D-Wave D-Wave Systems Inc.

Μέγεθος: px
Εμφάνιση ξεκινά από τη σελίδα:

Download "D-Wave D-Wave Systems Inc."

Transcript

1 D-Wave D-Wave sems Inc. Anaol Yu. mirnov D-Wave sems Inc. Vancouver Briish Columbia HE QUANUM COMPUING COMPANY M Decoherence and Noise Conrol in rongl Driven uperconducing Quanum Bis Collaboraion: M. Grajcar E. Il ichev A. Imalkov IPH Jena German M.H.. Amin A. Maassen van den Brink A. Zagoskin D-Wave sems Inc.

2 D-Wave D-Wave sems Inc. HE QUANUM COMPUING COMPANY M Ouline:. Quanum Brownian moion of a driven wo-sae ssem.. abi oscillaions and decoherence suppression in a superconducing flu qubi. 3. abi specroscop and noise manipulaion. 4. Conclusions.

3 & & & D-Wave D-Wave sems Inc. HE QUANUM COMPUING COMPANY M Qubi { } Hea bah Q Driving force FF cos Hamilonian and Heisenberg equaions: H Q F cos H Hea bah: Q F. cos Q F ϕ M i [ ] Q Q B cos [ ] Q Q χ" coh. θ. X E ± χ χ" ±. s A e / / / E E / /. c

4 D-Wave sems Inc. D-Wave sems Inc. HE QUANUM COMPUING COMPANY M Non-Markovian Heisenberg-Langevin equaions Flucuaion forces: [ ] [ ]. Q M d F Q M d F ϕ δ δ ξ ϕ δ δ ξ & & & [ ] [ ]. Q M d Q Q M d Q δ δ ξ δ δ ξ ξ ξ G.F. Efremov A.Yu. mirnov ov.phs. JEP

5 D-Wave sems Inc. D-Wave sems Inc. HE QUANUM COMPUING COMPANY M Qubi wih hea bah no driving force : / e X X X [ ] [ ] cos cos / / / / e e e e Populaion difference: Evoluion of -polariaion: eq eq X anh X X Equilibrium relaaion and dephasing raes :

6 wih he frequenc: D-Wave D-Wave sems Inc. abi oscillaions of he ecied level populaion P Ec : and he damping rae P Ec X F HE QUANUM COMPUING COMPANY M Qubi wih hea bah and driving force. Eac resonance Weak qubi-bah coupling oaing Wave Approimaion : E E Γ <<. / e cos >>. P Ec.

7 D-Wave D-Wave sems Inc. HE QUANUM COMPUING COMPANY M abi oscillaions of he dipole momen a ero bias: wih he sead-sae -polariaion: Z χ" Γ e cos / e sin sin Z Z cos χ" and he addiional decoherence rae non-ero bias: Γ. A.Yu. mirnov Phs.ev. B ; Phs.ev. B

8 D-Wave D-Wave sems Inc. HE QUANUM COMPUING COMPANY M For he srongl driven qubi >> - abi oscillaions of boh populaion and -polariaion disappear for he same relaaion ime : Wihou he driving force: eq eq : defines a imescale for relaaion of populaion : defines a dephasing rae deca of a dipole momen.

9 D-Wave D-Wave sems Inc. HE QUANUM COMPUING COMPANY M abi oscillaions in a flu superconducing qubi. Quanum aes: L lef roaing curren righ roaing curren I I q uperconducing Loop: Macroscopic wo-level ssem I. Chiorescu e al. cience ; ime domain Bias: e I q / π Φ Φ E. Il ichev e al. Phs. ev. Le Frequenc domain /

10 Measuremens: Deca ime of abi oscillaions: τ abi 5ns elaaion ime of undriven qubi: eq τ rela 9 Dephasing ime of undriven qubi: abi oscillaions of upper level populaion. ns D-Wave D-Wave sems Inc. HE QUANUM COMPUING COMPANY M F eq τ ns ϕ π 6.6GH >> MH π I. Chiorescu e al. cience ;

11 D-Wave D-Wave sems Inc. HE QUANUM COMPUING COMPANY M Deca rae of abi oscillaions: 9 s 5 3 elaaion rae of undriven qubi: eq 9 s 9 Dephasing ime of undriven qubi: eq s 9 eq τ c Frequenc dispersion of he hea bah specrum τ c / π MH For he fla specrum i should be: fla 39.5ns / 3.8 Difference beween and fla poins o he decoherence suppression in 3.8 imes b eernal driving field

12 D-Wave D-Wave sems Inc. HE QUANUM COMPUING COMPANY M Much higher suppression of decoherence b he high-frequenc field - pin / irradiaed b circularl polaried ligh roaing magneic field: r r H elaaion rae a cos sin Q H B << 4χ" coh 4 " coh << 4 χ eq χ" A s e / c s A.Yu. mirnov Phs.ev.B

13 D-Wave D-Wave sems Inc. abi specroscop and noise manipulaion in a flu qubi coupled o a ank circui HE QUANUM COMPUING COMPANY M Qubi: Γ ank as a low-frequenc linear deecor of curren flucuaions in he qubi d d γ d d V >> ank: λ & γ L C E. Il ichev e al. Phs. ev. Le

14 D-Wave D-Wave sems Inc. HE QUANUM COMPUING COMPANY M pecrum of volage flucuaions in he ank heor VQ k Peak value of he specrum a L q C I q Γ V ma γ ~ Γ Γ >> >> γ Direc deecion of radiaion a abi frequenc : F. γ << Γ A.Yu. mirnov Phs.ev.B

15 D-Wave D-Wave sems Inc. HE QUANUM COMPUING COMPANY M pecrum of volage flucuaions in he ank eperimen Τ /π 6.84 MH Q Τ /γ Τ 85 L q 4 ph I q 5 na k -3 mk Decoherence imes:.5µs Jena/D-Wave.5µs Delf pecrum / VQ Peak value of he specrum as a funcion of HF ampliude F a differen HF power heor V ma / P / P P / P /

16 D-Wave sems Inc. D-Wave sems Inc. HE QUANUM COMPUING COMPANY M abi specroscop as a weak coninuous measuremen Measuremen-induced decoherence backacion of he ank on he qubi: << Γ < Γ Γ << γ 4 q q I L k γ γ Γ Γ ignal-o-noise raio: Γ Γ q q V VQ I L k γ abi specroscop is a weak quanum measuremen if: V C γ γ Inernal noise of he ank circui:

17 D-Wave D-Wave sems Inc. HE QUANUM COMPUING COMPANY M Conclusions. ecen measuremens of abi oscillaions in superconducing flu qubis have demonsraed a possibili o suppress decoherence and conrol a noise level in he flu qubis b appling a srong driving field.

