one an only moving part (MP) in the swith. This part in general an e move linearly or rotationally as shown in a priniple seth in Fig. a, with FC an FC eing the fixe ontats. a) Linear ) Rotational A FC m s v MP FC l Swithing Meium m rot MP FC v,ω A s + FC Fig. :Priniple esign of linearly an rotationally operate elementary swithes an the notations use throughout this wor. Per efinition, a swith is terme an elementary swith, if it only fulfills its elementary funtions. These are: ithstan the esign voltage if open Carry the esign urrent if lose Performing mehanial opening an losing operations. Note that aoring to the aove-mentione iea, ar ooling an extinguishing is not an elementary funtion, as it e.g. is the ase for a isonnetor. For the following theoretial onsierations on elementary swithes it is not reasonale to wor with rate values as given y stanars. Hene, the terms esign voltage an esign urrent are given to istinguish from rate values. A efinition for the esign values for elementary swithes is given as follows: The esign voltage U im is the reaown voltage of an elementary swith in the fully OPEN position. The esign urrent I im is the ontinuous thermal limiting urrent through the elementary swith in the CLOSE position. The average reaown fiel strength E is given y the ratio of U im over ontat gap s for a given swithing meium an pressure. The average ontat urrent ensity J is given y the ratio I im over the ross setion of the moving part A (see Fig. ). The average reaown fiel strength of the oil insulation material is terme E iso. These efinitions are use in the following setion for an estimation of the main imensions of suh swithes. Estimating the main imensions of elementary swithes A ieletri reaown mehanism is assume to alulate the minimum ontat gap in the open position for a given esign voltage U im. Therefore, the minimum ontat gap s in fully open position results from Eq. with the esign voltage U im, the average reaown fiel strength of the utilize swithing meium E, the pressure p of the swithing meium an a safety fator safe. U safe s im Eq. p E The safety fator safe is manatory, eause U im is efine aove as reaown voltage. As the ontat gap oes not show a homogeneous eletri fiel, E is unerstoo to e an average value, whih an e erive from fiel alulations or from experimental ata for a speifie geometry. Eq. gives the ross setion A of the moving part, where I im is the imensioning urrent an J is the average ontat urrent ensity appliale. Iim A l Eq. J Eq. presumes a homogenous istriution of urrent, what isregars the onstrition of a urrent path at the ontat points. Therefore, to apply Eq., the ontat fore, the numer of ontat points an the mass of the fixe ontats have to e hosen suffiiently high so that the thermal limit for the ontat region is not exeee for a urrent ensity equal or smaller than J. These assumptions are inlue in the efinition for J. Given the ontat gap s an its ross setion A, the minimum for the moving mass m of a linearly moving part is otaine y Eq. 3, whereas ρ is the mass ensity of the moving part. ρ safe m ρ A s U im I im Eq. 3 p E J hen using a rotationally operate swith aoring to Fig., the moving part remains in the ontat gap after a 9 turn. Consequently, the istane etween the fixe ontats has to e inrease to s +. Therefore, the moving mass of rotationally operate swithes m rot is (slightly) higher than at linear motion an shows more epeneny on the imensioning urrent, see Eq. 4.

3 mrot ρ A ( s safe ρ p E J + ) U im I im I + l J im Eq. 4 To show what values result for the moving mass, Fig. 3 gives m alulate (Eq. 3) as a funtion of U im I im for opper an aluminium an various fiel strengths. It an e seen, that using p E 5 V / m, e.g., air at ar an J A/mm whih oth are useful values the mass of a moving part out of aluminium is aroun m g/m. The values for m rot (Eq. 4) are nearly iential to m in the given range. mm [g]) Cu, 5 V/m 5 V/m 3 V/m V/m 4 V/m Aluminum safe.5 JUim*Iim [M] A/mm 5 5 U im I im [M]) 5 3 Fig. 3: Theoretial minimum for the moving mass in an elementary swith as a funtion of U im I im aoring to Eq. 3. The mass alulate in Eq. 3 an Eq. 4 only ontains the mass of the moving part itself, ase on the efinitions an the approximate imensioning formula given aove. Neither rive omponents (springs, hyrauli oil, valves, gear lever ) nor aitional mass for ontating, mounting or ontat oating is ontaine herein. All aitional funtional, - ieletri, -rive, -material, -ontat an aring requirements relate to high power swithes will a mass to this theoretial minimum. For this reasons, m an m rot are unerstoo to e the theoretially minimal (possile) moving mass. An elementary swith having a esign power U im I im as given in Fig. 3 is essentially not apale of interrupting this power. It is aleit assume, that this very small inertia m in omination with a repulsion rive leas to a high ontat separation veloity. It is then the high opening an losing veloity, whih is the ey parameter for suessful appliation. 3. DRIVE SYSTEM AND ENERGY The repulsion rive was foun to e est suitale to operate fast-ating swithes []. But most esigns for fast ating swithes equippe with a repulsion rive use separate parts for the ey-urrent loop an the ontat system an a mehanial linage in etween them. Only reently, a esign for a fast opening swith was presente in literature, whih uses the moving ontat rige as ey urrent loop at the same time [4]. This multiple use of the moving part allows swith esigns, where this part Synonyms are: Thomson rive, eletroynami rive stays the only moving part in the swith an therefore shows a minimal moving mass aoring to Eq. 3 an Eq. 4. Now, omining the iea of the elementary swith with a repulsion rive, where the ey urrent loop ats as moving ontat at the same time, results in a esign presente in Fig. 4. It shows the ross setion of an elementary swith with linear movement that is opene an lose y repulsion. A rief summary of an operation proess is given elow; see [] for a etaile isussion. Opening an losing elementary swithes y repulsion The ring-shape moving part MP is shown in the lose position. hen triggering the losing swith T, the rive apaitor C isharge through the opening rive oil. The rive urrent i together with the inue ey urrents in the moving part are generating a repulsion fore on MP, whih is then pushe upwars in a narrowing gap. The moving part is eelerate an arreste in the open position y frition on the narrowing walls. To lose this swith, the losing oil is energize the same way. The loa urrent is flowing in raial iretion aross the moving part. MP FC MP i T insulation i C FC... opening oil... losing oil U Fig. 4: Applying a repulsion rive for opening an losing a linearly operate elementary swith. Applying the repulsion rive to the asi geometry for elementary swithes with rotational operation (Fig. ) leas to another feasile esign. This esign for opening an losing elementary swithes with rotational movement is given in Fig. 5. Here, the moving part is of uois shape an its entre of rotation has to e fixe on oth ens. Opening an losing is ahieve aoringly y energizing the opening oil or the losing oil. The rive oils are woun elow the moving part on one sie an aove the moving part on the other sie of the axis of rotation. FC i T C U MP insulation i FC Fig. 5: Applying a repulsion rive for opening an losing a rotationally operate elementary swith. It is now to e isusse, whether the linear or the rotational priniple, whih has not yet een treate in literature, is etter suitale for ultra-fast swithes. This is first one y a omparison of the require rive energy.

