Solution of the Heat Equation for transient conduction by LaPlace Transform
|
|
- Lucas Marshall
- 7 years ago
- Views:
Transcription
1 Solution of the Heat Equation for tranient conduction by LaPlace Tranform Thi notebook ha been written in Mathematica by Mark J. McCready Profeor and Chair of Chemical Engineering Univerity of Notre Dame Notre Dame IN USA It i copyrighted to the extent allowed by whatever law pertain to the World Wide Web and the Internet. I would hope that a a profeional courtey, that if you ue it, that thi notice remain viible to other uer. There i no charge for copying and diemination Verion: 3/7/98
2 2 heat.laplace.nb Thi notebook how how to olve tranient heat conduction in a emi-infinite lab. It i intended a a upplement to L. G. Leal (992) Laminar flow and Convective Tranport Procee, Butterworth pp Leal mention the poible ue of linear tranform technique but doe not give example. Many tudent are not familiar with thee. Thi notebook i intended to illutrate the ue of the LaPlace tranform to olve a imple PDE, and to how how it i implemented in Mathematica. Thi problem i the heat tranfer analog to the "Rayleigh" problem that tart on page 9. Problem formulation Conider a emi-infinite lab where the ditance variable, y, goe from 0 to. The temperature i initially uniform within the lab and we can conider it to be 0. At t=0, the temperature at y=0 i uddenly increaed to. We would like to calculate the temperature a a function of time, t, within the lab. Thi problem i commonly olved by a imilarity variable technique that arie becaue the abence of a phyical length cale. In thi notebook we ue the Laplace Tranform, which i an integral tranform that effectively convert (linear) PDE, (if we wih to ue it on ay time), to a et of ODE in frequency pace. I ay a "et" of problem becaue the tranform create an explict parameter,, which i effectively a frequency and the equation need to be olved for all poitive. Equation heateq t Θ t, y y,2 Θ t, y Θ,0 t, y Θ 0,2 t, y boundary condition the boundary condition are Θ(t,y)=0 t < 0, Θ(t,y)=0 a y-->, Θ(t, y=0) = for t > 0. initialization of Mathematica, load a package Need "Calculu`LaplaceTranform` "
3 heat.laplace.nb 3 Here i the analyi If we ue a tranform technique, we intend to implify the problem by tranforming the pde to an ode (or an algebraic equation from an ode). Once the tranform i done, we will need to evaluate the integral that arie a the boundarie. So the boundary condition and the domain of the problem mut be in a form conducive to thi. The Laplace tranform i defined from 0 to. In thi problem both of the domain are from 0 to, however firt try to do the tranform in time. In Mathematica thi command i LaplaceTranform[heateq,t,] and the new parameter i. LaplaceTranform heateq, t, LaplaceTranform Θ t, y, t, LaplaceTranform Θ 0,2 t, y, t, Θ 0, y The firt two term make an ode in the tranformed Θ(t,y). Let' call thi Θ. The lat term, which aroe from integration by part of the Θ(t,y)/ t term, mut be evaluated from the boundary condition. The temperature for all y at t=0 i zero, thu thi term i 0. Note that the t--> boundary term i uually zero (we don't ee it in thi calculation) becaue it i multiplied by Exp[- t] (and thu Mathematica automatically make it 0). Thu we have an ode in Θ (y), and have generated an explicit parameter,. The LaplaceTranform[t,] doe not affect any y derivative. We can write eq Θ y y,2 Θ y Θ y Θ y Thi i eaily olved by doing an DSolve eq 0, Θ y, y y Θ y c y c 2 Now get the olution out of the {{ }}'. oln Θ y. an y c y c 2 We ee that we cannot tand an exponentially increaing part o that c 2 =0. Now, we need to evaluate Θ (y,) at y= 0 or at ome place that we know it. Well, we know y=0 (=). Thu, we can tranform thi to get a value for Θ[y=0,]. bc0 LaplaceTranform, t, Now find the value of C[] after etting C[2] = 0 and evaluating the expreion at y=0.
