Theoretische Chemie (TC II) Computational Chemistry
|
|
- Catrin Voss
- vor 5 Jahren
- Abrufe
Transkript
1 Theoretische Chemie (TC II) Computational Chemistry Lecture 12 27/01/2012 Irene Burghardt Vorlesung: 27/01/2012, 01/02/2012, Mi 11h45-13h15, Fr 8h-9h30 Praktikum (gemäß Ankündigung, statt Vorlesung): Fr Computing Center (BCC) Web site: 1
2 Starting point: the molecular Hamiltonian all electrons and nuclei Ĥ = ˆT e + ˆT N + ˆV e + ˆV N + ˆV en = N e i=1 h 2 2m e 2 i N N a=1 + e2 { Ne 4πɛ 0 i=1 h 2 2M a 2 a N e j>i 1 r ij + N N N N a=1 b>a Z a Z b r ab N e i=1 N N a=1 Z } a r ia i h t ψ = Ĥψ Ĥψ = Eψ 2
3 But we might eventually do classical molecular dynamics (MD) simulations, e.g., for proteins Quantum classical transition due to decoherence Do any quantum effects survive? 3
4 Of course the electrons always need a quantum mechanical treatment but they are usually integrated out so as to yield effective potentials for the nuclear motion (Born-Oppenheimer approach) 4
5 Two Steps 1 Born-Oppenheimer approximation: separate the electronic and nuclear motions and generate effective potentials for the nuclear motion 2 follow the dynamics of the nuclei, either using quantum dynamics (time-dependent Schrödinger equation) or else using classical dynamics (Newton s equations)( ) ( )... or else using a variety of semiclassical and mixed quantum-classical approaches 5
6 Step 1: the Born-Oppenheimer approximation Max Born Robert Oppenheimer perturbative expansion in orders of the mass ratio m/m 1/1836 6
7 Born-Oppenheimer basics Using the idea of an adiabatic separability of the time scales for electronic vs. nuclear motion, separate the total Hamiltonian Ĥ T = ˆT e + ˆV e + ˆT N + ˆV N + ˆV en = ˆT N + Ĥ el and solve the electronic Schrödinger equation first disregarding ˆT N : Ĥ el ψ n (r el R) = ɛ n (R)ψ n (r el R) The eigenvalues ɛ n (R) depend parametrically on the nuclear coordinate(s) and constitute the Born-Oppenheimer surfaces 7
8 Born-Oppenheimer, cont d If we assume that the overall wavefunction (electronic + nuclear) can be written as Ψ T (r el, R) = ψ n (r el R)χ n (R) we obtain nuclear motion in terms of the TDSE for the nuclear wavefunction χ n (R, t) on the nth Born-Oppenheimer surface: i h χ ( n t = h2 ) 2M 2 R + ɛ n(r) χ n Thus we have separated the electronic-nuclear problem into two parts: Ĥ el ψ n (r el R) = ɛ n (R)ψ n (r el R) ; i h χ n = ( ˆT N + ɛ n (R)) χ n 8
9 BO surfaces for the hydrogen molecule molecular orbitals = bonding and non-bonding combinations of atomic orbitals parametric dependence on the internuclear distance potentials 9
10 Born-Oppenheimer surfaces for the I 2 molecule note that in the BO picture, the nuclei move only on a given BO surface at a time thus, the multiple crossings of the I 2 poentials are indicative of a breakdown of the BO approximation (see Lecture 2) 10
11 Step 2: calculate the dynamics of the nuclei i h Ψ t = ( ˆT + ˆV )Ψ or q = p m ṗ = V In many applications, Newton s equations are used! 11
12 Trajectory dynamics: the Heisenberg picture of classical mechanics trajectory = chronological sequence of (coordinate-space or phase-space) configurations 12
13 Trajectories in phase space Hamilton s equations: (yielding Newton s equations, m q = ( V / q)): q = p/m ṗ = V / q or: q ṗ = H p H q = H q H p where we used the classical Hamiltonian: H = T + V = p2 2m + V (q) the antisymmetric matrix ((0, 1), ( 1, 0)) reflects the symplectic structure of classical mechanics 13
14 Time-evolving phase-space densities: the Schrödinger picture of classical mechanics f(q, p, t) = dq dp δ(q q(t))δ(p p(t))f(q, p, t 0 ) Liouville equation: f t = {H, f} = H p = p m f q + H q f q + V q f p f p Lf picture: Martens & co where we introduced the Poisson bracket {, } and the Liouvillian L 14
15 Liouville s theorem df dt = 0 where df dt = f t + f q q + f pṗ phase space continuity equation the density keeps its size: it is incompressible each trajectory keeps its weight as a function of time 15
