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FR3131-LECTURE5SUM-2012

Course: FR 3131, Spring 2012
School: Minnesota
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Sensing Measuring Remote an object from a distance For GIS, that means using photographic or satellite images to gather spatial data Fundamental Variables Planimetric (x,y) location and dimensions Topographic (z) location Color (spectral reflectance) Surface Temperature Texture Surface Roughness Moisture Content Vegetation Biomass Two Main Image Types Aerial Photographs common relatively inexpensive...

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Sensing Measuring Remote an object from a distance For GIS, that means using photographic or satellite images to gather spatial data Fundamental Variables Planimetric (x,y) location and dimensions Topographic (z) location Color (spectral reflectance) Surface Temperature Texture Surface Roughness Moisture Content Vegetation Biomass Two Main Image Types Aerial Photographs common relatively inexpensive easy to interpret small area coverage can be geometrically corrected Satellite Images large area coverage broader spectral range digital formats inexpensive for large areas geometrically accurate Electromagnetic energy is a mixture of waves with different frequencies Each wave represents energy that varies at a given frequency. Source:http://www.cnr.berkeley.edu/~gong/textbook/chapter2/html/sect21.htm Plotting amplitude against the wavelength you get an electromagnetic curve, or spectrum Source:http://www.cnr.berkeley.edu/~gong/textbook/chapter2/html/sect21.htm Radiation (electromagnetic energy) is emitted by the Sun, and attenuated by the atmosphere. Specific bands of wavelengths are used for remote sensing xrays Blue .4 to.5 m Green .5 to .6 m Red .6 to .7 m (micrometers) (micrometers) (micrometers) Visible Light - How we see colors Emit/Reflect Addition of light waves of different frequencies Absorb Absorb some of the frequencies you see whats reflected (paint,pigments like chlorophyll) http://science.howstuffworks.com/light7.htm Energy, Atmosphere, and Surface Interactions Sources of Information Variations in electromagnetic fields that can be used to identify and characterize objects: Spectral-radiometric (color, temperature) Spatial (pattern, size, shape, texture, ...) Temporal Spectral Reflectance Curves % of energy reflected Wavelength (m) A B C Spectral Resolution and Spectral Sampling The three shaded bars A, B, and C represent three spectral bands. The width of each bar covers a spectral range within which no signal variation can be resolved. The width of each spectral band represents its spectral resolution. The resolution of A is coarser than the resolution of B. This is because spectral details within band A that cannot be discriminated may be partly discriminated with a spectral resolution as narrow as band B. The resolution relationships among the three bands are: Resolution of A < Resolution of C < Resolution of B Adapted from Source:http://www.cnr.berkeley.edu/~gong/textbook/chapter1/html/sect13.htm Concept Spectral of Bands A B Adapted from Source:http://www.cnr.berkeley.edu/~gong/textbook/chapter1/html/sect13.htm C Photo Scale Set by flying height, focal length Most mapping cameras use 6 lens Reduce scale by flying higher Increasing flying height reduces scale (objects get smaller, area covered by each photo increases) Increasing focal length increases scale (objects get larger, are covered decreases) Scale is NOT Constant Can be over flat terrain with perfectly vertical photographs - rarely occurs Terrain - some objects are closer to lens, hence larger scale Tilt - causes perspective distortion Perspective vs. Orthographic Views Terrain Variation Causes Relief Displacement Features are displaced radially from their planimetric position due to differences in relative elevation Tilt measured as the angle between a line perpendicular to the film and