4 4 heat.laplace.nb bc0 oln. y 0, C 2 0 c Thu our olution in tranformed pace i expreion oln. C,C 2 0 General::pell : Poible pelling error: new ymbol name "expreion" i imilar to exiting ymbol "Expreion". y Plot olution in frequency pace to ee what doe What doe thi look like?? p Plot expreion.,, y, 0, 3 p2 Plot expreion., 0, y, 0, 3 p3 Plot expreion.,., y, 0, 3 Show p, p2, p The top plot i for = 0. It i a difficult to tell for ure, but the different value of repreent different mode. The term i roughly a frequency o that higher ' decay fater!! Examine the iue of time to "frequency" We can ee more of what mean by tranforming t n
5 heat.laplace.nb 5 LaplaceTranform t n,t, n n LaplaceTranform t, t, 2 LaplaceTranform t, t, Π LaplaceTranform, t, So we ee the invere relation of t and -- which that i a little jutification for calling the "frequency". Plot olution in frequency pace to ee what doe Now if we make plot for different value of we get: p4 Plot expreion..,, y, 0, 3 p5 Plot expreion. 0,, y, 0, 3 p6 Plot expreion.,, y, 0, 3 Show p4, p5, p
6 6 heat.laplace.nb The top curve i for = 0. It i een that the value of give the rate of "diffuion" which we alo expect once the olution i tranformed back. Tranform back to time Now we mut tranform back to get the olution in phyical pace. There are 3 way. One i to get a table of tranform and invere tranform. A good table i in Spiegel' math handbook (M. R. Spiegel, Mathematical Handbook, Schaum' Ouline Serie, McGraw-Hill, 968). The econd way i to ue Mathematica or Maple, the problem would be, do you believe the anwer. The third way i to do the complex integration yourelf, the problem i, would you believe the anwer?? Anyway Mathematica agree with the table expreion y an InvereLaplaceTranform expreion,, t erfc y 2 t Plot the olution in phyical pace p7 Plot an. 0, t.2, y, 0, 5 p8 Plot an. 0, t.02, y, 0, 5 p9 Plot an. 0, t 2, y, 0, 5 Show p7, p8, p9, AxeLabel y, temp temp y Note that the bottom curve i for t =.02
7 heat.laplace.nb 7 p0 Plot an.., t.2, y, 0, 5 p Plot an.., t 2, y, 0, 5 p2 Plot an.., t.02, y, 0, 5 Show p0, p, p2, PlotRange All, AxeLabel y, temp temp y Again the bottom curve i for t = By comparing the two plot for different, we can ee that the value of the diffuivity control how fat heat tranfer occur. Why did we tranform the time variable intead of the pace variable? Now uppoe that we had initially tranformed the y variable LaplaceTranform t Θ t, y y,2 Θ t, y, y, LaplaceTranform Θ,0 t, y, y, LaplaceTranform Θ t, y, y, 2 Θ t,0 Θ 0, t, 0 Now we need to evaluate the boundary term. The firt one Θ[t,0] = for all t of interet. However, the econd one preent a bit of a problem. We don't really know the heat flux at the boundary o we don't know the derivative. Conequently, tranforming y to doe not help olve the problem!!
Unit 11 Using Linear Regression to Describe Relationships
Unit 11 Uing Linear Regreion to Decribe Relationhip Objective: To obtain and interpret the lope and intercept of the leat quare line for predicting a quantitative repone variable from a quantitative explanatory
More informationv = x t = x 2 x 1 t 2 t 1 The average speed of the particle is absolute value of the average velocity and is given Distance travelled t
Chapter 2 Motion in One Dimenion 2.1 The Important Stuff 2.1.1 Poition, Time and Diplacement We begin our tudy of motion by conidering object which are very mall in comparion to the ize of their movement
More informationMath 22B, Homework #8 1. y 5y + 6y = 2e t
Math 22B, Homework #8 3.7 Problem # We find a particular olution of the ODE y 5y + 6y 2e t uing the method of variation of parameter and then verify the olution uing the method of undetermined coefficient.
More informationA note on profit maximization and monotonicity for inbound call centers
A note on profit maximization and monotonicity for inbound call center Ger Koole & Aue Pot Department of Mathematic, Vrije Univeriteit Amterdam, The Netherland 23rd December 2005 Abtract We conider an
More informationMECH 2110 - Statics & Dynamics
Chapter D Problem 3 Solution 1/7/8 1:8 PM MECH 11 - Static & Dynamic Chapter D Problem 3 Solution Page 7, Engineering Mechanic - Dynamic, 4th Edition, Meriam and Kraige Given: Particle moving along a traight
More information2. METHOD DATA COLLECTION
Key to learning in pecific ubject area of engineering education an example from electrical engineering Anna-Karin Cartenen,, and Jonte Bernhard, School of Engineering, Jönköping Univerity, S- Jönköping,
More informationOptical Illusion. Sara Bolouki, Roger Grosse, Honglak Lee, Andrew Ng
