Laser Safety. Safe clinical application of laser radiation. Frits F.M. de Mul ffmdemul(at)gmail.

Size: px
Start display at page:

Download "Laser Safety. Safe clinical application of laser radiation. Frits F.M. de Mul ffmdemul(at)gmail."

Transcription

1 Lser Sfety Sfe clinicl ppliction of lser rdition Frits F.M. de Mul emil: ffmdemul(t)gmil.com

2 Lser Sfety Sfe clinicl ppliction of lser rdition Contents: 1. Physicl / mthemticl explntion of the clcultion 2. The computer progrm: exmple of clcultions. Progrm options (similr clcultions): 1. Subprogrm of the Hygird -pckge (stnd-lone). 2. Web-ppliction. More informtion nd downlods: ; Avilble softwre....

3 Lser Sfety uses : NOHD: Nominl Oculr Hzrd Distnce NOHD: sfe distnce to void eye (or skin) dmge Stndrd distnce for eye sfety: 0.25 m for 10 s exposure time. If lser intensity [W/m 2 ] t the stndrd distnce is too high: protection glsses compulsory. 3

4 Dmge of excessive lser exposure to eye nd skin eye skin Wvelength Photochemicl Retin Therml Erythem formtion Therml < 400 nm >

5 NOHD: Nominl Oculr Hzrd Distnce lser trget focus Sfety condition t trget: Intensity I MUST be Mximum Permissible Exposure MPE I nd MPE in W/m 2 MPE is tbulted by EU NOHD is minimum distnce where I MPE 5

6 MPE: mximum permissible exposure MPE is function of: Wvelength Pulse durtion (or continuous) Pulse frequency Angulr subtense (viewing ngle of light source from trget) MPE-formule re tbulted in Directive 2006/25/EU of Europen Prliment nd Commission IEC NEN

7 MPE: mximum permissible exposure : eye α = ngulr subtense (ngle of lser wist, s seen from trget) α = 1, 10, 100 mrd (0.06, 0.6, 6 0 ) NB. Logrithmic scles 7

8 MPE: mximum permissible exposure : eye α = ngulr subtense (ngle of wist, s seen from trget) α = 1, 10, 100 mrd (0.06, 0.6, 6 0 ) If α smller: brighter lser spot, MPE smller. 8

9 NOHD: Nominl Oculr Hzrd Distnce: Clcultion Sfety condition: I MPE in W/m 2 I = intensity [W/m 2 ] I ~ lser power P [W] I ~ 1/ trget re S [m 2 ] I dependent on type of lser bem: PC = lser Profile Correltion Fctor [-]. I = (P/S). PC = P.PC / S 9

10 PC: Profile Correltion Fctor PC depends on lser mode structure Cylindricl trnsverse modes Rectngulr trnsverse modes Locl intensity in modes is lrger thn verged over the mode envelope. Profile Correltion Fctor PC > 1. 10

11 NOHD: Nominl Oculr Hzrd Distnce Sfety condition: I = intensity t trget P = power PC= prof.corr.fctor S = trget re. lser R focus, width w P PC I. MPE S Effective trget re: θ/2 D trget P. PC S MPE 2 S D, D D w 4 D = effective dimeter S 4S ( D w) 4 D w 2 2 Sfety condition for trget dimeter : D 4S w 4P. PC. MPE w 11

12 NOHD: Nominl Oculr Hzrd Distnce lser R focus, width w θ/2 trget D Effective trget re: 2 S D, D D w 4 Sfety condition for trget dimeter : D 4S w 4P. PC. MPE w NOHD R D 2.tn( / 2) NOHD 1 4P. PC - 2. tn( / 2). MPE w 12

13 NOHD: Nominl Oculr Hzrd Distnce lser R focus, width w θ/2 trget D NOHD depends on: D, or θ P PC 1/MPE w NOHD 1 4P. PC - 2. tn( / 2). MPE w 13

14 NOHD: Nominl Oculr Hzrd Distnce NOHD is lso dependent on α : ngulr subtense ngulr subtense α = ngle to view the source (= lser focus) from the trget position lser w /2 R focus, width w D Focus s seen from the trget 1 2 tn 1 w 2 R 2( w NOHD ) A smller wist will led to shrper (intenser) spot on the trget, thus MPE lower. For certin situtions (e.g. visible light): MPE depends on α (tbulted in EU-Directive), nd thus on NOHD 14

15 NOHD: Nominl Oculr Hzrd Distnce Two reltions between NOHD nd MPE : lser w /2 R focus, width w D 1 tn 2 w 2R 2( So, NOHD =f (α) w NOHD ) lser R focus, width w θ/2 trget D But lso: NOHD = f (MPE) =f (α)! from Sfety Condition: I MPE 1 4P. PC NOHD R - 2.tn( / 2). MPE w Thus: itertive pproch necessry!! 15

16 NOHD: Nominl Oculr Hzrd Distnce Two reltions between NOHD nd MPE : lser θ/2 D focus, width w trget R lser w /2 R focus, width w D (1): NOHD = f (MPE) = f (α) (2): NOHD =f (α) Itertive pproch: ε = tolernce Strt α -vlue Clc NOHD 1 from (1) nd NOHD 2 from (2) NOHD 1 NOHD 2 < ε? yes redy no α α ±Δα 16

17 Trnsmission of sfety goggles lser R focus, width w θ/2 trget D NOHD = R + In cse NOHD > sfety distnce b (from focus): sfety goggles necessry! Trnsmission T of sfety goggles nd Opticl density OD: T b NOHD 2 ; OD 10 log T trget re ~R 2 Stndrd sfety distnce = 0.25 m for 10 sec exposure. 17

18 Lser tretment In generl: pulsed lser tretment will consist of 1 seprte trins of 1 seprte pulses I I I I I I I I I I I I I I I I I I I I I Trin 1 Trin 2 Trin 3 Lser pulses Totl tretment Time Continuous lser: 1 long trin of 1 long pulse. 18