Non-Markovian dynamics of an open quantum system in fermionic environments

Non-Markovian dynamics of an open quantum system in fermionic environments Non-Marovian dynamics of an open quanum sysem in fermionic environmens J. Q. You Deparmen of Physics, Fudan Universiy, Shanghai, and Beijing Compuaional Science Research Cener, Beijing Mi Chen (PhD suden

Διαβάστε περισσότερα

ΣΤΟΧΑΣΤΙΚΑ ΣΥΣΤΗΜΑΤΑ & ΕΠΙΚΟΙΝΩΝΙΕΣ 1o Τμήμα (Α - Κ): Αμφιθέατρο 4, Νέα Κτίρια ΣΗΜΜΥ Διαμόρφωση Γωνίας (Angle Modulation) - 3

ΣΤΟΧΑΣΤΙΚΑ ΣΥΣΤΗΜΑΤΑ & ΕΠΙΚΟΙΝΩΝΙΕΣ 1o Τμήμα (Α - Κ): Αμφιθέατρο 4, Νέα Κτίρια ΣΗΜΜΥ Διαμόρφωση Γωνίας (Angle Modulation) - 3 ΣΤΟΧΑΣΤΙΚΑ ΣΥΣΤΗΜΑΤΑ & ΕΠΙΚΟΙΝΩΝΙΕΣ 1o Τμήμα (Α - Κ): Αμφιθέατρο 4, Νέα Κτίρια ΣΗΜΜΥ Διαμόρφωση Γωνίας (Angle Modulaion) - 3 4.4: Βρόχος Κλειδωμένης Φάσης (Phase-Locked Loop - PLL) 4.5: Μη Γραμμικά Φαινόμενα

Διαβάστε περισσότερα

Anti-aliasing Prefilter (6B) Young Won Lim 6/8/12

Anti-aliasing Prefilter (6B) Young Won Lim 6/8/12 ni-aliasing Prefiler (6B) Copyrigh (c) Young W. Lim. Permission is graned o copy, disribue and/or modify his documen under he erms of he GNU Free Documenaion License, Version. or any laer version published

Διαβάστε περισσότερα

Lecture 12 Modulation and Sampling

Lecture 12 Modulation and Sampling EE 2 spring 2-22 Handou #25 Lecure 2 Modulaion and Sampling The Fourier ransform of he produc of wo signals Modulaion of a signal wih a sinusoid Sampling wih an impulse rain The sampling heorem 2 Convoluion

Διαβάστε περισσότερα

6.003: Signals and Systems

6.003: Signals and Systems 6.3: Signals and Sysems Modulaion December 6, 2 Communicaions Sysems Signals are no always well mached o he media hrough which we wish o ransmi hem. signal audio video inerne applicaions elephone, radio,

Διαβάστε περισσότερα

Analysis of optimal harvesting of a prey-predator fishery model with the limited sources of prey and presence of toxicity

Analysis of optimal harvesting of a prey-predator fishery model with the limited sources of prey and presence of toxicity ES Web of Confeences 7, 68 (8) hps://doiog/5/esconf/8768 ICEIS 8 nalsis of opimal havesing of a pe-pedao fishe model wih he limied souces of pe and pesence of oici Suimin,, Sii Khabibah, and Dia nies Munawwaoh

Διαβάστε περισσότερα

d dt S = (t)si d dt R = (t)i d dt I = (t)si (t)i

d dt S = (t)si d dt R = (t)i d dt I = (t)si (t)i d d S = ()SI d d I = ()SI ()I d d R = ()I d d S = ()SI μs + fi + hr d d I = + ()SI (μ + + f + ())I d d R = ()I (μ + h)r d d P(S,I,) = ()(S +1)(I 1)P(S +1, I 1, ) +()(I +1)P(S,I +1, ) (()SI + ()I)P(S,I,)

Διαβάστε περισσότερα

6.003: Signals and Systems. Modulation

6.003: Signals and Systems. Modulation 6.3: Signals and Sysems Modulaion December 6, 2 Subjec Evaluaions Your feedback is imporan o us! Please give feedback o he saff and fuure 6.3 sudens: hp://web.mi.edu/subjecevaluaion Evaluaions are open

Διαβάστε περισσότερα

Jesse Maassen and Mark Lundstrom Purdue University November 25, 2013

Jesse Maassen and Mark Lundstrom Purdue University November 25, 2013 Notes on Average Scattering imes and Hall Factors Jesse Maassen and Mar Lundstrom Purdue University November 5, 13 I. Introduction 1 II. Solution of the BE 1 III. Exercises: Woring out average scattering

Διαβάστε περισσότερα

From the course textbook, Power Electronics Circuits, Devices, and Applications, Fourth Edition, by M.S. Rashid, do the following problems

From the course textbook, Power Electronics Circuits, Devices, and Applications, Fourth Edition, by M.S. Rashid, do the following problems ECE 427 Homework #2 From he course exbook, Power Elecronics Circuis, Devices, and Applicaions, Fourh Ediion, by M.S. Rashid, do he following problems 1. Problem.1 on page 1. Draw he oupu volage and inpu

Διαβάστε περισσότερα

3 Frequency Domain Representation of Continuous Signals and Systems

3 Frequency Domain Representation of Continuous Signals and Systems 3 Frequency Domain Represenaion of Coninuous Signals and Sysems 3. Fourier Series Represenaion of Periodic Signals............. 2 3.. Exponenial Fourier Series.................... 2 3..2 Discree Fourier

Διαβάστε περισσότερα

The Euler Equations! λ 1. λ 2. λ 3. ρ ρu. E = e + u 2 /2. E + p ρ. = de /dt. = dh / dt; h = h( T ); c p. / c v. ; γ = c p. p = ( γ 1)ρe. c v.

The Euler Equations! λ 1. λ 2. λ 3. ρ ρu. E = e + u 2 /2. E + p ρ. = de /dt. = dh / dt; h = h( T ); c p. / c v. ; γ = c p. p = ( γ 1)ρe. c v. hp://www.nd.ed/~gryggva/cfd-corse/ The Eler Eqaions The Eler Eqaions The Eler eqaions for D flow: + + p = x E E + p where Define E = e + / H = h + /; h = e + p/ Gréar Tryggvason Spring 3 Ideal Gas: p =

Διαβάστε περισσότερα

Radiation Stress Concerned with the force (or momentum flux) exerted on the right hand side of a plane by water on the left hand side of the plane.