a line perpendicular to the datum. Typically specified to be less than 3o on vertical aerial photos. Parallax Relative shift in position with a change in viewing location. Closer (taller) objects shift more. We measure parallax to estimate height. Relief Displacement Height affects horizontal position Displacement are radial higher outward shift Lower inward shift In a planimetric map, A should occur at the same location as B But is displace by d Question: how much is d? Use similar triangles to find out Big triangle CNS Small triangle 1 - Cna Small triangle 2 - ABS We may see: D/P = d / p and D/P = h/H So d/p = h/H d=p*h/H So We know H Measure p on photo Know h from DEM Apply equation d = p* h/H Apply for every spot (cell, pixel) on the photo, yielding an ortho-corrected image Time of Year and Film Type Black and white (Panchromatic) lower costs, wide sensitivity "True" color Enhanced interpretation Color infrared film (also near-IR or color-IR) Enhanced vegetation, more contrast Two Main Types of Films Photo Interpretation This is the process of identifying and mapping the features that appear on the photos Use characteristics of the objects observed, plus knowledge of acquisition (scale, time of year, film type) to identify features Characteristics used include: Shape Size Color (or tone) Texture Shadows and Context Satellite Systems High Resolution Sensing Systems Ikonos, Quickbird Spot Medium Resolution Sensing Systems Landsat Thematic Mapper (TM, ETM+) Multispectral Scanner (MSS) SPOT coarse modes COARSE RESOLUTION LAND SENSORS AVHRR (since the 1970s) MODIS
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Minnesota - FR - 3131
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Minnesota - FR - 3131
Homework2; dueMarch23,2012DownloadfromWebUse.docfiletorecordyouranswers;submitviaMoodleCanload.dbfinArcMapanduseSelectbyAttributes12Homework2OntheWebandLabComputers3ExtraCredit:ExtraLab LabX(practicedigitizing)15ptsExtraHomework (moredataquer
Minnesota - FR - 3131
A SmallExercise inNormal FormsMaple without WormsMaple with WormsEarthworm InvasionsStudy to identify the cause and extent of exotic earthworminfestations Many sample sites, 10 meters in diameter, over a range ofconditions. The worms present were
Minnesota - FR - 3131
Spatial data analysisInput -&gt; spatial operation -&gt; outputSpatial data analysisInput -&gt; spatial operation -&gt; outputInput ScopeLocal point to pointNeighborhood adjacent regions haveinputGlobal the entire inputdata layer may influenceoutputSpatia
Minnesota - FR - 3131
Raster AnalysisRaster cells store data (nominal, ordinal, interval/ratio)Complex constructs built from raster dataConnected cells can be formed in to networksRelated cells can be grouped into neighborhoods or regionsExamples:Predict fate of pollutan
Minnesota - FR - 3131
Map AlgebraKernalsCost SurfaceFriction SurfaceThere will bequestions aboutthese on the test[(-1*2)+ (-1*2)+ (-1*3)+ (-1*2)+ (3*9) + (-1*3)+ (-1*2)+ (-1*4)+ (-1*3)]/9[(1*2) + (1*2) + (1*3)+(1*2) +(1*3) + (1*3)+(1*2) + (1*4) + (1*3)]/9Spatial C
Minnesota - FR - 3131
Map AlgebraKernalsCost SurfaceFriction SurfaceSlopeThere will bequestions aboutthese on the test(Use Calculator)SlopeCalculationhttp:/www.cut-the-knot.org/Generalization/pythagoras.shtmlhttp:/wright.nasa.gov/airplane/trig.htmlIf you know the
Minnesota - FR - 3131
TerrainModeling:HowtodelineateawatershedusingaprintedtopographicalmapSeeNRCShandout:HowtoReadaTopographicMapandDelineateaWatershedMarktheoutlet(circle);Markthehighpointsadjacenttothestreamorlake(xs)Startingatthecircle,drawalineconnectingthex's&quot;alo
Minnesota - FR - 3131
INTERPOLATIONProcedure to predict values of attributes atunsampled pointsWhy?Cant measure all locations:TimeMoneyImpossible (physical- legal)Changing cell sizeMissing/unsuitable dataPast date (eg. temperature)Systematic sampling patternEasySa
Minnesota - FR - 3131