19 Hygird-progrm: Exmple of clcultions LASER INPUT DATA VALUE Wvelength 532 nm (full) Divergence ngle rd Profile correltion fctor 2 - Wist(spot)dimeter 400e-6 m Distnce lser to focus(wist) 0.3 m Bsic pulse: pulse power 1.000E+06 W...: pulse energy 5.000E-03 J...: durtion 5.000E-09 s...: rep.freq Hz Trin of pulses: power 5.000E+00 W...: energy 5.000E+01 J...: durtion 1.000E+01 s...: rep.freq Hz...: pulse t end of trin (yes/no=1/0) : nr. of pulses per trin Totl tretment: power 5.000E+00 W...: energy 5.000E+01 J...: durtion 1.000E+01 s...: nr. of trins in totl 1 - Sfe distnce from focus (for OD-glsses) m 19

20 Hygird-progrm: Exmple of clcultions OUTPUT of clcultions: For this wvelength the dmge is: EYE: photochemicl nd retin (therml) nd therml SKIN: therml RESULTS: (H in J/m^2 - E=MPE in W/m^2) CALCULATION formul MPE [W/m^2] lph [rd] NOHD [m] T-glsses OD-glss eye: pulse H=5E-3.CE 1.000E E E id. with CF1.. N= 10000, CF= 1.000E E E E id. with CF2.. N= 10000, CF= 1.000E E E E eye: trin H=18.CE.t^ E E E eye: totl H=18.CE.t^ E E E skin: pulse H=200.CA 4.000E E E id. with CF1.. N= 10000, CF= 1.000E E E E id. with CF2.. N= 10000, CF= 1.000E E E E skin: trin H=1.1E4.CA.t^ E E E skin: totl H=1.1E4.CA.t^ E E E CF = correction fctor, needed for therml dmge when >1 pulse in Tmin. (Tmin is 1.8E-5 s for 532 nm). 20

21 the end 21

Laser Safety: Safe clinical application of laser radiation

Laser Safety: Safe clinical application of laser radiation Lser Sfety: Sfe clinicl ppliction of lser rdition Frits F.M. de Mul MEPHYS Softwre & Services 2012 www.medphys.nl emil: info(t)medphys.nl NOH: Nominl Oculr Hzrd istnce NOH: sfe distnce to void eye dmge

More information

Acceptance Sampling by Attributes

Acceptance Sampling by Attributes Introduction Acceptnce Smpling by Attributes Acceptnce smpling is concerned with inspection nd decision mking regrding products. Three spects of smpling re importnt: o Involves rndom smpling of n entire

More information

New data structures to reduce data size and search time

New data structures to reduce data size and search time New dt structures to reduce dt size nd serch time Tsuneo Kuwbr Deprtment of Informtion Sciences, Fculty of Science, Kngw University, Hirtsuk-shi, Jpn FIT2018 1D-1, No2, pp1-4 Copyright (c)2018 by The Institute

More information

Motion of Electrons in Electric and Magnetic Fields & Measurement of the Charge to Mass Ratio of Electrons

Motion of Electrons in Electric and Magnetic Fields & Measurement of the Charge to Mass Ratio of Electrons n eperiment of the Electron topic Motion of Electrons in Electric nd Mgnetic Fields & Mesurement of the Chrge to Mss Rtio of Electrons Instructor: 梁生 Office: 7-318 Emil: shling@bjtu.edu.cn Purposes 1.

More information

19 th INTERNATIONAL CONGRESS ON ACOUSTICS MADRID, 2-7 SEPTEMBER 2007 A NON-CONTACT SYSTEM FOR TRANSPORTING OBJECTS USING ULTRASONIC LEVITATION

19 th INTERNATIONAL CONGRESS ON ACOUSTICS MADRID, 2-7 SEPTEMBER 2007 A NON-CONTACT SYSTEM FOR TRANSPORTING OBJECTS USING ULTRASONIC LEVITATION 19 th INTERNATIONAL CONGRESS ON ACOUSTICS MADRID, -7 SEPTEMBER 007 A NON-CONTACT SYSTEM FOR TRANSPORTING OBJECTS USING ULTRASONIC LEVITATION PACS: 3.5.Uv Gudr, Tdeusz 1 ; Perkowski, Dniel ; Opielinski,

More information

Measuring Electron Work Function in Metal

Measuring Electron Work Function in Metal n experiment of the Electron topic Mesuring Electron Work Function in Metl Instructor: 梁生 Office: 7-318 Emil: shling@bjtu.edu.cn Purposes 1. To understnd the concept of electron work function in metl nd

More information

Light and Optics Propagation of light Electromagnetic waves (light) in vacuum and matter Reflection and refraction of light Huygens principle

Light and Optics Propagation of light Electromagnetic waves (light) in vacuum and matter Reflection and refraction of light Huygens principle Light nd Optics Propgtion of light Electromgnetic wves (light) in vcuum nd mtter Reflection nd refrction of light Huygens principle Polristion of light Geometric optics Plne nd curved mirrors Thin lenses

More information

PLK VICWOOD K.T. CHONG SIXTH FORM COLLEGE Form Six AL Physics Optical instruments

PLK VICWOOD K.T. CHONG SIXTH FORM COLLEGE Form Six AL Physics Optical instruments AL Pysics/pticl instruments/p.1 PLK VICW K.T. CHNG SIXTH FRM CLLEGE Form Six AL Pysics pticl Instruments pticl instruments Mgniying glss Microscope Rercting telescope Grting spectrometer Qulittive understnding

More information

CLOSED EXPRESSIONS FOR COEFFICIENTS IN WEIGHTED NEWTON-COTES QUADRATURES

CLOSED EXPRESSIONS FOR COEFFICIENTS IN WEIGHTED NEWTON-COTES QUADRATURES Filomt 27:4 (2013) 649 658 DOI 10.2298/FIL1304649M Published by Fculty of Sciences nd Mthemtics University of Niš Serbi Avilble t: http://www.pmf.ni.c.rs/filomt CLOSED EXPRESSIONS FOR COEFFICIENTS IN WEIGHTED

More information

Pre-Calculus TMTA Test 2018

Pre-Calculus TMTA Test 2018 . For the function f ( x) ( x )( x )( x 4) find the verge rte of chnge from x to x. ) 70 4 8.4 8.4 4 7 logb 8. If logb.07, logb 4.96, nd logb.60, then ).08..867.9.48. For, ) sec (sin ) is equivlent to

More information

Simulation of Eclipsing Binary Star Systems. Abstract

Simulation of Eclipsing Binary Star Systems. Abstract Simultion of Eclipsing Binry Str Systems Boris Yim 1, Kenny Chn 1, Rphel Hui 1 Wh Yn College Kowloon Diocesn Boys School Abstrct This report briefly introduces the informtion on eclipsing binry str systems.

