Hydrogen Production with Mixed Protonic-Electronic Conducting Perovskite Membranes

Size: px
Start display at page:

Download "Hydrogen Production with Mixed Protonic-Electronic Conducting Perovskite Membranes"

Transcription

1 ydrogen roducon wh Mxed roonc-elecronc Conducng erovske Membranes Erc D. achsman UF-DE gh Temperaure Elecrochemsry Cener Deparmen of Maerals Scence and Engneerng Unversy of Florda Ganesvlle, FL 36 UF-DE TEC UF-DE TEC

2 ulne Inroducon Fundamenals and Maerals Developmen Membrane eacor Fabrcaon and esuls ecen Membrane Maerals Advances Conclusons UF-DE TEC

3 Concep - Auohermal Caalyc Membrane eacor for roducon of ure C N-SrCe 3 porous ubular suppor Suppor for hydrogen membrane N caalyzes endohermc seam reformng or waer gas-shf reacon SrCe -x x 3-δ dense hydrogen membrane Mxed proon-elecron conducor ~0 µm dense layer xygen ranspor membrane Exohermc oxdaon of hydrocarbon feed gas Ulmaely can produce pure from any hydrocarbon feed sock: Naural gas Coal based syn gas Bomass UF-DE TEC

4 Cos of ydrogen roducon from Naural Gas* C = C /C C ~ 0.0C$/m 3 ~$0.5/m 3 ~0.05 /ler * Assumes 00% converson and selecvy, ar and waer are free, and gnores capal cos UF-DE TEC

5 DE s Fuure Gen ydrogen and elecrcy co-generaon from coal Zero emssons and C capure ydrogen roducon from Fossl Fuels wh roon and xygen-ion Transpor Membranes, E. D. achsman and M. C. llams, Inerface, Volume 3, No.3, Fall 00 UF-DE TEC

6 ulne Inroducon Fundamenals and Maerals Developmen Membrane eacor Fabrcaon and esuls ecen Membrane Maerals Advances Conclusons UF-DE TEC

7 XIDE-IN CNDUCTING MIEC s ermeaon Membrane arally xdzed ydrocarbon Effluen C, Cnm Vo h N, N ydrocarbon Feed σ and σ e of La 0.8 Sr 0. Co 0.8 Fe 0. 3-d Teraoka, e al (998) J of La 0.6 Sr 0. Co 0.8 B 0. 3-d Teraoka, e al (998) Ionc and elecronc conducvy resuls n permeaon lmed by oxde-on conducvy σ Vo UF-DE TEC

8 XIDE-IN vs. TNIC CNDUCTIN M M x x V xygen ons jump from a flled ( x ) o a vacan (V ) se -bonded proons form an group ( ) roons move around x and jump o neghborng x UF-DE TEC

9 TNIC vs. XIDE-IN CNDUCTS ermeaon Membrane ydrogen Depleed Effluen C, C+ e o C,, C arally xdzed ydrocarbon Feed SrCe 3-δ layer N-GDC porous suppor Iwahara, e al. σ and σ e of La 0.8 Sr 0. Co 0.8 Fe 0. 3-d Teraoka, e al (998) roonc conducors have comparable onc conducvy bu neglgble elecronc conducvy flux lmed by elecronc conducvy (σ e ) UF-DE TEC

10 Addng Elecronc Conducvy o a roon Conducor Add elecronc conducvy by dopng Ce se wh mulvalen caon (M 3+/+ ) ha can be reduced o + M Ce = M Ce + e (n-ype conducon) E. D. achsman and N. Jang, cober, 00, U.S. aen No. 6,96, Mach onc rad for hase sably roon conducvy > 3+/+ Conducvy of BaCe -x M x 3-d as a funcon r M, Iwahara e al (993) UF-DE TEC

11 Flux elaonshp J // // T T =! # ln +! ( + / / / ) ln d # d V V e L F F roon flux across calculaed usng agner equaon: Assumes ha bulk dffuson s rae lmng sep σ s he oal conducvy σ = z q u, ( =, V, e ) Transference number, = σ / σ gh flux requres boh hgh proonc and hgh elecronc conducvy F s Faraday s consan L s he membrane hckness Inegrae boh and poenal gradens UF-DE TEC

12 UF-DE TEC Complex Defec Equlbra n p!! V! / Ce // Ce 6 3 { 6 3 { 6 3 ) ( 6 3 { 6 3 { A Ce // = { { { 3 { A Ce // = 6 3 { A 6 3 { A 6 3 { A 3 { { A // / Ce Ce = 6 3 { A { { { Ce / = { A 8 { 8 { { 8 { 8 { A Ce / = { { { A! { { { A! 8 { A 8 { A { A 8 { A // Ce = 8 { A { { A Charge Neuraly = V n // = V Ce = n / = V Ce A p << A p << A p >> A p >> // = V Ce / = Ce // = Ce // = Ce p Ce = /

13 Modelng Defec Equlbra and Transpor -effec of,, S. J. Song, E. D. achsman, S. E. Dorrs, and U. Balachandran, Sold Sae Ioncs, 9, -0 (00). UF-DE TEC

14 Modelng Defec Equlbra and Transpor σ = z q u UF-DE TEC

15 Selecon of Dopan - Conducvy as a Funcon of n-ype p-ype BaCe 0.85 Gd Neglgble n-ype elecronc conducvy excep a very hgh emperaure >000 C N. Bonanos (99) log σ (S/cm) -.6 ) -.65 m c / S -.7 ( g o! l C 600 C BaCe Sgnfcan n-ype elecronc conducvy a much lower emperaure and hgher J. hodes and E.D. achsman (00) log o UF-DE TEC

16 Flux elaonshp J // // T T =! # ln +! ( + / / / ) ln d # d V V e L F F Flux ~ /membrane hckness (L) YDGEN FLUX (cc/cm -mn) % 0.75 mm 90%.00 mm 90%.00 mm TEMEATUE ( o C) YDGEN FLUX (cc/cm -mn) o C 800 o C 750 o C /TICNESS (mm) A hgh emperaure (>750 C) permeaon s bulk ranspor conrolled Flux s lnear wh /L A lower emperaure permeaon s surface knec conrolled UF-DE TEC

17 ulne Inroducon Fundamenals and Maerals Developmen Membrane eacor Fabrcaon and esuls ecen Membrane Maerals Advances Conclusons UF-DE TEC

18 ydrogen Membrane Cell Fabrcaon Co-frng Slurry Snered coang suppor hydrogen for and membrane hn hn cell flm flm UF-DE TEC

19 Fabrcaon of Membrane eacor UF-DE TEC

20 ydrogen Membrane Evaluaon All ubes are connuously leak checked by Ar racer n feed gas UF-DE TEC