Optical Illuion Sara Bolouki, Roger Groe, Honglak Lee, Andrew Ng. Introduction The goal of thi proect i to explain ome of the illuory phenomena uing pare coding and whitening model. Intead of the pare
More informationA new definition of the fractional Laplacian
A new efinition of the fractional Laplacian W. Chen imula Reearch Laboratory, P. O. Box. 34, NO-325 Lyaker, Norway (9 eptember 2002) Keywor: fractional Laplacian, fractional erivative, Riez potential,
More informationName: SID: Instructions
CS168 Fall 2014 Homework 1 Aigned: Wedneday, 10 September 2014 Due: Monday, 22 September 2014 Name: SID: Dicuion Section (Day/Time): Intruction - Submit thi homework uing Pandagrader/GradeScope(http://www.gradecope.com/
More informationOn Reference RIAA Networks by Jim Hagerman
On eference IAA Network by Jim Hagerman You d think there would be nothing left to ay. Everything you need to know about IAA network ha already been publihed. However, a few year back I came acro an intereting
More informationTRANSFORM AND ITS APPLICATION
LAPLACE TRANSFORM AND ITS APPLICATION IN CIRCUIT ANALYSIS C.T. Pan. Definition of the Laplace Tranform. Ueful Laplace Tranform Pair.3 Circuit Analyi in S Domain.4 The Tranfer Function and the Convolution
More informationMassachusetts Institute of Technology Department of Electrical Engineering and Computer Science
aachuett Intitute of Technology Department of Electrical Engineering and Computer Science 6.685 Electric achinery Cla Note 10: Induction achine Control and Simulation c 2003 Jame L. Kirtley Jr. 1 Introduction
More informationHeat transfer to or from a fluid flowing through a tube
Heat tranfer to or from a fluid flowing through a tube R. Shankar Subramanian A common ituation encountered by the chemical engineer i heat tranfer to fluid flowing through a tube. Thi can occur in heat
More information6. Friction, Experiment and Theory
6. Friction, Experiment and Theory The lab thi wee invetigate the rictional orce and the phyical interpretation o the coeicient o riction. We will mae ue o the concept o the orce o gravity, the normal
More informationSolutions to Sample Problems for Test 3
22 Differential Equation Intructor: Petronela Radu November 8 25 Solution to Sample Problem for Tet 3 For each of the linear ytem below find an interval in which the general olution i defined (a) x = x
More informationMixed Method of Model Reduction for Uncertain Systems
SERBIAN JOURNAL OF ELECTRICAL ENGINEERING Vol 4 No June Mixed Method of Model Reduction for Uncertain Sytem N Selvaganean Abtract: A mixed method for reducing a higher order uncertain ytem to a table reduced
More informationMSc Financial Economics: International Finance. Bubbles in the Foreign Exchange Market. Anne Sibert. Revised Spring 2013. Contents
MSc Financial Economic: International Finance Bubble in the Foreign Exchange Market Anne Sibert Revied Spring 203 Content Introduction................................................. 2 The Mone Market.............................................
More informationA Note on Profit Maximization and Monotonicity for Inbound Call Centers
OPERATIONS RESEARCH Vol. 59, No. 5, September October 2011, pp. 1304 1308 in 0030-364X ein 1526-5463 11 5905 1304 http://dx.doi.org/10.1287/opre.1110.0990 2011 INFORMS TECHNICAL NOTE INFORMS hold copyright
More information1D STEADY STATE HEAT
D SEADY SAE HEA CONDUCION () Prabal alukdar Aociate Profeor Department of Mechanical Engineering II Delhi E-mail: prabal@mech.iitd.ac.in Convection Boundary Condition Heat conduction at the urface in a
More informationAssessing the Discriminatory Power of Credit Scores
Aeing the Dicriminatory Power of Credit Score Holger Kraft 1, Gerald Kroiandt 1, Marlene Müller 1,2 1 Fraunhofer Intitut für Techno- und Wirtchaftmathematik (ITWM) Gottlieb-Daimler-Str. 49, 67663 Kaierlautern,
More information12.4 Problems. Excerpt from "Introduction to Geometry" 2014 AoPS Inc. Copyrighted Material CHAPTER 12. CIRCLES AND ANGLES
HTER 1. IRLES N NGLES Excerpt from "Introduction to Geometry" 014 os Inc. onider the circle with diameter O. all thi circle. Why mut hit O in at leat two di erent point? (b) Why i it impoible for to hit
More informationThe Nonlinear Pendulum
The Nonlinear Pendulum D.G. Simpon, Ph.D. Department of Phyical Science and Enineerin Prince Geore ommunity ollee December 31, 1 1 The Simple Plane Pendulum A imple plane pendulum conit, ideally, of a
More informationCHARACTERISTICS OF WAITING LINE MODELS THE INDICATORS OF THE CUSTOMER FLOW MANAGEMENT SYSTEMS EFFICIENCY
Annale Univeritati Apuleni Serie Oeconomica, 2(2), 200 CHARACTERISTICS OF WAITING LINE MODELS THE INDICATORS OF THE CUSTOMER FLOW MANAGEMENT SYSTEMS EFFICIENCY Sidonia Otilia Cernea Mihaela Jaradat 2 Mohammad
