Haptic Manipulation of Virtual Materials for Medical Application


 Beatrix Baker
 2 years ago
 Views:
Transcription
1 Haptic Manipulation of Virtual Materials for Medical Application HIDETOSHI WAKAMATSU, SATORU HONMA Graduate Scool of Healt Care Sciences Tokyo Medical and Dental University, JAPAN ttp://www.tmd.ac.jp/med/mtec/wakamatsu/e_index.tm Abstract:  Te aptic and force display system is available for medical training despite some simple matematical models are required in order to realize various kinds of necessary environment. Our matematical model of mass, elasticity, viscosity and plasticity is applied to represent te various deformations of materials including teir destruction. We propose te metod for description of arbitral complicated forms of virtual organs and/or tools, introducing lattice planes for te construction and simple andling of virtual objects. Ten, we analyze te mutual interaction of virtual objects to clarify teir dynamical features. In consequence, we propose te new metods of kinetic process of contact and collision wit calculation of generating moments, wic yield te basic application of our metods to medical fields. KeyWords : Haptic and force display, Virtual material, Viscoelastoplastic model, Cutting tools, Deformation and destruction of objects 1 Introduction Pysical penomena ave been matematically described to clarify teir relating dynamics under te various kinds of conditions. However, tis kind of analysis as been sometimes purely matematical, and not used for te description of real time dynamic analysis because of computing restriction. Tat is, various penomena could not be treated simultaneously as a wole system to present teir dynamics even under te simple calculating condition. Meanwile, a force display system was useful to manipulate artificially realized environment, wic partly made it possible to feel dynamics as visual and aptic sense by te outside operation of virtual objects. [3,4,7]. But, te cutting of te objects was forced to perform in a restricted form of destruction, for wic we ave ever tried to use practically matematical model for te convenient calculation. Our recent tecnology of artificial reality as ensured te realization of various penomena as a wole[14,15]. Consequently, important pysical properties can be really taken into account in order to ave virtual experience and training in medical domain. Tat is, tis kind of tecnology is useful for te teme from te point of actual treatment of complicated systematic penomena. If we would apply te system to even unrealizable experience in simulated micro and macro spaces, tere would be still lots of difficulties practically from te various viewpoints. However, it is useful for suc temes, in wic aptic and force display systems are used as te one providing te experience by uman visual, aptic sense and so on [5,6]. Actually, we ave ever developed scissorstype[8,9], knifetype[13,14] and sawtype cutting tools wit teir control systems[16] and te matematical formulation of objects representing irreversible dynamics[16]. Considering te computing ability, te calculating time ave to be reduced by using appropriate matematical models, wic are accepted by users as smoot operation of going on time. 2 Syntesis of virtual material as viscoelastoplastic model 2.1 Development and improvement of model Te viscoelastic KelvinVoigt model was used for te dynamical representation of virtual objects [1,11]. Furter, extended distinct element metod was proposed[1], in wic rigid body was divided into teir certain size of portions beforeand. Aside from tem, a particle metod[2] was proposed, in wic liquid was represented by te mutual action of particle masses witin te definite distance among tem. It as ISBN:
2 been confirmed appropriate to describe fluid dynamics of destroyed objects represented by te set of a certain size of particles. However, tey are not always effective to represent te deformation and destruction of a rigid body. Tus, te syntesis of materials was extended to versatile ones wit plasticity in teir dynamic caracteristics beyond te elasticity. Te metod can realize te mutual action of objects, considering te collision of masses on te elements wic yield te kinds of destruction under te various conditions [14]. By te syntesis of concerning models in a virtual space, teir deformation and destruction including teir position and attitude are appropriately represented on te basis of pysical properties. 2.2 Needs of general matematical model Te pysically more appropriate reality could ave been described by te introduction of oter metods to realize te penomena, providing users wit teir actual experiences in a virtual space. However, te pysical and logical processes are not easy to describe exactly and precisely. Tus, it is reasonable to make analysis by extracting of substantial feature as our proposed metod [9,12,13]. By te way, in many aptic and force display systems, operational tools as rigid bodies ave been implemented, wic sometimes forced us to do unreasonable operation. Indeed, we proposed lots of utilities to medical system from te points of safety and etic problems, even if we would only apply te concerning systems as a pseudoclinical practice in need of education. Hereby, some internal organs and tools are syntesized reflecting sape and caracteristics by using te viscoelastoplastic model, and furter develop medical training systems by wic operational feeling is experienced reasonably wit aptic sense and reactive force on blood sampling and on cutting of brain tissues. Hereby, we sould be careful for te unnecessary tecniques to keep safety and to avoid etical problems, even if tey would be developed only for training. 