21 ydrogen ermeaon and Leak Tesng Confrms membranes are leak free Capable of producng 00% pury UF-DE TEC

22 ydrogen ermeaon ydrogen flux ~ / UF-DE TEC

23 ydrogen ermeaon (am) average value Acvaon energy,e (ev) Acvaon energy of ~0.9 ev ndcaes flux lmed by σ e σ acvaon energy ~ 0.5 ev UF-DE TEC

24 ydrogen ermeaon Membrane ubes produce 7 cc/mn of pure -3% balance Ar / SrCe /e UF-DE TEC

25 ydrogen ermeaon Area normalzed membrane flux comparable o bes n leraure. owever -3% balance Ar / SrCe /e balance e / SrCe 0.95 Tm / 0% balance e S. Cheng, V.. Gupa, and J. Y. S. Ln, Sold Sae Ioncs 76 (005) 653. % -3% balance e / N-BaCe 0.8 Y 0. 3 / N wh 00ppm C. Zuo, T.. Lee, S.-J. Song, L. Chen, S. E. Dorrs, U. Balachandran, and M. Lu, Elecrochem. Sold-Sae Le., 8 (005) J35 UF-DE TEC

26 ydrogen roducon C / ~ ure produced drecly by nernal seam reformng C flux even hgher han from comparable feed UF-DE TEC

27 ydrogen roducon Converson (%) h permeaon hou permeaon Thermodynamc calculaon ermeaon ydrogen producon and ermeaon Flux (cc/mn) Temperaure ( o C) aer gas shf reacon: C + -> C + 3% C and balance e Sold lnes are /C=, dashed lnes are /C UF-DE TEC

28 ulne Inroducon Fundamenals and Maerals Developmen Membrane eacor Fabrcaon and esuls ecen Membrane Maerals Advances Conclusons UF-DE TEC

29 Conducvy of -doped SrCe o C Log σ roon (Scm - ) o C 700 o C 600 o C Acvaon Energy 0 mol% 0.9 ev 5 mol% 0.5 ev 0 mol% 0.87 ev Dopng concenraon of on SrCe 3 (mol %) Toal conducvy maxmum a ~0% UF-DE TEC

30 roon vs. Elecron Conducvy - roon Conducvy - Elecron Conducvy o C 900 o C Log σ roon (Scm - ) o C 700 o C 600 o C Log σ Elecron (Scm - ) o C 700 o C 600 o C Dopng concenraon of (mol %) Dopng concenraon of (mol %) Increasng concenraon: Decreases σ Increases σ e UF-DE TEC

31 Increased Elecronc Transference Number roon Transference number roon 5 roon 0 Elecron 0 Elecron 5 = e # = + # e # e + # e 0. Elecron Temperaure ( o C) flux lmed by elecronc conducvy UF-DE TEC

32 Conclusons gh emperaure proonc conducors offer remendous poenal for producon Addng elecronc conducvy sgnfcanly ncreases flux Demonsraed permeaon flux of ~0 cc/mn flux s proporonal o / flux s lmed by elecronc conducon Demonsraed pure producon from nernal seam reformed C Demonsraed pure producon from waer-gas-shf reacon Increased producon of membrane reacor - La Chaler Increasng -dopan concenraon wll sgnfcanly ncrease permeaon and producon Demonsraed >0X ncrease n e Should resul n 6 ler/hr producon per ube UF-DE TEC

33 Acknowledgemens NASA Conrac NAG3-930 DE TEC Conrac DE-AC05-76L0830 eesung Yoon Takeun h Janln L Sun Ju Song Jame hodes UF-DE TEC

34 ydrogen roducon, Transpor, and Sorage Symposum B The Elecrochemcal Socey Chcago, May 6-, 007 Absracs should be submed va he ECS webse by January 3, 007. Commens and nqures abou he symposum may be sen o he organzers: E. D. achsman, Unversy of Florda, ewach@mse.ufl.edu M. C. llams, NETL, mark.wllams@nel.doe.gov M. eben, NEL, Mchael_heben@nrel.gov A. Manvannan, NETL, manvana@nel.doe.gov B.. Maupn, U.S. Deparmen of Energy, paul.maupn@scence.doe.gov C. V. aman, Illnos Insue of Technology, raman@.edu UF-DE TEC

Multi-Fuel and Mixed-Mode IC Engine Combustion Simulation with a Detailed Chemistry Based Progress Variable Library Approach

Multi-Fuel and Mixed-Mode IC Engine Combustion Simulation with a Detailed Chemistry Based Progress Variable Library Approach Mul-Fuel and Med-Mode IC Engne Combuson Smulaon wh a Dealed Chemsry Based Progress Varable Lbrary Approach Conens Inroducon Approach Resuls Conclusons 2 Inroducon New Combuson Model- PVM-MF New Legslaons

More information

Comprehensive Integrated Simulation and Optimization of LPP for EUV Lithography Devices

Comprehensive Integrated Simulation and Optimization of LPP for EUV Lithography Devices Comprehense Inegraed Smulaon and Opmaon of LPP for EUV Lhograph Deces A. Hassanen V. Su V. Moroo T. Su B. Rce (Inel) Fourh Inernaonal EUVL Smposum San Dego CA Noember 7-9 2005 Argonne Naonal Laboraor Offce

More information

Transcription: Messenger RNA, mrna, is produced and transported to Ribosomes

Transcription: Messenger RNA, mrna, is produced and transported to Ribosomes Quanave Cenral Dogma I Reference hp//book.bonumbers.org Inaon ranscrpon RNA polymerase and ranscrpon Facor (F) s bnds o promoer regon of DNA ranscrpon Meenger RNA, mrna, s produced and ranspored o Rbosomes

More information

Solution in semi infinite diffusion couples (error function analysis)

Solution in semi infinite diffusion couples (error function analysis) Soluon n sem nfne dffuson couples (error funcon analyss) Le us consder now he sem nfne dffuson couple of wo blocks wh concenraon of and I means ha, n a A- bnary sysem, s bondng beween wo blocks made of

More information

Nonequilibrium models for a multi component reactive distillation column

Nonequilibrium models for a multi component reactive distillation column onequlbrum models for a mul componen reacve dsllaon column D. ROUZIEAU, M. PREVOST, M. MEYER IP/E..S.I.G.C LGC Equpe Séparaon Gaz Lqude 8 Chemn de la Loge, 3078 Toulouse Cedex 4, France Absrac A nonequlbrum

More information

Optimal Operation of the Cyclic Claus Process

Optimal Operation of the Cyclic Claus Process 17 h European Symposum on Compuer Aded Process Engneerng ESCAPE17 V. Plesu and P.S. Agach (Edors) 7 Elsever B.V. All rghs reserved. 1 Opmal Operaon of he Cyclc Claus Process Assanous Abufares a and Sebasan