More informationQueueing systems with scheduled arrivals, i.e., appointment systems, are typical for frontal service systems,
MANAGEMENT SCIENCE Vol. 54, No. 3, March 28, pp. 565 572 in 25-199 ein 1526-551 8 543 565 inform doi 1.1287/mnc.17.82 28 INFORMS Scheduling Arrival to Queue: A Single-Server Model with No-Show INFORMS
More informationThree Phase Theory - Professor J R Lucas
Three Phae Theory - Profeor J Luca A you are aware, to tranit power with ingle phae alternating current, we need two wire live wire and neutral. However you would have een that ditribution line uually
More informationTransient turbulent flow in a pipe
Tranient turbulent flow in a pipe M. S. Ghidaoui A. A. Kolyhkin Rémi Vaillancourt CRM-3176 January 25 Thi work wa upported in part by the Latvian Council of Science, project 4.1239, the Natural Science
More informationQueueing Models for Multiclass Call Centers with Real-Time Anticipated Delays
Queueing Model for Multicla Call Center with Real-Time Anticipated Delay Oualid Jouini Yve Dallery Zeynep Akşin Ecole Centrale Pari Koç Univerity Laboratoire Génie Indutriel College of Adminitrative Science
More informationDISTRIBUTED DATA PARALLEL TECHNIQUES FOR CONTENT-MATCHING INTRUSION DETECTION SYSTEMS
DISTRIBUTED DATA PARALLEL TECHNIQUES FOR CONTENT-MATCHING INTRUSION DETECTION SYSTEMS Chritopher V. Kopek Department of Computer Science Wake Foret Univerity Winton-Salem, NC, 2709 Email: kopekcv@gmail.com
More informationChapter 10 Stocks and Their Valuation ANSWERS TO END-OF-CHAPTER QUESTIONS
Chapter Stoc and Their Valuation ANSWERS TO EN-OF-CHAPTER QUESTIONS - a. A proxy i a document giving one peron the authority to act for another, typically the power to vote hare of common toc. If earning
More informationAvailability of WDM Multi Ring Networks
Paper Availability of WDM Multi Ring Network Ivan Rado and Katarina Rado H d.o.o. Motar, Motar, Bonia and Herzegovina Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture, Univerity
More informationDISTRIBUTED DATA PARALLEL TECHNIQUES FOR CONTENT-MATCHING INTRUSION DETECTION SYSTEMS. G. Chapman J. Cleese E. Idle
DISTRIBUTED DATA PARALLEL TECHNIQUES FOR CONTENT-MATCHING INTRUSION DETECTION SYSTEMS G. Chapman J. Cleee E. Idle ABSTRACT Content matching i a neceary component of any ignature-baed network Intruion Detection
More informationIMPORTANT: Read page 2 ASAP. *Please feel free to email (longo.physics@gmail.com) me at any time if you have questions or concerns.
rev. 05/4/16 AP Phyic C: Mechanic Summer Aignment 016-017 Mr. Longo Foret Park HS longo.phyic@gmail.com longodb@pwc.edu Welcome to AP Phyic C: Mechanic. The purpoe of thi ummer aignment i to give you a
More informationScheduling of Jobs and Maintenance Activities on Parallel Machines
Scheduling of Job and Maintenance Activitie on Parallel Machine Chung-Yee Lee* Department of Indutrial Engineering Texa A&M Univerity College Station, TX 77843-3131 cylee@ac.tamu.edu Zhi-Long Chen** Department
More informationChapter 10 Velocity, Acceleration, and Calculus
Chapter 10 Velocity, Acceleration, and Calculu The firt derivative of poition i velocity, and the econd derivative i acceleration. Thee derivative can be viewed in four way: phyically, numerically, ymbolically,
More informationProject Management Basics
Project Management Baic A Guide to undertanding the baic component of effective project management and the key to ucce 1 Content 1.0 Who hould read thi Guide... 3 1.1 Overview... 3 1.2 Project Management
More informationTwo Dimensional FEM Simulation of Ultrasonic Wave Propagation in Isotropic Solid Media using COMSOL
Excerpt from the Proceeding of the COMSO Conference 0 India Two Dimenional FEM Simulation of Ultraonic Wave Propagation in Iotropic Solid Media uing COMSO Bikah Ghoe *, Krihnan Balaubramaniam *, C V Krihnamurthy
More informationStochasticity in Transcriptional Regulation: Origins, Consequences, and Mathematical Representations
36 Biophyical Journal Volume 8 December 200 36 336 Stochaticity in Trancriptional Regulation: Origin, Conequence, and Mathematical Repreentation Thoma B. Kepler* and Timothy C. Elton *Santa Fe Intitute,
More informationThe Cash Flow Statement: Problems with the Current Rules
A C C O U N T I N G & A U D I T I N G accounting The Cah Flow Statement: Problem with the Current Rule By Neii S. Wei and Jame G.S. Yang In recent year, the tatement of cah flow ha received increaing attention
More informationApigee Edge: Apigee Cloud vs. Private Cloud. Evaluating deployment models for API management
Apigee Edge: Apigee Cloud v. Private Cloud Evaluating deployment model for API management Table of Content Introduction 1 Time to ucce 2 Total cot of ownerhip 2 Performance 3 Security 4 Data privacy 4