2.3 Appropriate matematical description Virtual material is syntesized as a matematical model in order to represent its real time deformation and destruction in a virtual space. It is necessary to keep speedy calculation of all te state cange, because te operator as relations wit te cange of virtual materials at real time. In order to overcome suc difficulties, particularly in destruction wit its wole movement including structural cange, Honma and Wakamatsu introduced viscoelastoplastic model as a modified KelvinVoigt. In te basic tetraedron units, eac element as te modified KelvinVoigt model wit mass on eac apex. Tese elements are connected in a series and formed in an arbitrary sape, wic lead us to describe deformation and destruction due to te collision of te objects made of above materials. Tis kind deformation of objects is sufficiently enoug speedy calculated in a real time duration by using PC, wic is appropriate for te force display systems. 3 Matematical model of virtual material based on viscoelastoplasticity 3.1 Matematical explanation of pysically relating penomena As illustrated by Fig.1, stress and strain caracteristic curve of a material suc a metal is experimentally obtained concerning te expansion as indicated by solid lines [14]. In te case of te range witin limit of elasticity, a material as proportionally elastic deformation according to te applied force. Te limit of elasticity is a (a)yield point, beyond wic plastic deformation occurs by te furter stress wit never back to its original state as represented by te figure. From tis state, te stress is differently effective in nonlinear way corresponding to te exerting force, and it breaks after all on te limited point, namely (b)breaking point. Considering te force generation due to a different elasticity k 2 beyond te limit of specific elasticity, variable y p is defined as yielding distance ratio by using te ratio l/l of lengt l and mass L b p L y p l Stress Coefficient of elasticity k 2 (1) (2) (3) (b) breaking (a) yield point point Strain Coefficient of y ' 1 p b p 1 elasticity k 1 y p 1 Lengt corresponding to plastic strain l c Bauscinger effect l : Lengt of viscoelastoplastic element at time t L : Original lengt of viscoelastoplastic element l c : Lengt corresponding to plastic strain y p : Yielding distance ratio b p : Breaking distance ratio Pysical Value Approximate Value y p < l / L < b p y p y p ' Fig.1 Approximate representation based on te pysical property of material ISBN:
3 natural lengt L, and l/l at (b)breaking point is defined as breaking distance ratio b p (1< y p < b p ). If te force is taken off from te element wit te lengt between yielding ratio y p and breaking distance ratio b p, its lengt becomes sort according to specific elasticity k 1, but longer by l c tan natural lengt L, even if te force is taken off in tis case. Te state of an element, namely a modified 1dimemtional KelvinVoigt model is described by te picture on te superior region and by te explanation on te rigt region in Fig.1. Te lengt cange l c is a stretc lengt corresponding to plastic strain, were yielding distance ratio y p canges to y p ' = (l+l c )/L. For tis calculation of plastic strain related to stress, te metod as been proposed on te basis of broken line approximation as designated in te figure [14]. Te proposing model as strain according to Hooke's law, proportional to a given stress were te elastic constant is k 1. Beyond te limit of elasticity its elastic constant is regarded as k 2 proportional to stress. On te removal of te force in tis area, its lengt decreases by elastic constant k 1 proportional to te stress. It is remarked tat nonlinear cange of elastic constant from k 1 to k 2, in actual material, wit less or around natural lengt as Bauscinger effect, is not taken into account for te present discussion [14]. Tus, model of tetraedron unit does not completely correspond to actual caracteristics of material, but te virtual objects consisting of teir continuous arrangement can be syntesized by coosing appropriate pysical parameters to represent teir macro caracteristics. 3.2 Description of condition by matematical formulation In order to explain te broken line in Fig.1 matematically, te following dynamical kinetics are described in tree stages, taking into account te ratio of te lengt l /L of te element l and natural lengt L concerning t element at time t. <1> y p >l / L Tis is stress and strain of te element witin limit of elasticity and wen te stress is taken off from te unbroken element after te state beyond te limit of elasticity. In suc cases te strain is proportional to stress f wic is described by eq.(1) using own specific elastic constant k 1 and viscosity coefficient γ. f = k 1 ( l L lc ) γ dl dt (1) Hereby, l c is a stretc lengt by plastic strain. It is zero owever, if te element does not ave a ysteresis of stress and strain, but it is no longer zero, if tey are once beyond te limit of its elasticity. <2> y p <l / L < b p It is interpreted as te state of a concerning element around (a) yield point beyond te limit of elasticity. Te stress f is represented by eq.