Radiation Stress Concerned with the force (or momentum flux) exerted on the right hand side of a plane by water on the left hand side of the plane. upplement on Radiation tress and Wave etup/et down Radiation tress oncerned wit te force (or momentum flu) eerted on te rit and side of a plane water on te left and side of te plane. plane z "Radiation

Διαβάστε περισσότερα

LONGITUDINAL INSTABILITIES

LONGITUDINAL INSTABILITIES 1) Inroducion ) Impedances and wake funcions 3) Longiudinal dynamics 4) Robinson insabiliy 5) Poenial well bunch lenghening LONGITUDINAL INSTABILITIES CAS 7, Daresbury; A Hofmann cas7li-1 1) INTRODUCTION

Διαβάστε περισσότερα

Electronic Companion to Supply Chain Dynamics and Channel Efficiency in Durable Product Pricing and Distribution

Electronic Companion to Supply Chain Dynamics and Channel Efficiency in Durable Product Pricing and Distribution i Eleconic Copanion o Supply Chain Dynaics and Channel Efficiency in Duable Poduc Picing and Disibuion Wei-yu Kevin Chiang College of Business Ciy Univesiy of Hong Kong wchiang@ciyueduh I Poof of Poposiion

Διαβάστε περισσότερα

(b) flat (continuous) fins on an array of tubes

(b) flat (continuous) fins on an array of tubes (a) Individually finned ues () fla (coninuous) fins on an array of ues Eample Fins Fins on Segosaurus 3 Rekangulär fläns, Recangular fin. Z d f 4 Rekangulär fläns, Recangular fin. Z d f d αc d λ ( f )

Διαβάστε περισσότερα

ω = radians per sec, t = 3 sec

ω = radians per sec, t = 3 sec Secion. Linear and Angular Speed 7. From exercise, =. A= r A = ( 00 ) (. ) = 7,00 in 7. Since 7 is in quadran IV, he reference 7 8 7 angle is = =. In quadran IV, he cosine is posiive. Thus, 7 cos = cos

Διαβάστε περισσότερα

wave energy Superposition of linear plane progressive waves Marine Hydrodynamics Lecture Oblique Plane Waves:

wave energy Superposition of linear plane progressive waves Marine Hydrodynamics Lecture Oblique Plane Waves: 3.0 Marine Hydrodynamics, Fall 004 Lecture 0 Copyriht c 004 MIT - Department of Ocean Enineerin, All rihts reserved. 3.0 - Marine Hydrodynamics Lecture 0 Free-surface waves: wave enery linear superposition,

Διαβάστε περισσότερα

The Student s t and F Distributions Page 1

The Student s t and F Distributions Page 1 The Suden s and F Disribuions Page The Fundamenal Transformaion formula for wo random variables: Consider wo random variables wih join probabiliy disribuion funcion f (, ) simulaneously ake on values in

Διαβάστε περισσότερα

( ) ( ) ( ) Fourier series. ; m is an integer. r(t) is periodic (T>0), r(t+t) = r(t), t Fundamental period T 0 = smallest T. Fundamental frequency ω

( ) ( ) ( ) Fourier series. ; m is an integer. r(t) is periodic (T>0), r(t+t) = r(t), t Fundamental period T 0 = smallest T. Fundamental frequency ω Fourier series e jm when m d when m ; m is an ineger. jm jm jm jm e d e e e jm jm jm jm r( is periodi (>, r(+ r(, Fundamenal period smalles Fundamenal frequeny r ( + r ( is periodi hen M M e j M, e j,

Διαβάστε περισσότερα

16. 17. r t te 2t i t 1. 18 19 Find the derivative of the vector function. 19. r t e t cos t i e t sin t j ln t k. 31 33 Evaluate the integral.

16. 17. r t te 2t i t 1. 18 19 Find the derivative of the vector function. 19. r t e t cos t i e t sin t j ln t k. 31 33 Evaluate the integral. SECTION.7 VECTOR FUNCTIONS AND SPACE CURVES.7 VECTOR FUNCTIONS AND SPACE CURVES A Click here for answers. S Click here for soluions. Copyrigh Cengage Learning. All righs reserved.. Find he domain of he

Διαβάστε περισσότερα

X-Y COUPLING GENERATION WITH AC/PULSED SKEW QUADRUPOLE AND ITS APPLICATION

X-Y COUPLING GENERATION WITH AC/PULSED SKEW QUADRUPOLE AND ITS APPLICATION X-Y COUPLING GENERATION WITH AC/PULSED SEW QUADRUPOLE AND ITS APPLICATION # Takeshi Nakamura # Japan Synchrotron Radiation Research Institute / SPring-8 Abstract The new method of x-y coupling generation

Διαβάστε περισσότερα

ΕΡΓΑΣΙΑ ΜΑΘΗΜΑΤΟΣ: ΘΕΩΡΙΑ ΒΕΛΤΙΣΤΟΥ ΕΛΕΓΧΟΥ ΦΙΛΤΡΟ KALMAN ΜΩΥΣΗΣ ΛΑΖΑΡΟΣ

ΕΡΓΑΣΙΑ ΜΑΘΗΜΑΤΟΣ: ΘΕΩΡΙΑ ΒΕΛΤΙΣΤΟΥ ΕΛΕΓΧΟΥ ΦΙΛΤΡΟ KALMAN ΜΩΥΣΗΣ ΛΑΖΑΡΟΣ ΑΡΙΣΤΟΤΕΛΕΙΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΘΕΣΣΑΛΟΝΙΚΗΣ ΤΜΗΜΑ ΜΑΘΗΜΑΤΙΚΩΝ ΜΕΤΑΠΤΥΧΙΑΚΟ ΠΡΟΓΡΑΜΜΑ ΣΠΟΥΔΩΝ ΘΕΩΡΗΤΙΚΗ ΠΛΗΡΟΦΟΡΙΚΗ ΚΑΙ ΘΕΩΡΙΑ ΣΥΣΤΗΜΑΤΩΝ & ΕΛΕΓΧΟΥ ΕΡΓΑΣΙΑ ΜΑΘΗΜΑΤΟΣ: ΘΕΩΡΙΑ ΒΕΛΤΙΣΤΟΥ ΕΛΕΓΧΟΥ ΦΙΛΤΡΟ KALMAN ΜΩΥΣΗΣ

Διαβάστε περισσότερα

The canonical 2nd order transfer function is expressed as. (ω n

The canonical 2nd order transfer function is expressed as. (ω n Second order ransfer funcions nd Order ransfer funcion - Summary of resuls The canonical nd order ransfer funcion is expressed as H(s) s + ζ s + is he naural frequency; ζ is he damping coefficien. The

Διαβάστε περισσότερα

Appendix. The solution begins with Eq. (2.15) from the text, which we repeat here for 1, (A.1)

Appendix. The solution begins with Eq. (2.15) from the text, which we repeat here for 1, (A.1) Aenix Aenix A: The equaion o he sock rice. The soluion egins wih Eq..5 rom he ex, which we reea here or convenience as Eq.A.: [ [ E E X, A. c α where X u ε, α γ, an c α y AR. Take execaions o Eq. A. as

Διαβάστε περισσότερα

BandPass (4A) Young Won Lim 1/11/14

BandPass (4A) Young Won Lim 1/11/14 BandPass (4A) Copyright (c) 22 Young W. Lim. Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version.2 or any later version

Διαβάστε περισσότερα

ΣΤΟΧΑΣΤΙΚΑ ΣΥΣΤΗΜΑΤΑ & ΕΠΙΚΟΙΝΩΝΙΕΣ 1o Τμήμα (Α - Κ): Αμφιθέατρο 4, Νέα Κτίρια ΣΗΜΜΥ Διαμόρφωση Γωνίας (Angle Modulation) - 2

