Surfaces with holes in them: new plasmonic metamaterials

Size: px
Start display at page:

Download "Surfaces with holes in them: new plasmonic metamaterials"

Transcription

1 INSTITUTE OF PHYSICS PUBLISHING JOURNAL OF OPTICS A: PURE AND APPLIED OPTICS J Opt A: Pure Appl Opt 7 5 S97 S oi:88/ /7//3 Surfaces with holes in them: new plasmonic metamaterials FJGarcia-Vial,LMartín-Moreno an J B Penry 3 Departamento e Fisica Teorica e la Materia Conensaa, Universia Autonoma e Mari, E-849 Mari, Spain Departamento e Fisica e la Materia Conensaa, ICMA-CSIC, Universia e Zaragoza, E-59 Zaragoza, Spain 3 Imperial College Lonon, Department of Physics, The Blackett Laboratory, Lonon SW7 AZ, UK Receive June 4, accepte for publication 7 August 4 Publishe January 5 Online at stacksioporg/jopta/7/s97 Abstract In this paper weeplore the eistence of surface electromagnetic moes in corrugate surfaces of perfect conuctors We analyse two cases: one-imensional arrays of grooves an two-imensional arrays of holes In both cases we fin that these structures support surface boun states an that the ispersions of these moes have strong similarities with the ispersion of the surface plasmon polariton bans of real metals Importantly, the ispersion relation of these surface states is mainly ictate by the geometry of the grooves or holes an these results open the possibility of tailoring the properties of these moes by just tuning the geometrical parameters of the surface Keywors: surface plasmons, metamaterials, enhance transmission Some figures in this article are in colour only in the electronic version Introuction Since the appearance of the paper by Ebbesen et al [] reporting etraorinary optical transmission EOT in twoimensional D arrays of subwavelength holes in metallic films, the stuy of the optical properties of subwavelength apertures has become one of the most eciting areas in optics research In this seminal paper [], the relation between transmission resonances appearing in the spectra an the ecitation of the surface plasmon polaritons SPPs of the metallic surface was alreay pointe out The link between EOT an surface plasmons was corroborate theoretically three years after that [] Interestingly, in this last paper we also showe that similar anomalous transmission appears in arrays of subwavelength hole arrays perforate in a perfect conuctor It is well known that the surface of a perfect conuctor oes not support surface plasmons This seeme to suggest that the physical origins of EOT in real metals an in perfect conuctors were ifferent, leaing to iscussions asregars the true origin of the EOT phenomenon In this paper we solve this parao by showing that although a flat perfectly conucting surface supports no boun states, the presence of any perioic inentation of the flat surface for eample, D arrays of grooves or D hole arrays provokes the appearance of surface boun states that have strong similarities with the canonical SPPs of a flat metal surface [3, 4] Importantly, we also show that, as long as the size an spacing of the holes are much smaller than the wavelength, a perforate perfectly conucting surface behaves as an effective meium This meium is characterize by an effective ielectric function that has a plasmon form with a plasma frequency ictate by the geometry of the hole or the groove In other wors, the system behaves as a plasmonic metamaterial in which its electromagnetic response is governe by the surface moes that ecorate its surface It is worth commenting that this new class of metamaterials has some links with the metallic metamaterials invente in recent years in connection with the concept of negative refraction [5] D arrays of grooves First, we analyse the case of a D array of grooves rille in aperfect conuctor see figure a; a is the with of the grooves, h is the epth an the perio of the array We are intereste in looking at the surface EM moes supporte by /5/97+5$3 5 IOP Publishing Lt Printe in the UK S97

2 FJGarcia-Vial et al a b Figure a A one-imensional array of grooves of with a an epth h separate by a istance Weareintereste in p-polarize surface moes running in the irection with E lying in the z plane b In the effective meium approimation the structure isplaye in a behaves as an homogeneous but anisotropic layer of thickness h on top of a perfect conuctor this structure The proceure for calculating the ispersion relation of these surface moes, ωk,isthefollowing First, we calculate the reflectance of an incient p-polarize incient plane wave with parallel momentum k Asweareintereste in a truly surface moe, we will then analyse the epression for the reflectance for the particular case in which the incient plane wave is evanescent, k >ω/c a truly surface moe has tolive outsie the light cone The locations of the ivergences in the reflectance will give us the esire ispersion relation for the surface EM moes The electromagnetic EM fiels associate with the incient wave are E inc e ik e ikz z k /k z H inc e ik e ikz z k /k z where k is the wavenumber, ω/c,ank z k k The reflecte wave associate with the n-iffraction orer can be written as E ref,n e ikn H ref,n e ikn e ikn z z e ikn z z k n /k z n k /k z n where k n k +πn/ n,,,, an k z n k kn As we assume that the wavelength of light is much larger than the with of the grooves λ a, in the moal epansion of the EM fiels insie the grooves we only consier the funamental TE moe: E TE,± e ±ikz a H TE,± a e ±ik z Then, the EM fiels in region I vacuum can be epresse as a sum of the incient plane wave an the reflecte ones: E I E inc + H I H inc + n n ρ n E ref,n 3 ρ n H ref,n 4 where ρ n is the reflection coefficient associate with the iffraction orer n InregionIIinsiethe grooves, the EM fiels can be written as a linear combination of the forwar an backwar propagating TE moes: E II C + E TE,+ + C E TE, H II C + H TE,+ + C H TE, By applying the stanar matching bounary conitions at z continuity of E at every point of the unit cell an continuity of H y only at the groove s location an at z h; E must be zero, we can easily etract the reflection coefficients, ρ n : i tank hs S n k /k z ρ n δ n itank h n S n k /k z n 6 where S n is the overlap integral between the nth-orer plane wave an the TE moe: S n a a/ e ikn a/ a sink n k n a/ 5 a/ 7 In principle, we coul calculate the surface bans of our system by just analysing the zeros of the enominator of equation 6 [6] The calculation is much simpler if we assume λ Then, all the iffraction orers can be safely neglecte ecept the specular one an ρ takes the form ρ +is tank hk /k z is tank 8 hk /k z For the case k > k k z i k k,wecan calculate the ispersion relation of the surface boun state by calculating the location of the ivergences of ρ : k k S k tank h 9 This is the ispersion relation of the surface EM moes supporte by a D array of grooves in the limit λ an λ a It is interesting to note here that the same ispersion relation coul be obtaine if we replace the array of grooves S98