More information

Math 113 Exam 1-Review

Math 113 Exam 1-Review Mth 113 Exm 1-Review September 26, 2016 Exm 1 covers 6.1-7.3 in the textbook. It is dvisble to lso review the mteril from 5.3 nd 5.5 s this will be helpful in solving some of the problems. 6.1 Are Between

More information

WMAP satellite. 16 Feb Feb Feb 2012

WMAP satellite. 16 Feb Feb Feb 2012 16 Feb 2012 21 Feb 2012 23 Feb 2012 è Announcements è Problem 5 (Hrtle 18.3). Assume V * is nonreltivistic. The reltivistic cse requires more complicted functions. è Outline è WMAP stellite è Dipole nisotropy

More information

Numerical Integration

Numerical Integration Chpter 1 Numericl Integrtion Numericl differentition methods compute pproximtions to the derivtive of function from known vlues of the function. Numericl integrtion uses the sme informtion to compute numericl

More information

Laser polishing of vidicon s glass substrates

Laser polishing of vidicon s glass substrates Lser polishing of vidicon s glss substrtes Sidorenko S.P., Fedosovsky M.E., Veiko V.P. 3, Golubok A.O. 3, Levichev V.V. 3, Chuiko V.A. 3, Ykovlev E.B. 3, Shkhno E.A. 3 Joint stock compny «Dikont», joint

More information

Precalculus Spring 2017

Precalculus Spring 2017 Preclculus Spring 2017 Exm 3 Summry (Section 4.1 through 5.2, nd 9.4) Section P.5 Find domins of lgebric expressions Simplify rtionl expressions Add, subtrct, multiply, & divide rtionl expressions Simplify

More information

Selection of bearing type

Selection of bearing type Selection of ering type Aville spce... 35 Lods... 37 Mgnitude of lod... 37 Direction of lod... 37 Mislignment... 40 Precision... 40 Speed... 42 Quiet running... 42 Stiffness... 42 Axil displcement... 43

More information

Trigonometric Functions

Trigonometric Functions Exercise. Degrees nd Rdins Chpter Trigonometric Functions EXERCISE. Degrees nd Rdins 4. Since 45 corresponds to rdin mesure of π/4 rd, we hve: 90 = 45 corresponds to π/4 or π/ rd. 5 = 7 45 corresponds

More information

Data Provided: A formula sheet and table of physical constants are attached to this paper.

Data Provided: A formula sheet and table of physical constants are attached to this paper. PHY472 Dt Provided: Formul sheet nd physicl constnts Dt Provided: A formul sheet nd tble of physicl constnts re ttched to this pper. DEPARTMENT OF PHYSICS & Autumn Semester 2009-2010 ASTRONOMY DEPARTMENT

More information

Studies on Nuclear Fuel Rod Thermal Performance

Studies on Nuclear Fuel Rod Thermal Performance Avilble online t www.sciencedirect.com Energy Procedi 1 (1) 1 17 Studies on Nucler Fuel od herml Performnce Eskndri, M.1; Bvndi, A ; Mihndoost, A3* 1 Deprtment of Physics, Islmic Azd University, Shirz

More information

The Properties of Stars

The Properties of Stars 10/11/010 The Properties of Strs sses Using Newton s Lw of Grvity to Determine the ss of Celestil ody ny two prticles in the universe ttrct ech other with force tht is directly proportionl to the product

More information

Today s summary. MIT 2.71/2.710 Optics 10/24/05 wk8-a-1

Today s summary. MIT 2.71/2.710 Optics 10/24/05 wk8-a-1 Tody s summry Multiple bem interferometers: Fbry-Perot resontors Stokes reltionships Trnsmission nd reflection coefficients for dielectric slb Opticl resonnce Principles of lsers Coherence: sptil / temporl

More information

Shear and torsion interaction of hollow core slabs

Shear and torsion interaction of hollow core slabs Competitive nd Sustinble Growth Contrct Nº G6RD-CT--6 Sher nd torsion interction of hollow core slbs HOLCOTORS Technicl Report, Rev. Anlyses of hollow core floors December The content of the present publiction

More information

Department of Physical Pharmacy and Pharmacokinetics Poznań University of Medical Sciences Pharmacokinetics laboratory

Department of Physical Pharmacy and Pharmacokinetics Poznań University of Medical Sciences Pharmacokinetics laboratory Deprtment of Physicl Phrmcy nd Phrmcoinetics Poznń University of Medicl Sciences Phrmcoinetics lbortory Experiment 1 Phrmcoinetics of ibuprofen s n exmple of the first-order inetics in n open one-comprtment

More information

x = b a N. (13-1) The set of points used to subdivide the range [a, b] (see Fig. 13.1) is

x = b a N. (13-1) The set of points used to subdivide the range [a, b] (see Fig. 13.1) is Jnury 28, 2002 13. The Integrl The concept of integrtion, nd the motivtion for developing this concept, were described in the previous chpter. Now we must define the integrl, crefully nd completely. According

More information

Physics 2135 Exam 3 April 21, 2015

Physics 2135 Exam 3 April 21, 2015 Em Totl hysics 2135 Em 3 April 21, 2015 Key rinted Nme: 200 / 200 N/A Rec. Sec. Letter: Five multiple choice questions, 8 points ech. Choose the best or most nerly correct nswer. 1. C Two long stright

More information

Data Provided: A formula sheet and table of physical constants is attached to this paper.