(2) using coefficient k 1 before aving reaced te yield point and using coefficient k 2 once on passing troug te yield point. f = k {( y p 1 ) L lc} + k ( l y pl ) γ dl dt (2) 1 2 After f is derived from eq.(2), variable y p as yielding distance ratio y p and plastic strain l c are substituted for y ' = l L andlc' = l L f k, respectively. 1 p <3>l / L > b p Te element is broken down in tis case, i.e. te stress f exposed to mass on te element is f = (3) were te connection coefficient η c = 1 canges to η c =, and dynamic state of te element is not calculated and displayed. 4 Virtual objects based on virtual materials on lattice planes 4.1 Arbitrary formation by te combination of matematical models As sown in Fig.2(a) a virtual material is syntesized by arranging tetraedrons consisting of masses and elements caracterized by te elasticity, viscosity and plasticity as illustrated by Fig.2(b). Te appropriate area covering anticipated objects are first given to fulfill its inside wit teir tetraedron units as aligns on planes. Tat is, virtual materials are arranged inside of te given envelop, in wic te cange in parameters of pysical properties can be easily described as nonuniformity of teir inner states. Te set of 2dimensional points on eac plane forms 1layer virtual material as described by (a) and (c) in Fig.2. In oter words, concerning layers of material on te plane are combined using elements wit te ones on next parallel planes. Te virtual object basically consists of virtual materials wit continuous regular arrangements of masses on te apexes of tetraedrons. Te arrangement forms a kind of lattice wit te straigt lines on te plane, wic are connected to te next one by te elements. If some parts of tetraedron units are expected out of te given area, te concerning masses on te elements are regarded not existing in te area. ISBN:
4 elasticity mass viscosity plasticity (b) elastoviscoplastic model (a) lattice plane Odd Layer Even Layer Connecting Edge Fig.2 Virtual material syntesized by te 2dimensionally continuous connection of tetraedron units on te settingup lattice plane ()original (3)disunion (1)restitution (4)crus (c) (2)crack (5)smas Fig.3 Classification of destructions after te collision of virtual materials to te floor Te syntesis of an object is explained on te basis of te equallydistance arrayed planes, on wic te parallel aligns of apexes are set. Terefore, it is possible to construct an arbitral form of object using virtual materials on lattice planes, on wic te apexes of tetraedrons actually mounted[9]. Even if te sape of object is complicated, te various sizes of lattice planes are set in every concerning section of te object in te same way. Te empty area after te above operation is regarded in existence of no material. 4.2 Te dynamical state of virtual objects obtained from virtual material According to Fig.3 we ereby mention te collision of () original spere illustrated falling down on te floor as an example. An object witin te limit of elastic deformation comes back to te (1)restitution form in an original state. Te states of objects are classified into five categories after te collisions of virtual spere to te floor including te state before te collision. Tat is, te plastic deformations of objects are largely classified into four states as (2)crack, (3)disunion, (4)crus and (5)smas. Hereby, te collision between masses is regarded as perfectly elastic, but as a wole, our metod does not represent perfectly elastic collision, because te elements contain viscosity and plasticity. Te ligt line represents te element wic moves witin te limit of elasticity given as initial condition. Te dark line represents not broken element beyond te limit of elasticity. Te (1)restitution is an illustration of sligt deformation by te stress after te collision. If y p is big enoug, te deformation is likely witin te limit of elasticity, tus te object tends to old te original sape, even after te colliding stress is taken off. Tat is, te object comes back to te original sape by its elastic stress, altoug deformation is observed in te process of collision. In te case of (2)crack, a certain site of te concerning spere will partly break down elements, wose stress are transmitted to te neigboring elements, causing furter deviation beyond te limit of elasticity but wit little destruction to keep its almost original sape. Tat is, te site of y p in greater tan te definite value as an exceeding strain beyond its elasticity. Incidentally te near site wit its easy impact propagation as te deviation beyond te limit of elasticity, so tat te relating elements may partly ave breaking damage. In te case of (3)disunion, some breaking occurs in a certain direction on a certain site of an object. In consequence, te spere divides into relatively big and small parts. Comparing wit te latter case of (5)smas, y p is a little bigger, even wit small difference between y p and b p. Tus, te definitely larger impact causes te state beyond te limit of elasticity. Te force impact propagates to some elements to ave mecanical effects in some rate of tem. On one side, it breaks tem in parts, but on te oter and some are not broken. Consequently, some sites break down by propagation of impact and te oter undestroyed ones witout propagation of stress are divided into several parts as illustrated in te figure. In te case of (4)crus, almost all te elements ave deviation from te limit of elasticity witout breaking down. Tat is, small y p wit relatively big difference between y p and b p, give te unbreakable ISBN:
5 caracteristics beyond te limit of elasticity, and it easily forms a kind of soft deformation as a wole. In (5)smas, te broken particles are largely stretced out and te spere objects are almost all fragmented into small scattering pieces. Te reason of above caracteristics is small y p wit a small difference between y p and b p, Tat is, te elements easily break down as a wole, even toug strains remain small, as tey readily ave strain beyond te limit of elasticity due to certain impact. 5 Representation of various objects consisting of virtual materials 5.1 Virtual objects in various state All possible forces exerted on masses are used for te dynamical calculation of previously mentioned models. Tereby, te mutual interaction of concerning parts of objects can be calculated as a wole, taking into account te collisions and/or cutting of teir elements as given by te positional relation of teir masses concerning virtual materials. To be more precise, outer masses of object are defined as ones to possibly collide wit eac oter. Tat is, te collision is tougt to occur wen te distance of masses becomes sorter tan te definite value. As tis metod is useful to compreend te mutual relation and interaction among objects in a virtual space, it is now rational to syntesize organs and tools by our previously mentioned virtual materials. 5.2 Relation of virtual organs and tools in various state In tis section, virtual organs and tools are mainly concerned, because it is necessary to cut open skins and teir neigboring area in some kinds of surgery, for wic scissors, knife and saw were developed as basic cutting tools depending on te situation. Indeed, Wakamatsu and Honma ave developed scissorstype, knifetype, sawtype tools and teir control systems for te joint use of suc file, cisel and rasp in training practice[6,7]. But te deformation and destruction of te tools temselves ad not been examined from teir availability in te aptic and force display systems, altoug tey ad to be considered from te various viewpoints of te caracteristics of teir tools. Tat is, for te use of above tools tere are still found problems in movements. Tat will be good discussions of te practical movement of operational tools, as tere are practically various surgical actions to organs in medical treatments In blood sampling, one of te most basic medical practices, skin area near blood vessel are in a kind of invasion process and te cutting of brain tissues are seriously invasive in te terapeutic operation. Te virtual operating tools ave dynamic interactions mutually wit te concerning organs according to teir matematical models on te basis of pysical properties of te site of action. Te invasive process by te system will be discussed in te next study. Hereby only te objects mainly wit te sapes of organs and tools are discussed, suc as blood vessel wit puncture needle and syringe and as brain wit knifetype tools in practice. 5.3 Objects in movement and deformation Internal organs are not easy to represent teir forms including pysical properties, because many different kinds of tissues suc as smoot muscle and striated muscle must be taken into account. In addition, teir matematical models may be very different to syntesize considering teir individual variations. However, it is practically possible to describe teir matematical outline, altoug tere must be required more calculation and operation, in order to display and feel reactive force resulting from mecanism of deformation and destruction of materials. Twist angle θ Center of axis 2n Sarpened angle θ 4n Diameter 2r Virtual object 1 Needlesape device Virtual object 2 Blood vessel Needle lengt l Swing angle θ 1n Point P Rotation angle θ 3n Fig. 4 Syntesis of puncture needle and blood vessel needle blood vessel (a) (b) Fig.5 Te virtual rigid puncture needle into blood vessel as tubular type objects ISBN:
6 Here, te objects are in appropriate sapes composed of te previously mentioned virtual materials in suitable areas. Teir concerning masses belonging to te same lattice plane are tereby continuously connected to form arranged segments between every regularly spaced planes. Te organs inclusive of pysical properties are generally classified into tubular, cavity or ollow type and solid type of tissues. Tus, in te process of deformation, cutting and perforation of te organs by te virtual operating tools, a blood vessel as a tubular organ and a brainlike spere as a solid organ were given by Fig.4(b) and Fig.6(b), respectively. Here, te sape and pysical properties are given by te parameters, wic do not always correspond to te actual caracteristics. In te present case, elastic coefficients are given smaller one to represent soft materials. 