More information

CONTAMINATION OF QUARTZ GLASS SAMPLE SURFACES UNDER IRRADIATION BY OUTGASSED VOLATILE PRODUCTS

CONTAMINATION OF QUARTZ GLASS SAMPLE SURFACES UNDER IRRADIATION BY OUTGASSED VOLATILE PRODUCTS CONTAMINATION OF QUARTZ GLASS SAMPLE SURFACES UNDER IRRADIATION BY OUTGASSED VOLATILE PRODUCTS R.H. Khasanshn (1), A.N. Galygn (1), N.G. Alexandrov (2) (1) Jon-sock company Kompoz 4, Ponerskay sr., 141070

More information

Polymerization Technology Laboratory Course

Polymerization Technology Laboratory Course Prakkum Polymer Scence/Polymersaonsechnk Versuch Resdence Tme Dsrbuon Polymerzaon Technology Laboraory Course Resdence Tme Dsrbuon of Chemcal Reacors If molecules or elemens of a flud are akng dfferen

More information

Ion Transport Numbers

Ion Transport Numbers 4/8/17 A quoe of he week (or camel of he week): A lfe spen makng msakes s no only more honorable, bu more useful han a lfe spen dong nohng. George Bernard Shaw 1 Ion Transpor Numbers Ion ranspor number

More information

THERMODYNAMICS 1. The First Law and Other Basic Concepts (part 2)

THERMODYNAMICS 1. The First Law and Other Basic Concepts (part 2) Company LOGO THERMODYNAMICS The Frs Law and Oher Basc Conceps (par ) Deparmen of Chemcal Engneerng, Semarang Sae Unversy Dhon Harano S.T., M.T., M.Sc. Have you ever cooked? Equlbrum Equlbrum (con.) Equlbrum

More information

On One Analytic Method of. Constructing Program Controls

On One Analytic Method of. Constructing Program Controls Appled Mahemacal Scences, Vol. 9, 05, no. 8, 409-407 HIKARI Ld, www.m-hkar.com hp://dx.do.org/0.988/ams.05.54349 On One Analyc Mehod of Consrucng Program Conrols A. N. Kvko, S. V. Chsyakov and Yu. E. Balyna

More information

National Exams December 2015 NOTES: 04-BS-13, Biology. 3 hours duration

National Exams December 2015 NOTES: 04-BS-13, Biology. 3 hours duration Naonal Exams December 205 04-BS-3 Bology 3 hours duraon NOTES: f doub exss as o he nerpreaon of any queson he canddae s urged o subm wh he answer paper a clear saemen of any assumpons made 2 Ths s a CLOSED

More information

Lecture 9: Dynamic Properties

Lecture 9: Dynamic Properties Shor Course on Molecular Dynamcs Smulaon Lecure 9: Dynamc Properes Professor A. Marn Purdue Unversy Hgh Level Course Oulne 1. MD Bascs. Poenal Energy Funcons 3. Inegraon Algorhms 4. Temperaure Conrol 5.

More information

SUPPLEMENTARY INFORMATION

SUPPLEMENTARY INFORMATION In he orma provded y he auhors and uneded. SUPPLEMENTRY INFORMTION OI: 1.138/NMT4968 Nanoduson n Elecrocaalyc Flms Cyrlle Cosenn 1 *, Carlo Govann 1, Maron Graud, Jean-Mchel Savéan 1 *, and Céc Tard 1

More information

Robustness Experiments with Two Variance Components

Robustness Experiments with Two Variance Components Naonal Insue of Sandards and Technology (NIST) Informaon Technology Laboraory (ITL) Sascal Engneerng Dvson (SED) Robusness Expermens wh Two Varance Componens by Ana Ivelsse Avlés avles@ns.gov Conference

More information

Numerical Simulation of the Dispersion of a Plume of Exhaust Gases from Diesel and Petrol Engine Vehicles

Numerical Simulation of the Dispersion of a Plume of Exhaust Gases from Diesel and Petrol Engine Vehicles World Academy of Scence, Engneerng and Technology 67 01 Numercal Smulaon of he Dsperson of a Plume of Exhaus Gases from Desel and Perol Engne Vehcles H. ZAHLOUL, and M. MERIEM-BENZIANE Absrac The obecve

More information

Attribute Reduction Algorithm Based on Discernibility Matrix with Algebraic Method GAO Jing1,a, Ma Hui1, Han Zhidong2,b

Attribute Reduction Algorithm Based on Discernibility Matrix with Algebraic Method GAO Jing1,a, Ma Hui1, Han Zhidong2,b Inernaonal Indusral Informacs and Compuer Engneerng Conference (IIICEC 05) Arbue educon Algorhm Based on Dscernbly Marx wh Algebrac Mehod GAO Jng,a, Ma Hu, Han Zhdong,b Informaon School, Capal Unversy

More information

Diffusion of Heptane in Polyethylene Vinyl Acetate: Modelisation and Experimentation

Diffusion of Heptane in Polyethylene Vinyl Acetate: Modelisation and Experimentation IOSR Journal of Appled hemsry (IOSR-JA) e-issn: 78-5736.Volume 7, Issue 6 Ver. I. (Jun. 4), PP 8-86 Dffuson of Hepane n Polyehylene Vnyl Aceae: odelsaon and Expermenaon Rachd Aman *, Façal oubarak, hammed

More information

Numerical simulation of a solar chimney power plant in the southern region of Iran

Numerical simulation of a solar chimney power plant in the southern region of Iran Energy Equp. Sys./ Vol. 5/No.4/December 2017/ 431-437 Energy Equpmen and Sysems hp://energyequpsys.u.ac.r www.energyequpsys.com Numercal smulaon of a solar chmney power plan n he souhern regon of Iran

More information

Power Electronics 7. Diode and Diode Circuits

Power Electronics 7. Diode and Diode Circuits Module 7 Dode and Dode Crcus. Inroducon 2. DC and swchng characerscs 3. Types of Power Dode 4. Dode Crcu 4.. Seres Conneced Dodes 4.2. Parallel Conneced Dodes 5. Dode behavor for dfferen loads 6. Freewheelng

More information

Material Science Simulations using PWmat

Material Science Simulations using PWmat Maeral Scence Smulaons usng PWma Ln-Wang Wang Chef Techncal Advsor, LongXu Oulne 1 Charge pachng mehod for nanosrucure calculaons 2 Shockley-Read-Hall nonradave decay calculaons 3 Real-me TDDFT smulaons

More information

Track Properities of Normal Chain

Track Properities of Normal Chain In. J. Conemp. Mah. Scences, Vol. 8, 213, no. 4, 163-171 HIKARI Ld, www.m-har.com rac Propes of Normal Chan L Chen School of Mahemacs and Sascs, Zhengzhou Normal Unversy Zhengzhou Cy, Hennan Provnce, 4544,