Data Provided: A formula sheet and table of physical constants is attached to this paper. PHY15-B PHY47 Dt Provided: Formul sheet nd physicl constnts Dt Provided: A formul sheet nd tble of physicl constnts is ttched to this pper. DEPARTMENT OF PHYSICS & Autumn Semester 009-010 ASTRONOMY DEPARTMENT

More information

8Similarity UNCORRECTED PAGE PROOFS. 8.1 Kick off with CAS 8.2 Similar objects 8.3 Linear scale factors. 8.4 Area and volume scale factors 8.

8Similarity UNCORRECTED PAGE PROOFS. 8.1 Kick off with CAS 8.2 Similar objects 8.3 Linear scale factors. 8.4 Area and volume scale factors 8. 8.1 Kick off with S 8. Similr ojects 8. Liner scle fctors 8Similrity 8. re nd volume scle fctors 8. Review U N O R R E TE D P G E PR O O FS 8.1 Kick off with S Plese refer to the Resources t in the Prelims

More information

Main topics for the First Midterm

Main topics for the First Midterm Min topics for the First Midterm The Midterm will cover Section 1.8, Chpters 2-3, Sections 4.1-4.8, nd Sections 5.1-5.3 (essentilly ll of the mteril covered in clss). Be sure to know the results of the

More information

Lecture 20: Numerical Integration III

Lecture 20: Numerical Integration III cs4: introduction to numericl nlysis /8/0 Lecture 0: Numericl Integrtion III Instructor: Professor Amos Ron Scribes: Mrk Cowlishw, Yunpeng Li, Nthnel Fillmore For the lst few lectures we hve discussed

More information

Electric Potential. Concepts and Principles. An Alternative Approach. A Gravitational Analogy

Electric Potential. Concepts and Principles. An Alternative Approach. A Gravitational Analogy . Electric Potentil Concepts nd Principles An Alterntive Approch The electric field surrounding electric chrges nd the mgnetic field surrounding moving electric chrges cn both be conceptulized s informtion

More information

8Similarity ONLINE PAGE PROOFS. 8.1 Kick off with CAS 8.2 Similar objects 8.3 Linear scale factors. 8.4 Area and volume scale factors 8.

8Similarity ONLINE PAGE PROOFS. 8.1 Kick off with CAS 8.2 Similar objects 8.3 Linear scale factors. 8.4 Area and volume scale factors 8. 8.1 Kick off with S 8. Similr ojects 8. Liner scle fctors 8Similrity 8.4 re nd volume scle fctors 8. Review Plese refer to the Resources t in the Prelims section of your eookplus for comprehensive step-y-step

More information

(See Notes on Spontaneous Emission)

(See Notes on Spontaneous Emission) ECE 240 for Cvity from ECE 240 (See Notes on ) Quntum Rdition in ECE 240 Lsers - Fll 2017 Lecture 11 1 Free Spce ECE 240 for Cvity from Quntum Rdition in The electromgnetic mode density in free spce is

More information

Emission of K -, L - and M - Auger Electrons from Cu Atoms. Abstract

Emission of K -, L - and M - Auger Electrons from Cu Atoms. Abstract Emission of K -, L - nd M - uger Electrons from Cu toms Mohmed ssd bdel-rouf Physics Deprtment, Science College, UEU, l in 17551, United rb Emirtes ssd@ueu.c.e bstrct The emission of uger electrons from

More information

Soft switching 4/2 and 4/3 directional valves with DC solenoids Model WE /A12..

Soft switching 4/2 and 4/3 directional valves with DC solenoids Model WE /A12.. R 3 183/06.98 Replces: R 3 18/05.9 R 3 183/06.98 Soft switching / nd /3 directionl vlves with DC solenoids Model WE...73 -.. /1.. Nominl sizes 6 nd 10 Series 6X (size 6)/3X (size 10) Mximum operting pressure

More information

25 Which of the following summarises the change in wave characteristics on going from infra-red to ultraviolet in the electromagnetic spectrum?

25 Which of the following summarises the change in wave characteristics on going from infra-red to ultraviolet in the electromagnetic spectrum? PhysicsndMthsTutor.com 25 Which of the following summrises the chnge in wve chrcteristics on going from infr-red to ultrviolet in the electromgnetic spectrum? 972//M/J/2 frequency speed (in vcuum) decreses

More information

Year 12 Mathematics Extension 2 HSC Trial Examination 2014

Year 12 Mathematics Extension 2 HSC Trial Examination 2014 Yer Mthemtics Etension HSC Tril Emintion 04 Generl Instructions. Reding time 5 minutes Working time hours Write using blck or blue pen. Blck pen is preferred. Bord-pproved clcultors my be used A tble of

More information

Modelling of the near infra-red radiation pulse propagation in biological tissues for medical imaging application

Modelling of the near infra-red radiation pulse propagation in biological tissues for medical imaging application JOURNAL OF INTENSE PULSED LASERS AND APPLICATIONS IN ADVANCED PHYSICS Vol. 3, No. 4, p. 4-45 Modelling of the ner infr-red rdition pulse propgtion in biologicl tissues for medicl imging ppliction A. SAOULI

More information

potentials A z, F z TE z Modes We use the e j z z =0 we can simply say that the x dependence of E y (1)

potentials A z, F z TE z Modes We use the e j z z =0 we can simply say that the x dependence of E y (1) 3e. Introduction Lecture 3e Rectngulr wveguide So fr in rectngulr coordintes we hve delt with plne wves propgting in simple nd inhomogeneous medi. The power density of plne wve extends over ll spce. Therefore

More information

The Basic Functional 2 1

The Basic Functional 2 1 2 The Bsic Functionl 2 1 Chpter 2: THE BASIC FUNCTIONAL TABLE OF CONTENTS Pge 2.1 Introduction..................... 2 3 2.2 The First Vrition.................. 2 3 2.3 The Euler Eqution..................