4 The ineti energy of the moving part An elementary swith is efine to e OPEN if the istane etween fixe ontats an moving ontat is larger than the istane etween the fixe ontats. Thus, the opening gap x (on eah sie) has to e larger than half of the maximal ontat gap inrease y the thiness of the moving part as given y Eq. 5: s a) linear: x + Eq. 5 ) rotational α + sin s + Given an opening time t an the opening gap x alulate y Eq. 5, the neessary veloity v (ω if rotationally operate) for fully opening the ontats within t an e alulate using Eq. 6. This presumes that v respetively ω are onstant uring opening, whih is a goo approximation aoring to measurements an simulations on several esigns. x s a) v onst. + to to Eq. 6 ) ω α + sin onst. to t o s + The require opening veloity therefore is a funtion of the swith parameters s an an it is inversely proportional to the require opening time. Comining Eq. 3 an Eq. 6a leas to the ineti energy lin of linearly opene swithes as a funtion of the opening time, see Eq. 7. lin m v ρ s + l s t o Eq. 7 Therefore, the ineti energy lin strongly epens on l, an s, ut ontat length l an thiness are not separately etermine y Eq., whih gives possiilities for optimisation. For rotationally operate swithes, the moving part is approximate y a uoi an the moment of inertia J of uois. Thus, the ineti energy results from Eq. 8; mainly epening on ontat gap s an ontat thiness. rot J ρ l ω ( + ) ( s + ) ( s + ) + sin s + t o Eq. 8 For omparing linear or rotational operation, the ineti energy of oth priniples is to e ompare. Fig. 6 shows the asolute values of lin an rot (ompute using Eq. 7 an Eq. 8) as a funtion of the ontat istane s for an opening time of t o.5 ms while varying the ontat thiness. The ontat ross setion was hosen to A m, whih is suitale for urrents in the A-range lin, rot [J] Constants: Aluminum, t o.5 ms A m rot, 5 mm lin, 5 mm lin, 3mm rot, 3 mm lin, mm rot, mm s,[mm] s,[mm] lin, rot [J] lin, 5 mm lin, mm lin, 3mm rot, 5 mm rot, 3 mm rot, mm Fig. 6: Kineti energy of the moving part uring opening as a funtion of ontat istane s when opene within t.5 ms. Parameter is the thiness of the moving part, whih is of aluminum for oth linear an rotational operation. It an e rawn from Fig. 6, that the ineti energy of linearly moving ontats is notieale higher at high ontat gaps s, for all values of mass ensity an opening time. At small ontat gaps, there is small ifferene etween the ineti energy for linear an for rotational movement. The resulting values of ineti energy are within several J. Aluminum was hosen as ul material for the moving part as it shows high onutivity an low mass ensity. Using opper instea of aluminium for the moving part woul lea to three times higher energy values ue to higher mass ensity. Require rive energy for elementary swithes The values erive from Eq. 7 an Eq. 8 are giving the ineti energy of the moving part in motion. These have to e ivie y the rive effiieny whih is nown to e only aroun % for repulsion rives to get the require rive energy for the elementary swithes. From theoretial onsierations on repulsion rives foun in literature [5] an from measurements, the following epenene of rive effiieny η from esign parameters applie: η η U im δ e e E iso, η 8 % Eq. 9 inf inf δ is the sin epth of the ey urrents in the moving part an E iso is the reaown fiel for the rive oil insulation an η inf is the maximum rive effiieny. Comining Eq. 7 an Eq. 9 no leas to the require rive energy for linear movement Dlin Dlin η lin ρ l s η s + t C U Eq. Aoringly, the require rive energy for rotational movement Drot results to

5 Drot η ρ l rot ( + ) ( s + ) ( s + ) sin 4 + η t s + o Eq. One question to e answere y this erivation was, whether linear or rotational operation etter fits for ultrafast elementary swithes. The ratio of require rive energy Dlin / Drot for the same rive- an iruit parameters given in Fig. 7 shows, that using linear operation requires up to three times more rive energy. 3.5 Dlin / Drot ar 3 ar 5 ar ar Constants:.5 E 5 V/m l 3 mm mm J 4 A/mm I im 4 A U im [V] Fig. 7: Ratio of require rive energy of linear over rotational movement. Parameter is the pressure p of the swithing meium (see Eq. ). From this omparison it is onlue that aoring to rive energy requirements, rotational operation is superior to linear operation for most esigns. The lower the ieletri strength of the swithing meium an the higher the system voltage, the etter is rotational. A seon question arises from the a rive effiieny of the repulsion rive an the fat, that the rive energy is to e store in apaitors, whih itself have a low energy ensity: hat asolute values for the rive energy result for elementary swithes at higher voltage levels? Fig. 8 showing the require rive energy for imensioning voltage levels up to 5 V answers this question. The values erive for elementary swithes exponentially inrease with the esign voltage an are ompare to the rive energy of stanar iruit reaer, assuming U im eing omparale to the asi insulation level (BIL) in stanars. Fig. 8 shows, that a typial rive apaitor has to have a store energy of several J; for instane a isharge apaitor with C 5 µf, U 5 V, whih gives D 3 J. This apaitor has a volume of V 4.44 liter whih is reasonale an omparale to the require volume of the rive systems of stanar meium voltage iruit reaers. However, it is onlue for higher voltage levels that it maes soun sense to inrease the ieletri strength of the utilize swithing meium rather than rive energy. Inreasing the pressure p of the swithing meium or using one with higher ieletri strength, as e.g. SF 6, ahieves this. Dlin, Drot [J] For omparison: Drive energy for puffer-reaer (approx.) Self-last tehnology (approx.) Lin. ar Rot. ar Lin. 3 ar Rot. 3 ar Lin. 5 ar Rot. 5 ar U im [V] Fig. 8: Require rive energy as a funtion of imensioning voltage for linear un rotational movement. Parameter: E iso 5 V/mm, E.5 V/m, η inf 8%, mm, l 5 mm, t open ms, I im A. For omparison: Self-last: J/M, Puffer-reaer: 7 J/M from [6] 4. OPENING VELOCITY For the erivation of the main imensions of elementary swithes it was foun, that the ontinuous urrent efines the ontat ross setion A l ut not l an iniviually, see Fig. an Eq. aove. Therefore, there are possiilities for optimisation of the swith geometry, whih are isusse in the following. Opening veloity as a funtion of esign parameters As the vital harateristi of elementary swithes is fast operation, optimisation is arrie out for its opening veloity. Using the ineti energy Dlin from Eq., the minimal moving mass m from Eq. 3 an the rive effiieny given in Eq. 9, one an erive the opening veloity for linear operation as a funtion of swith esign an rive parameters as given in Eq.. U lin η im inf Dlin Eiso δ v, lin e e m Eq. ρ l s Aoringly, the opening veloities for rotational operation as a funtion of swith esign an rive parameters are given in Eq. 3. U 6 η ( + ) Drot s im inf Eiso δ v, rot e e ρ l ( + s ) + Eq. 3 ( ) Eq. an Eq. 3 are wiely appliale equations to alulate the opening veloity of elementary swithes as a funtion of swith esign, rive values an ontat material. These equations an e use as an optimisation tool for a qui he on the imensions for a speifi rating. Some speifi values alulate using Eq. an Eq. 3, for aluminium, magnesium an opper an the same rive energy for oth operating priniples Dlin Drot D J are given in Fig. 9. The veloity is at most 6 % higher if using aluminum or magnesium as ontat material instea of opper.