3 Surfaces with holes in them: new plasmonic metamaterials y z Figure 3 Atwo-imensional square array ofsquare holes sie aperforate on a semi-infinite perfect conuctor Figure The ispersion relation ωk ofthe surface boun states supporte by a D array of grooves with geometrical parameters a/ anh/ asobtaine with equation 4 by a single homogeneous but anisotropic layer of thickness h on top of the surface of a perfect conuctor see the schematic rawing in figure b The homogeneous layer woul have the following parameters: ɛ /a ɛ y ɛ z As light propagates in the grooves in the y or z irections with the velocity of light, ɛ µ y ɛ µ z an, hence, µ y µ z ɛ µ After some straightforwar algebra the specular reflection coefficient, R, for a p-polarize plane wave impinging at the surface of a homogeneous layer of thickness h with ɛ an µ given by equations an can be written as R ɛ k z k + k + ɛ k z e ikh 3 ɛ k z + k k ɛ k z eikh Again, by etening this formula to the case k > k an looking at the zeros of the enominator of R we can calculate the ispersion relation of the surface moes: k k a k tank h 4 Note that this epression coincies with equation 9 in the limit k a In figure we plot the ispersion relation equation 4 for the particular case a/ anh/ We have checke that this epression equation 4 gives accurate results for the range of wavelengths analyse in this case λ > 4h bycomparing them with the ispersion relation obtaine by calculating the zeros of the enominator of equation 6 in which the approimation λ is not applie It is worth commenting on the similarities between this ispersion an the one associate with the bans of SPPs supporte by the surfaces of real metals In a SPP ban, at large k, ω approaches ω p /, whereas in this case, ω approaches πc /h that is, the frequency location of a cavity waveguie moe insie the groove in the limit a/, the locations of the ifferent cavity waveguie moes correspon to the conition cos k h 3 D hole array Now we consier the caseofsquare holes of sie a arrange on a lattice perforate on a perfect conuctor semi-infinite structure see figure 3 [7] We assume that the holes are fille with a material whose ielectric constant is ɛ h Asinthe case of the array of grooves, we are intereste in looking at the possible surface states supporte by this system by looking at ivergences of the reflection coefficient of a p-polarize plane wave impinging at the perforate surface As we are intereste in the long wavelength limit λ, now we only take into account the specular reflecte wave The normalize EM fiels associate with the incient an specular reflecte waves are E inc eik e ikz z k /k z H inc eik e ikz z k /k z E ref e eik ikz z k /k z H ref e eik ikz z k /k z 5 6 Insie the holes, as we are intereste in the limit λ a, we assume that the funamental eigenmoe will ominate because it is the least strongly ecaying The EM fiels are zero insie the perfect metal but insie the holes they take the form E TE a eiqzz sin πy a where q z H TE ɛ h k π /a a eiqzz sin πy q z /k a iπ/ak 7 S99

4 FJGarcia-Vial et al Again, the EM fiels in region I can be epresse as a sum of the incient plane wave an the reflecte one: E I E inc + ρ E ref H I H inc + ρ H ref 8 where ρ is the specular reflection coefficient, an in region II insie the holes, as we are ealing with a semi-infinite structure, we only have to consier the ecaying moe: E II τ E TE H II τ H TE 9 where τ is the transmission coefficient In the matching proceure at z, E must be continuous over the entire unit cell an y ranging from an whereas H y has to be continuous only at the hole This woul yiel ρ k S q zk z k S + q zk z where S is the overlap integral of the incient plane wave an the funamental moe insie the hole: a a S e ik y sin πy a a y a sink a/ π k a/ By analysing the zeros of the enominator of ρ an etening the epression to k > k, we can etract the ispersion relation of the surface states supporte by the D hole array: k k k S k π /a ɛ h k As in the case of D arrays of grooves, we woul like to test whether the semi-infinite perfect conuctor perforate with holes coul be replace by a semi-infinite homogeneous system, characterize by an effective ielectric constant an an effective magnetic permeability Due to the symmetry of the structure, ɛ eff ɛ yeff ɛ eff an µ eff µ yeff µ eff Asthe ispersion of the waveguie moe insie the hole is unaffecte by parallel momentum, ɛ zeff µ zeff In a homogeneous structure, the reflection coefficient for a normally incient plane wave can be epresse as a function of the impeance of the meium, Z µ ɛ : R Z Z + 3 Then, the effective impeance of a D hole array perforate on a perfect conuctor can be easily calculate by analysing equation in the particular case of a normally incient plane wave k, k z k : µeff Z eff S k 4 ɛ eff q z where S S k a/π The other equation linking ɛ eff an µ eff can be obtaine from π q z k ɛeff µ eff i a ɛ hk 5 Figure 4 The ispersion relation ωk ofthep-polarize surface boun states supporte by a D array of holes with a/ 6an fille with a ielectric material with ine of refraction n h 3, as obtaine with equation 9 Combining equations 4 an 5 we can write own the effective magnetic permeability an effective ielectric permittivity of our system: µ eff µ yeff S 6 ɛ eff ɛ yeff ɛ h π S a ɛ h k ɛ h π c 7 S a ɛ h ω which isthe canonical plasmon form with a plasma frequency, ω pl πc / ɛ h athisfrequency is just the cut-off frequency of a square waveguie of sie a fille with a material characterize by a ielectric constant ɛ h The net step is to calculate the ispersion relation of the surface moes supporte by this effective meium an compare it with equation For an interface between vacuum an a semi-infinite structure characterize by ɛ eff,thesurface moes have to fulfil the equation k z + q z ɛ eff 8 where k z k i k is the inverse of the ecaying length of the surface moe insie the vacuum, e k z z,anq z is the analogue magnitue in the effective meium By using ɛ eff from equation 7 we obtain k k k S k π /a ɛ h k 9 which coincies with equation in the long wavelength limit when the effective meium approimation makes sense, k a In figure 4 we plot the ispersion relation of these surface moes for the particular case a/ 6 anɛ h 9 3 D arrays of holes of finite epth imples It is quite interesting to analyse also the case of a D square array ofsquare holes sie a offiniteepth, h The proceure for calculating the ispersion relation of the surface S