More information

Atmospheric Radiation Fall 2008

Atmospheric Radiation Fall 2008 MIT OpenCourseWre http://ocw.mit.edu.85 Atmospheric Rdition Fll 008 For informtion bout citing these mterils or our Terms of Use, visit: http://ocw.mit.edu/terms. .85, Atmospheric Rdition Dr. Robert A.

More information

HT Module 2 Paper solution. Module 2. Q6.Discuss Electrical analogy of combined heat conduction and convection in a composite wall.

HT Module 2 Paper solution. Module 2. Q6.Discuss Electrical analogy of combined heat conduction and convection in a composite wall. HT Module 2 Pper solution Qulity Solutions wwwqulitytutorilin Module 2 Q6Discuss Electricl nlogy of combined het conduction nd convection in composite wll M-16-Q1(c)-5m Ans: It is frequently convient to

More information

1 Which of the following summarises the change in wave characteristics on going from infra-red to ultraviolet in the electromagnetic spectrum?

1 Which of the following summarises the change in wave characteristics on going from infra-red to ultraviolet in the electromagnetic spectrum? Which of the following summrises the chnge in wve chrcteristics on going from infr-red to ultrviolet in the electromgnetic spectrum? frequency speed (in vcuum) decreses decreses decreses remins constnt

More information

MIXED MODELS (Sections ) I) In the unrestricted model, interactions are treated as in the random effects model:

MIXED MODELS (Sections ) I) In the unrestricted model, interactions are treated as in the random effects model: 1 2 MIXED MODELS (Sections 17.7 17.8) Exmple: Suppose tht in the fiber breking strength exmple, the four mchines used were the only ones of interest, but the interest ws over wide rnge of opertors, nd

More information

Unexplored Indoors method for pyranometers calibration traceable to SI

Unexplored Indoors method for pyranometers calibration traceable to SI Journl of Physics: Conference Series OPEN CCESS Unexplored ndoors method for pyrnometers clirtion trcele to S To cite this rticle: H Cstillo-Mtdms et l 15 J. Phys.: Conf. Ser. 58 151 View the rticle online

More information

Remarks to the H-mode workshop paper

Remarks to the H-mode workshop paper 2 nd ITPA Confinement Dtbse nd Modeling Topicl Group Meeting, Mrch 11-14, 2002, Princeton Remrks to the H-mode workshop pper The development of two-term model for the confinement in ELMy H-modes using

More information

99/105 Comparison of OrcaFlex with standard theoretical results

99/105 Comparison of OrcaFlex with standard theoretical results 99/105 Comprison of OrcFlex ith stndrd theoreticl results 1. Introduction A number of stndrd theoreticl results from literture cn be modelled in OrcFlex. Such cses re, by virtue of being theoreticlly solvble,

More information

6.2 CONCEPTS FOR ADVANCED MATHEMATICS, C2 (4752) AS

6.2 CONCEPTS FOR ADVANCED MATHEMATICS, C2 (4752) AS 6. CONCEPTS FOR ADVANCED MATHEMATICS, C (475) AS Objectives To introduce students to number of topics which re fundmentl to the dvnced study of mthemtics. Assessment Emintion (7 mrks) 1 hour 30 minutes.

More information

A new algorithm for generating Pythagorean triples 1

A new algorithm for generating Pythagorean triples 1 A new lgorithm for generting Pythgoren triples 1 RH Dye 2 nd RWD Nicklls 3 The Mthemticl Gzette (1998; 82 (Mrch, No. 493, pp. 86 91 http://www.nicklls.org/dick/ppers/mths/pythgtriples1998.pdf 1 Introduction

More information

Chapter 7 Notes, Stewart 8e. 7.1 Integration by Parts Trigonometric Integrals Evaluating sin m x cos n (x) dx...

Chapter 7 Notes, Stewart 8e. 7.1 Integration by Parts Trigonometric Integrals Evaluating sin m x cos n (x) dx... Contents 7.1 Integrtion by Prts................................... 2 7.2 Trigonometric Integrls.................................. 8 7.2.1 Evluting sin m x cos n (x)......................... 8 7.2.2 Evluting

More information

Physics 1402: Lecture 7 Today s Agenda

Physics 1402: Lecture 7 Today s Agenda 1 Physics 1402: Lecture 7 Tody s gend nnouncements: Lectures posted on: www.phys.uconn.edu/~rcote/ HW ssignments, solutions etc. Homework #2: On Msterphysics tody: due Fridy Go to msteringphysics.com Ls:

More information

Introduction to ISAR imaging systems. Elaborazione Sistemi Radar delle immagini radar

Introduction to ISAR imaging systems. Elaborazione Sistemi Radar delle immagini radar Introduction to ISAR imging systems SAR_RANGE 1 Rdr imging systems More in generl rdr imges re obtined by exploiting the reltive motion between the rdr ntenn nd the scene to be imged. SAR: KNOWN reltive

More information

, MATHS H.O.D.: SUHAG R.KARIYA, BHOPAL, CONIC SECTION PART 8 OF

, MATHS H.O.D.: SUHAG R.KARIYA, BHOPAL, CONIC SECTION PART 8 OF DOWNLOAD FREE FROM www.tekoclsses.com, PH.: 0 903 903 7779, 98930 5888 Some questions (Assertion Reson tpe) re given elow. Ech question contins Sttement (Assertion) nd Sttement (Reson). Ech question hs

More information

Nuclear Reactions. Shape, interaction, and excitation structures of nuclei scattering expt. cf. Experiment by Rutherford (α scatt.