Models in GISA model is a description of realityIt may be:Dynamic or StaticDynamic spatial models e.g., hydrologicflowStatic spatial models (or point in time)e.g., land suitability analysesSpatial ModelsFocus on computer based models ofspatial p
Minnesota - FR - 3131
StandardsAn established or sanctioned measure, form, ormethod; an agreedupon way of doing, describing ordelivering somethingData standards(used to format, assess, document and delivery spatial data)Analysis standards(ensure most appropriate methods
Minnesota - FR - 3131
everything happenssomewhereSpatial ThinkingSpatial ThinkingWalking: controlled fallingSpatial ThinkingWalking: controlled fallingWe are geospatially oriented lifeformsSpatial Thinkinggeographic knowledge ispervasiveGIS Futurevery promising ra
Minnesota - CHEM - 4502
AThe correct answer is in red. For exams B,C,D the order of the questions change but thequestions and the answers are the same.1.(a)(b)(c)(d)Which of the following phenomena could not be explained by classical physicsand required a quantum hypoth
Minnesota - CHEM - 4502
A1.For the diatomic molecule LiF, where Li has atomic mass 3 and F has atomicmass 9, what is the reduced mass?(a)(b)(c)12 / 79/41/7(e)(f)(g)(d)4/9(h)2.Which of the following statements is/are false for a given set of QMHO wavefunctions c
Minnesota - CHEM - 4502
ATests A, B, C and D1.Whichofthebelowstatementsaboutthewavefunctiona(1) (1) b(1) (1)is/are true if the spatial functions a and b are(1, 2) =a(2) (2) b(2) (2)normalized?Its normalization constant is 2(e)&lt; | S2 | &gt; = 0(b)It is symmetric
Minnesota - CHEM - 4502
Some Potentially Useful Mathematical FormulaeTrigonometric Relationssin sin =Some Operators1[cos( ) cos( + )]2cos cos =1[cos( ) + cos( + )]2sin cos =1[sin( ) + sin( + )]2x multiply by xr multiply by rp x iddxsin( ) = sin cos sin cos H
Minnesota - CHEM - 4502
Chem 4502Introduction to Quantum Mechanics and SpectroscopySpring Semester 2012Laura GagliardiLecture 1, January 18, 20123 CreditsThe state of Physics and Chemistry at the turn of the 20th CenturyTo appreciate quantum mechanics, it is important to
Minnesota - CHEM - 4502
Chem 4502Introduction to Quantum Mechanics and SpectroscopySpring Semester 2012Laura Gagliardi3 CreditsLecture 2, January 20, 2012Solved HomeworkThe total power emitted by a blackbody is obtained by integrating the frequencydependent energy density
Minnesota - CHEM - 4502
Chem 4502Introduction to Quantum Mechanics and SpectroscopySpring Semester 2012Laura Gagliardi3 CreditsLecture 3, January 23 and 25, 2012Solved HomeworkIf an electron has a de Broglie wavelength of 1 (0.1 nm), then we can compute itsmomentum ash
Minnesota - CHEM - 4502
Chem 4502Introduction to Quantum Mechanics and SpectroscopySpring Semester 2012Laura Gagliardi3 CreditsLecture 5, January 30, 2012Solved Homework (Homework for grading is also due today)We are told that the probability of a random variable taking o
Minnesota - CHEM - 4502
Chem 4502Introduction to Quantum Mechanics and SpectroscopySpring Semester 2012Laura Gagliardi3 CreditsLecture 6, February 01, 2012Solved HomeworkWe are given that A = a and A* = a where a is a real number. As bothA and A* are equal to the same th
Minnesota - CHEM - 4502
Chem 4502Introduction to Quantum Mechanics and SpectroscopySpring Semester 2012Laura Gagliardi3 CreditsLecture 7, February 03, 2012Solved HomeworkWe are given that A is a Hermitian operator such that A1 = a1, A2 = b2, A3 =b3, and A4 = c4, a b c, a
Minnesota - CHEM - 4502
Chem 4502Introduction to Quantum Mechanics and SpectroscopySpring Semester 2012Laura Gagliardi3 CreditsLecture 8, February 06, 2012Solved HomeworkEvaluate &lt;x&gt; and &lt;x2&gt; for a particle-in-a-box wave function. These expectation valuesare, generically
Minnesota - CHEM - 4502
Chem 4502Introduction to Quantum Mechanics and SpectroscopySpring Semester 2012Laura Gagliardi3 CreditsLecture 9, February 13, 2012The Harmonic OscillatorConsider a diatomic molecule. Such a molecule has a single degree of freedom,the bond length.