More informationResearch Article An (s, S) Production Inventory Controlled Self-Service Queuing System
Probability and Statitic Volume 5, Article ID 558, 8 page http://dxdoiorg/55/5/558 Reearch Article An (, S) Production Inventory Controlled Self-Service Queuing Sytem Anoop N Nair and M J Jacob Department
More informationOhm s Law. Ohmic relationship V=IR. Electric Power. Non Ohmic devises. Schematic representation. Electric Power
Ohm Law Ohmic relationhip V=IR Ohm law tate that current through the conductor i directly proportional to the voltage acro it if temperature and other phyical condition do not change. In many material,
More informationCASE STUDY ALLOCATE SOFTWARE
CASE STUDY ALLOCATE SOFTWARE allocate caetud y TABLE OF CONTENTS #1 ABOUT THE CLIENT #2 OUR ROLE #3 EFFECTS OF OUR COOPERATION #4 BUSINESS PROBLEM THAT WE SOLVED #5 CHALLENGES #6 WORKING IN SCRUM #7 WHAT
More informationJanuary 21, 2015. Abstract
T S U I I E P : T R M -C S J. R January 21, 2015 Abtract Thi paper evaluate the trategic behavior of a monopolit to influence environmental policy, either with taxe or with tandard, comparing two alternative
More informationSenior Thesis. Horse Play. Optimal Wagers and the Kelly Criterion. Author: Courtney Kempton. Supervisor: Professor Jim Morrow
Senior Thei Hore Play Optimal Wager and the Kelly Criterion Author: Courtney Kempton Supervior: Profeor Jim Morrow June 7, 20 Introduction The fundamental problem in gambling i to find betting opportunitie
More informationPerformance of a Browser-Based JavaScript Bandwidth Test
Performance of a Brower-Baed JavaScript Bandwidth Tet David A. Cohen II May 7, 2013 CP SC 491/H495 Abtract An exiting brower-baed bandwidth tet written in JavaScript wa modified for the purpoe of further
More informationTIME SERIES ANALYSIS AND TRENDS BY USING SPSS PROGRAMME
TIME SERIES ANALYSIS AND TRENDS BY USING SPSS PROGRAMME RADMILA KOCURKOVÁ Sileian Univerity in Opava School of Buine Adminitration in Karviná Department of Mathematical Method in Economic Czech Republic
More informationIn this paper, we investigate toll setting as a policy tool to regulate the use of roads for dangerous goods
Vol. 43, No. 2, May 2009, pp. 228 243 in 0041-1655 ein 1526-5447 09 4302 0228 inform doi 10.1287/trc.1080.0236 2009 INFORMS Toll Policie for Mitigating Hazardou Material Tranport Rik Patrice Marcotte,
More informationA technical guide to 2014 key stage 2 to key stage 4 value added measures
A technical guide to 2014 key tage 2 to key tage 4 value added meaure CONTENTS Introduction: PAGE NO. What i value added? 2 Change to value added methodology in 2014 4 Interpretation: Interpreting chool
More informationA Spam Message Filtering Method: focus on run time
, pp.29-33 http://dx.doi.org/10.14257/atl.2014.76.08 A Spam Meage Filtering Method: focu on run time Sin-Eon Kim 1, Jung-Tae Jo 2, Sang-Hyun Choi 3 1 Department of Information Security Management 2 Department
More informationRisk Management for a Global Supply Chain Planning under Uncertainty: Models and Algorithms
Rik Management for a Global Supply Chain Planning under Uncertainty: Model and Algorithm Fengqi You 1, John M. Waick 2, Ignacio E. Gromann 1* 1 Dept. of Chemical Engineering, Carnegie Mellon Univerity,
More informationTap Into Smartphone Demand: Mobile-izing Enterprise Websites by Using Flexible, Open Source Platforms
Tap Into Smartphone Demand: Mobile-izing Enterprie Webite by Uing Flexible, Open Source Platform acquia.com 888.922.7842 1.781.238.8600 25 Corporate Drive, Burlington, MA 01803 Tap Into Smartphone Demand:
More informationGrowing Self-Organizing Maps for Surface Reconstruction from Unstructured Point Clouds
Growing Self-Organizing Map for Surface Recontruction from Untructured Point Cloud Renata L. M. E. do Rêgo, Aluizio F. R. Araújo, and Fernando B.de Lima Neto Abtract Thi work introduce a new method for
More informationCASE STUDY BRIDGE. www.future-processing.com
CASE STUDY BRIDGE TABLE OF CONTENTS #1 ABOUT THE CLIENT 3 #2 ABOUT THE PROJECT 4 #3 OUR ROLE 5 #4 RESULT OF OUR COLLABORATION 6-7 #5 THE BUSINESS PROBLEM THAT WE SOLVED 8 #6 CHALLENGES 9 #7 VISUAL IDENTIFICATION
More informationSupport Vector Machine Based Electricity Price Forecasting For Electricity Markets utilising Projected Assessment of System Adequacy Data.
The Sixth International Power Engineering Conference (IPEC23, 27-29 November 23, Singapore Support Vector Machine Baed Electricity Price Forecating For Electricity Maret utiliing Projected Aement of Sytem
More informationIntroduction to the article Degrees of Freedom.