6 3 Sin epth opper 5 v [m/s] 5 Sin epth aluminum Sin epth magnesium Rotating, magnesium Rotating, aluminum Linear, magnesium Rotating, opper Linear, aluminum Constants: Linear, opper D J l. m Measure: linear, aluminum 5 η inf 8 % Measure: linear, opper s 7 mm f 3.5 Hz s i mm [mm] Fig. 9: Calulate opening veloity of elementary swithes with repulsion rive as a funtion of ontat thiness. Linearly- an rotationally operate swithes of Al, Mg an Cu are shown in omparison to measure values. From Fig. 9 it turns out, that the optimum ontat thiness to get highest veloity is in the range of some mm for all three materials. The opening veloity shows a flattish optimum at a thiness whih is little larger than the sin epth δ an thus epens on the rive frequeny f. In general, the optimal ontat thiness is within opt (.5 ) δ for linear an rotational movement; thus the optimum thiness if using opper is slightly smaller. In Fig. 9 also the measure opening veloities for mm of an implemente swith with the given parameters an equippe with a opper, respetively an aluminum moving ontat are given for. The measurements are in goo agreement with the alulate values. Comparison to measure values A omparison of the measure opening veloity of a rotationally operate swith to alulate values (Eq. 3) for a wie range of rive energy is given in Fig v [m/s] alulate using Eq measure values for a rotationally operate swith D [J] Fig. : Comparison of measure opening veloity with alulate values from Eq. 3 for a rotationally operate swith. An average opening veloity up to 5 m/s oul e measure on this rotationally operate swith, whih is a very high value. The omparison shows a very goo agreement etween measure an alulate values at high rive energy. At lower rive energy, what opes with lower opening veloity, the measure values are muh smaller than the alulate ones. This is suppose to originate from the ontat fore, whih ats as a retaration on the moving part. A onstant ontat fore eomes more effetive at low riving fores, i.e. at low rive energy. 5. CONCLUSIONS Base on the presumption that the esign voltage only etermines ontat gap an the esign urrent only etermines the ross setion of the moving part, a esign guieline for the so-alle elementary swithes with repulsion rive was given. The minimal moving mass of an elementary swith was alulate to e aroun g/m. The rive apaitor nees to store less than J energy for ontat veloities up to 5 m/s. The optimum thiness of the moving part is.5 times the sin epth for oth linear an rotational movement. ith regar to low rive energy an high ontat veloity, rotational operation tops linear operation an aluminum an magnesium are the most suitale materials for the moving part. As oth are worse ontat materials, they are to e oate with a suitale ontat material. A wiely appliale equation for alulating the opening veloity of elementary swithes as a funtion of swith esign, rive values an ontat material was given an the results show are in goo agreement with measure ata. This equation an e use as an optimization tool for a qui he on the imensions for a speifi rating. Possile appliations of ultra-fast swithes with the presente esign are in hyri systems for fault urrent limitation, for synhronous urrent interruption, for fast isonnetors or for fast losing swithes at meium voltage levels. The interruption apaility of suh swithes in these appliations is remarale an isusse in [] [4]. 6. REFERENCES [] M. Linmayer, Shaltgeräte: Grunlagen, Aufau, irungsweise (Springer Verlag, Berlin 987). [] M. Steurer, Ein hyries Shaltsystem für Mittelspannung zur stromegrenzenen Kurzshlussunterrehung (Thesis ETH Zürih, ). [3] M. Steurer, K. Fröhlih,. Holaus, K. Kaltenegger, A Novel Hyri Current Limiting Ciruit Breaer for Meium Voltage: Priniple an Test Results, Sumitte to: IEEE Transations on Power Systems. [4]. Holaus, K. Fröhlih, Ultra-Fast Swithes A New Element for Meium Voltage Fault Current Limiting Swithgear, Sumitte to: IEEE-PES inter Meeting, New Yor. [5] P. Zieve, High fore ensity ey urrent riven atuator. IEEE Transations on magnetis, 4, 988, [6] D.S. Johnson,. Hofauer, J. Steharth, Development of the type 45 PM self-last iruit reaer, 99 Dole Client Conferene, Boston 99.

Chapter 2: One-dimensional Steady State Conduction

Chapter 2: One-dimensional Steady State Conduction 1 Chapter : One-imensional Steay State Conution.1 Eamples of One-imensional Conution Eample.1: Plate with Energy Generation an Variable Conutivity Sine k is variable it must remain insie the ifferentiation

More information

Supplementary Materials for A universal data based method for reconstructing complex networks with binary-state dynamics

Supplementary Materials for A universal data based method for reconstructing complex networks with binary-state dynamics Supplementary Materials for A universal ata ase metho for reonstruting omplex networks with inary-state ynamis Jingwen Li, Zhesi Shen, Wen-Xu Wang, Celso Greogi, an Ying-Cheng Lai 1 Computation etails

More information

Chapter 9. There are 7 out of 50 measurements that are greater than or equal to 5.1; therefore, the fraction of the

Chapter 9. There are 7 out of 50 measurements that are greater than or equal to 5.1; therefore, the fraction of the Pratie questions 6 1 a y i = 6 µ = = 1 i = 1 y i µ i = 1 ( ) = 95 = s n 95 555. x i f i 1 1+ + 5+ n + 5 5 + n µ = = = f 11+ n 11+ n i 7 + n = 5 + n = 6n n = a Time (minutes) 1.6.1.6.1.6.1.6 5.1 5.6 6.1

More information

Euler and Hamilton Paths

Euler and Hamilton Paths Euler an Hamilton Paths The town of Königserg, Prussia (now know as Kaliningra an part of the Russian repuli), was ivie into four setion y ranhes of the Pregel River. These four setions C A D B Figure:

More information

Implementing the Law of Sines to solve SAS triangles

Implementing the Law of Sines to solve SAS triangles Implementing the Law of Sines to solve SAS triangles June 8, 009 Konstantine Zelator Dept. of Math an Computer Siene Rhoe Islan College 600 Mount Pleasant Avenue Proviene, RI 0908 U.S.A. e-mail : kzelator@ri.eu

More information

Determination the Invert Level of a Stilling Basin to Control Hydraulic Jump

Determination the Invert Level of a Stilling Basin to Control Hydraulic Jump Global Avane Researh Journal of Agriultural Siene Vol. (4) pp. 074-079, June, 0 Available online http://garj.org/garjas/inex.htm Copyright 0 Global Avane Researh Journals Full Length Researh Paper Determination

More information

CSIR-UGC NET/JRF JUNE - 6 PHYSICAL SCIENCES OOKLET - [A] PART. The raius of onvergene of the Taylor series epansion of the funtion (). The value of the ontour integral the anti-lokwise iretion, is 4z e

More information

Sensitivity Analysis of Resonant Circuits

Sensitivity Analysis of Resonant Circuits 1 Sensitivity Analysis of Resonant Ciruits Olivier Buu Abstrat We use first-orer perturbation theory to provie a loal linear relation between the iruit parameters an the poles of an RLC network. The sensitivity

More information

Answers to Coursebook questions Chapter J2

Answers to Coursebook questions Chapter J2 Answers to Courseook questions Chapter J 1 a Partiles are produed in ollisions one example out of many is: a ollision of an eletron with a positron in a synhrotron. If we produe a pair of a partile and

More information

2. Properties of Functions

2. Properties of Functions 2. PROPERTIES OF FUNCTIONS 111 2. Properties of Funtions 2.1. Injetions, Surjetions, an Bijetions. Definition 2.1.1. Given f : A B 1. f is one-to-one (short han is 1 1) or injetive if preimages are unique.