16 Special case: equilibrium distribution f t = 0 The distribution function does not evolve in time but the trajectories do! Typical equilibrium ensembles: microcanonical ensemble (NVE): all microstates with fixed total energy: Q NV E = Γ δ(h(γ) E) canonical ensemble (NVT): assembly of all microstates with fixed N, V, but energy can fluctuate according to T : Q NV T = Γ exp( H(Γ)/kT ) 16
17 MD: Solve Newton s Equations in a Simulation Box Each atom feels forces on it from other atoms: F 1 = dv(x 1,...,x N ) dx 1 where V(x 1,...,x N ) is the interaction potential Newton s Equations: the acceleration of the particle is proportional to the force: F 1 = mẍ 1 ma 1 where a 1 is the acceleration experienced by particle 1 17
18 Newton s Equations at Work calculate force at given particle position x 1 update position (x) and velocity (v = ẋ) from Newton s equation: x 2 = x 1 + v 1 t v 2 = v 1 + a 1 t = v 1 1 m dv dx t x1 the sequence of positions (x 1,x 2,...) define the particle s trajectory 18
19 Which Potentials (Force Fields)? dihedral angle typical force fields: V bond (r) = 1 2 k(r r 0) 2 V angular (φ) = 1 (1 + cos(mφ δ))2 2 V vdw (r ij ) = C 12 r 12 ij C 6 r 6 ij nonbonded interaction 19
20 Harmonic oscillator potential (V ) vs. kinetic energy (K) change in the course of the trajectory while the total energy (E) remains constant 20
21 Phase space picture y(t) = b cosωt p(t) = b mω sinωt ẏ = p m ṗ = dv dy V (y) = mω 2 y 2 21
22 Potential landscapes characteristic points: minima, maxima, saddle points 22
23 Potentials in 2D V (x, y) = 1 2 k xx k yy 2 V (x, y) = 1 2 k xx k yy 2 minimum saddle point 23
24 Equilibrium ensembles Typical equilibrium ensembles: microcanonical ensemble (NVE): all microstates with fixed total energy: Q NV E = q,p δ(h(q, p) E) canonical ensemble (NVT): assembly of all microstates with fixed N, V, but energy can fluctuate according to T : Q NV T = q,p exp( H(q, p))/kt ) 24
25 Properties = ensemble averages A = dq dp A(q, p)p (q, p) where P (q, p) = probability of being at a given phase-space point: P NV T (q, p) = 1 ( Q exp E(q, p) ) kt phase space averages in many dimensions may be hard to calculate! 25
26 Ergodic theorem: ensemble averages are equivalent to time averages A ensemble = 1 τobs τ obs τ =1 A(q(τ ), p(τ )) if trajectories explore all of phase space with time 26
27 Conformational analysis Ramachandran map = conformational energy surface usually represented as contour map showing accessible conformations example above: dipeptide as model for protein conformation 27
28 Correlation functions e.g., 2-time velocity autocorrelation function 28
Theoretische Chemie (TC II) Computational Chemistry
Theoretische Chemie (TC II) Computational Chemistry Irene Burghardt (burghardt@chemie.uni-frankfurt.de) Praktikumsbetreuung: Dr. Matthias Ruckenbauer (matruc@theochem.uni-frankfurt.de) Dr. Haleh Hashemi
Allgemeine Mechanik Musterlösung 11.
Allgemeine Mechanik Musterlösung 11. HS 2014 Prof. Thomas Gehrmann Übung 1. Poisson-Klammern 1 Zeigen Sie mithilfe der Poisson-Klammern, dass folgendes gilt: a Für das Potential V ( r = α r 1+ε ist der
Finite Difference Method (FDM)
Finite Difference Method (FDM) home/lehre/vl-mhs-1-e/folien/vorlesung/2a_fdm/cover_sheet.tex page 1 of 15. p.1/15 Table of contents 1. Problem 2. Governing Equation 3. Finite Difference-Approximation 4.
Theoretische Chemie (TC II) Computational Chemistry
Theoretische Chemie (TC II) Computational Chemistry Irene Burghardt (burghardt@chemie.uni-frankfurt.de) Praktikumsbetreuung: Dr. Matthias Ruckenbauer (matruc@theochem.uni-frankfurt.de) Dr. Haleh Hashemi
FEM Isoparametric Concept
FEM Isoparametric Concept home/lehre/vl-mhs--e/folien/vorlesung/4_fem_isopara/cover_sheet.tex page of 25. p./25 Table of contents. Interpolation Functions for the Finite Elements 2. Finite Element Types
Allgemeine Mechanik Musterlösung 7.