ΣΤΟΧΑΣΤΙΚΑ ΣΥΣΤΗΜΑΤΑ & ΕΠΙΚΟΙΝΩΝΙΕΣ 1o Τμήμα (Α - Κ): Αμφιθέατρο 4, Νέα Κτίρια ΣΗΜΜΥ Διαμόρφωση Γωνίας (Angle Modulation) - 2 ΣΤΟΧΑΣΤΙΚΑ ΣΥΣΤΗΜΑΤΑ & ΕΠΙΚΟΙΝΩΝΙΕΣ 1o Τμήμα (Α - Κ): Αμφιθέατρο 4, Νέα Κτίρια ΣΗΜΜΥ Διαμόρφωση Γωνίας (Angle Modulaion) - 4.3: Διαμόρφωση Συχνότητας (Frequency Modulaion FM) καθ. Βασίλης Μάγκλαρης maglaris@nemode.nua.gr

Διαβάστε περισσότερα

Fourier transform of continuous-time signals

Fourier transform of continuous-time signals Fourier ransform of coninuous-ime signals Specral represenaion of non-periodic signals Fourier ransform: aperiodic signals repeiion of a finie-duraion signal x()> periodic signals. x x T x kt x kt k k

Διαβάστε περισσότερα

GEEPLUS VM1614. Force (N) vs Displacement (mm) Peak. Max 'ON' time. Force. Model No. VM

GEEPLUS VM1614. Force (N) vs Displacement (mm) Peak. Max 'ON' time. Force. Model No. VM VM1614 2 VM1614 18 VM1614 125 VM1614 1 GEEPLUS VM1614 P 1 is the continuous (1% ED) excitation power at mounted to a massive heatsink at 2 C P 1 5 W Total Mass 15 g T max 13 C Coil Mass 3 g R 2 2.8.2 mh.7

Διαβάστε περισσότερα

Second Order Partial Differential Equations

Second Order Partial Differential Equations Chapter 7 Second Order Partial Differential Equations 7.1 Introduction A second order linear PDE in two independent variables (x, y Ω can be written as A(x, y u x + B(x, y u xy + C(x, y u u u + D(x, y

Διαβάστε περισσότερα

IXGK64N60B3D1 IXGX64N60B3D1

IXGK64N60B3D1 IXGX64N60B3D1 GenX3 TM 6V IGBT wih Diode Medium speed low Vsa PT IGBTs 5-4 khz swiching IXGK64N6B3D1 IXGX64N6B3D1 V CES = 6V 11 = 64A V CE(sa) 1.8V fi(yp) = 88ns TO-264 (IXGK) Symbol Tes Condiions Maximum Raings V CES

Διαβάστε περισσότερα

Reminders: linear functions

Reminders: linear functions Reminders: linear functions Let U and V be vector spaces over the same field F. Definition A function f : U V is linear if for every u 1, u 2 U, f (u 1 + u 2 ) = f (u 1 ) + f (u 2 ), and for every u U

Διαβάστε περισσότερα

Rektangulär fläns, Rectangular fin

Rektangulär fläns, Rectangular fin Rekangulär fläns, Recangular fin. Z d f d αc d λ ( f ) (3 3) m αc λ α Z λz α λ Randvillkor, Boundary condiions: : d : λ ( f ) d unn och lång fläns, long and hin fin d d f Rekangulär fläns, recangular fin

Διαβάστε περισσότερα

( ) ( t) ( 0) ( ) dw w. = = β. Then the solution of (1.1) is easily found to. wt = t+ t. We generalize this to the following nonlinear differential

( ) ( t) ( 0) ( ) dw w. = = β. Then the solution of (1.1) is easily found to. wt = t+ t. We generalize this to the following nonlinear differential Periodic oluion of van der Pol differenial equaion. by A. Arimoo Deparmen of Mahemaic Muahi Iniue of Technology Tokyo Japan in Seminar a Kiami Iniue of Technology January 8 9. Inroducion Le u conider a

Διαβάστε περισσότερα

Monolithic Crystal Filters (M.C.F.)

Monolithic Crystal Filters (M.C.F.) Monolithic Crystal Filters (M.C.F.) MCF (MONOLITHIC CRYSTAL FILTER) features high quality quartz resonators such as sharp cutoff characteristics, low loss, good inter-modulation and high stability over

Διαβάστε περισσότερα

6.4 Superposition of Linear Plane Progressive Waves

6.4 Superposition of Linear Plane Progressive Waves .0 - Marine Hydrodynamics, Spring 005 Lecture.0 - Marine Hydrodynamics Lecture 6.4 Superposition of Linear Plane Progressive Waves. Oblique Plane Waves z v k k k z v k = ( k, k z ) θ (Looking up the y-ais

Διαβάστε περισσότερα

A Control Method of Errors in Long-Term Integration

A Control Method of Errors in Long-Term Integration 1,a) Hamilon Runge Kua Hamilonian 1/2 Runge Kua (Brouwer s law) Runge Kua Runge Kua Hamilonian 1/2 Brouwer 3 A Conrol Mehod of Errors in Long-Term Inegraion Ozawa Kazufumi 1,a) Absrac: When solving he

Διαβάστε περισσότερα

= 0.927rad, t = 1.16ms

= 0.927rad, t = 1.16ms P 9. [a] ω = 2πf = 800rad/s, f = ω 2π = 27.32Hz [b] T = /f = 7.85ms [c] I m = 25mA [d] i(0) = 25cos(36.87 ) = 00mA [e] φ = 36.87 ; φ = 36.87 (2π) = 0.6435 rad 360 [f] i = 0 when 800t + 36.87 = 90. Now

Διαβάστε περισσότερα

Χρονοσειρές Μάθημα 3

Χρονοσειρές Μάθημα 3 Χρονοσειρές Μάθημα 3 Ασυσχέτιστες (λευκός θόρυβος) και ανεξάρτητες (iid) παρατηρήσεις Chafield C., The Analysis of Time Series, An Inroducion, 6 h ediion,. 38 (Chaer 3): Some auhors refer o make he weaker

Διαβάστε περισσότερα

TRM +4!5"2# 6!#!-!2&'!5$27!842//22&'9&2:1*;832<

TRM +4!52# 6!#!-!2&'!5$27!842//22&'9&2:1*;832< TRM!"#$%& ' *,-./ *!#!!%!&!3,&!$-!$./!!"#$%&'*" 4!5"# 6!#!-!&'!5$7!84//&'9&:*;83< #:4

Διαβάστε περισσότερα

Space Physics (I) [AP-3044] Lecture 1 by Ling-Hsiao Lyu Oct Lecture 1. Dipole Magnetic Field and Equations of Magnetic Field Lines