More information

ECE Microwave Engineering

ECE Microwave Engineering ECE 5317-6351 Mirowave Engineering Aapte from notes by Prof. Jeffery T. Williams Fall 18 Prof. Davi R. Jakson Dept. of ECE Notes 7 Waveguiing Strutures Part : Attenuation ε, µσ, 1 Attenuation on Waveguiing

More information

Stochastic Analysis of a Compound Redundant System Involving Human Failure

Stochastic Analysis of a Compound Redundant System Involving Human Failure Journal of Matheatis an Statistis (3): 47-43, 6 ISSN 549-3644 6 Siene Publiations Stohasti nalysis of a Copoun Reunant Syste Involving uan Failure Ritu Gupta, S.. Mittal an 3 C. M. Batra,3 Departent of

More information

An Algorithm to Remove Asynchronous ROMs in Circuits with Cycles

An Algorithm to Remove Asynchronous ROMs in Circuits with Cycles 211 eon nternational Conferene on Networking an Computing An Algorithm to emove Asynhronous Ms in Ciruits with Cyles M. Nazrul slam Monal, Koji Nakano, an Yasuaki to Department of nformation Engineering,

More information

Performance Evaluation of atall Building with Damped Outriggers Ping TAN

Performance Evaluation of atall Building with Damped Outriggers Ping TAN Performane Evaluation of atall Builing with Dampe Outriggers Ping TAN Earthquake Engineering Researh an Test Center Guangzhou University, Guangzhou, China OUTLINES RESEARCH BACKGROUND IMPROVED ANALYTICAL

More information

Duct Acoustics. Chap.4 Duct Acoustics. Plane wave

Duct Acoustics. Chap.4 Duct Acoustics. Plane wave Chap.4 Dut Aoustis Dut Aoustis Plane wave A sound propagation in pipes with different ross-setional area f the wavelength of sound is large in omparison with the diameter of the pipe the sound propagates

More information

Math 225B: Differential Geometry, Homework 6

Math 225B: Differential Geometry, Homework 6 ath 225B: Differential Geometry, Homework 6 Ian Coley February 13, 214 Problem 8.7. Let ω be a 1-form on a manifol. Suppose that ω = for every lose urve in. Show that ω is exat. We laim that this onition

More information

Constraint-free Analog Placement with Topological Symmetry Structure

Constraint-free Analog Placement with Topological Symmetry Structure Constraint-free Analog Plaement with Topologial Symmetry Struture Qing DONG Department of Information an Meia Sienes University of Kitakyushu Wakamatsu, Kitakyushu, Fukuoka, 808-0135, Japan e-mail: ongqing@env.kitakyu-u.a.jp

More information

Optimal torque control of permanent magnet synchronous machines using magnetic equivalent circuits

Optimal torque control of permanent magnet synchronous machines using magnetic equivalent circuits This oument ontains a post-print version of the paper Optimal torque ontrol of permanent magnet synhronous mahines using magneti equivalent iruits authore by W. Kemmetmüller, D. Faustner, an A. Kugi an

More information

On the Reverse Problem of Fechnerian Scaling

On the Reverse Problem of Fechnerian Scaling On the Reverse Prolem of Fehnerian Saling Ehtiar N. Dzhafarov Astrat Fehnerian Saling imposes metris on two sets of stimuli relate to eah other y a isrimination funtion sujet to Regular Minimality. The

More information

Malaysian Journal of Civil Engineering 22(2) : (2010) Skudai, Johor, Malaysia. *Corresponding Author:

Malaysian Journal of Civil Engineering 22(2) : (2010) Skudai, Johor, Malaysia. *Corresponding Author: A STUDY ON FLXURAL MODULUS AND DUCTILITY OF LAMINATD CMNTITIOUS COMPOSITS M. Zakaria Hossain 1, A.S.M. Aul Awal 2* 1 Grauate Shool of Bioresoures, Mie University, Japan 2 Faulty of Civil ngineering, Universiti

More information

Reliability Optimization With Mixed Continuous-Discrete Random Variables and Parameters

Reliability Optimization With Mixed Continuous-Discrete Random Variables and Parameters Subroto Gunawan Researh Fellow Panos Y. Papalambros Professor e-mail: pyp@umih.eu Department of Mehanial Engineering, University of Mihigan, Ann Arbor, MI 4809 Reliability Optimization With Mixe Continuous-Disrete

More information

Conveyor trajectory discharge angles

Conveyor trajectory discharge angles University of Wollongong Researh Online Faulty of Engineering - Papers (Arhive) Faulty of Engineering and Information Sienes 007 Conveyor trajetory disharge angles David B. Hastie University of Wollongong,

More information

Math 151 Introduction to Eigenvectors

Math 151 Introduction to Eigenvectors Math 151 Introdution to Eigenvetors The motivating example we used to desrie matrixes was landsape hange and vegetation suession. We hose the simple example of Bare Soil (B), eing replaed y Grasses (G)

More information

The Laws of Acceleration

The Laws of Acceleration The Laws of Aeleration The Relationships between Time, Veloity, and Rate of Aeleration Copyright 2001 Joseph A. Rybzyk Abstrat Presented is a theory in fundamental theoretial physis that establishes the

More information

Heat exchangers: Heat exchanger types:

Heat exchangers: Heat exchanger types: Heat exhangers: he proess of heat exhange between two fluids that are at different temperatures and separated by a solid wall ours in many engineering appliations. he devie used to implement this exhange

More information

Combined Electric and Magnetic Dipoles for Mesoband Radiation, Part 2

Combined Electric and Magnetic Dipoles for Mesoband Radiation, Part 2 Sensor and Simulation Notes Note 53 3 May 8 Combined Eletri and Magneti Dipoles for Mesoband Radiation, Part Carl E. Baum University of New Mexio Department of Eletrial and Computer Engineering Albuquerque

More information

Variable Impedance Control with an Artificial Muscle Manipulator Using Instantaneous Force and MR Brake

Variable Impedance Control with an Artificial Muscle Manipulator Using Instantaneous Force and MR Brake 1 IEEE/RSJ International Conferene on Intelligent Robots an Systems (IROS) November -7, 1. Tokyo, Japan ariable Impeane Control with an Artifiial Musle Manipulator Using Instantaneous Fore an MR Brake