5 Surfaces with holes in them: new plasmonic metamaterials moes supporte by this type of structure is quite similar to the one presente for the previous case The only ifference is that in equation 9 we have to consier not only the ecaying moe e qz z but also the growing one, e + qz z : E II C + E TE,+ + C E TE, H II C + H TE,+ + C H TE, 3 Apart from the continuity equations at z, we have to a the conition E atthebottom of the hole, z h By oing straightforwar algebra, we en up with a ispersion relation of the surface moes: k k k S k π /a ɛ h k e qz h 3 +e qz h Note that in the limit h, k k light line an for h we recover equation 9, as we shoul 4 Conclusions We have emonstrate that a semi-infinite perfect conuctor perforate with a one-imensional array of grooves or a twoimensional array of holes can be optically escribe in the long wavelength limit as an effective meium characterize by a ielectric function of plasmon form in which the plasma frequency only epens on the geometry of the inentation groove or hole The surface moes supporte by this system have close resemblances with the surface plasmon polaritons of a real metal In these new plasmonic metamaterials, their electromagnetic response coul be engineere by tuning the geometrical parameters efining the corrugate surface Then, these tailore surface plasmons coul be moifie at will at almost any frequency because metals are nearly perfect conuctors from zero frequency up to the threshol of the THz regime Surface electromagnetic moes ecite at a metal surface can also be analyse as propagating waves in two imensions [8, 9] Our results coul be use as an alternative way to control the flow of light in the surface of a metal by just playing with the geometry size an separation of the inentations ispose at the surface Acknowlegments Financial support by the Spanish MCyT uner grant BES an contracts MAT-534 an MAT- 39 an by EC project FP6-NMP4-CT Surface Plasmon Photonics is gratefully acknowlege References [] Ebbesen T W, Lezec H J, Ghaemi H F, Thio T an Wolff P A 998 Nature [] Martín-Moreno L, Garcia-Vial F J, Lezec H J, Pellerin K M, Thio T, Penry J B an Ebbesen T W Phys RevLett 86 4 [3] Ritchie R H 957 Phys Rev [4] A very recent review of works relate to surface plasmons can be foun in: Barnes W L, Dereu A an Ebbesen T W 3 Nature [5] Penry J B, Holen A J, Robbins D J an Stewart W J 998 J Phys: Conens Matter 4785 Penry J B, Holen A J, Robbins D J an Stewart W J 999 IEEE Trans Microw Theory Tech [6] Garcia-Vial F J an Martín-Moreno L Phys Rev B [7] A previous theoretical analysis of this case although using a slightly ifferent approach can be foun in: Penry J B, Martín-Moreno L an Garcia-Vial F J 4 Science [8] Bozhevolnyi S I, Erlan J, Leosson K, Skovgaar P M an Hvam J M Phys RevLett [9] Ditlbacher H, Krenn J R, Schier G, Leitner A an Aussenegg F R Appl Phys Lett S

SOLUTIONS TO CONCEPTS CHAPTER 17

SOLUTIONS TO CONCEPTS CHAPTER 17 1. Given that, 400 m < < 700 nm. 1 1 1 700nm 400nm SOLUTIONS TO CONCETS CHATER 17 1 1 1 3 10 c 3 10 (Where, c = spee of light = 3 10 m/s) 7 7 7 7 7 10 4 10 7 10 4 10 4.3 10 14 < c/ < 7.5 10 14 4.3 10 14

More information

PHY101 Electricity and Magnetism I Course Summary

PHY101 Electricity and Magnetism I Course Summary TOPIC 1 ELECTROSTTICS PHY11 Electricity an Magnetism I Course Summary Coulomb s Law The magnitue of the force between two point charges is irectly proportional to the prouct of the charges an inversely

More information

Lecture L25-3D Rigid Body Kinematics

Lecture L25-3D Rigid Body Kinematics J. Peraire, S. Winall 16.07 Dynamics Fall 2008 Version 2.0 Lecture L25-3D Rigi Boy Kinematics In this lecture, we consier the motion of a 3D rigi boy. We shall see that in the general three-imensional

More information

Lagrangian and Hamiltonian Mechanics

Lagrangian and Hamiltonian Mechanics Lagrangian an Hamiltonian Mechanics D.G. Simpson, Ph.D. Department of Physical Sciences an Engineering Prince George s Community College December 5, 007 Introuction In this course we have been stuying

More information

DIFFRACTION AND INTERFERENCE

DIFFRACTION AND INTERFERENCE DIFFRACTION AND INTERFERENCE In this experiment you will emonstrate the wave nature of light by investigating how it bens aroun eges an how it interferes constructively an estructively. You will observe

More information

Answers to the Practice Problems for Test 2

Answers to the Practice Problems for Test 2 Answers to the Practice Problems for Test 2 Davi Murphy. Fin f (x) if it is known that x [f(2x)] = x2. By the chain rule, x [f(2x)] = f (2x) 2, so 2f (2x) = x 2. Hence f (2x) = x 2 /2, but the lefthan

More information

Terahertz transmission properties of an individual slit in a thin metallic plate

Terahertz transmission properties of an individual slit in a thin metallic plate Terahertz transmission properties of an individual slit in a thin metallic plate J. W. Lee, 1 T. H. Park, 2 Peter Nordlander, 2 and Daniel M. Mittleman 1,* 1 Department of Electrical and Computer Engineering,

More information

arxiv:1309.1857v3 [gr-qc] 7 Mar 2014

arxiv:1309.1857v3 [gr-qc] 7 Mar 2014 Generalize holographic equipartition for Friemann-Robertson-Walker universes Wen-Yuan Ai, Hua Chen, Xian-Ru Hu, an Jian-Bo Deng Institute of Theoretical Physics, LanZhou University, Lanzhou 730000, P.

More information

Inverse Trig Functions

Inverse Trig Functions Inverse Trig Functions c A Math Support Center Capsule February, 009 Introuction Just as trig functions arise in many applications, so o the inverse trig functions. What may be most surprising is that

More information

Measures of distance between samples: Euclidean

Measures of distance between samples: Euclidean 4- Chapter 4 Measures of istance between samples: Eucliean We will be talking a lot about istances in this book. The concept of istance between two samples or between two variables is funamental in multivariate

More information

Reading: Ryden chs. 3 & 4, Shu chs. 15 & 16. For the enthusiasts, Shu chs. 13 & 14.

Reading: Ryden chs. 3 & 4, Shu chs. 15 & 16. For the enthusiasts, Shu chs. 13 & 14. 7 Shocks Reaing: Ryen chs 3 & 4, Shu chs 5 & 6 For the enthusiasts, Shu chs 3 & 4 A goo article for further reaing: Shull & Draine, The physics of interstellar shock waves, in Interstellar processes; Proceeings

More information

On Adaboost and Optimal Betting Strategies

On Adaboost and Optimal Betting Strategies On Aaboost an Optimal Betting Strategies Pasquale Malacaria 1 an Fabrizio Smerali 1 1 School of Electronic Engineering an Computer Science, Queen Mary University of Lonon, Lonon, UK Abstract We explore

More information

10.2 Systems of Linear Equations: Matrices

10.2 Systems of Linear Equations: Matrices SECTION 0.2 Systems of Linear Equations: Matrices 7 0.2 Systems of Linear Equations: Matrices OBJECTIVES Write the Augmente Matrix of a System of Linear Equations 2 Write the System from the Augmente Matrix

More information

Definition of the spin current: The angular spin current and its physical consequences

Definition of the spin current: The angular spin current and its physical consequences Definition of the spin current: The angular spin current an its physical consequences Qing-feng Sun 1, * an X. C. Xie 2,3 1 Beijing National Lab for Conense Matter Physics an Institute of Physics, Chinese

More information

Chalcopyrite CuGaJn, -se2 semiconducting thin films produced by radio frequency sputtering