Introduction to the article Degree of Freedom. The article by Walker, H. W. Degree of Freedom. Journal of Educational Pychology. 3(4) (940) 53-69, wa trancribed from the original by Chri Olen, George Wahington
More informationRotation of an Object About a Fixed Axis
Chapter 1 Rotation of an Object About a Fixed Axi 1.1 The Important Stuff 1.1.1 Rigid Bodie; Rotation So far in our tudy of phyic we have (with few exception) dealt with particle, object whoe patial dimenion
More informationBio-Plex Analysis Software
Multiplex Supenion Array Bio-Plex Analyi Software The Leader in Multiplex Immunoaay Analyi Bio-Plex Analyi Software If making ene of your multiplex data i your challenge, then Bio-Plex data analyi oftware
More informationReview of Multiple Regression Richard Williams, University of Notre Dame, http://www3.nd.edu/~rwilliam/ Last revised January 13, 2015
Review of Multiple Regreion Richard William, Univerity of Notre Dame, http://www3.nd.edu/~rwilliam/ Lat revied January 13, 015 Aumption about prior nowledge. Thi handout attempt to ummarize and yntheize
More informationInternational Journal of Heat and Mass Transfer
International Journal of Heat and Ma Tranfer 5 (9) 14 144 Content lit available at ScienceDirect International Journal of Heat and Ma Tranfer journal homepage: www.elevier.com/locate/ijhmt Technical Note
More informationBob York. Simple FET DC Bias Circuits
Bob York Simple FET DC Bia Circuit Loa-Line an Q-point Conier the effect of a rain reitor in the comnon-ource configuration: Smaller + g D out KL: Thi i the equation of a line that can be uperimpoe on
More informationMorningstar Fixed Income Style Box TM Methodology
Morningtar Fixed Income Style Box TM Methodology Morningtar Methodology Paper Augut 3, 00 00 Morningtar, Inc. All right reerved. The information in thi document i the property of Morningtar, Inc. Reproduction
More informationRedesigning Ratings: Assessing the Discriminatory Power of Credit Scores under Censoring
Redeigning Rating: Aeing the Dicriminatory Power of Credit Score under Cenoring Holger Kraft, Gerald Kroiandt, Marlene Müller Fraunhofer Intitut für Techno- und Wirtchaftmathematik (ITWM) Thi verion: June
More informationMBA 570x Homework 1 Due 9/24/2014 Solution
MA 570x Homework 1 Due 9/24/2014 olution Individual work: 1. Quetion related to Chapter 11, T Why do you think i a fund of fund market for hedge fund, but not for mutual fund? Anwer: Invetor can inexpenively
More informationFEDERATION OF ARAB SCIENTIFIC RESEARCH COUNCILS
Aignment Report RP/98-983/5/0./03 Etablihment of cientific and technological information ervice for economic and ocial development FOR INTERNAL UE NOT FOR GENERAL DITRIBUTION FEDERATION OF ARAB CIENTIFIC
More informationCHAPTER 5 BROADBAND CLASS-E AMPLIFIER
CHAPTER 5 BROADBAND CLASS-E AMPLIFIER 5.0 Introduction Cla-E amplifier wa firt preented by Sokal in 1975. The application of cla- E amplifier were limited to the VHF band. At thi range of frequency, cla-e
More informationLinear Momentum and Collisions
Chapter 7 Linear Momentum and Colliion 7.1 The Important Stuff 7.1.1 Linear Momentum The linear momentum of a particle with ma m moving with velocity v i defined a p = mv (7.1) Linear momentum i a vector.