Allgemeine Mechanik Musterlösung 7. HS 204 Prof. Thomas Gehrmann Übung. Lagrange-Funktion eines geladenen Teilchens Die Lagrange-Funktion für ein Teilchen der Ladung q in elektrischen und magnetischen
Introduction FEM, 1D-Example
Introduction FEM, 1D-Example home/lehre/vl-mhs-1-e/folien/vorlesung/3_fem_intro/cover_sheet.tex page 1 of 25. p.1/25 Table of contents 1D Example - Finite Element Method 1. 1D Setup Geometry 2. Governing
Introduction FEM, 1D-Example
Introduction FEM, D-Example /home/lehre/vl-mhs-/inhalt/cover_sheet.tex. p./22 Table of contents D Example - Finite Element Method. D Setup Geometry 2. Governing equation 3. General Derivation of Finite
Bayesian Networks. Syntax Semantics Parametrized Distributions Inference in Bayesian Networks. Exact Inference. Approximate Inference
Syntax Semantics Parametrized Distributions Inference in Exact Inference Approximate Inference enumeration variable elimination stochastic simulation Markov Chain Monte Carlo (MCMC) 1 Includes many slides
TC1 Grundlagen der Theoretischen Chemie
TC1 Grundlagen der Theoretischen Chemie Irene Burghardt (burghardt@chemie.uni-frankfurt.de) Praktikumsbetreuung: Sarah Römer (roemer@em.uni-frankfurt.de) Simona Scheit (simona.scheit@googlemail.com) Juanma
Theoretische Chemie (TC II) Computational Chemistry
Theoretische Chemie (TC II) Computational Chemistry Lecture 2 28/10/2011 Irene Burghardt (burghardt@chemie.uni-frankfurt.de) Vorlesung: Mi 11h30-13h, Fr 8h-9h30 Praktikum (gemäß Ankündigung, statt Vorlesung):
Bohmian Mechanics. The Physics and Mathematics of Quantum Theory. Bearbeitet von Detlef Dürr, Stefan Teufel
Bohmian Mechanics The Physics and Mathematics of Quantum Theory Bearbeitet von Detlef Dürr, Stefan Teufel 1. Auflage 2009. Buch. xii, 393 S. Hardcover ISBN 978 3 540 89343 1 Format (B x L): 15,5 x 23,5
Theoretische Chemie (TC II) Computational Chemistry
Theoretische Chemie (TC II) Computational Chemistry Irene Burghardt (burghardt@chemie.uni-frankfurt.de) Praktikumsbetreuung: Dr. Matthias Ruckenbauer (matruc@theochem.uni-frankfurt.de) Dr. Haleh Hashemi
a) Name and draw three typical input signals used in control technique.
12 minutes Page 1 LAST NAME FIRST NAME MATRIKEL-NO. Problem 1 (2 points each) a) Name and draw three typical input signals used in control technique. b) What is a weight function? c) Define the eigen value
LS Kopplung. = a ij l i l j. W li l j. = b ij s i s j. = c ii l i s i. W li s j J = L + S. L = l i L = L(L + 1) J = J(J + 1) S = s i S = S(S + 1)
LS Kopplung in many electron systems there are many li and si the coupling to for total momentum J depends on the energetic ordering of the interactions orbital momenta interaction W li l j = a ij l i
Theoretische Chemie (TC II) Computational Chemistry
Theoretische Chemie (TC II) Computational Chemistry Irene Burghardt (burghardt@chemie.uni-frankfurt.de) Praktikumsbetreuung: Konstantin Falahati (falahati@theochem.uni-frankfurt.de) Pierre Eisenbrandt
Übungsblatt 6. Analysis 1, HS14
Übungsblatt 6 Analysis, HS4 Ausgabe Donnerstag, 6. Oktober. Abgabe Donnerstag, 23. Oktober. Bitte Lösungen bis spätestens 7 Uhr in den Briefkasten des jeweiligen Übungsleiters am J- oder K-Geschoss von
Snap-in switch for switches PSE, MSM and MCS 30
Product manual Snap-in switch for switches PSE, MSM and MCS 30 CONTENTS 1. PRODUCT DESCRIPTION 2. DATA AND DIMENSIONAL DRAWINGS 2.1. Technical Data 2.2. Dimensions of PSE with a Mounting Diameter 19 mm
Theoretische Chemie (TC II) Computational Chemistry
Theoretische Chemie (TC II) Computational Chemistry Irene Burghardt (burghardt@chemie.uni-frankfurt.de) Praktikumsbetreuung: Robert Binder (rbinder@theochem.uni-frankfurt.de) Pierre Eisenbrandt (peisenbr@theochem.uni-frankfurt.de)
Computational Chemistry
The fundamental laws necessary for the mathematical treatment of a large part of physics and the whole of chemistry are thus completely known, and the difficulty lies only in the fact that application
Field-Circuit Coupling for Mechatronic Systems: Some Trends and Techniques
Field-Circuit Coupling for Mechatronic Systems: Some Trends and Techniques Stefan Kurz Robert Bosch GmbH, Stuttgart Now with the University of the German Federal Armed Forces, Hamburg stefan.kurz@unibw-hamburg.de
Efficient Monte Carlo Simulation of Tunnel Currents in MOS Structures
Efficient Monte Carlo Simulation of Tunnel Currents in MOS Structures D. Grgec, M.I. Vexler, C. Jungemann, B. Meinerhagen Grg-P/02-1 Presentation Outline Introduction: quantum effects in MOS structures
Attention: Give your answers to problem 1 and problem 2 directly below the questions in the exam question sheet. ,and C = [ ].