Minnesota - CHEM - 4502
Chem 4502Introduction to Quantum Mechanics and SpectroscopySpring Semester 2012Laura Gagliardi3 CreditsLecture 10, February 13, 2012Solved HomeworkWe are asked to find &lt;x&gt; and &lt;x2&gt; for the first two harmonic oscillator wavefunctions, which are k
Minnesota - CHEM - 4502
Chem 4502Introduction to Quantum Mechanics and SpectroscopySpring Semester 2012Laura Gagliardi3 CreditsLecture 11, February 15, 2012Solved HomeworkWe are asked to find &lt;T&gt; for the first harmonic oscillator wave function k 1 / 4 k x 2 / 20 ( x ) =
Minnesota - CHEM - 4502
Chem 4502Introduction to Quantum Mechanics and SpectroscopySpring Semester 2012Laura Gagliardi3 CreditsLecture 12, February 17, 2012Solved HomeworkWe are allowed to know any one component of the total angular momentum toperfect accuracy. Although
Minnesota - CHEM - 4502
Chem 4502Introduction to Quantum Mechanics and SpectroscopySpring Semester 2012Laura Gagliardi3 CreditsLecture 13, February 20, 2012Solved HomeworkWe are asked to demonstrate the orthogonality of the functions () that are the-dependent components
Minnesota - CHEM - 4502
Chem 4502Introduction to Quantum Mechanics and SpectroscopySpring Semester 2012Laura Gagliardi3 CreditsLecture 14, February 22, 2012Solved HomeworkWe are given that the lowest microwave absorption of carbon monoxide (CO,withand 16O specified) is
Minnesota - CHEM - 4502
Chem 4502Introduction to Quantum Mechanics and SpectroscopySpring Semester 2012Laura Gagliardi3 CreditsLecture 15, February 24, 2012Solved HomeworkWe are asked to give the minimum energy required for the ionization reactionBe3+ Be4+ + eSince Be i
Minnesota - CHEM - 4502
Chem 4502Introduction to Quantum Mechanics and SpectroscopySpring Semester 2012Laura Gagliardi3 CreditsLecture 16, February 27, 2012Solved HomeworkGiven that for a hydrogenic atomH=T+V1= 2 Z r 12where we have explicitly written the proper kine
Minnesota - CHEM - 4502
Chem 4502Introduction to Quantum Mechanics and SpectroscopySpring Semester 2012Laura Gagliardi3 CreditsLecture 17, February 29, 2012(Some material in this lecture has been adapted from Cramer, C. J. Essentials ofComputational Chemistry, Wiley, Chic
Minnesota - CHEM - 4502
Chem 4502Introduction to Quantum Mechanics and SpectroscopySpring Semester 2012Laura Gagliardi3 CreditsLecture 18, March 02, 2012Solved HomeworkIf the approximate energy is given by&lt;H&gt; = 3a4 4a3 36a2 + 10where a is a variational parameter, local
Minnesota - CHEM - 4502
Chem 4502Introduction to Quantum Mechanics and SpectroscopySpring Semester 2012Laura Gagliardi3 CreditsLecture 19, March 19, 2012Solved HomeworkWe seekd 1( x ;a ) px (x ;a ) = N 2 0 x a (1 x ) i x a (1 x ) dxdx []where N is the normalization
Minnesota - CHEM - 4502
Chem 4502Introduction to Quantum Mechanics and SpectroscopySpring Semester 2012Laura Gagliardi3 CreditsLecture 20, March 21, 2012Solved HomeworkWe determined that the two coefficients in our two-gaussian wave function werec1 = 0.3221 and c2 = 0.76
Minnesota - CHEM - 4502
Chem 4502Introduction to Quantum Mechanics and SpectroscopySpring Semester 2012Laura Gagliardi3 CreditsLecture 21, March 23, 2012(Some material in this lecture has been adapted from Cramer, C. J. Essentials ofComputational Chemistry, Wiley, Chiches
Minnesota - CHEM - 4502