More informationEngineering Bernoulli Equation
Engineering Bernoulli Equation R. Shankar Subramanian Department of Chemical and Biomolecular Engineering Clarkon Univerity The Engineering Bernoulli equation can be derived from the principle of conervation
More informationDesign of Compound Hyperchaotic System with Application in Secure Data Transmission Systems
Deign of Compound Hyperchaotic Sytem with Application in Secure Data Tranmiion Sytem D. Chantov Key Word. Lyapunov exponent; hyperchaotic ytem; chaotic ynchronization; chaotic witching. Abtract. In thi
More informationSTRUCTURAL DESIGN NOTES TOPIC C PRESSURE VESSEL STRESS ANALYSIS J. E. Meyer revision of August 1996
STRUCTURAL DESIGN NOTES TOPIC C PRESSURE VESSEL STRESS ANALYSIS J. E. Meyer reviion of Augut 1996 1. INTRODUCTION Thee note upplement cla lecture on "thin hell" preure veel tre analyi. The ue of the implified
More informationTurbulent Mixing and Chemical Reaction in Stirred Tanks
Turbulent Mixing and Chemical Reaction in Stirred Tank André Bakker Julian B. Faano Blend time and chemical product ditribution in turbulent agitated veel can be predicted with the aid of Computational
More informationPartial optimal labeling search for a NP-hard subclass of (max,+) problems
Partial optimal labeling earch for a NP-hard ubcla of (max,+) problem Ivan Kovtun International Reearch and Training Center of Information Technologie and Sytem, Kiev, Uraine, ovtun@image.iev.ua Dreden
More informationSimulation of Power Systems Dynamics using Dynamic Phasor Models. Power Systems Laboratory. ETH Zürich Switzerland
X SEPOPE 2 a 25 de maio de 26 May 2 rt to 25 th 26 FLORIANÓPOLIS (SC) BRASIL X SIMPÓSIO DE ESPECIALISTAS EM PLANEJAMENTO DA OPERAÇÃO E EXPANSÃO ELÉTRICA X SYMPOSIUM OF SPECIALISTS IN ELECTRIC OPERATIONAL
More informationProfitability of Loyalty Programs in the Presence of Uncertainty in Customers Valuations
Proceeding of the 0 Indutrial Engineering Reearch Conference T. Doolen and E. Van Aken, ed. Profitability of Loyalty Program in the Preence of Uncertainty in Cutomer Valuation Amir Gandomi and Saeed Zolfaghari
More informationA model for the relationship between tropical precipitation and column water vapor
Click Here for Full Article GEOPHYSICAL RESEARCH LETTERS, VOL. 36, L16804, doi:10.1029/2009gl039667, 2009 A model for the relationhip between tropical precipitation and column water vapor Caroline J. Muller,
More informationModule 8. Three-phase Induction Motor. Version 2 EE IIT, Kharagpur
Module 8 Three-phae Induction Motor Verion EE IIT, Kharagpur Leon 33 Different Type of Starter for Induction Motor (IM Verion EE IIT, Kharagpur Inructional Objective Need of uing arter for Induction motor
More informationPublic Transportation Systems: Basic Principles of System Design, Operations Planning and Real-Time Control
INSTITUTE OF TRANSPORTATION STUDIES UNIVERSITY OF CALIFORNIA, BERKELEY Public Tranportation Sytem: Baic Principle of Sytem Deign, Operation Planning and Real-Time Control Carlo F. Daganzo Coure Note UCB-ITS-CN-00-
More informationBUILT-IN DUAL FREQUENCY ANTENNA WITH AN EMBEDDED CAMERA AND A VERTICAL GROUND PLANE
Progre In Electromagnetic Reearch Letter, Vol. 3, 51, 08 BUILT-IN DUAL FREQUENCY ANTENNA WITH AN EMBEDDED CAMERA AND A VERTICAL GROUND PLANE S. H. Zainud-Deen Faculty of Electronic Engineering Menoufia
More informationMobile Network Configuration for Large-scale Multimedia Delivery on a Single WLAN
Mobile Network Configuration for Large-cale Multimedia Delivery on a Single WLAN Huigwang Je, Dongwoo Kwon, Hyeonwoo Kim, and Hongtaek Ju Dept. of Computer Engineering Keimyung Univerity Daegu, Republic
More informationThe Import-Export Paradigm for High-Quality College Courses
Public Policy Editor: Stephen Ruth ruth@gmu.edu The Import-Export Paradigm for High-Quality College Coure An Anwer to Tuition Through-the- Roof Cot Spiral? Stephen Ruth George Maon Univerity Three new
More informationINTERACTIVE TOOL FOR ANALYSIS OF TIME-DELAY SYSTEMS WITH DEAD-TIME COMPENSATORS
INTERACTIVE TOOL FOR ANALYSIS OF TIMEDELAY SYSTEMS WITH DEADTIME COMPENSATORS Joé Lui Guzmán, Pedro García, Tore Hägglund, Sebatián Dormido, Pedro Alberto, Manuel Berenguel Dep. de Lenguaje y Computación,
More informationCapital Investment. Decisions: An Overview Appendix. Introduction. Analyzing Cash Flows for Present Value Analysis
f. Capital Invetment Deciion: An Overview Appendix Introduction Capital invetment deciion are the reponibility of manager of invetment center (ee Chapter 12). The analyi of capital invetment deciion i
More informationBidding for Representative Allocations for Display Advertising
Bidding for Repreentative Allocation for Diplay Advertiing Arpita Ghoh, Preton McAfee, Kihore Papineni, and Sergei Vailvitkii Yahoo! Reearch. {arpita, mcafee, kpapi, ergei}@yahoo-inc.com Abtract. Diplay
More informationProgress 8 measure in 2016, 2017, and 2018. Guide for maintained secondary schools, academies and free schools
Progre 8 meaure in 2016, 2017, and 2018 Guide for maintained econdary chool, academie and free chool July 2016 Content Table of figure 4 Summary 5 A ummary of Attainment 8 and Progre 8 5 Expiry or review