Space Physics (I) [AP-3044] Lecture 1 by Ling-Hsiao Lyu Oct Lecture 1. Dipole Magnetic Field and Equations of Magnetic Field Lines Space Physics (I) [AP-344] Lectue by Ling-Hsiao Lyu Oct. 2 Lectue. Dipole Magnetic Field and Equations of Magnetic Field Lines.. Dipole Magnetic Field Since = we can define = A (.) whee A is called the

Διαβάστε περισσότερα

Reservoir modeling. Reservoir modelling Linear reservoirs. The linear reservoir, no input. Starting up reservoir modeling

Reservoir modeling. Reservoir modelling Linear reservoirs. The linear reservoir, no input. Starting up reservoir modeling Reservoir modeling Reservoir modelling Linear reservoirs Paul Torfs Basic equaion for one reservoir:) change in sorage = sum of inflows minus ouflows = Q in,n Q ou,n n n jus an ordinary differenial equaion

Διαβάστε περισσότερα

Forced Pendulum Numerical approach

Forced Pendulum Numerical approach Numerical approach UiO April 8, 2014 Physical problem and equation We have a pendulum of length l, with mass m. The pendulum is subject to gravitation as well as both a forcing and linear resistance force.

Διαβάστε περισσότερα

University of Washington Department of Chemistry Chemistry 553 Spring Quarter 2010 Homework Assignment 3 Due 04/26/10

University of Washington Department of Chemistry Chemistry 553 Spring Quarter 2010 Homework Assignment 3 Due 04/26/10 Universiy of Washingon Deparmen of Chemisry Chemisry 553 Spring Quarer 1 Homework Assignmen 3 Due 4/6/1 v e v e A s ds: a) Show ha for large 1 and, (i.e. 1 >> and >>) he velociy auocorrelaion funcion 1)

Διαβάστε περισσότερα

Errata (Includes critical corrections only for the 1 st & 2 nd reprint)

Errata (Includes critical corrections only for the 1 st & 2 nd reprint) Wedesday, May 5, 3 Erraa (Icludes criical correcios oly for he s & d repri) Advaced Egieerig Mahemaics, 7e Peer V O eil ISB: 978474 Page # Descripio 38 ie 4: chage "w v a v " "w v a v " 46 ie : chage "y

Διαβάστε περισσότερα

ΕΙΣΑΓΩΓΗ ΣΤΗ ΣΤΑΤΙΣΤΙΚΗ ΑΝΑΛΥΣΗ

ΕΙΣΑΓΩΓΗ ΣΤΗ ΣΤΑΤΙΣΤΙΚΗ ΑΝΑΛΥΣΗ ΕΙΣΑΓΩΓΗ ΣΤΗ ΣΤΑΤΙΣΤΙΚΗ ΑΝΑΛΥΣΗ ΕΛΕΝΑ ΦΛΟΚΑ Επίκουρος Καθηγήτρια Τµήµα Φυσικής, Τοµέας Φυσικής Περιβάλλοντος- Μετεωρολογίας ΓΕΝΙΚΟΙ ΟΡΙΣΜΟΙ Πληθυσµός Σύνολο ατόµων ή αντικειµένων στα οποία αναφέρονται

Διαβάστε περισσότερα

Fractional Calculus. Student: Manal AL-Ali Dr. Abdalla Obeidat

Fractional Calculus. Student: Manal AL-Ali Dr. Abdalla Obeidat Fracional Calculu Suen: Manal AL-Ali Dr. Aballa Obeia Deignaion Deignaion mean inegraion an iffereniaion of arbirary orer, In oher ereion i mean ealing wih oeraor like,, i arbirary real or Comle value.

Διαβάστε περισσότερα

INDEX HOESUNG COIL PARTS

INDEX HOESUNG COIL PARTS 1. Metal Molding High Current SMD Power Inductor PART NO DEMINSION(mm) Inductance Range Rated DC Current Page MMI 06518 SERIES 6.5 7.1 1.8 1.0uH ~ 4.7uH 9.8A ~ 5.0A 5 MMI 06524 SERIES 6.5 7.1 2.4 0.47uH

Διαβάστε περισσότερα

6.003: Signals and Systems. Modulation

6.003: Signals and Systems. Modulation 6.003: Signals and Systems Modulation May 6, 200 Communications Systems Signals are not always well matched to the media through which we wish to transmit them. signal audio video internet applications

Διαβάστε περισσότερα

ECE Spring Prof. David R. Jackson ECE Dept. Notes 2

ECE Spring Prof. David R. Jackson ECE Dept. Notes 2 ECE 634 Spring 6 Prof. David R. Jackson ECE Dept. Notes Fields in a Source-Free Region Example: Radiation from an aperture y PEC E t x Aperture Assume the following choice of vector potentials: A F = =

Διαβάστε περισσότερα

Magnetically Coupled Circuits

Magnetically Coupled Circuits DR. GYURCSEK ISTVÁN Magnetically Coupled Circuits Sources and additional materials (recommended) Dr. Gyurcsek Dr. Elmer: Theories in Electric Circuits, GlobeEdit, 2016, ISBN:978-3-330-71341-3 Ch. Alexander,

Διαβάστε περισσότερα

Example Sheet 3 Solutions

Example Sheet 3 Solutions Example Sheet 3 Solutions. i Regular Sturm-Liouville. ii Singular Sturm-Liouville mixed boundary conditions. iii Not Sturm-Liouville ODE is not in Sturm-Liouville form. iv Regular Sturm-Liouville note

Διαβάστε περισσότερα

5. Αυτεπαγωγή-Χωρητικότητα Inductance Capacitance

5. Αυτεπαγωγή-Χωρητικότητα Inductance Capacitance 5. Αυτεπαγγή-Χρητικότητα nucance Capaciance Εδώ εισάγουµε τα δύο τελευταία στοιχεία κυκλµάτν, τα πηνία και τους πυκντές. Οι τεχνικές ανάλυσης κυκλµάτν που εισήχθικαν νρίτερα ακόµα ισχύουν εδώ. Ένα πηνίο

Διαβάστε περισσότερα

ECE 222b Applied Electromagnetics Notes Set 3a

ECE 222b Applied Electromagnetics Notes Set 3a C b lid lcomagnics Nos S 3a Insuco: Pof. Viali Lomakin Damn of lcical and Comu ngining Univsi of Califonia San Digo Unifom Plan Wavs Consid Mawll s quaions: In a losslss mdium ε and µ a al and σ : Sinc

Διαβάστε περισσότερα

Multimodal Oscillations: from Dopamine Neurons to Solid Fuel Combustion. Georgi Medvedev. Department of Mathematics, Drexel University

Multimodal Oscillations: from Dopamine Neurons to Solid Fuel Combustion. Georgi Medvedev. Department of Mathematics, Drexel University Mulimodal Oscillaions: from Dopamine Neurons o Solid Fuel Combusion Georgi Medvedev Deparmen of Mahemaics, Drexel Universiy Dopamine Neurons and Solid Fuel Wha? A mahemaician is he one, who finds analogies