Chalcopyrite CuGaJn, -se2 semiconducting thin films produced by radio frequency sputtering Chalcopyrite CuGaJn, -se2 semiconucting thin films prouce by raio frequency sputtering J. L. HernAnez-Rojas, M. L. Lucfa, I. M&N, J. Santamaria, G. GonzAlez-Dfaaz, an F. Sgnchez-Quesaa Departamento e Electricia

More information

Introduction to Integration Part 1: Anti-Differentiation

Introduction to Integration Part 1: Anti-Differentiation Mathematics Learning Centre Introuction to Integration Part : Anti-Differentiation Mary Barnes c 999 University of Syney Contents For Reference. Table of erivatives......2 New notation.... 2 Introuction

More information

Unsteady Flow Visualization by Animating Evenly-Spaced Streamlines

Unsteady Flow Visualization by Animating Evenly-Spaced Streamlines EUROGRAPHICS 2000 / M. Gross an F.R.A. Hopgoo Volume 19, (2000), Number 3 (Guest Eitors) Unsteay Flow Visualization by Animating Evenly-Space Bruno Jobar an Wilfri Lefer Université u Littoral Côte Opale,

More information

FAST JOINING AND REPAIRING OF SANDWICH MATERIALS WITH DETACHABLE MECHANICAL CONNECTION TECHNOLOGY

FAST JOINING AND REPAIRING OF SANDWICH MATERIALS WITH DETACHABLE MECHANICAL CONNECTION TECHNOLOGY FAST JOINING AND REPAIRING OF SANDWICH MATERIALS WITH DETACHABLE MECHANICAL CONNECTION TECHNOLOGY Jörg Felhusen an Sivakumara K. Krishnamoorthy RWTH Aachen University, Chair an Insitute for Engineering

More information

Electronically Controlled Surface Plasmon Dispersion and Optical Transmission through Metallic Hole Arrays Using Liquid Crystal

Electronically Controlled Surface Plasmon Dispersion and Optical Transmission through Metallic Hole Arrays Using Liquid Crystal Electronically Controlled Surface Plasmon Dispersion and Optical Transmission through Metallic Hole Arrays Using Liquid Crystal NANO LETTERS 2008 Vol. 8, No. 1 281-286 Wayne Dickson,* Gregory A. Wurtz,

More information

Calculating Viscous Flow: Velocity Profiles in Rivers and Pipes

Calculating Viscous Flow: Velocity Profiles in Rivers and Pipes previous inex next Calculating Viscous Flow: Velocity Profiles in Rivers an Pipes Michael Fowler, UVa 9/8/1 Introuction In this lecture, we ll erive the velocity istribution for two examples of laminar

More information

Reflectance of a layered system with a gaussian distribution of the refractive index and inserted metamaterial

Reflectance of a layered system with a gaussian distribution of the refractive index and inserted metamaterial Reflectance of a layered system with a gaussian distribution of the refractive index and inserted metamaterial Xóchitl Saldaña Saldaña Instituto de Física de la Benemérita Universidad Autónoma de Puebla

More information

Exponential Functions: Differentiation and Integration. The Natural Exponential Function

Exponential Functions: Differentiation and Integration. The Natural Exponential Function 46_54.q //4 :59 PM Page 5 5 CHAPTER 5 Logarithmic, Eponential, an Other Transcenental Functions Section 5.4 f () = e f() = ln The inverse function of the natural logarithmic function is the natural eponential

More information

Lecture 10: TEM, TE, and TM Modes for Waveguides. Rectangular Waveguide.

Lecture 10: TEM, TE, and TM Modes for Waveguides. Rectangular Waveguide. Whites, EE 481/581 Lecture 10 Page 1 of 10 Lecture 10: TEM, TE, and TM Modes for Waveguides. Rectangular Waveguide. We will now generalie our discussion of transmission lines by considering EM waveguides.

More information

A Generalization of Sauer s Lemma to Classes of Large-Margin Functions

A Generalization of Sauer s Lemma to Classes of Large-Margin Functions A Generalization of Sauer s Lemma to Classes of Large-Margin Functions Joel Ratsaby University College Lonon Gower Street, Lonon WC1E 6BT, Unite Kingom J.Ratsaby@cs.ucl.ac.uk, WWW home page: http://www.cs.ucl.ac.uk/staff/j.ratsaby/

More information

JON HOLTAN. if P&C Insurance Ltd., Oslo, Norway ABSTRACT

JON HOLTAN. if P&C Insurance Ltd., Oslo, Norway ABSTRACT OPTIMAL INSURANCE COVERAGE UNDER BONUS-MALUS CONTRACTS BY JON HOLTAN if P&C Insurance Lt., Oslo, Norway ABSTRACT The paper analyses the questions: Shoul or shoul not an iniviual buy insurance? An if so,

More information

Purpose of the Experiments. Principles and Error Analysis. ε 0 is the dielectric constant,ε 0. ε r. = 8.854 10 12 F/m is the permittivity of

Purpose of the Experiments. Principles and Error Analysis. ε 0 is the dielectric constant,ε 0. ε r. = 8.854 10 12 F/m is the permittivity of Experiments with Parallel Plate Capacitors to Evaluate the Capacitance Calculation an Gauss Law in Electricity, an to Measure the Dielectric Constants of a Few Soli an Liqui Samples Table of Contents Purpose

More information

Ultra-broadband Microwave Metamaterial Absorber

Ultra-broadband Microwave Metamaterial Absorber Ultra-broadband Microwave Metamaterial Absorber Fei Ding 1, Yanxia Cui 1,3, Xiaochen Ge 1, Feng Zhang 1, Yi Jin 1*, and Sailing He 1,2 1 Centre for Optical and Electromagnetic Research, State Key Laboratory

More information

Achieving quality audio testing for mobile phones

Achieving quality audio testing for mobile phones Test & Measurement Achieving quality auio testing for mobile phones The auio capabilities of a cellular hanset provie the funamental interface between the user an the raio transceiver. Just as RF testing

More information

Example Optimization Problems selected from Section 4.7

Example Optimization Problems selected from Section 4.7 Example Optimization Problems selecte from Section 4.7 19) We are aske to fin the points ( X, Y ) on the ellipse 4x 2 + y 2 = 4 that are farthest away from the point ( 1, 0 ) ; as it happens, this point

More information

Products no longer available

Products no longer available Technical ata sheet R6..R haracterize control valves, 2-way, with flange PN 6 for open an close col an warm water systems for moulating control on the water sie of air-hanling an heating systems air bubble-tight

More information

An intertemporal model of the real exchange rate, stock market, and international debt dynamics: policy simulations

An intertemporal model of the real exchange rate, stock market, and international debt dynamics: policy simulations This page may be remove to conceal the ientities of the authors An intertemporal moel of the real exchange rate, stock market, an international ebt ynamics: policy simulations Saziye Gazioglu an W. Davi