Chem 4502Introduction to Quantum Mechanics and SpectroscopySpring Semester 2012Laura Gagliardi3 CreditsLecture 22, March 28, 2012(Some material in this lecture has been adapted from Cramer, C. J. Essentials ofComputational Chemistry, Wiley, Chiches
Minnesota - CHEM - 4502
Chem 4502Introduction to Quantum Mechanics and SpectroscopySpring Semester 2012Laura Gagliardi3 CreditsLecture 23, April 02, 2012(Some material in this lecture has been adapted from Cramer, C. J. Essentials ofComputational Chemistry, Wiley, Chiches
Minnesota - CHEM - 4502
Chem 4502Introduction to Quantum Mechanics and SpectroscopySpring Semester 2012Laura Gagliardi3 CreditsLecture 24, April 04, 2012Solved HomeworkWe are given a perturbing potential V = k ( 1 x ) for a particle in an otherwise&quot;normal&quot; box of length
Minnesota - CHEM - 4502
Chem 4502Introduction to Quantum Mechanics and SpectroscopySpring Semester 2012Laura Gagliardi3 CreditsLecture 25, April 06, 2012(Some material in this lecture has been adapted from Cramer, C. J. Essentials ofComputational Chemistry, Wiley, Chiches
Minnesota - CHEM - 4502
Chem 4502Introduction to Quantum Mechanics and SpectroscopySpring Semester 2012Laura Gagliardi3 CreditsLecture 26, April 16, 2012(Some material in this lecture has been adapted from Cramer, C. J. Essentials ofComputational Chemistry, Wiley, Chiches
Minnesota - CHEM - 4502
Chem 4502Introduction to Quantum Mechanics and SpectroscopySpring Semester 2012Laura Gagliardi3 CreditsLecture 27, April 18, 2012(Some material in this lecture has been adapted from Cramer, C. J. Essentials ofComputational Chemistry, Wiley, Chiches
Minnesota - CHEM - 4502
Chem 4502Introduction to Quantum Mechanics and SpectroscopySpring Semester 2012Laura Gagliardi3 CreditsLecture 28, April 20, 2012(Some material in this lecture has been adapted from Cramer, C. J. Essentials ofComputational Chemistry, Wiley, Chiches
Minnesota - CHEM - 4502
Chem 4502Introduction to Quantum Mechanics and SpectroscopySpring Semester 2012Laura Gagliardi3 CreditsLecture 31, May 02, 2012(Some material in this lecture has been adapted from Cramer, C. J. Essentials ofComputational Chemistry, Wiley, Chicheste
Minnesota - CHEM - 4502
Chem 4502Introduction to Quantum Mechanics and SpectroscopySpring Semester 2012Laura Gagliardi3 CreditsLecture 32, May 04, 2012(Some material in this lecture has been adapted from Cramer, C. J. Essentials ofComputational Chemistry, Wiley, Chicheste
Minnesota - CHEM - 4502
Lecture 1Thank youProfessor Cramer!The state of Physics and Chemistry at the turn of the20th CenturyWhat is Quantization?The First Quantum AssumptionsBlackbody RadiationThe Photoelectric EffectHeat Capacity of Perfect CrystalsHydrogen Emission S
Minnesota - CHEM - 4502
Lecture 2The Orbiting Electron Model of the Hydrogen AtomKinetic Energy of the Hydrogen AtomPotential Energy of the Hydrogen AtomThe Total Energy of the Bohr Model for the AtomWave-particle DualityChapter 1 McQuarrie Simon pp 1-25January 20 2012ht
Minnesota - CHEM - 4502
Lecture 3The Wave Function for a Material SystemThe Schrdinger EquationWhat is a Wave Function?Expectation ValuesCollapse of the Wave FunctionPages 31-72 McQuarrie and SimonJanuary 23 and 25 2012http:/www.chem.umn.edu/groups/gagliardi/teaching.htm
Minnesota - CHEM - 4502
Lecture 5Mathematical Tools:Complex numbersVectors of complex numbersHermitian OperatorsEigenvalues and EigenvectorsHermitian Operators CommutatorsofMath Chapters A,B,C McQuarrie SimonJanuary 30 2012http:/www.chem.umn.edu/groups/gagliardi/teach