Διαβάστε περισσότερα

George S. A. Shaker ECE477 Understanding Reflections in Media. Reflection in Media

George S. A. Shaker ECE477 Understanding Reflections in Media. Reflection in Media Geoge S. A. Shake C477 Udesadg Reflecos Meda Refleco Meda Ths hadou ages a smplfed appoach o udesad eflecos meda. As a sude C477, you ae o equed o kow hese seps by hea. I s jus o make you udesad how some

Διαβάστε περισσότερα

Breaking capacity: ~200kA Rated voltage: ~690V, 550V. Operating I 2 t-value (A 2 s) Power

Breaking capacity: ~200kA Rated voltage: ~690V, 550V. Operating I 2 t-value (A 2 s) Power SYSTEM NV-NH NV/NH SERIES TYPES gr UQ M M, M-striker pin ~ 5V ~9V Technical data on page 8 Technical data: Application: MCUQ/5A/9V Standards: IEC 9- Breaking capacity: ~ka Rated voltage: ~9V, 55V For battery

Διαβάστε περισσότερα

4.4 Superposition of Linear Plane Progressive Waves

4.4 Superposition of Linear Plane Progressive Waves .0 Marine Hydrodynamics, Fall 08 Lecture 6 Copyright c 08 MIT - Department of Mechanical Engineering, All rights reserved..0 - Marine Hydrodynamics Lecture 6 4.4 Superposition of Linear Plane Progressive

Διαβάστε περισσότερα

Second Order RLC Filters

Second Order RLC Filters ECEN 60 Circuits/Electronics Spring 007-0-07 P. Mathys Second Order RLC Filters RLC Lowpass Filter A passive RLC lowpass filter (LPF) circuit is shown in the following schematic. R L C v O (t) Using phasor

Διαβάστε περισσότερα

Derivation of Optical-Bloch Equations

Derivation of Optical-Bloch Equations Appendix C Derivation of Optical-Bloch Equations In this appendix the optical-bloch equations that give the populations and coherences for an idealized three-level Λ system, Fig. 3. on page 47, will be

Διαβάστε περισσότερα

Το άτομο του Υδρογόνου

Το άτομο του Υδρογόνου Το άτομο του Υδρογόνου Δυναμικό Coulomb Εξίσωση Schrödinger h e (, r, ) (, r, ) E (, r, ) m ψ θφ r ψ θφ = ψ θφ Συνθήκες ψ(, r θφ, ) = πεπερασμένη ψ( r ) = 0 ψ(, r θφ, ) =ψ(, r θφ+, ) π Επιτρεπτές ενέργειες

Διαβάστε περισσότερα

Dimensions in inches (mm)

Dimensions in inches (mm) SGMH Dimensions in inches (mm) () 3-Bit Incremental Encoder, without Brake 30 (0.04hp), 50 (0.07hp), 00 (0.3hp) ENCODER CBE, Φ0.24 (Φ6) U20276.8 (300) ±.8 (30) MOTOR CBE, Φ0.28 (Φ7) U88 or U3535.38 (35)

Διαβάστε περισσότερα

2.019 Design of Ocean Systems. Lecture 6. Seakeeping (II) February 21, 2011

2.019 Design of Ocean Systems. Lecture 6. Seakeeping (II) February 21, 2011 2.019 Design of Ocean Systems Lecture 6 Seakeeping (II) February 21, 2011 ω, λ,v p,v g Wave adiation Problem z ζ 3 (t) = ζ 3 cos(ωt) ζ 3 (t) = ω ζ 3 sin(ωt) ζ 3 (t) = ω 2 ζ3 cos(ωt) x 2a ~n Total: P (t)

Διαβάστε περισσότερα

DiracDelta. Notations. Primary definition. Specific values. General characteristics. Traditional name. Traditional notation

DiracDelta. Notations. Primary definition. Specific values. General characteristics. Traditional name. Traditional notation DiracDelta Notations Traditional name Dirac delta function Traditional notation x Mathematica StandardForm notation DiracDeltax Primary definition 4.03.02.000.0 x Π lim ε ; x ε0 x 2 2 ε Specific values

Διαβάστε περισσότερα

ITU-R BT ITU-R BT ( ) ITU-T J.61 (

ITU-R BT ITU-R BT ( ) ITU-T J.61 ( ITU-R BT.439- ITU-R BT.439- (26-2). ( ( ( ITU-T J.6 ( ITU-T J.6 ( ( 2 2 2 3 ITU-R BT.439-2 4 3 4 K : 5. ITU-R BT.24 :. ITU-T J.6. : T u ( ) () (S + L = M) :A :B :C : D :E :F :G :H :J :K :L :M :S :Tsy :Tlb

Διαβάστε περισσότερα

What happens when two or more waves overlap in a certain region of space at the same time?

What happens when two or more waves overlap in a certain region of space at the same time? Wave Superposition What happens when two or more waves overlap in a certain region of space at the same time? To find the resulting wave according to the principle of superposition we should sum the fields

Διαβάστε περισσότερα

Matrices and Determinants

Matrices and Determinants Matrices and Determinants SUBJECTIVE PROBLEMS: Q 1. For what value of k do the following system of equations possess a non-trivial (i.e., not all zero) solution over the set of rationals Q? x + ky + 3z

Διαβάστε περισσότερα

Analiza reakcji wybranych modeli

Analiza reakcji wybranych modeli Bank i Kredy 43 (4), 202, 85 8 www.bankikredy.nbp.pl www.bankandcredi.nbp.pl Analiza reakcji wybranych modeli 86 - - - srice - - - per capia research and developmen dynamic sochasic general equilibrium

Διαβάστε περισσότερα

Œ ˆ Œ Ÿ Œˆ Ÿ ˆŸŒˆ Œˆ Ÿ ˆ œ, Ä ÞŒ Å Š ˆ ˆ Œ Œ ˆˆ

Œ ˆ Œ Ÿ Œˆ Ÿ ˆŸŒˆ Œˆ Ÿ ˆ œ, Ä ÞŒ Å Š ˆ ˆ Œ Œ ˆˆ ˆ ˆŠ Œ ˆ ˆ Œ ƒ Ÿ 018.. 49.. 4.. 907Ä917 Œ ˆ Œ Ÿ Œˆ Ÿ ˆŸŒˆ Œˆ Ÿ ˆ œ, Ä ÞŒ Å Š ˆ ˆ Œ Œ ˆˆ.. ³μ, ˆ. ˆ. Ë μ μ,.. ³ ʲ μ ± Ë ²Ó Ò Ö Ò Í É Å μ ± ÊÎ μ- ² μ É ²Ó ± É ÉÊÉ Ô± ³ É ²Ó μ Ë ±, μ, μ Ö μ ² Ìμ μé Ê Ö ±

Διαβάστε περισσότερα

D Alembert s Solution to the Wave Equation

D Alembert s Solution to the Wave Equation D Alembert s Solution to the Wave Equation MATH 467 Partial Differential Equations J. Robert Buchanan Department of Mathematics Fall 2018 Objectives In this lesson we will learn: a change of variable technique

Διαβάστε περισσότερα

Introduction to Time Series Analysis. Lecture 16.