More informationTrusted Document Signing based on use of biometric (Face) keys
Truted Document Signing baed on ue of biometric (Face) Ahmed B. Elmadani Department of Computer Science Faculty of Science Sebha Univerity Sebha Libya www.ebhau.edu.ly elmadan@yahoo.com ABSTRACT An online
More informationAbstract parsing: static analysis of dynamically generated string output using LR-parsing technology
Abtract paring: tatic analyi of dynamically generated tring output uing LR-paring technology Kyung-Goo Doh 1, Hyunha Kim 1, David A. Schmidt 2 1 Hanyang Univerity, Anan, South Korea 2 Kana State Univerity,
More informationA Review On Software Testing In SDlC And Testing Tools
www.ijec.in International Journal Of Engineering And Computer Science ISSN:2319-7242 Volume - 3 Iue -9 September, 2014 Page No. 8188-8197 A Review On Software Teting In SDlC And Teting Tool T.Amruthavalli*,
More informationCluster-Aware Cache for Network Attached Storage *
Cluter-Aware Cache for Network Attached Storage * Bin Cai, Changheng Xie, and Qiang Cao National Storage Sytem Laboratory, Department of Computer Science, Huazhong Univerity of Science and Technology,
More informationA) When two objects slide against one another, the magnitude of the frictional force is always equal to μ
Phyic 100 Homewor 5 Chapter 6 Contact Force Introduced ) When two object lide againt one another, the magnitude of the frictional force i alway equal to μ B) When two object are in contact with no relative
More informationReturn on Investment and Effort Expenditure in the Software Development Environment
International Journal of Applied Information ytem (IJAI) IN : 2249-0868 Return on Invetment and Effort Expenditure in the oftware Development Environment Dineh Kumar aini Faculty of Computing and IT, ohar
More informationFour Ways Companies Can Use Open Source Social Publishing Tools to Enhance Their Business Operations
Four Way Companie Can Ue Open Source Social Publihing Tool to Enhance Their Buine Operation acquia.com 888.922.7842 1.781.238.8600 25 Corporate Drive, Burlington, MA 01803 Four Way Companie Can Ue Open
More informationSCM- integration: organiational, managerial and technological iue M. Caridi 1 and A. Sianei 2 Dipartimento di Economia e Produzione, Politecnico di Milano, Italy E-mail: maria.caridi@polimi.it Itituto
More informationT-test for dependent Samples. Difference Scores. The t Test for Dependent Samples. The t Test for Dependent Samples. s D
The t Tet for ependent Sample T-tet for dependent Sample (ak.a., Paired ample t-tet, Correlated Group eign, Within- Subject eign, Repeated Meaure,.. Repeated-Meaure eign When you have two et of core from
More informationLecture 14: Transformers. Ideal Transformers
White, EE 3 Lecture 14 Page 1 of 9 Lecture 14: Tranforer. deal Tranforer n general, a tranforer i a ultiort ac device that convert voltage, current and iedance fro one value to another. Thi device only
More informationAlgorithms for Advance Bandwidth Reservation in Media Production Networks
Algorithm for Advance Bandwidth Reervation in Media Production Network Maryam Barhan 1, Hendrik Moen 1, Jeroen Famaey 2, Filip De Turck 1 1 Department of Information Technology, Ghent Univerity imind Gaton
More informationControl of Wireless Networks with Flow Level Dynamics under Constant Time Scheduling
Control of Wirele Network with Flow Level Dynamic under Contant Time Scheduling Long Le and Ravi R. Mazumdar Department of Electrical and Computer Engineering Univerity of Waterloo,Waterloo, ON, Canada
More informationLinear energy-preserving integrators for Poisson systems
BIT manucript No. (will be inerted by the editor Linear energy-preerving integrator for Poion ytem David Cohen Ernt Hairer Received: date / Accepted: date Abtract For Hamiltonian ytem with non-canonical
More informationPipe Flow Calculations
Pipe Flow Calculation R. Shankar Subramanian epartment o Chemical and Biomolecular Engineering Clarkon Univerity We begin with ome reult that we hall ue when making riction lo calculation or teady, ully
More informationApplication of Fourier Transform to PDE (I) Fourier Sine Transform (application to PDEs defined on a semi-infinite domain)
Application of Fourier Transform to PDE (I) Fourier Sine Transform (application to PDEs defined on a semi-infinite domain) The Fourier Sine Transform pair are F. T. : U = 2/ u x sin x dx, denoted as U
More informationYou may use a scientific calculator (non-graphing, non-programmable) during testing.
TECEP Tet Decription College Algebra MAT--TE Thi TECEP tet algebraic concept, procee, and practical application. Topic include: linear equation and inequalitie; quadratic equation; ytem of equation and
More informationPRESENTATION OF THE PROJECT ACTIVITY SCHEDULE
Newletter 1 A FEASIBLE PROCESS A SUSTAINABLE FUTURE. Welcome to the firt iue of the METABIORE- SOR (LIFE08 ENV/ES/000113) project wletter. The aim of thi wletter i to dieminate, on a regular bai, both
More information