Nuclear Reactions. Shape, interaction, and excitation structures of nuclei scattering expt. cf. Experiment by Rutherford (α scatt. Nucler Rections Shpe, interction, nd excittion structures of nuclei scttering expt. cf. Experiment by Rutherford (α sctt.) scttered prticles detector solid ngle projectile trget trnsmitted prticles http://www.th.phys.titech.c.jp/~muto/lectures/qmii11/qmii11_chp21.pdf

More information

13: Diffusion in 2 Energy Groups

13: Diffusion in 2 Energy Groups 3: Diffusion in Energy Groups B. Rouben McMster University Course EP 4D3/6D3 Nucler Rector Anlysis (Rector Physics) 5 Sept.-Dec. 5 September Contents We study the diffusion eqution in two energy groups

More information

a * a (2,1) 1,1 0,1 1,1 2,1 hkl 1,0 1,0 2,0 O 2,1 0,1 1,1 0,2 1,2 2,2

a * a (2,1) 1,1 0,1 1,1 2,1 hkl 1,0 1,0 2,0 O 2,1 0,1 1,1 0,2 1,2 2,2 18 34.3 The Reciprocl Lttice The inverse of the intersections of plne with the unit cell xes is used to find the Miller indices of the plne. The inverse of the d-spcing etween plnes ppers in expressions

More information

Rolling Contact Bearings (pg 599)

Rolling Contact Bearings (pg 599) Bering V9.xmcd [Pg / 6] Title [234] The Units used s stndrd: m, kg, N, P, sec, wtts N, kg, m, P, sec/min, wtts/kw Rolling Contct Berings (pg 599) This note is only guideline for using the text book. Detiled

More information

TO: Next Year s AP Calculus Students

TO: Next Year s AP Calculus Students TO: Net Yer s AP Clculus Students As you probbly know, the students who tke AP Clculus AB nd pss the Advnced Plcement Test will plce out of one semester of college Clculus; those who tke AP Clculus BC

More information

THE KENNESAW STATE UNIVERSITY HIGH SCHOOL MATHEMATICS COMPETITION PART I MULTIPLE CHOICE NO CALCULATORS 90 MINUTES

THE KENNESAW STATE UNIVERSITY HIGH SCHOOL MATHEMATICS COMPETITION PART I MULTIPLE CHOICE NO CALCULATORS 90 MINUTES THE 08 09 KENNESW STTE UNIVERSITY HIGH SHOOL MTHEMTIS OMPETITION PRT I MULTIPLE HOIE For ech of the following questions, crefully blcken the pproprite box on the nswer sheet with # pencil. o not fold,

More information

Industrial Electrical Engineering and Automation

Industrial Electrical Engineering and Automation CODEN:LUTEDX/(TEIE-719)/1-7/(7) Industril Electricl Engineering nd Automtion Estimtion of the Zero Sequence oltge on the D- side of Dy Trnsformer y Using One oltge Trnsformer on the D-side Frncesco Sull

More information

Temperature influence compensation in microbolometer detector for image quality enhancement

Temperature influence compensation in microbolometer detector for image quality enhancement .26/qirt.26.68 Temperture influence compenstion in microolometer detector for imge qulity enhncement More info out this rticle: http://www.ndt.net/?id=2647 Astrct y M. Krupiński*, T. Sosnowski*, H. Mdur*

More information

Data Structures and Algorithms CMPSC 465

Data Structures and Algorithms CMPSC 465 Dt Structures nd Algorithms CMPSC 465 LECTURE 10 Solving recurrences Mster theorem Adm Smith S. Rskhodnikov nd A. Smith; bsed on slides by E. Demine nd C. Leiserson Review questions Guess the solution

More information

PKK Energy chains. PKK 320 / 200 x 2340 / 200; 5Pz, 1PT55

PKK Energy chains. PKK 320 / 200 x 2340 / 200; 5Pz, 1PT55 Energy cins Te order for plstic energy cin sould contin te following dt: Type / dius x Lengt / Widt "Arrngement"; Seprtor rrngement 1 3 Type selection is in ccordnce wit dimeter nd quntity of te lines

More information

SUPPLEMENTARY INFORMATION

SUPPLEMENTARY INFORMATION DOI:.38/NMAT343 Hybrid Elstic olids Yun Li, Ying Wu, Ping heng, Zho-Qing Zhng* Deprtment of Physics, Hong Kong University of cience nd Technology Cler Wter By, Kowloon, Hong Kong, Chin E-mil: phzzhng@ust.hk

More information

Data Provided: A formula sheet and table of physical constants are attached to this paper.

Data Provided: A formula sheet and table of physical constants are attached to this paper. PHY472 Dt Provided: Formul sheet nd physicl constnts Dt Provided: A formul sheet nd tble of physicl constnts re ttched to this pper. DEPARTMENT OF PHYSICS & Autumn Semester 2009-2010 ASTRONOMY DEPARTMENT

More information

Teaching Modelica for Mathematicians and Engineers Modelica Educational Workshop Berlin

Teaching Modelica for Mathematicians and Engineers Modelica Educational Workshop Berlin Teching Modelic for Mthemticins nd Modelic Eductionl Workshop Berlin Bernhrd Bchmnn University of Applied Sciences Bielefeld Outline Pst Teching Experience Mthemticins precognition, course objectives Course

More information

DIFFRACTION OF LIGHT

DIFFRACTION OF LIGHT DIFFRACTION OF LIGHT The phenomenon of bending of light round the edges of obstcles or nrrow slits nd hence its encrochment into the region of geometricl shdow is known s diffrction. P Frunhofer versus

More information

Monte Carlo method in solving numerical integration and differential equation

Monte Carlo method in solving numerical integration and differential equation Monte Crlo method in solving numericl integrtion nd differentil eqution Ye Jin Chemistry Deprtment Duke University yj66@duke.edu Abstrct: Monte Crlo method is commonly used in rel physics problem. The

More information

THERMAL EXPANSION COEFFICIENT OF WATER FOR VOLUMETRIC CALIBRATION

THERMAL EXPANSION COEFFICIENT OF WATER FOR VOLUMETRIC CALIBRATION XX IMEKO World Congress Metrology for Green Growth September 9,, Busn, Republic of Kore THERMAL EXPANSION COEFFICIENT OF WATER FOR OLUMETRIC CALIBRATION Nieves Medin Hed of Mss Division, CEM, Spin, mnmedin@mityc.es