More information

The Dynamic Programming Models for Inventory Control System with Time-varying Demand

The Dynamic Programming Models for Inventory Control System with Time-varying Demand The Dynamc Programmng Models for Invenory Conrol Sysem wh Tme-varyng Demand Truong Hong Trnh (Correspondng auhor) The Unversy of Danang, Unversy of Economcs, Venam Tel: 84-236-352-5459 E-mal: rnh.h@due.edu.vn

More information

Mobile Ion Effects on SiC MOS Bias- Temperature Instability Measurements

Mobile Ion Effects on SiC MOS Bias- Temperature Instability Measurements 14-15 Aug 2014 1 U.S. Army Research, Developmen and Engineering Command Mobile Ion Effecs on SiC MOS Bias- Temperaure Insabiliy Measuremens Daniel B. Habersa Neil Goldsman (UMD), and Aivars Lelis 14-15

More information

ELASTIC MODULUS ESTIMATION OF CHOPPED CARBON FIBER TAPE REINFORCED THERMOPLASTICS USING THE MONTE CARLO SIMULATION

ELASTIC MODULUS ESTIMATION OF CHOPPED CARBON FIBER TAPE REINFORCED THERMOPLASTICS USING THE MONTE CARLO SIMULATION THE 19 TH INTERNATIONAL ONFERENE ON OMPOSITE MATERIALS ELASTI MODULUS ESTIMATION OF HOPPED ARBON FIBER TAPE REINFORED THERMOPLASTIS USING THE MONTE ARLO SIMULATION Y. Sao 1*, J. Takahash 1, T. Masuo 1,

More information

V R. Electronics and Microelectronics AE4B34EM. Electronics and Microelectronics AE4B34EM. Voltage. Basic concept. Voltage.

V R. Electronics and Microelectronics AE4B34EM. Electronics and Microelectronics AE4B34EM. Voltage. Basic concept. Voltage. Elecroncs and Mcroelecroncs AEBEM. lecure basc elecronc crcu conceps ressors, capacors, nducors Elecroncs and Mcroelecroncs AEBEM Sudng maerals: server MOODLE hp://moodle.kme.fel.cvu.cz AEBEM Elecroncs

More information

Fall 2009 Social Sciences 7418 University of Wisconsin-Madison. Problem Set 2 Answers (4) (6) di = D (10)

Fall 2009 Social Sciences 7418 University of Wisconsin-Madison. Problem Set 2 Answers (4) (6) di = D (10) Publc Affars 974 Menze D. Chnn Fall 2009 Socal Scences 7418 Unversy of Wsconsn-Madson Problem Se 2 Answers Due n lecure on Thursday, November 12. " Box n" your answers o he algebrac quesons. 1. Consder

More information

HEAT CONDUCTION PROBLEM IN A TWO-LAYERED HOLLOW CYLINDER BY USING THE GREEN S FUNCTION METHOD

HEAT CONDUCTION PROBLEM IN A TWO-LAYERED HOLLOW CYLINDER BY USING THE GREEN S FUNCTION METHOD Journal of Appled Mahemacs and Compuaonal Mechancs 3, (), 45-5 HEAT CONDUCTION PROBLEM IN A TWO-LAYERED HOLLOW CYLINDER BY USING THE GREEN S FUNCTION METHOD Sansław Kukla, Urszula Sedlecka Insue of Mahemacs,

More information

[ ] 2. [ ]3 + (Δx i + Δx i 1 ) / 2. Δx i-1 Δx i Δx i+1. TPG4160 Reservoir Simulation 2018 Lecture note 3. page 1 of 5

[ ] 2. [ ]3 + (Δx i + Δx i 1 ) / 2. Δx i-1 Δx i Δx i+1. TPG4160 Reservoir Simulation 2018 Lecture note 3. page 1 of 5 TPG460 Reservor Smulaon 08 page of 5 DISCRETIZATIO OF THE FOW EQUATIOS As we already have seen, fne dfference appromaons of he paral dervaves appearng n he flow equaons may be obaned from Taylor seres

More information

V.Abramov - FURTHER ANALYSIS OF CONFIDENCE INTERVALS FOR LARGE CLIENT/SERVER COMPUTER NETWORKS

V.Abramov - FURTHER ANALYSIS OF CONFIDENCE INTERVALS FOR LARGE CLIENT/SERVER COMPUTER NETWORKS R&RATA # Vol.) 8, March FURTHER AALYSIS OF COFIDECE ITERVALS FOR LARGE CLIET/SERVER COMPUTER ETWORKS Vyacheslav Abramov School of Mahemacal Scences, Monash Unversy, Buldng 8, Level 4, Clayon Campus, Wellngon

More information

Modern Time-Rate Relations

Modern Time-Rate Relations Modern Tme-Rae Relaons Slde 1 Orenaon Tme-Rae Relaons: New me-rae relaons whch ulze he followng componens: Hyperbolc and modfed-hyperbolc relaons, Power-law/sreched exponenal relaons, and Exponenal relaons

More information

P R = P 0. The system is shown on the next figure:

P R = P 0. The system is shown on the next figure: TPG460 Reservor Smulaon 08 page of INTRODUCTION TO RESERVOIR SIMULATION Analycal and numercal soluons of smple one-dmensonal, one-phase flow equaons As an nroducon o reservor smulaon, we wll revew he smples

More information

Relative controllability of nonlinear systems with delays in control

Relative controllability of nonlinear systems with delays in control Relave conrollably o nonlnear sysems wh delays n conrol Jerzy Klamka Insue o Conrol Engneerng, Slesan Techncal Unversy, 44- Glwce, Poland. phone/ax : 48 32 37227, {jklamka}@a.polsl.glwce.pl Keywor: Conrollably.