More information

i( t) L i( t) 56mH 1.1A t = τ ln 1 = ln 1 ln 1 6.67ms

i( t) L i( t) 56mH 1.1A t = τ ln 1 = ln 1 ln 1 6.67ms Exam III PHY 49 Summer C July 16, 8 1. In the circuit shown, L = 56 mh, R = 4.6 Ω an V = 1. V. The switch S has been open for a long time then is suenly close at t =. At what value of t (in msec) will

More information

The one-year non-life insurance risk

The one-year non-life insurance risk The one-year non-life insurance risk Ohlsson, Esbjörn & Lauzeningks, Jan Abstract With few exceptions, the literature on non-life insurance reserve risk has been evote to the ultimo risk, the risk in the

More information

Almost Everything You Always Wanted to Know About the Toda Equation

Almost Everything You Always Wanted to Know About the Toda Equation Jahresber. Deutsch. Math.-Verein. 103, no. 4, 149-162 (2001) Mathematics Subject Classification: 35Q51, 37K10; 37K15, 39A70 Keywors an Phrases: Toa equation, Kac van Moerbeke equation, Solitons, Lax pair

More information

As customary, choice (a) is the correct answer in all the following problems.

As customary, choice (a) is the correct answer in all the following problems. PHY2049 Summer 2012 Instructor: Francisco Rojas Exam 1 As customary, choice (a) is the correct answer in all the following problems. Problem 1 A uniformly charge (thin) non-conucting ro is locate on the

More information

Analysis of Electromagnetic Propulsion on a Two-Electric-Dipole System

Analysis of Electromagnetic Propulsion on a Two-Electric-Dipole System Electronics and Communications in Japan, Part 2, Vol. 83, No. 4, 2000 Translated from Denshi Joho Tsushin Gakkai Ronbunshi, Vol. J82-C-I, No. 6, June 1999, pp. 310 317 Analysis of Electromagnetic Propulsion

More information

11 CHAPTER 11: FOOTINGS

11 CHAPTER 11: FOOTINGS CHAPTER ELEVEN FOOTINGS 1 11 CHAPTER 11: FOOTINGS 11.1 Introuction Footings are structural elements that transmit column or wall loas to the unerlying soil below the structure. Footings are esigne to transmit

More information

ELECTROMAGNETIC ANALYSIS AND COLD TEST OF A DISTRIBUTED WINDOW FOR A HIGH POWER GYROTRON

ELECTROMAGNETIC ANALYSIS AND COLD TEST OF A DISTRIBUTED WINDOW FOR A HIGH POWER GYROTRON ELECTROMAGNETIC ANALYSIS AND COLD TEST OF A DISTRIBUTED WINDOW FOR A HIGH POWER GYROTRON M.A.Shapiro, C.P.Moeller, and R.J.Temkin Plasma Science and Fusion Ceer, Massachusetts Institute of Technology,

More information

Inductors and Capacitors Energy Storage Devices

Inductors and Capacitors Energy Storage Devices Inuctors an Capacitors Energy Storage Devices Aims: To know: Basics of energy storage evices. Storage leas to time elays. Basic equations for inuctors an capacitors. To be able to o escribe: Energy storage

More information

Cross-Over Analysis Using T-Tests

Cross-Over Analysis Using T-Tests Chapter 35 Cross-Over Analysis Using -ests Introuction his proceure analyzes ata from a two-treatment, two-perio (x) cross-over esign. he response is assume to be a continuous ranom variable that follows

More information

Web Appendices to Selling to Overcon dent Consumers

Web Appendices to Selling to Overcon dent Consumers Web Appenices to Selling to Overcon ent Consumers Michael D. Grubb MIT Sloan School of Management Cambrige, MA 02142 mgrubbmit.eu www.mit.eu/~mgrubb May 2, 2008 B Option Pricing Intuition This appenix

More information

Fluid Pressure and Fluid Force

Fluid Pressure and Fluid Force 0_0707.q //0 : PM Page 07 SECTION 7.7 Section 7.7 Flui Pressure an Flui Force 07 Flui Pressure an Flui Force Fin flui pressure an flui force. Flui Pressure an Flui Force Swimmers know that the eeper an

More information

Homework 8. problems: 10.40, 10.73, 11.55, 12.43

Homework 8. problems: 10.40, 10.73, 11.55, 12.43 Hoework 8 probles: 0.0, 0.7,.55,. Proble 0.0 A block of ass kg an a block of ass 6 kg are connecte by a assless strint over a pulley in the shape of a soli isk having raius R0.5 an ass M0 kg. These blocks

More information

Math 230.01, Fall 2012: HW 1 Solutions

Math 230.01, Fall 2012: HW 1 Solutions Math 3., Fall : HW Solutions Problem (p.9 #). Suppose a wor is picke at ranom from this sentence. Fin: a) the chance the wor has at least letters; SOLUTION: All wors are equally likely to be chosen. The

More information

MASSACHUSETTS INSTITUTE OF TECHNOLOGY 6.436J/15.085J Fall 2008 Lecture 14 10/27/2008 MOMENT GENERATING FUNCTIONS

MASSACHUSETTS INSTITUTE OF TECHNOLOGY 6.436J/15.085J Fall 2008 Lecture 14 10/27/2008 MOMENT GENERATING FUNCTIONS MASSACHUSETTS INSTITUTE OF TECHNOLOGY 6.436J/15.085J Fall 2008 Lecture 14 10/27/2008 MOMENT GENERATING FUNCTIONS Contents 1. Moment generating functions 2. Sum of a ranom number of ranom variables 3. Transforms

More information

2 Metamaterials: Fundamental Revolution and Potential Future

2 Metamaterials: Fundamental Revolution and Potential Future 3 2 Metamaterials: Fundamental Revolution and Potential Future Materials properties have troubled scientists since old ages [1]. From an electromagnetic outlook, researchers have had different concerns

More information

MODELING OF PLANAR METAMATERIAL STRUCTURE AND ITS EFFECTIVE PARAMETER EXTRACTION

MODELING OF PLANAR METAMATERIAL STRUCTURE AND ITS EFFECTIVE PARAMETER EXTRACTION International Journal of Electronics and Communication Engineering & Technology (IJECET) Volume 7, Issue 1, Jan-Feb 2016, pp. 55-62, Article ID: IJECET_07_01_006 Available online at http://www.iaeme.com/ijecetissues.asp?jtype=ijecet&vtype=7&itype=1

More information

State of Louisiana Office of Information Technology. Change Management Plan

State of Louisiana Office of Information Technology. Change Management Plan State of Louisiana Office of Information Technology Change Management Plan Table of Contents Change Management Overview Change Management Plan Key Consierations Organizational Transition Stages Change

More information

The Classical Particle Coupled to External Electromagnetic Field Symmetries and Conserved Quantities. Resumo. Abstract