More information

PHYSICS 212 FINAL EXAM 21 March 2003

PHYSICS 212 FINAL EXAM 21 March 2003 PHYSIS INAL EXAM Marh 00 Eam is losed book, losed notes. Use only the provided formula sheet. Write all work and answers in eam booklets. The baks of pages will not be graded unless you so ruest on the

More information

A population of 50 flies is expected to double every week, leading to a function of the x

A population of 50 flies is expected to double every week, leading to a function of the x 4 Setion 4.3 Logarithmi Funtions population of 50 flies is epeted to doule every week, leading to a funtion of the form f ( ) 50(), where represents the numer of weeks that have passed. When will this

More information

l. For adjacent fringes, m dsin m

l. For adjacent fringes, m dsin m Test 3 Pratie Problems Ch 4 Wave Nature of Light ) Double Slit A parallel beam of light from a He-Ne laser, with a wavelength of 656 nm, falls on two very narrow slits that are 0.050 mm apart. How far

More information

PN Code Tracking Loops

PN Code Tracking Loops Wireless Information Transmission System Lab. PN Coe Traking Loops Institute of Communiations Engineering National Sun Yat-sen University Introution Coe synhronization is generally arrie out in two steps

More information

Millennium Relativity Acceleration Composition. The Relativistic Relationship between Acceleration and Uniform Motion

Millennium Relativity Acceleration Composition. The Relativistic Relationship between Acceleration and Uniform Motion Millennium Relativity Aeleration Composition he Relativisti Relationship between Aeleration and niform Motion Copyright 003 Joseph A. Rybzyk Abstrat he relativisti priniples developed throughout the six

More information

The optimization of kinematical response of gear transmission

The optimization of kinematical response of gear transmission Proeeings of the 7 WSEAS Int. Conferene on Ciruits, Systems, Signal an Teleommuniations, Gol Coast, Australia, January 7-9, 7 The optimization of inematial response of gear transmission VINCENZO NIOLA

More information

Optimal Distributed Estimation Fusion with Transformed Data

Optimal Distributed Estimation Fusion with Transformed Data Optimal Distribute Estimation Fusion with Transforme Data Zhansheng Duan X. Rong Li Department of Eletrial Engineering University of New Orleans New Orleans LA 70148 U.S.A. Email: {zuanxli@uno.eu Abstrat

More information

Buckling loads of columns of regular polygon cross-section with constant volume and clamped ends

Buckling loads of columns of regular polygon cross-section with constant volume and clamped ends 76 Bukling loads of olumns of regular polygon ross-setion with onstant volume and lamped ends Byoung Koo Lee Dept. of Civil Engineering, Wonkwang University, Iksan, Junuk, 7-79, Korea Email: kleest@wonkwang.a.kr

More information

τ = 10 seconds . In a non-relativistic N 1 = N The muon survival is given by the law of radioactive decay N(t)=N exp /.

τ = 10 seconds . In a non-relativistic N 1 = N The muon survival is given by the law of radioactive decay N(t)=N exp /. Muons on the moon Time ilation using ot prouts Time ilation using Lorentz boosts Cheking the etor formula Relatiisti aition of eloities Why you an t eee the spee of light by suessie boosts Doppler shifts

More information

McCreight s Suffix Tree Construction Algorithm. Milko Izamski B.Sc. Informatics Instructor: Barbara König

McCreight s Suffix Tree Construction Algorithm. Milko Izamski B.Sc. Informatics Instructor: Barbara König 1. Introution MCreight s Suffix Tree Constrution Algorithm Milko Izamski B.S. Informatis Instrutor: Barbara König The main goal of MCreight s algorithm is to buil a suffix tree in linear time. This is

More information

MCG 3341 FLUID MECHANICS II LABORATORY MANUAL

MCG 3341 FLUID MECHANICS II LABORATORY MANUAL MG 334 UI MEHANIS II ABORATORY MANUA January Professor S. Tavoularis epartment of Mehanial Engineering University of Ottawa MG 334 UI MEHANIS II / aboratory Manual / Professor S. Tavoularis /p.. Objetive

More information

The Complete Energy Translations in the Detailed. Decay Process of Baryonic Sub-Atomic Particles. P.G.Bass.

The Complete Energy Translations in the Detailed. Decay Process of Baryonic Sub-Atomic Particles. P.G.Bass. The Complete Energy Translations in the Detailed Deay Proess of Baryoni Su-Atomi Partiles. [4] P.G.Bass. PGBass P12 Version 1..3 www.relativitydomains.om August 218 Astrat. This is the final paper on the

More information

Designing Against Size Effect on Shear Strength of Reinforced Concrete Beams Without Stirrups

Designing Against Size Effect on Shear Strength of Reinforced Concrete Beams Without Stirrups Designing Against Size Effet on Shear Strength of Reinfore Conrete Beams Without Stirrups By Zeněk P. Bažant an Qiang Yu Abstrat: The shear failure of reinfore onrete beams is a very omplex frature phenomenon

More information

Comparison of Alternative Equivalent Circuits of Induction Motor with Real Machine Data

Comparison of Alternative Equivalent Circuits of Induction Motor with Real Machine Data Comparison of Alternative Equivalent Ciruits of Indution Motor with Real Mahine Data J. radna, J. auer, S. Fligl and V. Hlinovsky Abstrat The algorithms based on separated ontrol of the motor flux and

More information

A Theorem of Mass Being Derived From Electrical Standing Waves (Adapted for a test by Jerry E. Bayles)

A Theorem of Mass Being Derived From Electrical Standing Waves (Adapted for a test by Jerry E. Bayles) EleMaEMCD A Theorem of Mass Being Derived From Eletrial Standing Waves (Adapted for a test by Jerry E Bayles) - by - Jerry E Bayles May 1, 000 This paper formalizes a onept presented in my book, "Eletrogravitation

More information

Extended Spectral Nonlinear Conjugate Gradient methods for solving unconstrained problems

Extended Spectral Nonlinear Conjugate Gradient methods for solving unconstrained problems International Journal of All Researh Euation an Sientifi Methos IJARESM ISSN: 55-6 Volume Issue 5 May-0 Extene Spetral Nonlinear Conjuate Graient methos for solvin unonstraine problems Dr Basim A Hassan

More information

The numbers inside a matrix are called the elements or entries of the matrix.

The numbers inside a matrix are called the elements or entries of the matrix. Chapter Review of Matries. Definitions A matrix is a retangular array of numers of the form a a a 3 a n a a a 3 a n a 3 a 3 a 33 a 3n..... a m a m a m3 a mn We usually use apital letters (for example,

More information

Thermal runaway during blocking

Thermal runaway during blocking Thermal runaway uring blocking CES_stable CES ICES_stable ICES k 6.5 ma 13 6. 12 5.5 11 5. 1 4.5 9 4. 8 3.5 7 3. 6 2.5 5 2. 4 1.5 3 1. 2.5 1. 6 12 18 24 3 36 s Thermal runaway uring blocking Application

More information

The Nonlinear Accuracy Model of Electro-Hydrostatic Actuator

The Nonlinear Accuracy Model of Electro-Hydrostatic Actuator The Nonlinear Auray Model of Eletro-Hydrostati Atuator Rongjie Kang, Zongxia Jiao, Shuai Wu Yaoxing Shang Shool of Automation Siene and Eletrial Engineering Beihang University Beijing, China E-mail: angrongjie@vip.163.om

More information

Is the Free Vacuum Energy Infinite?