More information

II. Light is a Ray (Geometrical Optics)

II. Light is a Ray (Geometrical Optics) II Lgh s a Ray (Geomercal Opcs) IIB Reflecon and Refracon Hero s Prncple of Leas Dsance Law of Reflecon Hero of Aleandra, who lved n he 2 nd cenury BC, posulaed he followng prncple: Prncple of Leas Dsance:

More information

Midterm Exam. Thursday, April hour, 15 minutes

Midterm Exam. Thursday, April hour, 15 minutes Economcs of Grow, ECO560 San Francsco Sae Unvers Mcael Bar Sprng 04 Mderm Exam Tursda, prl 0 our, 5 mnues ame: Insrucons. Ts s closed boo, closed noes exam.. o calculaors of an nd are allowed. 3. Sow all

More information

Motion in Two Dimensions

Motion in Two Dimensions Phys 1 Chaper 4 Moon n Two Dmensons adzyubenko@csub.edu hp://www.csub.edu/~adzyubenko 005, 014 A. Dzyubenko 004 Brooks/Cole 1 Dsplacemen as a Vecor The poson of an objec s descrbed by s poson ecor, r The

More information

FTCS Solution to the Heat Equation

FTCS Solution to the Heat Equation FTCS Soluon o he Hea Equaon ME 448/548 Noes Gerald Reckenwald Porland Sae Unversy Deparmen of Mechancal Engneerng gerry@pdxedu ME 448/548: FTCS Soluon o he Hea Equaon Overvew Use he forward fne d erence

More information

Ordinary Differential Equations in Neuroscience with Matlab examples. Aim 1- Gain understanding of how to set up and solve ODE s

Ordinary Differential Equations in Neuroscience with Matlab examples. Aim 1- Gain understanding of how to set up and solve ODE s Ordnary Dfferenal Equaons n Neuroscence wh Malab eamples. Am - Gan undersandng of how o se up and solve ODE s Am Undersand how o se up an solve a smple eample of he Hebb rule n D Our goal a end of class

More information

Approximate Analytic Solution of (2+1) - Dimensional Zakharov-Kuznetsov(Zk) Equations Using Homotopy

Approximate Analytic Solution of (2+1) - Dimensional Zakharov-Kuznetsov(Zk) Equations Using Homotopy Arcle Inernaonal Journal of Modern Mahemacal Scences, 4, (): - Inernaonal Journal of Modern Mahemacal Scences Journal homepage: www.modernscenfcpress.com/journals/jmms.aspx ISSN: 66-86X Florda, USA Approxmae

More information

Synthesis and Characterization of Proton-Conducting Oxides as Hydrogen Transport Membranes

Synthesis and Characterization of Proton-Conducting Oxides as Hydrogen Transport Membranes Synthesis and Characterization of Proton-Conducting Oxides as ydrogen Transport Membranes Lin Li and Enrique Iglesia Department of Chemical Engineering, University of California at Berkeley, Division of

More information

J i-1 i. J i i+1. Numerical integration of the diffusion equation (I) Finite difference method. Spatial Discretization. Internal nodes.

J i-1 i. J i i+1. Numerical integration of the diffusion equation (I) Finite difference method. Spatial Discretization. Internal nodes. umercal negraon of he dffuson equaon (I) Fne dfference mehod. Spaal screaon. Inernal nodes. R L V For hermal conducon le s dscree he spaal doman no small fne spans, =,,: Balance of parcles for an nernal

More information

Graduate Macroeconomics 2 Problem set 5. - Solutions

Graduate Macroeconomics 2 Problem set 5. - Solutions Graduae Macroeconomcs 2 Problem se. - Soluons Queson 1 To answer hs queson we need he frms frs order condons and he equaon ha deermnes he number of frms n equlbrum. The frms frs order condons are: F K

More information

January Examinations 2012

January Examinations 2012 Page of 5 EC79 January Examnaons No. of Pages: 5 No. of Quesons: 8 Subjec ECONOMICS (POSTGRADUATE) Tle of Paper EC79 QUANTITATIVE METHODS FOR BUSINESS AND FINANCE Tme Allowed Two Hours ( hours) Insrucons

More information

EEL 6266 Power System Operation and Control. Chapter 5 Unit Commitment

EEL 6266 Power System Operation and Control. Chapter 5 Unit Commitment EEL 6266 Power Sysem Operaon and Conrol Chaper 5 Un Commmen Dynamc programmng chef advanage over enumeraon schemes s he reducon n he dmensonaly of he problem n a src prory order scheme, here are only N

More information

Q.1 Define work and its unit?

Q.1 Define work and its unit? CHP # 6 ORK AND ENERGY Q.1 Define work and is uni? A. ORK I can be define as when we applied a force on a body and he body covers a disance in he direcion of force, hen we say ha work is done. I is a scalar

More information

Chemical Engineering Thermodynamics

Chemical Engineering Thermodynamics Engi-3434 Chemical Engineering Thermodynamics Dr. Charles Xu @ Chemical Engineering, Lakehead Universiy Chemical Engineering Thermodynamics Insrucor: Dr. Charles Xu, P.Eng. Associae Professor Deparmen

More information

Effect of a Vector Wall on the Thermal Field in a SRU Thermal Reactor

Effect of a Vector Wall on the Thermal Field in a SRU Thermal Reactor Effec of a Vecor Wall on he Thermal Feld n a SRU Thermal Reacor Chun-Lang Yeh and Tzu-Ch Chen Absrac The effecs of a vecor wall on he hermal feld n a SRU hermal reacor are nvesgaed numercally. The FLUENT

More information

CH.3. COMPATIBILITY EQUATIONS. Continuum Mechanics Course (MMC) - ETSECCPB - UPC

CH.3. COMPATIBILITY EQUATIONS. Continuum Mechanics Course (MMC) - ETSECCPB - UPC CH.3. COMPATIBILITY EQUATIONS Connuum Mechancs Course (MMC) - ETSECCPB - UPC Overvew Compably Condons Compably Equaons of a Poenal Vecor Feld Compably Condons for Infnesmal Srans Inegraon of he Infnesmal

More information

Linear Response Theory: The connection between QFT and experiments

Linear Response Theory: The connection between QFT and experiments Phys540.nb 39 3 Lnear Response Theory: The connecon beween QFT and expermens 3.1. Basc conceps and deas Q: ow do we measure he conducvy of a meal? A: we frs nroduce a weak elecrc feld E, and hen measure

More information

Li An-Ping. Beijing , P.R.China

Li An-Ping. Beijing , P.R.China A New Type of Cpher: DICING_csb L An-Png Bejng 100085, P.R.Chna apl0001@sna.com Absrac: In hs paper, we wll propose a new ype of cpher named DICING_csb, whch s derved from our prevous sream cpher DICING.