Page 1 LAST NAME FIRST NAME MATRIKEL-NO. Attention: Give your answers to problem 1 and problem 2 directly below the questions in the exam question sheet. Problem 1 (15 points) a) (1 point) A system description
A Classification of Partial Boolean Clones
A Classification of Partial Boolean Clones DIETLINDE LAU, KARSTEN SCHÖLZEL Universität Rostock, Institut für Mathematik 25th May 2010 c 2010 UNIVERSITÄT ROSTOCK MATHEMATISCH-NATURWISSENSCHAFTLICHE FAKULTÄT,
FEM Isoparametric Concept
FEM Isoparametric Concept home/lehre/vl-mhs--e/cover_sheet.tex. p./26 Table of contents. Interpolation Functions for the Finite Elements 2. Finite Element Types 3. Geometry 4. Interpolation Approach Function
Algorithmische Bioinformatik II WS2004/05 Ralf Zimmer Part III Probabilistic Modeling IV Bayesian Modeling: Algorithms, EM and MC Methods HMMs
Algorithmische Bioinformatik II WS2004/05 Ralf Zimmer Part III Probabilistic Modeling IV Bayesian Modeling: Algorithms, EM and MC Methods HMMs Ralf Zimmer, LMU Institut für Informatik, Lehrstuhl für Praktische
Allgemeine Mechanik Musterlösung 5.
Allgemeine Mechanik Musterlösung 5. HS 014 Prof. Thomas Gehrmann Übung 1. Rotierende Masse. Eine Punktmasse m rotiere reibungslos auf einem Tisch (siehe Abb. 1). Dabei ist sie durch einen Faden der Länge
Magic Figures. We note that in the example magic square the numbers 1 9 are used. All three rows (columns) have equal sum, called the magic number.
Magic Figures Introduction: This lesson builds on ideas from Magic Squares. Students are introduced to a wider collection of Magic Figures and consider constraints on the Magic Number associated with such
4. Bayes Spiele. S i = Strategiemenge für Spieler i, S = S 1... S n. T i = Typmenge für Spieler i, T = T 1... T n
4. Bayes Spiele Definition eines Bayes Spiels G B (n, S 1,..., S n, T 1,..., T n, p, u 1,..., u n ) n Spieler 1,..., n S i Strategiemenge für Spieler i, S S 1... S n T i Typmenge für Spieler i, T T 1...
Unit 9. Prototype-Based Clustering. Knowledge-Based Methods in Image Processing and Pattern Recognition; Ulrich Bodenhofer 176
Unit 9 Prototype-Based Clustering Knowledge-Based Methods in Image Processing and Pattern Recognition; Ulrich Bodenhofer 176 Introduction Instead of a complete set description, every cluster C i is represented
1D-Example - Finite Difference Method (FDM)
D-Example - Finite Difference Method (FDM) h left. Geometry A = m 2 = m ents 4m q right x 2. Permeability k f = 5 m/s 3. Boundary Conditions q right = 4 m/s y m 2 3 4 5 h left = 5 m x x x x home/baumann/d_beispiel/folie.tex.
Computational Models
- University of Applied Sciences - Computational Models - CSCI 331 - Friedhelm Seutter Institut für Angewandte Informatik Part I Automata and Languages 0. Introduction, Alphabets, Strings, and Languages
Multicriterial Design Decision Making regarding interdependent Objectives in DfX
Overview Multicriterial Design Decision Making regarding interdependent Objectives in DfX S. Bauer The Design Process Support of the Design Process with Design for X Visualization of Decision Problems
Unit 1. Motivation and Basics of Classical Logic. Fuzzy Logic I 6
Unit 1 Motivation and Basics of Classical Logic Fuzzy Logic I 6 Motivation In our everyday life, we use vague, qualitative, imprecise linguistic terms like small, hot, around two o clock Even very complex
Eine kurze Geschichte der Polymerphysik von Naturkautschuk zu Nanostrukturen
Eine kurze Geschichte der Polymerphysik von Naturkautschuk zu Nanostrukturen Jens Uwe Sommer Leibniz Institut für Polymerforschung Dresden Hohe Straße 6 Institut für Theoretische Physik Technische Universität
Ressourcenmanagement in Netzwerken SS06 Vorl. 12,
Ressourcenmanagement in Netzwerken SS06 Vorl. 12, 30.6.06 Friedhelm Meyer auf der Heide Name hinzufügen 1 Prüfungstermine Dienstag, 18.7. Montag, 21. 8. und Freitag, 22.9. Bitte melden sie sich bis zum
Fundamentals of Electrical Engineering 1 Grundlagen der Elektrotechnik 1
Fundamentals of Electrical Engineering 1 Grundlagen der Elektrotechnik 1 Chapter: Operational Amplifiers / Operationsverstärker Michael E. Auer Source of figures: Alexander/Sadiku: Fundamentals of Electric
Hydroinformatik II: Grundlagen der Kontinuumsmechanik V3
Hydroinformatik II: Grundlagen der Kontinuumsmechanik V3 1 Helmholtz Centre for Environmental Research UFZ, Leipzig 2 Technische Universität Dresden TUD, Dresden Dresden, 21. April / 05. Mai 2017 1/18