Introduction to Time Series Analysis. Lecture 16. Introduction to Time Series Analysis. Lecture 16. 1. Review: Spectral density 2. Examples 3. Spectral distribution function. 4. Autocovariance generating function and spectral density. 1 Review: Spectral

Διαβάστε περισσότερα

!! " # $%&'() * & +(&( 2010

!!  # $%&'() * & +(&( 2010 !!" #$%&'() *& (&( 00 !! VISNIK OF HE VOLODYMYR DAL EAS UKRAINIAN NAIONAL UNIVERSIY 8 (50) 00 8 (50) 00 HE SCIENIFIC JOURNAL " 996 WAS FOUNDED IN 996 " - - " I IS ISSUED WELVE IMES A YEAR "#$% Founder

Διαβάστε περισσότερα

4.6 Autoregressive Moving Average Model ARMA(1,1)

4.6 Autoregressive Moving Average Model ARMA(1,1) 84 CHAPTER 4. STATIONARY TS MODELS 4.6 Autoregressive Moving Average Model ARMA(,) This section is an introduction to a wide class of models ARMA(p,q) which we will consider in more detail later in this

Διαβάστε περισσότερα

ITU-R P ITU-R P (ITU-R 204/3 ( )

ITU-R P ITU-R P (ITU-R 204/3 ( ) 1 ITU-R P.530-1 ITU-R P.530-1 (ITU-R 04/3 ) (007-005-001-1999-1997-1995-1994-199-1990-1986-198-1978)... ( ( ( 1 1. 1 : - - ) - ( 1 ITU-R P.530-1..... 6.3. :. ITU-R P.45 -. ITU-R P.619 -. ) (ITU-R P.55

Διαβάστε περισσότερα

Key Formulas From Larson/Farber Elementary Statistics: Picturing the World, Second Edition 2002 Prentice Hall

Key Formulas From Larson/Farber Elementary Statistics: Picturing the World, Second Edition 2002 Prentice Hall 64_INS.qxd /6/0 :56 AM Page Key Formulas From Larson/Farber Elemenary Saisics: Picuring he World, Second Ediion 00 Prenice Hall CHAPTER Class Widh = round up o nex convenien number Maximum daa enry - Minimum

Διαβάστε περισσότερα

UNIVERSITÀ DI PISA. Plane waves 07/10/2011 1

UNIVERSITÀ DI PISA. Plane waves 07/10/2011 1 UNIVERSITÀ DI PISA Electromagnetic Radiations and Biological i l Interactions Laurea Magistrale in Biomedical Engineering First semester (6 credits), academic ear 11/1 Prof. Paolo Nepa p.nepa@iet.unipi.it

Διαβάστε περισσότερα

Motion of an Incompressible Fluid. with Unit Viscosity

Motion of an Incompressible Fluid. with Unit Viscosity Nonl. Analsis and Diffeenial Equaions Vol. 1 013 no. 3 143-148 HIKARI Ld www.m-hikai.com Moion of an Incompessible Fluid wih Uni Viscosi V. G. Gupa and Kapil Pal Depamen of Mahemaics Univesi of Rajashan

Διαβάστε περισσότερα

The Early Universe Big Bang Cosmology: Einstein Universe Friedmann-Lemaître Universe Einstein-deSitter Universe

The Early Universe Big Bang Cosmology: Einstein Universe Friedmann-Lemaître Universe Einstein-deSitter Universe Seminr The Erly Universe Big Bng Cosmology: Einsein Universe Friemnn-Lemîre Universe Einsein-eSier Universe by Oliver Schmi Ouline The observe universe Meric of he universe Curvure Einsein Equion Cosmologicl

Διαβάστε περισσότερα

MULTILAYER CHIP VARISTOR JMV S & E Series: (SMD Surge Protection)

MULTILAYER CHIP VARISTOR JMV S & E Series: (SMD Surge Protection) INTRODUCTION Metal Oxide based chip varistors (JMVs) are used for transient suppression. JMVs have non-linear - behavior, which is similar to that of Zener Diode. Each grain in JMV exhibits small p-n junction

Διαβάστε περισσότερα

CONSULTING Engineering Calculation Sheet

CONSULTING Engineering Calculation Sheet E N G I N E E R S Consulting Engineers jxxx 1 Structure Design - EQ Load Definition and EQ Effects v20 EQ Response Spectra in Direction X, Y, Z X-Dir Y-Dir Z-Dir Fundamental period of building, T 1 5.00

Διαβάστε περισσότερα

Parametrized Surfaces

Parametrized Surfaces Parametrized Surfaces Recall from our unit on vector-valued functions at the beginning of the semester that an R 3 -valued function c(t) in one parameter is a mapping of the form c : I R 3 where I is some

Διαβάστε περισσότερα

3.5 - Boundary Conditions for Potential Flow

3.5 - Boundary Conditions for Potential Flow 13.021 Marine Hydrodynamics, Fall 2004 Lecture 10 Copyright c 2004 MIT - Department of Ocean Engineering, All rights reserved. 13.021 - Marine Hydrodynamics Lecture 10 3.5 - Boundary Conditions for Potential

Διαβάστε περισσότερα

If we restrict the domain of y = sin x to [ π, π ], the restrict function. y = sin x, π 2 x π 2

If we restrict the domain of y = sin x to [ π, π ], the restrict function. y = sin x, π 2 x π 2 Chapter 3. Analytic Trigonometry 3.1 The inverse sine, cosine, and tangent functions 1. Review: Inverse function (1) f 1 (f(x)) = x for every x in the domain of f and f(f 1 (x)) = x for every x in the

Διαβάστε περισσότερα

Solar Neutrinos: Fluxes

Solar Neutrinos: Fluxes Solar Neutrinos: Fluxes pp chain Sun shines by : 4 p 4 He + e + + ν e + γ Solar Standard Model Fluxes CNO cycle e + N 13 =0.707MeV He 4 C 1 C 13 p p p p N 15 N 14 He 4 O 15 O 16 e + =0.997MeV O17

Διαβάστε περισσότερα

Coupling of a Jet-Slot Oscillator With the Flow-Supply Duct: Flow-Acoustic Interaction Modeling

Coupling of a Jet-Slot Oscillator With the Flow-Supply Duct: Flow-Acoustic Interaction Modeling 1th AIAA/CEAS Aeroacoustics Conference, May 006 interactions Coupling of a Jet-Slot Oscillator With the Flow-Supply Duct: Interaction M. Glesser 1, A. Billon 1, V. Valeau, and A. Sakout 1 mglesser@univ-lr.fr