More information

Nuclear Reactors

Nuclear Reactors 501503747 Nucler Rectors Nucler Physics t BAU http://nucler.bu.edu.jo/ This course http://nucler.bu.edu.jo/rectors Prerequisites Nucler nd Rdition Physics 74 http://nucler.bu.edu.jo/nucler-rdition / l

More information

Tests for the Ratio of Two Poisson Rates

Tests for the Ratio of Two Poisson Rates Chpter 437 Tests for the Rtio of Two Poisson Rtes Introduction The Poisson probbility lw gives the probbility distribution of the number of events occurring in specified intervl of time or spce. The Poisson

More information

Lesson 8. Thermomechanical Measurements for Energy Systems (MENR) Measurements for Mechanical Systems and Production (MMER)

Lesson 8. Thermomechanical Measurements for Energy Systems (MENR) Measurements for Mechanical Systems and Production (MMER) Lesson 8 Thermomechnicl Mesurements for Energy Systems (MEN) Mesurements for Mechnicl Systems nd Production (MME) A.Y. 205-6 Zccri (ino ) Del Prete Mesurement of Mechnicl STAIN Strin mesurements re perhps

More information

KINEMATICS OF RIGID BODIES

KINEMATICS OF RIGID BODIES KINEMTICS OF RIGI OIES Introduction In rigid body kinemtics, e use the reltionships governing the displcement, velocity nd ccelertion, but must lso ccount for the rottionl motion of the body. escription

More information

1 Part II: Numerical Integration

1 Part II: Numerical Integration Mth 4 Lb 1 Prt II: Numericl Integrtion This section includes severl techniques for getting pproimte numericl vlues for definite integrls without using ntiderivtives. Mthemticll, ect nswers re preferble

More information

Testing categorized bivariate normality with two-stage. polychoric correlation estimates

Testing categorized bivariate normality with two-stage. polychoric correlation estimates Testing ctegorized bivrite normlity with two-stge polychoric correltion estimtes Albert Mydeu-Olivres Dept. of Psychology University of Brcelon Address correspondence to: Albert Mydeu-Olivres. Fculty of

More information

AP Calculus Multiple Choice: BC Edition Solutions

AP Calculus Multiple Choice: BC Edition Solutions AP Clculus Multiple Choice: BC Edition Solutions J. Slon Mrch 8, 04 ) 0 dx ( x) is A) B) C) D) E) Divergent This function inside the integrl hs verticl symptotes t x =, nd the integrl bounds contin this

More information

Chapter 4 Contravariance, Covariance, and Spacetime Diagrams

Chapter 4 Contravariance, Covariance, and Spacetime Diagrams Chpter 4 Contrvrince, Covrince, nd Spcetime Digrms 4. The Components of Vector in Skewed Coordintes We hve seen in Chpter 3; figure 3.9, tht in order to show inertil motion tht is consistent with the Lorentz

More information

Vertical uniformity of cells and nuclei in epithelial monolayers

Vertical uniformity of cells and nuclei in epithelial monolayers Supplementry informtion Verticl uniformity of cells nd nuclei in epithelil monolyers Srujn Neelm b, Peter Hyes, Qio Zhng, Richrd B. Dickinson nd Tnmy P. Lele, Figure S1. Histogrm plots compre the frequency

More information

Chapter 5 Waveguides and Resonators

Chapter 5 Waveguides and Resonators 5-1 Chpter 5 Wveguides nd Resontors Dr. Sturt Long 5- Wht is wveguide (or trnsmission line)? Structure tht trnsmits electromgnetic wves in such wy tht the wve intensity is limited to finite cross-sectionl

More information

Multi-objective optimization of dielectric layer photonic crystal filter

Multi-objective optimization of dielectric layer photonic crystal filter Optic Applict, Vol. XLVII, No. 1, 017 DOI: 10.577/o170103 Multi-objective optimiztion of dielectric lyer photonic crystl filter HONGWEI YANG *, CUIYING HUANG, SHANSHAN MENG College of Applied Sciences,

More information

Sufficient Response Time Analysis considering Dependencies between Rate-Dependent Tasks

Sufficient Response Time Analysis considering Dependencies between Rate-Dependent Tasks Sufficient Response Time Anlysis considering Dependencies between Rte-Dependent Tsks Timo Feld, Frnk Slomk Institute of Embedded Systems/Rel-Time Systems Ulm University, 89069 Ulm, Germny firstnme.lstnme@uni-ulm.de

More information

Diffraction. Diffraction and Polarization. Diffraction. Diffraction. Diffraction I. Angular Spread: θ ~ λ/a

Diffraction. Diffraction and Polarization. Diffraction. Diffraction. Diffraction I. Angular Spread: θ ~ λ/a 1 nd Polriztion Chpter 38 Rleigh s Criterion Polriztion n geometricl optics, we modeled rs like this! n fct wht hppens is this... A sphericl wve propgtes out from the perture. All wves do this.. For double

More information

Safety relay OA 5601, OA 5602, OA 5603

Safety relay OA 5601, OA 5602, OA 5603 Sfety rely OA 0, OA 0, OA 0 cc. to DIN EN 0 0, DIN EN 0-, DIN EN 0 - with positively driven contcts Clernce nd creepge distnces, contct-coil mm high voltge resistnce kv high switching relibility due to

More information

Chapter 0. What is the Lebesgue integral about?