The Classical Particle Coupled to External Electromagnetic Field Symmetries and Conserved Quantities. Resumo. Abstract The Classical Particle Couple to External Electromagnetic Fiel Symmetries an Conserve Quantities G. D. Barbosa R. Thibes, Universiae Estaual o Suoeste a Bahia Departamento e Estuos Básicos e Instrumentais

More information

5. Scanning Near-Field Optical Microscopy 5.1. Resolution of conventional optical microscopy

5. Scanning Near-Field Optical Microscopy 5.1. Resolution of conventional optical microscopy 5. Scanning Near-Field Optical Microscopy 5.1. Resolution of conventional optical microscopy Resolution of optical microscope is limited by diffraction. Light going through an aperture makes diffraction

More information

Hybrid Model Predictive Control Applied to Production-Inventory Systems

Hybrid Model Predictive Control Applied to Production-Inventory Systems Preprint of paper to appear in the 18th IFAC Worl Congress, August 28 - Sept. 2, 211, Milan, Italy Hybri Moel Preictive Control Applie to Prouction-Inventory Systems Naresh N. Nanola Daniel E. Rivera Control

More information

Progress In Electromagnetics Research, Vol. 138, 647 660, 2013

Progress In Electromagnetics Research, Vol. 138, 647 660, 2013 Progress In Electromagnetics Research, Vol. 138, 647 660, 2013 FAR-FIELD TUNABLE NANO-FOCUSING BASED ON METALLIC SLITS SURROUNDED WITH NONLINEAR- VARIANT WIDTHS AND LINEAR-VARIANT DEPTHS OF CIRCULAR DIELECTRIC

More information

Notes on tangents to parabolas

Notes on tangents to parabolas Notes on tangents to parabolas (These are notes for a talk I gave on 2007 March 30.) The point of this talk is not to publicize new results. The most recent material in it is the concept of Bézier curves,

More information

Near Field Imaging with Magnetic Wires

Near Field Imaging with Magnetic Wires Near Field Imaging with Magnetic Wires M C K Wiltshire and J V Hajnal Imaging Sciences Department, Imperial College London, Hammersmith Hospital, Du Cane Road, London W12 HS, UK michael.wiltshire@imperial.ac.uk;

More information

An Alternative Approach of Operating a Passive RFID Device Embedded on Metallic Implants

An Alternative Approach of Operating a Passive RFID Device Embedded on Metallic Implants An Alternative Approach of Operating a Passive RFID Device Embee on Metallic Implants Xiaoyu Liu, Ravi Yalamanchili, Ajay Ogirala an Marlin Mickle RFID Center of Excellence, Department of Electrical an

More information

Sensitivity Analysis of Non-linear Performance with Probability Distortion

Sensitivity Analysis of Non-linear Performance with Probability Distortion Preprints of the 19th Worl Congress The International Feeration of Automatic Control Cape Town, South Africa. August 24-29, 214 Sensitivity Analysis of Non-linear Performance with Probability Distortion

More information

Detecting Possibly Fraudulent or Error-Prone Survey Data Using Benford s Law

Detecting Possibly Fraudulent or Error-Prone Survey Data Using Benford s Law Detecting Possibly Frauulent or Error-Prone Survey Data Using Benfor s Law Davi Swanson, Moon Jung Cho, John Eltinge U.S. Bureau of Labor Statistics 2 Massachusetts Ave., NE, Room 3650, Washington, DC

More information

Modelling and Resolving Software Dependencies

Modelling and Resolving Software Dependencies June 15, 2005 Abstract Many Linux istributions an other moern operating systems feature the explicit eclaration of (often complex) epenency relationships between the pieces of software

More information

SAR REDUCTION IN HUMAN HEAD FROM MOBILE PHONE RADIATION USING SINGLE NEGATIVE META- MATERIALS

SAR REDUCTION IN HUMAN HEAD FROM MOBILE PHONE RADIATION USING SINGLE NEGATIVE META- MATERIALS J. of Electromagn. Waves and Appl., Vol. 23, 1385 1395, 2009 SAR REDUCTION IN HUMAN HEAD FROM MOBILE PHONE RADIATION USING SINGLE NEGATIVE META- MATERIALS M. B. Manapati and R. S. Kshetrimayum Department

More information

Factoring Dickson polynomials over finite fields

Factoring Dickson polynomials over finite fields Factoring Dickson polynomials over finite fiels Manjul Bhargava Department of Mathematics, Princeton University. Princeton NJ 08544 manjul@math.princeton.eu Michael Zieve Department of Mathematics, University

More information

MODELLING OF TWO STRATEGIES IN INVENTORY CONTROL SYSTEM WITH RANDOM LEAD TIME AND DEMAND

MODELLING OF TWO STRATEGIES IN INVENTORY CONTROL SYSTEM WITH RANDOM LEAD TIME AND DEMAND art I. robobabilystic Moels Computer Moelling an New echnologies 27 Vol. No. 2-3 ransport an elecommunication Institute omonosova iga V-9 atvia MOEING OF WO AEGIE IN INVENOY CONO YEM WIH ANOM EA IME AN

More information

A wave lab inside a coaxial cable

A wave lab inside a coaxial cable INSTITUTE OF PHYSICS PUBLISHING Eur. J. Phys. 25 (2004) 581 591 EUROPEAN JOURNAL OF PHYSICS PII: S0143-0807(04)76273-X A wave lab inside a coaxial cable JoãoMSerra,MiguelCBrito,JMaiaAlves and A M Vallera

More information

Experimental retrieval of the effective parameters of metamaterials based on a waveguide method

Experimental retrieval of the effective parameters of metamaterials based on a waveguide method Experimental retrieval of the effective parameters of metamaterials based on a waveguide method Hongsheng Chen 1,3, Jingjing Zhang 1,, Yang Bai 4, Yu Luo 1,, Lixin Ran 1,, Qin Jiang 1, and Jin Au Kong

More information

The Quick Calculus Tutorial

The Quick Calculus Tutorial The Quick Calculus Tutorial This text is a quick introuction into Calculus ieas an techniques. It is esigne to help you if you take the Calculus base course Physics 211 at the same time with Calculus I,

More information

Calculation of overvoltages and interference voltages

Calculation of overvoltages and interference voltages Calculation of overvoltages an interference voltages When installing telecom or computer systems close to heavy current equipment or traction power supplies, careful thought has to be given to the possibility

More information

Kater Pendulum. Introduction. It is well-known result that the period T of a simple pendulum is given by. T = 2π

Kater Pendulum. Introduction. It is well-known result that the period T of a simple pendulum is given by. T = 2π Kater Penulum ntrouction t is well-known result that the perio of a simple penulum is given by π L g where L is the length. n principle, then, a penulum coul be use to measure g, the acceleration of gravity.