Διαβάστε περισσότερα

Quartz Crystal Test Report

Quartz Crystal Test Report Quartz Crystal Test Report Abracon Part no. : Data Type: Page 2-3 Page 4-5 Page 6-7 Page 8-9 Page 10-11 ABM8-Series Crystal parameters & Spice Model ABM8-16.000MHz-10-1-U ABM8-13.000MHz-10-1-U ABM8-40.000MHz-10-1-U

Διαβάστε περισσότερα

If we restrict the domain of y = sin x to [ π 2, π 2

If we restrict the domain of y = sin x to [ π 2, π 2 Chapter 3. Analytic Trigonometry 3.1 The inverse sine, cosine, and tangent functions 1. Review: Inverse function (1) f 1 (f(x)) = x for every x in the domain of f and f(f 1 (x)) = x for every x in the

Διαβάστε περισσότερα

SOLUTIONS TO MATH38181 EXTREME VALUES AND FINANCIAL RISK EXAM

SOLUTIONS TO MATH38181 EXTREME VALUES AND FINANCIAL RISK EXAM SOLUTIONS TO MATH38181 EXTREME VALUES AND FINANCIAL RISK EXAM Solutions to Question 1 a) The cumulative distribution function of T conditional on N n is Pr T t N n) Pr max X 1,..., X N ) t N n) Pr max

Διαβάστε περισσότερα

Constitutive Relations in Chiral Media

Constitutive Relations in Chiral Media Constitutive Relations in Chiral Media Covariance and Chirality Coefficients in Biisotropic Materials Roger Scott Montana State University, Department of Physics March 2 nd, 2010 Optical Activity Polarization

Διαβάστε περισσότερα

First Sensor Quad APD Data Sheet Part Description QA TO Order #

First Sensor Quad APD Data Sheet Part Description QA TO Order # Responsivity (/W) First Sensor Quad PD Data Sheet Features Description pplication Pulsed 16 nm laser detection RoHS 211/65/EU Light source positioning Laser alignment ø mm total active area Segmented in

Διαβάστε περισσότερα

Π Ο Λ Ι Τ Ι Κ Α Κ Α Ι Σ Τ Ρ Α Τ Ι Ω Τ Ι Κ Α Γ Ε Γ Ο Ν Ο Τ Α

Π Ο Λ Ι Τ Ι Κ Α Κ Α Ι Σ Τ Ρ Α Τ Ι Ω Τ Ι Κ Α Γ Ε Γ Ο Ν Ο Τ Α Α Ρ Χ Α Ι Α Ι Σ Τ Ο Ρ Ι Α Π Ο Λ Ι Τ Ι Κ Α Κ Α Ι Σ Τ Ρ Α Τ Ι Ω Τ Ι Κ Α Γ Ε Γ Ο Ν Ο Τ Α Σ η µ ε ί ω σ η : σ υ ν ά δ ε λ φ ο ι, ν α µ ο υ σ υ γ χ ω ρ ή σ ε τ ε τ ο γ ρ ή γ ο ρ ο κ α ι α τ η µ έ λ η τ ο ύ

Διαβάστε περισσότερα

Large deviations of the density and of the current in non equilibrium steady states

Large deviations of the density and of the current in non equilibrium steady states Large deviaions of he densiy and of he curren in non equilibrium seady saes Bernard DERRIDA Universié Pierre e Marie Curie and Ecole Normale Supérieure, Paris June 2012 Lyon COLLABORATORS J.L. Lebowiz,

Διαβάστε περισσότερα

Review: Molecules = + + = + + Start with the full Hamiltonian. Use the Born-Oppenheimer approximation

Review: Molecules = + + = + + Start with the full Hamiltonian. Use the Born-Oppenheimer approximation Review: Molecules Start with the full amiltonian Ze e = + + ZZe A A B i A i me A ma ia, 4πε 0riA i< j4πε 0rij A< B4πε 0rAB Use the Born-Oppenheimer approximation elec Ze e = + + A A B i i me ia, 4πε 0riA

Διαβάστε περισσότερα

Vol. 40 No Journal of Jiangxi Normal University Natural Science Jul. 2016

Vol. 40 No Journal of Jiangxi Normal University Natural Science Jul. 2016 4 4 Vol 4 No 4 26 7 Journal of Jiangxi Normal Universiy Naural Science Jul 26-5862 26 4-349-5 3 2 6 2 67 3 3 O 77 9 A DOI 6357 /j cnki issn-5862 26 4 4 C q x' x /q G s = { α 2 - s -9 2 β 2 2 s α 2 - s

Διαβάστε περισσότερα

Χαρακτηρισµός Κυκλώµατος και Εκτίµηση Απόδοσης 2. Χαρακτηρισµός Κυκλώµατος

Χαρακτηρισµός Κυκλώµατος και Εκτίµηση Απόδοσης 2. Χαρακτηρισµός Κυκλώµατος 4 η Θεµατική Ενότητα : Χαρακτηρισµός Κυκλώµατος και Εκτίµηση Απόδοσης Επιµέλεια διαφανειών:. Μπακάλης Εισαγωγή Μια δοµή MOS προκύπτει από την υπέρθεση ενός αριθµού στρώσεων από µονωτικά και αγώγιµα υλικά

Διαβάστε περισσότερα

Lecture 2: Dirac notation and a review of linear algebra Read Sakurai chapter 1, Baym chatper 3

Lecture 2: Dirac notation and a review of linear algebra Read Sakurai chapter 1, Baym chatper 3 Lecture 2: Dirac notation and a review of linear algebra Read Sakurai chapter 1, Baym chatper 3 1 State vector space and the dual space Space of wavefunctions The space of wavefunctions is the set of all

Διαβάστε περισσότερα

linear motions: surge, sway, and heave rotations: roll, pitch, and yaw

linear motions: surge, sway, and heave rotations: roll, pitch, and yaw heave yaw when the ship is treated as a rigid body, it has six degrees of freedom: three linear motions and three rotations as indicated in the figure at the left: body-fixed axes pitch, v roll, u sway

Διαβάστε περισσότερα

INDIRECT ADAPTIVE CONTROL

INDIRECT ADAPTIVE CONTROL INDIREC ADAPIVE CONROL OULINE. Inroducion a. Main properies b. Running example. Adapive parameer esimaion a. Parameerized sysem model b. Linear parameric model c. Normalized gradien algorihm d. Normalized

Διαβάστε περισσότερα

Example 1: THE ELECTRIC DIPOLE

Example 1: THE ELECTRIC DIPOLE Example 1: THE ELECTRIC DIPOLE 1 The Electic Dipole: z + P + θ d _ Φ = Q 4πε + Q = Q 4πε 4πε 1 + 1 2 The Electic Dipole: d + _ z + Law of Cosines: θ A B α C A 2 = B 2 + C 2 2ABcosα P ± = 2 ( + d ) 2 2

Διαβάστε περισσότερα