Musterlösung 3. D-MATH Algebra I HS 2015 Prof. Richard Pink. Faktorielle Ringe, Grösster gemeinsamer Teiler, Ideale, Faktorringe
D-MATH Algebra I HS 2015 Prof. Richard Pink Musterlösung 3 Faktorielle Ringe, Grösster gemeinsamer Teiler, Ideale, Faktorringe 1. Sei K ein Körper. Zeige, dass K[X 2, X 3 ] K[X] ein Integritätsbereich,
Theoretische Chemie / Computerchemie
Theoretische Chemie / Computerchemie Bernd Hartke Theoretische Chemie Institut für Physikalische Chemie Christian-Albrechts-Universität Kiel Max-Eyth-Straße 2 Erdgeschoß, Raum 29 Tel.: 43/88-2753 hartke@pctc.uni-kiel.de
Open queueing network model of a computer system: completed jobs
E Queueing Networks E Queueing Networks Open queueing network model of a computer system: Stream of new jobs Disk CPU Printer Stream of completed jobs Magnetic Tape E.164 E Queueing Networks "Central-Server-Model
Number of Maximal Partial Clones
Number of Maximal Partial Clones KARSTEN SCHÖLZEL Universität Rostoc, Institut für Mathemati 26th May 2010 c 2010 UNIVERSITÄT ROSTOCK MATHEMATISCH-NATURWISSENSCHAFTLICHE FAKULTÄT, INSTITUT FÜR MATHEMATIK
Zentrum für Bioinformatik. Übung zur Vorlesung Grundlagen der Strukturanalyse Wintersemester 2013/2014. Übung 9: Revision 2
Andrew Torda Björn Hansen Iryna Bondarenko Zentrum für Bioinformatik Übung zur Vorlesung Grundlagen der Strukturanalyse Wintersemester 2013/2014 26.01.2015 Übung 9: Revision 2 Dies ist die zweite Übung,
Molecular dynamics simulation of confined multiphasic systems
VI. International Conference on Computational Fluid Dynamics Molecular dynamics simulation of confined multiphasic systems St. Petersburg, July 15, 2010 G. C. Lehmann, C. Dan, J. Harting, M. Heitzig, M.
Statistics, Data Analysis, and Simulation SS 2015
Mainz, June 11, 2015 Statistics, Data Analysis, and Simulation SS 2015 08.128.730 Statistik, Datenanalyse und Simulation Dr. Michael O. Distler Dr. Michael O. Distler
Level 2 German, 2015
91126 911260 2SUPERVISOR S Level 2 German, 2015 91126 Demonstrate understanding of a variety of written and / or visual German text(s) on familiar matters 2.00 p.m. Friday 4 December 2015 Credits: Five
Kursbuch Naturheilverfahren: Curriculum der Weiterbildung zur Erlangung der Zusatzbezeichnung Naturheilverfahren (German Edition)
Kursbuch Naturheilverfahren: Curriculum der Weiterbildung zur Erlangung der Zusatzbezeichnung Naturheilverfahren (German Edition) Click here if your download doesn"t start automatically Kursbuch Naturheilverfahren:
Einführung in die Finite Element Methode Projekt 2
Einführung in die Finite Element Methode Projekt 2 Juri Schmelzer und Fred Brockstedt 17.7.2014 Juri Schmelzer und Fred Brockstedt Einführung in die Finite Element Methode Projekt 2 17.7.2014 1 / 29 Project
Priorities (time independent and time dependent) Different service times of different classes at Type-1 nodes -
E.6 Approximate Analysis of Non-product-Form Queueing Networks Non exponentially distributed service times Priorities (time independent and time dependent) Different service times of different classes
Brand Label. Daimler Brand & Design Navigator
Daimler Brand & Design Navigator 30. März 2016 Brand Label FUSO Financial uses the FUSO letters in combination with the word Financial in the font Daimler CS for name and label. Black lettering is set
Algorithm Theory 3 Fast Fourier Transformation Christian Schindelhauer
Algorithm Theory 3 Fast Fourier Transformation Institut für Informatik Wintersemester 2007/08 Chapter 3 Fast Fourier Transformation 2 Polynomials Polynomials p over real numbers with a variable x p(x)
Mitglied der Leibniz-Gemeinschaft
Methods of research into dictionary use: online questionnaires Annette Klosa (Institut für Deutsche Sprache, Mannheim) 5. Arbeitstreffen Netzwerk Internetlexikografie, Leiden, 25./26. März 2013 Content
Interpolation Functions for the Finite Elements
Interpolation Functions for the Finite Elements For the finite elements method, the following is valid: The global function of a sought function consists of a sum of local functions: GALERKIN method: the
Causal Analysis in Population Studies
Causal Analysis in Population Studies Prof. Dr. Henriette Engelhardt Prof. Dr. Alexia Prskawetz Randomized experiments and observational studies for causal inference inference Historical dichotomy between