More information

Supporting Information: The integrated Global Temperature change Potential (igtp) and relationships between emission metrics

Supporting Information: The integrated Global Temperature change Potential (igtp) and relationships between emission metrics 2 3 4 5 6 7 8 9 Supporng Informaon: Te negraed Global Temperaure cange Poenal (GTP) and relaonsps beween emsson mercs Glen P. Peers *, Borgar Aamaas, Tere Bernsen,2, Jan S. Fuglesved Cener for Inernaonal

More information

MCTDH Approach to Strong Field Dynamics

MCTDH Approach to Strong Field Dynamics MCTDH ppoach o Song Feld Dynamcs Suen Sukasyan Thomas Babec and Msha Ivanov Unvesy o Oawa Canada Impeal College ondon UK KITP Sana Babaa. May 8 009 Movaon Song eld dynamcs Role o elecon coelaon Tunnel

More information

Cooling of a hot metal forging. , dt dt

Cooling of a hot metal forging. , dt dt Tranen Conducon Uneady Analy - Lumped Thermal Capacy Model Performed when; Hea ranfer whn a yem produced a unform emperaure drbuon n he yem (mall emperaure graden). The emperaure change whn he yem condered

More information

Online Supplement for Dynamic Multi-Technology. Production-Inventory Problem with Emissions Trading

Online Supplement for Dynamic Multi-Technology. Production-Inventory Problem with Emissions Trading Onlne Supplemen for Dynamc Mul-Technology Producon-Invenory Problem wh Emssons Tradng by We Zhang Zhongsheng Hua Yu Xa and Baofeng Huo Proof of Lemma For any ( qr ) Θ s easy o verfy ha he lnear programmng

More information

Variants of Pegasos. December 11, 2009

Variants of Pegasos. December 11, 2009 Inroducon Varans of Pegasos SooWoong Ryu bshboy@sanford.edu December, 009 Youngsoo Cho yc344@sanford.edu Developng a new SVM algorhm s ongong research opc. Among many exng SVM algorhms, we wll focus on

More information

NATIONAL UNIVERSITY OF SINGAPORE PC5202 ADVANCED STATISTICAL MECHANICS. (Semester II: AY ) Time Allowed: 2 Hours

NATIONAL UNIVERSITY OF SINGAPORE PC5202 ADVANCED STATISTICAL MECHANICS. (Semester II: AY ) Time Allowed: 2 Hours NATONAL UNVERSTY OF SNGAPORE PC5 ADVANCED STATSTCAL MECHANCS (Semeser : AY 1-13) Tme Allowed: Hours NSTRUCTONS TO CANDDATES 1. Ths examnaon paper conans 5 quesons and comprses 4 prned pages.. Answer all

More information

Tools for Analysis of Accelerated Life and Degradation Test Data

Tools for Analysis of Accelerated Life and Degradation Test Data Acceleraed Sress Tesng and Relably Tools for Analyss of Acceleraed Lfe and Degradaon Tes Daa Presened by: Reuel Smh Unversy of Maryland College Park smhrc@umd.edu Sepember-5-6 Sepember 28-30 206, Pensacola

More information

Superstructure-based Optimization for Design of Optimal PSA Cycles for CO 2 Capture

Superstructure-based Optimization for Design of Optimal PSA Cycles for CO 2 Capture Supersruure-asedOpmaonforDesgnof OpmalPSACylesforCO 2 Capure R. S. Kamah I. E. Grossmann L.. Begler Deparmen of Chemal Engneerng Carnege Mellon Unversy Psurgh PA 523 Marh 2 PSA n Nex Generaon Power Plans

More information

The topology and signature of the regulatory interactions predict the expression pattern of the segment polarity genes in Drosophila m elanogaster

The topology and signature of the regulatory interactions predict the expression pattern of the segment polarity genes in Drosophila m elanogaster The opology and sgnaure of he regulaory neracons predc he expresson paern of he segmen polary genes n Drosophla m elanogaser Hans Ohmer and Réka Alber Deparmen of Mahemacs Unversy of Mnnesoa Complex bologcal

More information

Lecture 11 SVM cont

Lecture 11 SVM cont Lecure SVM con. 0 008 Wha we have done so far We have esalshed ha we wan o fnd a lnear decson oundary whose margn s he larges We know how o measure he margn of a lnear decson oundary Tha s: he mnmum geomerc

More information

Multiphase CFD Modeling of Trickle-Bed Reactor Hydrodynamics

Multiphase CFD Modeling of Trickle-Bed Reactor Hydrodynamics Proceedngs of he World Congress on Engneerng and Compuer Scence 2007 WCECS 2007, Ocober 24-26, 2007, San Francsco, USA Mulphase CFD Modelng of Trckle-Bed Reacor Hydrodynamcs Rodrgo J.G. Lopes and Rosa

More information

A NEW TECHNIQUE FOR SOLVING THE 1-D BURGERS EQUATION

A NEW TECHNIQUE FOR SOLVING THE 1-D BURGERS EQUATION S19 A NEW TECHNIQUE FOR SOLVING THE 1-D BURGERS EQUATION by Xaojun YANG a,b, Yugu YANG a*, Carlo CATTANI c, and Mngzheng ZHU b a Sae Key Laboraory for Geomechancs and Deep Underground Engneerng, Chna Unversy

More information

Energy Storage Devices

Energy Storage Devices Energy Sorage Deces Objece of Lecure Descrbe he consrucon of a capacor and how charge s sored. Inroduce seeral ypes of capacors Dscuss he elecrcal properes of a capacor The relaonshp beween charge, olage,

More information

Bernoulli process with 282 ky periodicity is detected in the R-N reversals of the earth s magnetic field

Bernoulli process with 282 ky periodicity is detected in the R-N reversals of the earth s magnetic field Submed o: Suden Essay Awards n Magnecs Bernoull process wh 8 ky perodcy s deeced n he R-N reversals of he earh s magnec feld Jozsef Gara Deparmen of Earh Scences Florda Inernaonal Unversy Unversy Park,

More information

Measurement of liquid holdup and axial dispersion in trickle bed reactors using radiotracer technique

Measurement of liquid holdup and axial dispersion in trickle bed reactors using radiotracer technique NUKLEONIKA ;45(4):35 41 ORIGINAL PAPER Measuremen of lqud holdup and axal dsperson n rckle bed reacors usng radoracer echnque Harsh Jaga Pan, Anl Kumar Saroha, Krshna Deo Prasad Ngam Absrac The holdup

More information

Let s treat the problem of the response of a system to an applied external force. Again,

Let s treat the problem of the response of a system to an applied external force. Again, Page 33 QUANTUM LNEAR RESPONSE FUNCTON Le s rea he problem of he response of a sysem o an appled exernal force. Agan, H() H f () A H + V () Exernal agen acng on nernal varable Hamlonan for equlbrum sysem

More information

Comparison of Differences between Power Means 1

Comparison of Differences between Power Means 1 In. Journal of Mah. Analyss, Vol. 7, 203, no., 5-55 Comparson of Dfferences beween Power Means Chang-An Tan, Guanghua Sh and Fe Zuo College of Mahemacs and Informaon Scence Henan Normal Unversy, 453007,

More information

Suggested Problem Solutions Associated with Homework #5

Suggested Problem Solutions Associated with Homework #5 Suggesed Problem Soluions Associaed wih Homework #5 431 (a) 8 Si has proons and neurons (b) 85 3 Rb has 3 proons and 48 neurons (c) 5 Tl 81 has 81 proons and neurons 43 IDENTIFY and SET UP: The ex calculaes