More information

Scalar : Vector : Equal vectors : Negative vectors : Proper vector : Null Vector (Zero Vector): Parallel vectors : Antiparallel vectors :

Scalar : Vector : Equal vectors : Negative vectors : Proper vector : Null Vector (Zero Vector): Parallel vectors : Antiparallel vectors : ELEMENTS OF VECTOS 1 Scalar : physical quantity having only magnitue but not associate with any irection is calle a scalar eg: time, mass, istance, spee, work, energy, power, pressure, temperature, electric

More information

Stock Market Value Prediction Using Neural Networks

Stock Market Value Prediction Using Neural Networks Stock Market Value Preiction Using Neural Networks Mahi Pakaman Naeini IT & Computer Engineering Department Islamic Aza University Paran Branch e-mail: m.pakaman@ece.ut.ac.ir Hamireza Taremian Engineering

More information

Reducing the Synchrotron Radiation on RF Cavity Surfaces in the proposed Cornell Energy-Recovery Linac

Reducing the Synchrotron Radiation on RF Cavity Surfaces in the proposed Cornell Energy-Recovery Linac Reucing the Synchrotron Raiation on RF Cavity Surfaces in the propose Cornell Energy-Recovery Linac G. H. Hoffstaetter, T. Tanabe February 8, 4 Report: Cornell ERL-4- Abstract It has been suggeste to buil

More information

Risk Management for Derivatives

Risk Management for Derivatives Risk Management or Derivatives he Greeks are coming the Greeks are coming! Managing risk is important to a large number o iniviuals an institutions he most unamental aspect o business is a process where

More information

The waveguide adapter consists of a rectangular part smoothly transcending into an elliptical part as seen in Figure 1.

The waveguide adapter consists of a rectangular part smoothly transcending into an elliptical part as seen in Figure 1. Waveguide Adapter Introduction This is a model of an adapter for microwave propagation in the transition between a rectangular and an elliptical waveguide. Such waveguide adapters are designed to keep

More information

View Synthesis by Image Mapping and Interpolation

View Synthesis by Image Mapping and Interpolation View Synthesis by Image Mapping an Interpolation Farris J. Halim Jesse S. Jin, School of Computer Science & Engineering, University of New South Wales Syney, NSW 05, Australia Basser epartment of Computer

More information

Lagrange s equations of motion for oscillating central-force field

Lagrange s equations of motion for oscillating central-force field Theoretical Mathematics & Applications, vol.3, no., 013, 99-115 ISSN: 179-9687 (print), 179-9709 (online) Scienpress Lt, 013 Lagrange s equations of motion for oscillating central-force fiel A.E. Eison

More information

5 Isotope effects on vibrational relaxation and hydrogen-bond dynamics in water

5 Isotope effects on vibrational relaxation and hydrogen-bond dynamics in water 5 Isotope effects on vibrational relaxation an hyrogen-bon ynamics in water Pump probe experiments HDO issolve in liqui H O show the spectral ynamics an the vibrational relaxation of the OD stretch vibration.

More information

Given three vectors A, B, andc. We list three products with formula (A B) C = B(A C) A(B C); A (B C) =B(A C) C(A B);

Given three vectors A, B, andc. We list three products with formula (A B) C = B(A C) A(B C); A (B C) =B(A C) C(A B); 1.1.4. Prouct of three vectors. Given three vectors A, B, anc. We list three proucts with formula (A B) C = B(A C) A(B C); A (B C) =B(A C) C(A B); a 1 a 2 a 3 (A B) C = b 1 b 2 b 3 c 1 c 2 c 3 where the

More information

Theoretical Considerations on Compensation of the Accommodation- Vergence Mismatch by Refractive Power of Focus-Adjustable 3D Glasses

Theoretical Considerations on Compensation of the Accommodation- Vergence Mismatch by Refractive Power of Focus-Adjustable 3D Glasses Theoretical Consierations on Compensation of the Accommoation- Vergence Mismatch by Refractive Power of Focus-Ajustable 3D Glasses Dal-Young Kim* Department of Optometry, Seoul National University of Science

More information

Parameterized Algorithms for d-hitting Set: the Weighted Case Henning Fernau. Univ. Trier, FB 4 Abteilung Informatik 54286 Trier, Germany

Parameterized Algorithms for d-hitting Set: the Weighted Case Henning Fernau. Univ. Trier, FB 4 Abteilung Informatik 54286 Trier, Germany Parameterize Algorithms for -Hitting Set: the Weighte Case Henning Fernau Trierer Forschungsberichte; Trier: Technical Reports Informatik / Mathematik No. 08-6, July 2008 Univ. Trier, FB 4 Abteilung Informatik

More information

New Trade Models, New Welfare Implications

New Trade Models, New Welfare Implications New Trae Moels, New Welfare Implications Marc J. Melitz Harvar University, NBER an CEPR Stephen J. Reing Princeton University, NBER an CEPR August 13, 2014 Abstract We show that enogenous firm selection

More information

Here the units used are radians and sin x = sin(x radians). Recall that sin x and cos x are defined and continuous everywhere and

Here the units used are radians and sin x = sin(x radians). Recall that sin x and cos x are defined and continuous everywhere and Lecture 9 : Derivatives of Trigonometric Functions (Please review Trigonometry uner Algebra/Precalculus Review on the class webpage.) In this section we will look at the erivatives of the trigonometric

More information

APPLICATION OF CALCULUS IN COMMERCE AND ECONOMICS

APPLICATION OF CALCULUS IN COMMERCE AND ECONOMICS Application of Calculus in Commerce an Economics 41 APPLICATION OF CALCULUS IN COMMERCE AND ECONOMICS æ We have learnt in calculus that when 'y' is a function of '', the erivative of y w.r.to i.e. y ö

More information

Optimizing Multiple Stock Trading Rules using Genetic Algorithms

Optimizing Multiple Stock Trading Rules using Genetic Algorithms Optimizing Multiple Stock Traing Rules using Genetic Algorithms Ariano Simões, Rui Neves, Nuno Horta Instituto as Telecomunicações, Instituto Superior Técnico Av. Rovisco Pais, 040-00 Lisboa, Portugal.