Is the Free Vacuum Energy Infinite? Is the Free Vauum Energy Infite? H. Razmi () an S. M. Shirazi () Department of Physis, the University of Qom, Qom, I. R. Iran. () razmi@qom.a.ir & razmiha@hotmail.om () sms0@gmail.om Abstrat Consierg the

More information

Sufficient Conditions for a Flexible Manufacturing System to be Deadlocked

Sufficient Conditions for a Flexible Manufacturing System to be Deadlocked Paper 0, INT 0 Suffiient Conditions for a Flexile Manufaturing System to e Deadloked Paul E Deering, PhD Department of Engineering Tehnology and Management Ohio University deering@ohioedu Astrat In reent

More information

INFLUENCE OF OPERATING AND CONSTRUCTION PARAMETERS ON THE BEHAVIOR OF HYDRAULIC CYLINDER SUBJECTED TO JERKY MOTION

INFLUENCE OF OPERATING AND CONSTRUCTION PARAMETERS ON THE BEHAVIOR OF HYDRAULIC CYLINDER SUBJECTED TO JERKY MOTION Proeedings of ICFDP 8: 8 th International Congress of Fluid Dynamis & Propulsion Deember 14-17, 006, Sharm El-Shiekh, Sinai, Egypt ICFDP8-EG-154 INFLUENCE OF OPERATING AND CONSTRUCTION PARAMETERS ON THE

More information

Modern Physics I Solutions to Homework 4 Handout

Modern Physics I Solutions to Homework 4 Handout Moern Physis I Solutions to Homework 4 Hanout TA: Alvaro Núñez an33@sires.nyu.eu New York University, Department of Physis, 4 Washington Pl., New York, NY 0003. Bernstein, Fishbane, Gasiorowiz: Chapter

More information

Determination of the reaction order

Determination of the reaction order 5/7/07 A quote of the wee (or amel of the wee): Apply yourself. Get all the eduation you an, but then... do something. Don't just stand there, mae it happen. Lee Iaoa Physial Chemistry GTM/5 reation order

More information

Answers to Coursebook questions Chapter 5.6

Answers to Coursebook questions Chapter 5.6 Answers to Courseook questions Chapter 56 Questions marke with a star (*) use the formula for the magnetic fiel create y a current μi ( = ) which is not on the syllaus an so is not eaminale See Figure

More information

THEORETICAL PROBLEM No. 3 WHY ARE STARS SO LARGE?

THEORETICAL PROBLEM No. 3 WHY ARE STARS SO LARGE? THEORETICAL PROBLEM No. 3 WHY ARE STARS SO LARGE? The stars are spheres of hot gas. Most of them shine beause they are fusing hydrogen into helium in their entral parts. In this problem we use onepts of

More information

Time Domain Method of Moments

Time Domain Method of Moments Time Domain Method of Moments Massahusetts Institute of Tehnology 6.635 leture notes 1 Introdution The Method of Moments (MoM) introdued in the previous leture is widely used for solving integral equations

More information

Active Magnetic Bearings for Frictionless Rotating Machineries

Active Magnetic Bearings for Frictionless Rotating Machineries Ative Magneti Bearings for Fritionless Rotating Mahineries Joga Dharma Setiawan Abstrat Ative magneti bearing (AMB systems an support a rotor without physial ontat and enable users to preisely ontrol rotor

More information

MultiPhysics Analysis of Trapped Field in Multi-Layer YBCO Plates

MultiPhysics Analysis of Trapped Field in Multi-Layer YBCO Plates Exerpt from the Proeedings of the COMSOL Conferene 9 Boston MultiPhysis Analysis of Trapped Field in Multi-Layer YBCO Plates Philippe. Masson Advaned Magnet Lab *7 Main Street, Bldg. #4, Palm Bay, Fl-95,

More information

Econ 455 Answers - Problem Set Consider a small country (Belgium) with the following demand and supply curves for corn:

Econ 455 Answers - Problem Set Consider a small country (Belgium) with the following demand and supply curves for corn: Spring 004 Eon 455 Harvey Lapan Eon 455 Answers - Problem Set 4 1. Consier a small ountry (Belgium with the ollowing eman an supply urves or orn: Supply = 4P s ; Deman = 1000 Assume Belgium an import steel

More information

STUDY OF INHERENT FREQUENCY OF HELMHOLTZ RESONATOR

STUDY OF INHERENT FREQUENCY OF HELMHOLTZ RESONATOR 005 WJTA Amerian Waterjet Conferene August -3, 005! Houston, Texas Paper 6B-4 STUDY OF INHERENT FREQUENCY OF HELMHOLT RESONATOR Gong Weili An Liqian Cui Longlian Xie Guixin Shool of Mehanis, Arhiteture

More information

Review Topic 4: Cubic polynomials

Review Topic 4: Cubic polynomials Review Topi : ui polynomials Short answer Fatorise Px ( ) = x + 5x + x- 9 into linear fators. The polynomial Px ( ) = x - ax + x- leaves a remainer of when it is ivie y ( x - ) an a remainer of - when

More information

Class Test 1 ( ) Subject Code :Applied Physics (17202/17207/17210) Total Marks :25. Model Answer. 3. Photon travels with the speed of light

Class Test 1 ( ) Subject Code :Applied Physics (17202/17207/17210) Total Marks :25. Model Answer. 3. Photon travels with the speed of light Class Test (0-) Sujet Code :Applied Physis (70/707/70) Total Marks :5 Sem. :Seond Model Answer Q Attempt any FOUR of the following 8 a State the properties of photon Ans:.Photon is eletrially neutral.

More information

DIGITAL DISTANCE RELAYING SCHEME FOR PARALLEL TRANSMISSION LINES DURING INTER-CIRCUIT FAULTS

DIGITAL DISTANCE RELAYING SCHEME FOR PARALLEL TRANSMISSION LINES DURING INTER-CIRCUIT FAULTS CHAPTER 4 DIGITAL DISTANCE RELAYING SCHEME FOR PARALLEL TRANSMISSION LINES DURING INTER-CIRCUIT FAULTS 4.1 INTRODUCTION Around the world, environmental and ost onsiousness are foring utilities to install

More information

The simulation analysis of the bridge rectifier continuous operation in AC circuit

The simulation analysis of the bridge rectifier continuous operation in AC circuit Computer Appliations in Eletrial Engineering Vol. 4 6 DOI 8/j.8-448.6. The simulation analysis of the bridge retifier ontinuous operation in AC iruit Mirosław Wiślik, Paweł Strząbała Kiele University of

More information

Journal of Mathematical Analysis and Applications

Journal of Mathematical Analysis and Applications J. Math. Anal. Appl. 371 (010) 759 763 Contents lists available at SieneDiret Journal of Mathematial Analysis an Appliations www.elsevier.om/loate/jmaa Singular Sturm omparison theorems Dov Aharonov, Uri