More information

2.1 Constitutive Theory

2.1 Constitutive Theory Secon.. Consuve Theory.. Consuve Equaons Governng Equaons The equaons governng he behavour of maerals are (n he spaal form) dρ v & ρ + ρdv v = + ρ = Conservaon of Mass (..a) d x σ j dv dvσ + b = ρ v& +

More information

Discrete Markov Process. Introduction. Example: Balls and Urns. Stochastic Automaton. INTRODUCTION TO Machine Learning 3rd Edition

Discrete Markov Process. Introduction. Example: Balls and Urns. Stochastic Automaton. INTRODUCTION TO Machine Learning 3rd Edition EHEM ALPAYDI he MI Press, 04 Lecure Sldes for IRODUCIO O Machne Learnng 3rd Edon alpaydn@boun.edu.r hp://www.cmpe.boun.edu.r/~ehem/ml3e Sldes from exboo resource page. Slghly eded and wh addonal examples

More information

FI 3103 Quantum Physics

FI 3103 Quantum Physics /9/4 FI 33 Quanum Physcs Aleander A. Iskandar Physcs of Magnesm and Phooncs Research Grou Insu Teknolog Bandung Basc Conces n Quanum Physcs Probably and Eecaon Value Hesenberg Uncerany Prncle Wave Funcon

More information

A First Course on Kinetics and Reaction Engineering. Class 19 on Unit 18

A First Course on Kinetics and Reaction Engineering. Class 19 on Unit 18 A Firs ourse on Kineics and Reacion Engineering lass 19 on Uni 18 Par I - hemical Reacions Par II - hemical Reacion Kineics Where We re Going Par III - hemical Reacion Engineering A. Ideal Reacors B. Perfecly

More information

10. A.C CIRCUITS. Theoretically current grows to maximum value after infinite time. But practically it grows to maximum after 5τ. Decay of current :

10. A.C CIRCUITS. Theoretically current grows to maximum value after infinite time. But practically it grows to maximum after 5τ. Decay of current : . A. IUITS Synopss : GOWTH OF UNT IN IUIT : d. When swch S s closed a =; = d. A me, curren = e 3. The consan / has dmensons of me and s called he nducve me consan ( τ ) of he crcu. 4. = τ; =.63, n one

More information

Lesson 2 Transmission Lines Fundamentals

Lesson 2 Transmission Lines Fundamentals Lesson Transmsson Lnes Funamenals 楊尚達 Shang-Da Yang Insue of Phooncs Technologes Deparmen of Elecrcal Engneerng Naonal Tsng Hua Unersy Tawan Sec. -1 Inroucon 1. Why o scuss TX lnes srbue crcus?. Crera

More information

Dual Approximate Dynamic Programming for Large Scale Hydro Valleys

Dual Approximate Dynamic Programming for Large Scale Hydro Valleys Dual Approxmae Dynamc Programmng for Large Scale Hydro Valleys Perre Carpener and Jean-Phlppe Chanceler 1 ENSTA ParsTech and ENPC ParsTech CMM Workshop, January 2016 1 Jon work wh J.-C. Alas, suppored

More information

Assessing Customer Equity using Interval Estimation Method and Markov Chains (Case: An Internet Service Provider)

Assessing Customer Equity using Interval Estimation Method and Markov Chains (Case: An Internet Service Provider) Inernaonal Journal of Indusral Engneerng & Producon Managemen (2014) July 2014, Volume 25, Number 2 pp. 155-165 hp://ijiepm.us.ac.r/ Assessng Cusomer Equy usng Inerval Esmaon Mehod and Markov Chans (Case:

More information

MANY real-world applications (e.g. production

MANY real-world applications (e.g. production Barebones Parcle Swarm for Ineger Programmng Problems Mahamed G. H. Omran, Andres Engelbrech and Ayed Salman Absrac The performance of wo recen varans of Parcle Swarm Opmzaon (PSO) when appled o Ineger

More information

Response of MDOF systems

Response of MDOF systems Response of MDOF syses Degree of freedo DOF: he nu nuber of ndependen coordnaes requred o deerne copleely he posons of all pars of a syse a any nsan of e. wo DOF syses hree DOF syses he noral ode analyss

More information

Chapter 13 Homework Answers

Chapter 13 Homework Answers Chaper 3 Homework Answers 3.. The answer is c, doubling he [C] o while keeping he [A] o and [B] o consan. 3.2. a. Since he graph is no linear, here is no way o deermine he reacion order by inspecion. A

More information

Units. Chapter 1 Basic Concepts. Units. Example 1. Atoms. Example 2. Radiation Dosimetry I

Units. Chapter 1 Basic Concepts. Units. Example 1. Atoms. Example 2. Radiation Dosimetry I Unis Chaper Basic Conceps Radiaion Dosimery I Tex: H.E Johns and J.R. Cunningham, The physics of radiology, 4 h ed. Special uni of energy: elecron vol ev ev=.60x0-9 C x vol=.60x0-9 J Unis Absorbed dose:

More information

Mechanics Physics 151

Mechanics Physics 151 Mechancs Physcs 5 Lecure 9 Hamlonan Equaons of Moon (Chaper 8) Wha We Dd Las Tme Consruced Hamlonan formalsm H ( q, p, ) = q p L( q, q, ) H p = q H q = p H = L Equvalen o Lagrangan formalsm Smpler, bu

More information

Robustness of DEWMA versus EWMA Control Charts to Non-Normal Processes

Robustness of DEWMA versus EWMA Control Charts to Non-Normal Processes Journal of Modern Appled Sascal Mehods Volume Issue Arcle 8 5--3 Robusness of D versus Conrol Chars o Non- Processes Saad Saeed Alkahan Performance Measuremen Cener of Governmen Agences, Insue of Publc

More information

Solving the multi-period fixed cost transportation problem using LINGO solver

Solving the multi-period fixed cost transportation problem using LINGO solver Inernaonal Journal of Pure and Appled Mahemacs Volume 119 No. 12 2018, 2151-2157 ISSN: 1314-3395 (on-lne verson) url: hp://www.pam.eu Specal Issue pam.eu Solvng he mul-perod fxed cos ransporaon problem

More information

Learning Objectives. Self Organization Map. Hamming Distance(1/5) Introduction. Hamming Distance(3/5) Hamming Distance(2/5) 15/04/2015

Learning Objectives. Self Organization Map. Hamming Distance(1/5) Introduction. Hamming Distance(3/5) Hamming Distance(2/5) 15/04/2015 /4/ Learnng Objecves Self Organzaon Map Learnng whou Exaples. Inroducon. MAXNET 3. Cluserng 4. Feaure Map. Self-organzng Feaure Map 6. Concluson 38 Inroducon. Learnng whou exaples. Daa are npu o he syse