Final Exam. Friday June 4, 2008, 12:30, Magnus-HS
Stochastic Processes Summer Semester 2008 Final Exam Friday June 4, 2008, 12:30, Magnus-HS Name: Matrikelnummer: Vorname: Studienrichtung: Whenever appropriate give short arguments for your results. In
Unit 4. The Extension Principle. Fuzzy Logic I 123
Unit 4 The Extension Principle Fuzzy Logic I 123 Images and Preimages of Functions Let f : X Y be a function and A be a subset of X. Then the image of A w.r.t. f is defined as follows: f(a) = {y Y there
Rev. Proc Information
Rev. Proc. 2006-32 Information 2006, CPAs 1 Table 1-Total loss of the home Table 2- Near total loss is water to the roofline. Completely gut the home from floor to rafters - wiring, plumbing, electrical
Geometrie und Bedeutung: Kap 5
: Kap 5 21. November 2011 Übersicht Der Begriff des Vektors Ähnlichkeits Distanzfunktionen für Vektoren Skalarprodukt Eukidische Distanz im R n What are vectors I Domininic: Maryl: Dollar Po Euro Yen 6
Zentrum für Bioinformatik. Übung zur Vorlesung Grundlagen der Strukturanalyse Wintersemester 2015/2016. Übung 9: Revision 2
Andrew Torda Björn Hansen Zentrum für Bioinformatik Übung zur Vorlesung Grundlagen der Strukturanalyse Wintersemester 2015/2016 18./20. Januar 2016 Übung 9: Revision 2 Dies ist die zweite von zwei Übungen,
Titelmasterformat Object Generator durch Klicken bearbeiten
Titelmasterformat Object Generator durch Klicken bearbeiten How to model 82 screws in 2 minutes By Pierre-Louis Ruffieux 17.11.2014 1 Object Generator The object generator is usefull tool to replicate
ATEX-Check list. Compiled by: Date: Signature: Acceptable practice at the determination of flash point: Closed cup according to ISO 2719
Fire and explosion hazard ATEX 137 1999/92/EG und ATEX 95 2014/34/EU Danger assessment and determination of explosion protection zone for the test space as well as the installation site ATEX-Check list
TC1 Grundlagen der Theoretischen Chemie
TC1 Grundlagen der Theoretischen Chemie Irene Burghardt (burghardt@chemie.uni-frankfurt.de) Topic: Helium-Atom Vorlesung: Mo 10h-12h, Do9h-10h Übungen: Do 8h-9h Web site: http://www.theochem.uni-frankfurt.de/tc1
Quantenmechanik II Musterlösung 7.
Quantenmechanik II Musterlösung 7. FS 07 Prof. Thomas Gehrmann Übung. [Auswahlregeln] Beweise die Drehimpulsauswahlregeln m = 0, ± und l = ± für Dipolübergänge in wasserstoffähnlichen Atomen unter Verwendung
Analysis III Serie 13 Musterlösung
Ana-3 Hs 22 Analysis III Serie 3 Musterlösung Abgabe: Freitag, 2.2.22, Uhr, in der Vorlesung * Aufgabe Welche der folgenden Aussagen sind wahr und welche sind falsch? (Mit Begründung) (i) Sei A R 3 3 eine
Mathematics (M4) (English version) ORIENTIERUNGSARBEIT (OA 11) Gymnasium. Code-Nr.:
Gymnasium 2. Klassen MAR Code-Nr.: Schuljahr 2005/2006 Datum der Durchführung Donnerstag, 6.4.2006 ORIENTIERUNGSARBEIT (OA 11) Gymnasium Mathematics (M4) (English version) Lesen Sie zuerst Anleitung und
DICO Dimension Coupling
DICO Dimension Coupling 3D!" 1D and phase transition (liquid vapor) Jonathan Jung, Martina Friedrich, Claus-Dieter Munz, Jean-Marc Hérard, Philippe Helluy MAC days, Paris University of Stuttgart Institut
Supply Chain Management
Supply Chain Management Forecasting Methods Prof. Dr.-Ing. Burkhard Schmager Department of Industrial Engineering EAH Jena Sept 2016 SS 2016 Kapitel 2-1 Material Planning Approaches MRP - methods deterministical
VGM. VGM information. HAMBURG SÜD VGM WEB PORTAL USER GUIDE June 2016
Overview The Hamburg Süd VGM Web portal is an application that enables you to submit VGM information directly to Hamburg Süd via our e-portal Web page. You can choose to enter VGM information directly,
TC1 Grundlagen der Theoretischen Chemie
TC1 Grundlagen der Theoretischen Chemie Irene Burghardt (burghardt@chemie.uni-frankfurt.de) Topic: Wasserstoffatom Vorlesung: Mo 1h-12h, Do9h-1h Übungen: Do 8h-9h Web site: http://www.theochem.uni-frankfurt.de/tc1
Übungen zu Integrierter Kurs II - Festkörper und Statistische Physik Blatt 10 ( )
Fakultät für Physik WS 2014/15 Prof. Milena Grifoni, Prof. Jascha Repp Übungen zu Integrierter Kurs II - Festkörper und Statistische Physik Blatt 10 (03.12.2014) Übungsleiter: Prof. Jascha Repp (1.1.24,
Die einfachste Diät der Welt: Das Plus-Minus- Prinzip (GU Reihe Einzeltitel)