More information

Speed Regulation of a Small BLDC Motor using Genetic-Based Proportional Control

Speed Regulation of a Small BLDC Motor using Genetic-Based Proportional Control World Aademy of Siene, Engineering and Tehnology 47 8 Speed Regulation of a Small BLDC Motor using Geneti-Based Proportional Control S. Poonsawat, and T. Kulworawanihpong Abstrat This paper presents the

More information

Eigenvalues of tridiagonal matrix using Strum Sequence and Gerschgorin theorem

Eigenvalues of tridiagonal matrix using Strum Sequence and Gerschgorin theorem Eigenvalues o tridiagonal matrix using Strum Sequene and Gershgorin theorem T.D.Roopamala Department o Computer Siene and Engg., Sri Jayahamarajendra College o Engineering Mysore INDIA roopa_td@yahoo.o.in

More information

Part G-4: Sample Exams

Part G-4: Sample Exams Part G-4: Sample Exams 1 Cairo University M.S.: Eletronis Cooling Faulty of Engineering Final Exam (Sample 1) Mehanial Power Engineering Dept. Time allowed 2 Hours Solve as muh as you an. 1. A heat sink

More information

arxiv: v2 [hep-ex] 4 Feb 2013

arxiv: v2 [hep-ex] 4 Feb 2013 Measurement of the η η mixing angle in π an K eams with GAMS-4π Setup S.V. Donskov, 1 V.N. Kolosov, 1 A.A. Lenev, 1 Yu.V. Mikhailov, 1 V.A. Polyakov, 1 V.D. Samoylenko, 1, an G.V. Khaustov 1 1 Institute

More information

= ν L. C ν L. = ν R. P ν L. CP ν L. CP Violation. Standard Model contains only left-handed neutrinos and right-handed anti-neutrinos

= ν L. C ν L. = ν R. P ν L. CP ν L. CP Violation. Standard Model contains only left-handed neutrinos and right-handed anti-neutrinos Phy489 Leture 9 1 CP iolation Stanar Moel ontains only left-hane neutrinos an right-hane anti-neutrinos C ν L = ν L harge onjugation not a symmetry of the weak interation P ν L = ν R parity also not onserve

More information

TeSys contactors. Rated operational. current in AC V up to. kw kw kw kw kw kw kw A kg

TeSys contactors. Rated operational. current in AC V up to. kw kw kw kw kw kw kw A kg Referenes TeSys ontators TeSys D ontators for motor ontrol up to kw at 00 V, in ategory AC- For onnetion y srew lamp terminals and lugs D0pp Dpp -pole ontators Standard power ratings of -phase motors 0-0

More information

Appendix A Market-Power Model of Business Groups. Robert C. Feenstra Deng-Shing Huang Gary G. Hamilton Revised, November 2001

Appendix A Market-Power Model of Business Groups. Robert C. Feenstra Deng-Shing Huang Gary G. Hamilton Revised, November 2001 Appendix A Market-Power Model of Business Groups Roert C. Feenstra Deng-Shing Huang Gary G. Hamilton Revised, Novemer 200 Journal of Eonomi Behavior and Organization, 5, 2003, 459-485. To solve for the

More information

Calculation of Magnetic Field of Two Coaxially Located Circular Permanent Magnets Using a Method of Physical Analogies

Calculation of Magnetic Field of Two Coaxially Located Circular Permanent Magnets Using a Method of Physical Analogies World Applied Sienes Journal 3 (): 345-35, 3 ISSN 88-495 IDOSI Puliations, 3 DOI: 589/idosiwasj3335 Calulation of Magneti Field of Two Coaxially Loated Cirular Permanent Magnets Using a Method of Physial

More information

The influence of upstream weir slope on live-bed scour at submerged weir

The influence of upstream weir slope on live-bed scour at submerged weir The influene of upstream weir slope on live-be sour at submerge weir L. Wang, B.W. Melville & H. Frierih Department of Civil an Environmental Engineering, University of Auklan, New Zealan ABSTRACT: Shape

More information

Case I: 2 users In case of 2 users, the probability of error for user 1 was earlier derived to be 2 A1

Case I: 2 users In case of 2 users, the probability of error for user 1 was earlier derived to be 2 A1 MUTLIUSER DETECTION (Letures 9 and 0) 6:33:546 Wireless Communiations Tehnologies Instrutor: Dr. Narayan Mandayam Summary By Shweta Shrivastava (shwetash@winlab.rutgers.edu) bstrat This artile ontinues

More information

An Efficient Sequential SAT Solver With Improved Search Strategies

An Efficient Sequential SAT Solver With Improved Search Strategies An Effiient Sequential SAT Solver With Improved Searh Strategies F. Lu, M.K. Iyer, G. Parthasarathy, L.-C. Wang, and K.-T. Cheng K.C. Chen Department of ECE, Design Tehnology University of California at

More information

Edexcel GCSE Maths Foundation Skills Book Ratio, proportion and rates of change 1

Edexcel GCSE Maths Foundation Skills Book Ratio, proportion and rates of change 1 Guidane on the use of odes for this mark sheme ethod mark A C P ao oe ft Auray mark ark awarded independent of method Communiation mark Proof, proess or justifiation mark Corret answer only Or equivalent

More information

Theory. Coupled Rooms

Theory. Coupled Rooms Theory of Coupled Rooms For: nternal only Report No.: R/50/TCR Prepared by:. N. taey B.., MO Otober 00 .00 Objet.. The objet of this doument is present the theory alulations to estimate the reverberant

More information

ENERGY AND MOMENTUM IN ELECTROMAGNETIC WAVES

ENERGY AND MOMENTUM IN ELECTROMAGNETIC WAVES MISN-0-211 z ENERGY AND MOMENTUM IN ELECTROMAGNETIC WAVES y È B` x ENERGY AND MOMENTUM IN ELECTROMAGNETIC WAVES by J. S. Kovas and P. Signell Mihigan State University 1. Desription................................................

More information

Supporting Information

Supporting Information Supporting Information Multiple-beam interferene enable broaban metamaterial wave plates Junhao Li, Huijie Guo, Tao Xu, 3 Lin Chen,, * Zhihong Hang, 3 Lei Zhou, an Shuqi Chen 4 Wuhan National Laborator

More information

Class XII - Physics Electromagnetic Waves Chapter-wise Problems

Class XII - Physics Electromagnetic Waves Chapter-wise Problems Class XII - Physis Eletromagneti Waves Chapter-wise Problems Multiple Choie Question :- 8 One requires ev of energy to dissoiate a arbon monoxide moleule into arbon and oxygen atoms The minimum frequeny

More information

Evaluation of effect of blade internal modes on sensitivity of Advanced LIGO

Evaluation of effect of blade internal modes on sensitivity of Advanced LIGO Evaluation of effet of blade internal modes on sensitivity of Advaned LIGO T0074-00-R Norna A Robertson 5 th Otober 00. Introdution The urrent model used to estimate the isolation ahieved by the quadruple

More information

Chapter 6. Electromagnetic Oscillations and Alternating Current

Chapter 6. Electromagnetic Oscillations and Alternating Current hapter 6 Electromagnetic Oscillations an Alternating urrent hapter 6: Electromagnetic Oscillations an Alternating urrent (hapter 31, 3 in textbook) 6.1. Oscillations 6.. The Electrical Mechanical Analogy