More information

Time-interval analysis of β decay. V. Horvat and J. C. Hardy

Time-interval analysis of β decay. V. Horvat and J. C. Hardy Tme-nerval analyss of β decay V. Horva and J. C. Hardy Work on he even analyss of β decay [1] connued and resuled n he developmen of a novel mehod of bea-decay me-nerval analyss ha produces hghly accurae

More information

Modeling and Solving of Multi-Product Inventory Lot-Sizing with Supplier Selection under Quantity Discounts

Modeling and Solving of Multi-Product Inventory Lot-Sizing with Supplier Selection under Quantity Discounts nernaonal ournal of Appled Engneerng Research SSN 0973-4562 Volume 13, Number 10 (2018) pp. 8708-8713 Modelng and Solvng of Mul-Produc nvenory Lo-Szng wh Suppler Selecon under Quany Dscouns Naapa anchanaruangrong

More information

Mechanics Physics 151

Mechanics Physics 151 Mechancs Physcs 5 Lecure 9 Hamlonan Equaons of Moon (Chaper 8) Wha We Dd Las Tme Consruced Hamlonan formalsm Hqp (,,) = qp Lqq (,,) H p = q H q = p H L = Equvalen o Lagrangan formalsm Smpler, bu wce as

More information

Molecular Dynamics Simulation Study forgtransport Properties of Diatomic Liquids

Molecular Dynamics Simulation Study forgtransport Properties of Diatomic Liquids NpT EMD Smulaons of Daomc Lquds Bull. Korean Chem. Soc. 7, ol. 8, No. 697 Molecular Dynamcs Smulaon Sudy forgtranspor Properes of Daomc Lquds Song H Lee Deparmen of Chemsry, Kyungsung Unversy, Busan 68-736,

More information

Oligopoly with exhaustible resource input

Oligopoly with exhaustible resource input Olgopoly wh exhausble resource npu e, P-Y. 78 Olgopoly wh exhausble resource npu Recebmeno dos orgnas: 25/03/202 Aceação para publcação: 3/0/203 Pu-yan e PhD em Scences pela Chnese Academy of Scence Insução:

More information

AP Chemistry--Chapter 12: Chemical Kinetics

AP Chemistry--Chapter 12: Chemical Kinetics AP Chemisry--Chaper 12: Chemical Kineics I. Reacion Raes A. The area of chemisry ha deals wih reacion raes, or how fas a reacion occurs, is called chemical kineics. B. The rae of reacion depends on he

More information

TSS = SST + SSE An orthogonal partition of the total SS

TSS = SST + SSE An orthogonal partition of the total SS ANOVA: Topc 4. Orhogonal conrass [ST&D p. 183] H 0 : µ 1 = µ =... = µ H 1 : The mean of a leas one reamen group s dfferen To es hs hypohess, a basc ANOVA allocaes he varaon among reamen means (SST) equally

More information

Problem Set 5. Graduate Macro II, Spring 2017 The University of Notre Dame Professor Sims

Problem Set 5. Graduate Macro II, Spring 2017 The University of Notre Dame Professor Sims Problem Se 5 Graduae Macro II, Spring 2017 The Universiy of Nore Dame Professor Sims Insrucions: You may consul wih oher members of he class, bu please make sure o urn in your own work. Where applicable,

More information

Transient Numerical of Piston Wind in Subway Station. Haitao Bao

Transient Numerical of Piston Wind in Subway Station. Haitao Bao Appled Mechancs and Maerals Submed: 2014-07-20 ISSN: 1662-7482, Vols. 644-650, pp 467-470 Acceped: 2014-07-21 do:10.4028/www.scenfc.ne/amm.644-650.467 Onlne: 2014-09-22 2014 Trans Tech Publcaons, Swzerland

More information

Detection of Waving Hands from Images Using Time Series of Intensity Values

Detection of Waving Hands from Images Using Time Series of Intensity Values Deecon of Wavng Hands from Images Usng Tme eres of Inensy Values Koa IRIE, Kazunor UMEDA Chuo Unversy, Tokyo, Japan re@sensor.mech.chuo-u.ac.jp, umeda@mech.chuo-u.ac.jp Absrac Ths paper proposes a mehod

More information

( ) is the stretch factor, and x the

( ) is the stretch factor, and x the (Lecures 7-8) Liddle, Chaper 5 Simple cosmological models (i) Hubble s Law revisied Self-similar srech of he universe All universe models have his characerisic v r ; v = Hr since only his conserves homogeneiy

More information

THE PREDICTION OF COMPETITIVE ENVIRONMENT IN BUSINESS

THE PREDICTION OF COMPETITIVE ENVIRONMENT IN BUSINESS THE PREICTION OF COMPETITIVE ENVIRONMENT IN BUSINESS INTROUCTION The wo dmensonal paral dfferenal equaons of second order can be used for he smulaon of compeve envronmen n busness The arcle presens he

More information

Real time processing with low cost uncooled plane array IR camera-application to flash nondestructive

Real time processing with low cost uncooled plane array IR camera-application to flash nondestructive hp://dx.do.org/0.6/qr.000.04 Real me processng wh low cos uncooled plane array IR camera-applcaon o flash nondesrucve evaluaon By Davd MOURAND, Jean-Chrsophe BATSALE L.E.P.T.-ENSAM, UMR 8508 CNRS, Esplanade

More information

Homework 8: Rigid Body Dynamics Due Friday April 21, 2017

Homework 8: Rigid Body Dynamics Due Friday April 21, 2017 EN40: Dynacs and Vbraons Hoework 8: gd Body Dynacs Due Frday Aprl 1, 017 School of Engneerng Brown Unversy 1. The earh s roaon rae has been esaed o decrease so as o ncrease he lengh of a day a a rae of

More information

Cubic Bezier Homotopy Function for Solving Exponential Equations

Cubic Bezier Homotopy Function for Solving Exponential Equations Penerb Journal of Advanced Research n Compung and Applcaons ISSN (onlne: 46-97 Vol. 4, No.. Pages -8, 6 omoopy Funcon for Solvng Eponenal Equaons S. S. Raml *,,. Mohamad Nor,a, N. S. Saharzan,b and M.

More information

! ln 2xdx = (x ln 2x - x) 3 1 = (3 ln 6-3) - (ln 2-1)

! ln 2xdx = (x ln 2x - x) 3 1 = (3 ln 6-3) - (ln 2-1) 7. e - d Le u = and dv = e - d. Then du = d and v = -e -. e - d = (-e - ) - (-e - )d = -e - + e - d = -e - - e - 9. e 2 d = e 2 2 2 d = 2 e 2 2d = 2 e u du Le u = 2, hen du = 2 d. = 2 eu = 2 e2.! ( - )e

More information