Die einfachste Diät der Welt: Das Plus-Minus- Prinzip (GU Reihe Einzeltitel) Stefan Frà drich Click here if your download doesn"t start automatically Die einfachste Diät der Welt: Das Plus-Minus-Prinzip
Air-Sea Gas Transfer: Schmidt Number Dependency and Intermittency
Air-Sea Gas Transfer: Schmidt Number Dependency and Intermittency Bernd Jähne, Reinhard Nielsen, Christopher Pop, Uwe Schimpf, and Christoph Garbe Interdisziplinäres Zentrum für Wissenschaftliches Rechnen
Wie man heute die Liebe fürs Leben findet
Wie man heute die Liebe fürs Leben findet Sherrie Schneider Ellen Fein Click here if your download doesn"t start automatically Wie man heute die Liebe fürs Leben findet Sherrie Schneider Ellen Fein Wie
Grade 12: Qualifikationsphase. My Abitur
Grade 12: Qualifikationsphase My Abitur Qualifikationsphase Note 1 Punkte Prozente Note 1 15 14 13 85 % 100 % Note 2 12 11 10 70 % 84 % Note 3 9 8 7 55 % 69 % Note 4 6 5 4 40 % 54 % Note 5 3 2 1 20 % 39
Was heißt Denken?: Vorlesung Wintersemester 1951/52. [Was bedeutet das alles?] (Reclams Universal-Bibliothek) (German Edition)
Was heißt Denken?: Vorlesung Wintersemester 1951/52. [Was bedeutet das alles?] (Reclams Universal-Bibliothek) (German Edition) Martin Heidegger Click here if your download doesn"t start automatically Was
Duell auf offener Straße: Wenn sich Hunde an der Leine aggressiv verhalten (Cadmos Hundebuch) (German Edition)
Duell auf offener Straße: Wenn sich Hunde an der Leine aggressiv verhalten (Cadmos Hundebuch) (German Edition) Nadine Matthews Click here if your download doesn"t start automatically Duell auf offener
Web-Apps mit jquery Mobile: Mobile Multiplattform-Entwicklung mit HTML5 und JavaScript (German Edition)
Web-Apps mit jquery Mobile: Mobile Multiplattform-Entwicklung mit HTML5 und JavaScript (German Edition) Philipp Friberg Click here if your download doesn"t start automatically Web-Apps mit jquery Mobile:
Advanced Track and Tire Modeling using SIMPACK User Routines
Advanced Track and Tire Modeling using SIMPACK User Routines Werner, Jens Neubeck Forschungsinstitut für Kraftfahrwesen und www.fkfs.de SIMPACK User Meeting 2003 1 Introduction Continuous Track Model Implemented
Der Topos Mütterlichkeit am Beispiel Bertolt Brechts "Der kaukasische Kreidekreis" und "Mutter Courage und ihre Kinder" (German Edition)
Der Topos Mütterlichkeit am Beispiel Bertolt Brechts "Der kaukasische Kreidekreis" und "Mutter Courage und ihre Kinder" (German Edition) Filio Gavriilidou Click here if your download doesn"t start automatically
Oscillating drives generate oscillating motions of the output shaft through an evenly formed rotary motion of the drive How does it function?
Oscillating drives generate oscillating motions of the output shaft through an evenly formed rotary motion of the drive How does it function? the motion sequence in general: the input shaft rotates continuously,
EVANGELISCHES GESANGBUCH: AUSGABE FUR DIE EVANGELISCH-LUTHERISCHE LANDESKIRCHE SACHSEN. BLAU (GERMAN EDITION) FROM EVANGELISCHE VERLAGSAN
EVANGELISCHES GESANGBUCH: AUSGABE FUR DIE EVANGELISCH-LUTHERISCHE LANDESKIRCHE SACHSEN. BLAU (GERMAN EDITION) FROM EVANGELISCHE VERLAGSAN DOWNLOAD EBOOK : EVANGELISCHES GESANGBUCH: AUSGABE FUR DIE EVANGELISCH-LUTHERISCHE
H o c h s c h u l e D e g g e n d o r f H o c h s c h u l e f ü r a n g e w a n d t e W i s s e n s c h a f t e n
Time Aware Shaper Christian Boiger christian.boiger@hdu-deggendorf.de IEEE 802 Plenary September 2012 Santa Cruz, California D E G G E N D O R F U N I V E R S I T Y O F A P P L I E D S C I E N C E S Time
Multi-Lattice Approach to Kinetic Monte Carlo
Fakultät für Chemie Multi-Lattice Approach to Kinetic Monte Carlo Max J. Hoffmann Fritz-Haber Institut der Max-Planck-Gesellschaft TU München Jan 25, 2011 1 Outline introduction to DFT+kMC approach for
Mock Exam Behavioral Finance
Mock Exam Behavioral Finance For the following 4 questions you have 60 minutes. You may receive up to 60 points, i.e. on average you should spend about 1 minute per point. Please note: You may use a pocket
Functional Analysis Final Test, Funktionalanalysis Endklausur,
Spring term 2012 / Sommersemester 2012 Functional Analysis Final Test, 16.07.2012 Funktionalanalysis Endklausur, 16.07.2012 Name:/Name: Matriculation number:/matrikelnr.: Semester:/Fachsemester: Degree
25 teams will compete in the ECSG Ghent 2017 Senior Class Badminton.