Chapter 0. What is the Lebesgue integral about? Chpter 0. Wht is the Lebesgue integrl bout? The pln is to hve tutoril sheet ech week, most often on Fridy, (to be done during the clss) where you will try to get used to the ides introduced in the previous

More information

Emittance Partitioning in Photoinjectors

Emittance Partitioning in Photoinjectors Emittnce Prtitioning in Photoinjectors Bruce Crlsten, Robert Rne, Kip Bishofberger, Steven Russell, nd Nikoli Ympolsk Los Almos Ntionl Lbortor Lwrence Berkele Ntionl Lbortor Motivtion We need ver smll

More information

Design of T and L Beams in Flexure

Design of T and L Beams in Flexure Lecture 04 Design of T nd L Bems in Flexure By: Prof. Dr. Qisr Ali Civil Engineering Deprtment UET Peshwr drqisrli@uetpeshwr.edu.pk Prof. Dr. Qisr Ali CE 320 Reinforced Concrete Design Topics Addressed

More information

31.2. Numerical Integration. Introduction. Prerequisites. Learning Outcomes

31.2. Numerical Integration. Introduction. Prerequisites. Learning Outcomes Numericl Integrtion 3. Introduction In this Section we will present some methods tht cn be used to pproximte integrls. Attention will be pid to how we ensure tht such pproximtions cn be gurnteed to be

More information

Results of quality assessment tasks of the optical -electronic complex using complex instrumentation background and astroclimatic conditions

Results of quality assessment tasks of the optical -electronic complex using complex instrumentation background and astroclimatic conditions Results of qulity ssessment tsks of the opticl -electronic complex using complex instrumenttion bckground nd stroclimtic conditions Chirov D.S., Grigoroshenko V.M. Abstrct The report presents the results

More information

Information processing via physical soft body. Supplementary Information

Information processing via physical soft body. Supplementary Information Informtion processing vi physicl soft body Supplementry Informtion Kohei Nkjim 1, Helmut Huser 2, o Li 3, Rolf Pfeifer 4,5 1 he Hkubi Center for Advnced Reserch & Grdute School of Informtics, Kyoto University,

More information

Math 113 Exam 2 Practice

Math 113 Exam 2 Practice Mth 3 Exm Prctice Februry 8, 03 Exm will cover 7.4, 7.5, 7.7, 7.8, 8.-3 nd 8.5. Plese note tht integrtion skills lerned in erlier sections will still be needed for the mteril in 7.5, 7.8 nd chpter 8. This

More information

TMRT A thermal model reduction tool. Mathieu Bernard (EADS Astrium, France) Thierry Basset (Thales Alenia Space, France)

TMRT A thermal model reduction tool. Mathieu Bernard (EADS Astrium, France) Thierry Basset (Thales Alenia Space, France) 53 ppendix D MR therml model reduction tool Mthieu Bernrd (EDS strium, Frnce) hierry Bsset (hles leni Spce, Frnce) Sndrine Leroy Frnçois Brunetti (DORE, Frnce) Jmes Etchells (ES/ESE, he Netherlnds) 54

More information

THE SURFACE ROUGHNESS WAKEFIELD EFFECT

THE SURFACE ROUGHNESS WAKEFIELD EFFECT THE SURFACE ROUGHNESS WAKEFIELD EFFECT A. Novokhtski, M. Timm nd T. Weilnd, TU-Drmstdt, TEMF, Schlossgrtenstr. 8, 6489 Drmstdt, Germny Abstrct In the Liner Colliders FEL projects ultr short bunches re

More information

Vorticity. curvature: shear: fluid elements moving in a straight line but at different speeds. t 1 t 2. ATM60, Shu-Hua Chen

Vorticity. curvature: shear: fluid elements moving in a straight line but at different speeds. t 1 t 2. ATM60, Shu-Hua Chen Vorticity We hve previously discussed the ngulr velocity s mesure of rottion of body. This is suitble quntity for body tht retins its shpe but fluid cn distort nd we must consider two components to rottion:

More information

5.04 Principles of Inorganic Chemistry II

5.04 Principles of Inorganic Chemistry II MIT OpenCourseWre http://ocw.mit.edu 5.04 Principles of Inorgnic Chemistry II Fll 2008 For informtion bout citing these mterils or our Terms of Use, visit: http://ocw.mit.edu/terms. 5.04, Principles of

More information

Fault Modeling. EE5375 ADD II Prof. MacDonald

Fault Modeling. EE5375 ADD II Prof. MacDonald Fult Modeling EE5375 ADD II Prof. McDonld Stuck At Fult Models l Modeling of physicl defects (fults) simplify to logicl fult l stuck high or low represents mny physicl defects esy to simulte technology

More information

The Riemann-Lebesgue Lemma

The Riemann-Lebesgue Lemma Physics 215 Winter 218 The Riemnn-Lebesgue Lemm The Riemnn Lebesgue Lemm is one of the most importnt results of Fourier nlysis nd symptotic nlysis. It hs mny physics pplictions, especilly in studies of

More information

Multiple Integrals. Review of Single Integrals. Planar Area. Volume of Solid of Revolution

Multiple Integrals. Review of Single Integrals. Planar Area. Volume of Solid of Revolution Multiple Integrls eview of Single Integrls eding Trim 7.1 eview Appliction of Integrls: Are 7. eview Appliction of Integrls: olumes 7.3 eview Appliction of Integrls: Lengths of Curves Assignment web pge

More information

University of Texas MD Anderson Cancer Center Department of Biostatistics. Inequality Calculator, Version 3.0 November 25, 2013 User s Guide

University of Texas MD Anderson Cancer Center Department of Biostatistics. Inequality Calculator, Version 3.0 November 25, 2013 User s Guide University of Texs MD Anderson Cncer Center Deprtment of Biosttistics Inequlity Clcultor, Version 3.0 November 5, 013 User s Guide 0. Overview The purpose of the softwre is to clculte the probbility tht

More information

19 Optimal behavior: Game theory

19 Optimal behavior: Game theory Intro. to Artificil Intelligence: Dle Schuurmns, Relu Ptrscu 1 19 Optiml behvior: Gme theory Adversril stte dynmics hve to ccount for worst cse Compute policy π : S A tht mximizes minimum rewrd Let S (,

More information

3.1 Review of Sine, Cosine and Tangent for Right Angles

3.1 Review of Sine, Cosine and Tangent for Right Angles Foundtions of Mth 11 Section 3.1 Review of Sine, osine nd Tngent for Right Tringles 125 3.1 Review of Sine, osine nd Tngent for Right ngles The word trigonometry is derived from the Greek words trigon,

More information