Minnesota - CHEM - 4502
Lecture 6Stationary StatesMost Common OperatorsExpectation Values of operators that commute or donot commuteThe Uncertainty PrincipleChapter 3 McQuarrie and Simon pages 73-105Chapter 4 McQuarrie and Simon pages 115-147February 1 2012http:/www.che
Minnesota - CHEM - 4502
Lecture 7Free Particle Wave FunctionThe Particle in a BoxRepresenting Wave FunctionsChapter 3 McQuarrie and Simon pages 73-105February 03 2012Free ParticleTime-independent Schrdinger equation in one dimension 2 d 2+ V ( x )( x) = E( x)2 2m dx(
Minnesota - CHEM - 4502
Lecture 8ParitySpectroscopic TransitionsTunnelingMcQuarrie and Simonpp. 67-70problems 3-32 pp. 102-104February 06 2012http:/www.chem.umn.edu/groups/gagliardi/teaching.htmlParityIs a given integral zero or can it be non-zero?Explore a property k
Minnesota - CHEM - 4502
Lecture 9The Harmonic OscillatorShrdinger Equation for The Harmonic OscillatorProperties of the Harmonic OscillatorBook: M&amp;S: pp. 157-173!September 29 2010http:/www.chem.umn.edu/groups/gagliardi/teaching.htmlDiatomic MoleculesOne degree of freedom
Minnesota - CHEM - 4502
Lecture 10Analysis of the Harmonic Oscillator Wave FunctionsZero-Point EnergyNodes and Kinetic EnergySpectroscopy of the QM Harmonic OscillatorInfraredSpectroscopyM&amp;S pp. 157-173.!February 13 20121 and 2 for the Harmonic Oscillator2The Harmonic
Minnesota - CHEM - 4502
Lecture 11Angular MomentumEigenvaluesOperatorsoftheAngularMomentumMQ&amp;S: pp 105-120; 137; 200-206February 15 2012http:/www.chem.umn.edu/groups/gagliardi/teaching.html1Angular MomentumVector quantity: cross product of the position vector and th
Minnesota - CHEM - 4502
Lecture 12Polar CoordinatesAngular Momentum EigenfunctionsThe Initial Spherical HarmonicsMcQuarrie and Simon Chapter 6pp 191-230February 17 20121Polar coordinatesAngular momentum eigenfunctions.Transform the coordinate system to spherical polar
Minnesota - CHEM - 4502
Lecture 13The Rigid RotatorMicrowave SpectroscopyMcQuarrie and SimonChapter 5 pp 173-179and also Chapter 6February 20, 20121A Rotating SystemTwo masses connected by a spring: vibrational SchrdingerequationSolutions: QMHO wave functionsReplace
Minnesota - CHEM - 4502
Lecture 14The Hydrogen AtomExpression of the wave functionExpression of the energyMcQuarrie and SimonChapter 6 pp 191-231February 22, 2012The H atomA proton and an electron bound together.Quantum particles: they must be in motion.Center of mass
Minnesota - CHEM - 4502
Lecture 15Hydrogenic OrbitalsAtomic UnitsHydrogenic One-Electron Wave Functions and theirEnergiesFebruary 24, 2012Hydrogenic OrbitalsQuantum restrictions on the energy levels of one-electron atomsFinal step: pull out the eigenfunctionsGeneral wav
Minnesota - CHEM - 4502
Lecture 16Atomic SpectroscopyElectron SpinTotal Angular MomentumThe Zeeman Effect andSpectroscopyElectronSpinResonanceMcQuarrie and Simon Chapter 8 pages 275-321February 27, 2012Atomic SpectroscopyThe hydrogenic atom: three quantum numbersn l
Minnesota - CHEM - 4502
Lecture 17Recapitulation of the Schrdinger Equation and itsEigenfunctions and EigenvaluesThe Variational PrincipleThe Born-Oppenheimer ApproximationConstruction of Trial Wave Functions:ApproachCh 7 in the bookFebruary 29, 2012LCAO Basis SetThe S