More information

Effect of magnetization process on levitation force between a superconducting. disk and a permanent magnet

Effect of magnetization process on levitation force between a superconducting. disk and a permanent magnet Effet of magnetization proess on levitation fore between a superonduting disk and a permanent magnet L. Liu, Y. Hou, C.Y. He, Z.X. Gao Department of Physis, State Key Laboratory for Artifiial Mirostruture

More information

Models for the simulation of electronic circuits with hysteretic inductors

Models for the simulation of electronic circuits with hysteretic inductors Proeedings of the 5th WSEAS Int. Conf. on Miroeletronis, Nanoeletronis, Optoeletronis, Prague, Czeh Republi, Marh 12-14, 26 (pp86-91) Models for the simulation of eletroni iruits with hystereti indutors

More information

He s Semi-Inverse Method and Ansatz Approach to look for Topological and Non-Topological Solutions Generalized Nonlinear Schrödinger Equation

He s Semi-Inverse Method and Ansatz Approach to look for Topological and Non-Topological Solutions Generalized Nonlinear Schrödinger Equation Quant. Phys. Lett. 3, No. 2, 23-27 2014) 23 Quantum Physis Letters An International Journal http://x.oi.org/10.12785/qpl/030202 He s Semi-Inverse Metho an Ansatz Approah to look for Topologial an Non-Topologial

More information

Gravitational Theory with Local conservation of Energy ABSTRACT

Gravitational Theory with Local conservation of Energy ABSTRACT Gravitational Theory with Loal onservation of Energy D.T. Froege V00914 @ http://www.arxtf.org Formerly Auburn University Phys-tfroege@glasgow-ky.om ABSTRACT The presentation here is base on the presumption

More information

Thermal Power Density Barriers of Converter Systems

Thermal Power Density Barriers of Converter Systems Thermal Power Density Barriers of Converter Systems Uwe DOFENIK and Johann W. KOLA Power Eletroni Systems Laboratory (PES ETH Zurih ETH-Zentrum / ETL H CH-89 Zurih Switzerland Phone: +4--6-467 Fax: +4--6-

More information

Four-dimensional equation of motion for viscous compressible substance with regard to the acceleration field, pressure field and dissipation field

Four-dimensional equation of motion for viscous compressible substance with regard to the acceleration field, pressure field and dissipation field Four-dimensional equation of motion for visous ompressible substane with regard to the aeleration field, pressure field and dissipation field Sergey G. Fedosin PO box 6488, Sviazeva str. -79, Perm, Russia

More information

Click here to order this book in one of two formats: softcover ISBN: $50.00 ISBN: $50.00

Click here to order this book in one of two formats: softcover ISBN: $50.00 ISBN: $50.00 ere is a sample hapter from Letures on Radiation Dosimetry Physis: A Deeper Look into the Foundations of Clinial Protools his sample hapter is opyrighted and made availale for personal use only No part

More information

Sampler-B. Secondary Mathematics Assessment. Sampler 521-B

Sampler-B. Secondary Mathematics Assessment. Sampler 521-B Sampler-B Seonary Mathematis Assessment Sampler 51-B Instrutions for Stuents Desription This sample test inlues 15 Selete Response an 5 Construte Response questions. Eah Selete Response has a value of

More information

Some Useful Results for Spherical and General Displacements

Some Useful Results for Spherical and General Displacements E 5 Fall 997 V. Kumar Some Useful Results for Spherial an General Displaements. Spherial Displaements.. Eulers heorem We have seen that a spherial isplaement or a pure rotation is esribe by a 3 3 rotation

More information

UNIT 4:Capacitors and Dielectric

UNIT 4:Capacitors and Dielectric UNIT 4:apacitors an Dielectric SF7 4. apacitor A capacitor is a evice that is capable of storing electric charges or electric potential energy. It is consist of two conucting plates separate by a small

More information

To investigate the relationship between the work done to accelerate a trolley and the energy stored in the moving trolley.

To investigate the relationship between the work done to accelerate a trolley and the energy stored in the moving trolley. SP2h.1 Aelerating trolleys Your teaher may wath to see if you an follow instrutions safely take areful measurements. Introdution The work done y a fore is a measure of the energy transferred when a fore

More information

Problem set 6 for the course Theoretical Optics Sample Solutions

Problem set 6 for the course Theoretical Optics Sample Solutions Karlsruher Institut für Tehnologie KIT) Institut für theoretishe Festkörperphysik SS01 Prof. Dr. G. Shön, Dr. R. Frank 15.06.01 http://www.tfp.kit.eu/stuium-lehre.php Tutorial: Group 1, Name: Group, Group

More information

arxiv: v1 [math-ph] 19 Apr 2009

arxiv: v1 [math-ph] 19 Apr 2009 arxiv:0904.933v1 [math-ph] 19 Apr 009 The relativisti mehanis in a nonholonomi setting: A unifie approah to partiles with non-zero mass an massless partiles. Olga Krupková an Jana Musilová Deember 008

More information

Review of classical thermodynamics

Review of classical thermodynamics Review of lassial thermodynamis Fundamental Laws, roperties and roesses () First Law - Energy Balane hermodynami funtions of state Internal energy, heat and work ypes of paths (isobari, isohori, isothermal,

More information

Vectors in two dimensions

Vectors in two dimensions Vectors in two imensions Until now, we have been working in one imension only The main reason for this is to become familiar with the main physical ieas like Newton s secon law, without the aitional complication

More information

Study on the leak test technology of spacecraft using ultrasonic

Study on the leak test technology of spacecraft using ultrasonic SINCE2013 Singapore International NDT Conferene & Exhibition 2013, 19-20 July 2013 Study on the test tehnology of spaeraft using ultrasoni Yan Rongxin, Li Weidan Beijing Institute of Spaeraft Environment

More information

Force Reconstruction for Nonlinear Structures in Time Domain

Force Reconstruction for Nonlinear Structures in Time Domain Fore Reonstrution for Nonlinear Strutures in ime Domain Jie Liu 1, Bing Li 2, Meng Li 3, an Huihui Miao 4 1,2,3,4 State Key Laboratory for Manufaturing Systems Engineering, Xi an Jiaotong niversity, Xi

More information

Experiment 3: Basic Electronic Circuits II (tbc 1/7/2007)

Experiment 3: Basic Electronic Circuits II (tbc 1/7/2007) Experiment 3: Basi Eletroni iruits II (tb /7/007) Objetive: a) To study the first-order dynamis of a apaitive iruits with the appliation of Kirhoff s law, Ohm s law and apaitane formula. b) To learn how

More information

General Closed-form Analytical Expressions of Air-gap Inductances for Surfacemounted Permanent Magnet and Induction Machines

General Closed-form Analytical Expressions of Air-gap Inductances for Surfacemounted Permanent Magnet and Induction Machines General Closed-form Analytial Expressions of Air-gap Indutanes for Surfaemounted Permanent Magnet and Indution Mahines Ronghai Qu, Member, IEEE Eletroni & Photoni Systems Tehnologies General Eletri Company

More information