More information

Hull, Chapter 11 + Sections 17.1 and 17.2 Additional reference: John Cox and Mark Rubinstein, Options Markets, Chapter 5

Hull, Chapter 11 + Sections 17.1 and 17.2 Additional reference: John Cox and Mark Rubinstein, Options Markets, Chapter 5 Binomial Moel Hull, Chapter 11 + ections 17.1 an 17.2 Aitional reference: John Cox an Mark Rubinstein, Options Markets, Chapter 5 1. One-Perio Binomial Moel Creating synthetic options (replicating options)

More information

Using research evidence in mental health: user-rating and focus group study of clinicians preferences for a new clinical question-answering service

Using research evidence in mental health: user-rating and focus group study of clinicians preferences for a new clinical question-answering service DOI: 10.1111/j.1471-1842.2008.00833.x Using research evience in mental health: user-rating an focus group stuy of clinicians preferences for a new clinical question-answering service Elizabeth A. Barley*,

More information

BACKWARD WAVES AND NEGATIVE REFRACTION IN UNIAXIAL DIELECTRICS WITH NEGATIVE DIELECTRIC PERMITTIVITY ALONG THE ANISOTROPY AXIS

BACKWARD WAVES AND NEGATIVE REFRACTION IN UNIAXIAL DIELECTRICS WITH NEGATIVE DIELECTRIC PERMITTIVITY ALONG THE ANISOTROPY AXIS 2003 Wiley Periodicals, Inc. Reprinted, with permission, from P.A. Belov, Microwave and Optical Technology Letters, Vol. 37, No. 4, pp. 259-263, 2003. mere prototype; the same method can be extended to

More information

Heat-And-Mass Transfer Relationship to Determine Shear Stress in Tubular Membrane Systems Ratkovich, Nicolas Rios; Nopens, Ingmar

Heat-And-Mass Transfer Relationship to Determine Shear Stress in Tubular Membrane Systems Ratkovich, Nicolas Rios; Nopens, Ingmar Aalborg Universitet Heat-An-Mass Transfer Relationship to Determine Shear Stress in Tubular Membrane Systems Ratkovich, Nicolas Rios; Nopens, Ingmar Publishe in: International Journal of Heat an Mass Transfer

More information

Risk Adjustment for Poker Players

Risk Adjustment for Poker Players Risk Ajustment for Poker Players William Chin DePaul University, Chicago, Illinois Marc Ingenoso Conger Asset Management LLC, Chicago, Illinois September, 2006 Introuction In this article we consier risk

More information

4. Important theorems in quantum mechanics

4. Important theorems in quantum mechanics TFY4215 Kjemisk fysikk og kvantemekanikk - Tillegg 4 1 TILLEGG 4 4. Important theorems in quantum mechanics Before attacking three-imensional potentials in the next chapter, we shall in chapter 4 of this

More information

Metamaterials and Transformation Optics

Metamaterials and Transformation Optics AFRL-AFOSR-UK-TR-2011-0021 Metamaterials and Transformation Optics John Pendry Imperial College London Physics Department South Kensington Campus Exhibition Road London, United Kingdom SW7 2AZ EOARD GRANT

More information

Sage Match Terms and Conditions of Use (Last updated: 9 November 2015)

Sage Match Terms and Conditions of Use (Last updated: 9 November 2015) 1. Acknowlegement an Acceptance 1.1. This Agreement is between: (1) you, the person or organisation registere to use or using the Sage accountancy network service known as Sage Match ; an (2) us, as follows:

More information

Minimum-Energy Broadcast in All-Wireless Networks: NP-Completeness and Distribution Issues

Minimum-Energy Broadcast in All-Wireless Networks: NP-Completeness and Distribution Issues Minimum-Energy Broacast in All-Wireless Networks: NP-Completeness an Distribution Issues Mario Čagal LCA-EPFL CH-05 Lausanne Switzerlan mario.cagal@epfl.ch Jean-Pierre Hubaux LCA-EPFL CH-05 Lausanne Switzerlan

More information

Data Center Power System Reliability Beyond the 9 s: A Practical Approach

Data Center Power System Reliability Beyond the 9 s: A Practical Approach Data Center Power System Reliability Beyon the 9 s: A Practical Approach Bill Brown, P.E., Square D Critical Power Competency Center. Abstract Reliability has always been the focus of mission-critical

More information

Apertureless Near-Field Optical Microscopy

Apertureless Near-Field Optical Microscopy VI Apertureless Near-Field Optical Microscopy In recent years, several types of apertureless near-field optical microscopes have been developed 1,2,3,4,5,6,7. In such instruments, light scattered from

More information

1 High-Dimensional Space

1 High-Dimensional Space Contents High-Dimensional Space. Properties of High-Dimensional Space..................... 4. The High-Dimensional Sphere......................... 5.. The Sphere an the Cube in Higher Dimensions...........

More information

Mathematics. Circles. hsn.uk.net. Higher. Contents. Circles 119 HSN22400

Mathematics. Circles. hsn.uk.net. Higher. Contents. Circles 119 HSN22400 hsn.uk.net Higher Mathematics UNIT OUTCOME 4 Circles Contents Circles 119 1 Representing a Circle 119 Testing a Point 10 3 The General Equation of a Circle 10 4 Intersection of a Line an a Circle 1 5 Tangents

More information

Firewall Design: Consistency, Completeness, and Compactness

Firewall Design: Consistency, Completeness, and Compactness C IS COS YS TE MS Firewall Design: Consistency, Completeness, an Compactness Mohame G. Goua an Xiang-Yang Alex Liu Department of Computer Sciences The University of Texas at Austin Austin, Texas 78712-1188,

More information

Ch 10. Arithmetic Average Options and Asian Opitons

Ch 10. Arithmetic Average Options and Asian Opitons Ch 10. Arithmetic Average Options an Asian Opitons I. Asian Option an the Analytic Pricing Formula II. Binomial Tree Moel to Price Average Options III. Combination of Arithmetic Average an Reset Options

More information

15.2. First-Order Linear Differential Equations. First-Order Linear Differential Equations Bernoulli Equations Applications

15.2. First-Order Linear Differential Equations. First-Order Linear Differential Equations Bernoulli Equations Applications 00 CHAPTER 5 Differential Equations SECTION 5. First-Orer Linear Differential Equations First-Orer Linear Differential Equations Bernoulli Equations Applications First-Orer Linear Differential Equations

More information

Performance And Analysis Of Risk Assessment Methodologies In Information Security

Performance And Analysis Of Risk Assessment Methodologies In Information Security International Journal of Computer Trens an Technology (IJCTT) volume 4 Issue 10 October 2013 Performance An Analysis Of Risk Assessment ologies In Information Security K.V.D.Kiran #1, Saikrishna Mukkamala

More information

Optics and Spectroscopy at Surfaces and Interfaces

Optics and Spectroscopy at Surfaces and Interfaces Vladimir G. Bordo and Horst-Gunter Rubahn Optics and Spectroscopy at Surfaces and Interfaces WILEY- VCH WILEY-VCH Verlag GmbH & Co. KGaA Contents Preface IX 1 Introduction 1 2 Surfaces and Interfaces 5

More information

A Comparison of Performance Measures for Online Algorithms

A Comparison of Performance Measures for Online Algorithms A Comparison of Performance Measures for Online Algorithms Joan Boyar 1, Sany Irani 2, an Kim S. Larsen 1 1 Department of Mathematics an Computer Science, University of Southern Denmark, Campusvej 55,

More information