ECSG 2017 Badminton Briefing : Senior Class 25 teams will compete in the ECSG Ghent 2017 Senior Class Badminton. Including 8 Belgian, 1 Danish, 1 French, 21 German, and 1 Maltese Teams. Teams have been
PONS DIE DREI??? FRAGEZEICHEN, ARCTIC ADVENTURE: ENGLISCH LERNEN MIT JUSTUS, PETER UND BOB
Read Online and Download Ebook PONS DIE DREI??? FRAGEZEICHEN, ARCTIC ADVENTURE: ENGLISCH LERNEN MIT JUSTUS, PETER UND BOB DOWNLOAD EBOOK : PONS DIE DREI??? FRAGEZEICHEN, ARCTIC ADVENTURE: Click link bellow
Ultrakurze Lichtimpulse und THz Physik
Ultrakurze Lichtimpulse und THz Physik. Einleitung 2. Darstellung ultrakurzer Lichtimpulse 2. Prinzip der Modenkopplung 2.2 Komplexe Darstellung ultrakurzer Lichtimpulse 2.2. Fourier Transformation 2.2.2
Teil 2.2: Lernen formaler Sprachen: Hypothesenräume
Theorie des Algorithmischen Lernens Sommersemester 2006 Teil 2.2: Lernen formaler Sprachen: Hypothesenräume Version 1.1 Gliederung der LV Teil 1: Motivation 1. Was ist Lernen 2. Das Szenario der Induktiven
Keysight Technologies Using InfiniiMax Probes with Test Equipment other than Infiniium Oscilloscopes
Ihr Spezialist für Mess- und Prüfgeräte Keysight Technologies Using InfiniiMax Probes with Test Equipment other than Infiniium Oscilloscopes Configuration Guide Introduction The benefits of the Keysight
WP2. Communication and Dissemination. Wirtschafts- und Wissenschaftsförderung im Freistaat Thüringen
WP2 Communication and Dissemination Europa Programm Center Im Freistaat Thüringen In Trägerschaft des TIAW e. V. 1 GOALS for WP2: Knowledge information about CHAMPIONS and its content Direct communication
Logik für Informatiker Logic for computer scientists
Logik für Informatiker Logic for computer scientists Till Mossakowski WiSe 2007/08 2 Rooms Monday 13:00-15:00 GW2 B1410 Thursday 13:00-15:00 GW2 B1410 Exercises (bring your Laptops with you!) either Monday
Finite Difference Method (FDM) Integral Finite Difference Method (IFDM)
Finite Difference Method (FDM) Integral Finite Difference Method (IFDM) home/lehre/vl-mhs-1-e/cover sheet.tex. p.1/29 Table of contents 1. Finite Difference Method (FDM) 1D-Example (a) Problem and Governing
Fakultät III Univ.-Prof. Dr. Jan Franke-Viebach
1 Universität Siegen Fakultät III Univ.-Prof. Dr. Jan Franke-Viebach Klausur Monetäre Außenwirtschaftstheorie und politik / International Macro Wintersemester 2011-12 (2. Prüfungstermin) Bearbeitungszeit:
Level 1 German, 2014
90886 908860 1SUPERVISOR S Level 1 German, 2014 90886 Demonstrate understanding of a variety of German texts on areas of most immediate relevance 9.30 am Wednesday 26 November 2014 Credits: Five Achievement
Level 2 German, 2013
91126 911260 2SUPERVISOR S Level 2 German, 2013 91126 Demonstrate understanding of a variety of written and / or visual German text(s) on familiar matters 9.30 am Monday 11 November 2013 Credits: Five
Stochastic Processes SS 2010 Prof. Anton Wakolbinger. Klausur am 16. Juli 2010
Stochastic Processes SS 2010 Prof. Anton Wakolbinger Klausur am 16. Juli 2010 Vor- und Nachname: Matrikelnummer: Studiengang: Tutor(in): In der Klausur können 100 Punkte erreicht werden. Die Gesamtpunktezahl
Nürnberg und der Christkindlesmarkt: Ein erlebnisreicher Tag in Nürnberg (German Edition)
Nürnberg und der Christkindlesmarkt: Ein erlebnisreicher Tag in Nürnberg (German Edition) Karl Schön Click here if your download doesn"t start automatically Nürnberg und der Christkindlesmarkt: Ein erlebnisreicher
USBASIC SAFETY IN NUMBERS
USBASIC SAFETY IN NUMBERS #1.Current Normalisation Ropes Courses and Ropes Course Elements can conform to one or more of the following European Norms: -EN 362 Carabiner Norm -EN 795B Connector Norm -EN