6 Modeling of organs and tools as virtual objects 6.1 Blood vessel and puncture needle by matematical model A blood sampling is one of te commonly necessary, but relatively simple tecniques for medical staff. Te concerning training is not sometimes enoug for te incidental action of sting and bite by te needle, for wic operators must get used to make progress in teir skill. For tis complementary use, some kinds of training system are expected to realize as aptic and force display systems. On blood sampling te edge of needle comes into te inner side of vessel by cutting te tissue. Ten, te blood is inspired troug needle into te syringe. However, necessary liquid model was not taken into account in te present study. Hereby, only te needle in contact wit puncturing site provides operators its state and relation to te skin and blood vessels. Te puncture needle for te blood sampling is syntesized as a tangential form of an edge on unsymmetrical tube as sown in Fig.4. Te state of tangential sampling needle are caracterized by swinging angle θ 1n, twist angle θ 2n, rotational angle θ 3n, sarpened angle θ 4n and diameter r, wic are all to move in an arbitrarily position and attitude in any place in a virtual space by a mouse operation. Te needle is in te present study considered as 1layer of continuous tetraedron rigid body wit a balance of te matematical model of blood vessel. Movement of point by mouseoperation Velocity of origin V 1 +Representative velocity of inner particle v 1 Representative velocity of inner particle v 2 Twist Rotation angle θ angle θ 3k 2k Swing Virtual object 3 angle θ 1k Knifesape device Virtual floor Virtual object 4 Brain (spere) Fig. 6 Relation between virtual knife and spere object knife (a) brain (b) Fig.7 Te cutting of brainlike spere as a solid object It is remarked tat 1layer of tetraedrons on a plane can be regarded as consisting of two complimentary layers, because te complementary empty area can be regarded as if it were filled wit new concerning tetraedrons. It is natural tat various diameter and layers of a needle is introduced according to te medical purposes. Hereby, teir necessary parameters are given as nearly corresponding to rigid body. Figure 4 illustrates te blood sampling using te syntesized needle by te operation of te mouse. Figure 5(a) is a skit of movement for a puncture of needle and (b) illustrates te relating view during te puncture. In tis simulation of blood vessel, parameters are cosen to caracterize relatively fragile ones. Tat makes sometimes a ole on blood vessel by little strain suc a sligt tremble on te operation, incidentally destruction of te edge of needle. Te edge of needle is realized not broken so tat te strain by te concentrated force may appear on te very edge of blood vessel. 6.2 Brain and knife by matematical model Virtual knifetype cutting tool is syntesized as platelike one as illustrated by Fig.6, consisting of 1layer of tetraedrons seen as teir complimentary 2layers. As a knife of metal as little cange of form comparing wit various elastic objects, we treat ere it ISBN:
7 as viscoelastoplastic model, taking into account tat its edge is sometimes broken on its operation. In order to provide te caracteristics of a rigid body, its elasticity was given as a bigger one, and teir masses were cosen from 1 to 1, times bigger tan te masses of virtual objects as internal organs. In addition, te parameters were given as tangential angle, twist, direction of knife, θ 1k, θ 2k, θ 3k, by wic its position and attitude are arbitrarily controlled by using a mouse in a virtual space. Tis discussion can contribute to a basic condition for te unification of aptic and force display system wit organs in order to design operational knifetype cutting devices. Figure 7(a) is a skit of movement for a cutting and (b) illustrates te relating view during te cutting. In te simulation of brain, parameters are cosen to caracterize relatively fragile ones. 7 Reactive Forces during te deformation and destruction Wen some virtual materials are processed by virtual tools, all te forces appear on corresponding colliding masses wit eac oter in our proposed models. Tus, te moment are calculated around arbitrarily setting point by te forces on masses and teir distance from te setting point. According to te attitude cange of operational tool wit relative position to te objects, te numbers of masses cange in every sampling time concerning wit teir relating collision. In addition, te forces exerted on te masses continuously cange according to operational speed and direction of te tools. Tus, even if te same object is operated by te same knifetype tool in te same way, te output moment is different according to te operational condition. Figures 8 describe te calculated moments around 3 axes, wic are sown as examples during te operation of Fig.5(b). In Fig.8, mutual interaction of needle and blood vessel due to its puncture operation is illustrated wit cutting moments around eac axis on te point cosen in a virtual space. Figure 8 give te resulting moments from blood sampling by operations of te syringe wit puncture needle. In te present case, te angle to te vessel is set to remain uncanged. However, te measured moments are different in eac operation because different operational conditions. If te operation is sufficiently enoug performed, tere appear muc fluctuations of canging components of forces and moments. Tis may be a Moment [Nm] around xaxis around yaxis 55 around zaxis Time [msec] Fig.8 Moment calculated from a set point in a virtual space on te operation in blood sampling wit slow speed. Moment [Nm] 11 around xaxis 11 around yaxis 11 around zaxis Time [msec] Fig.9 Moment calculated from a set point in a virtual space on te cutting of virtual brain wit slow speed in a vertical direction. reason wit numerical results wy a strange feeling of a pain and/or a foreign body at blood sampling are often experienced depending on te skill of medical staff. Figures 9 are skits of calculated moments of brainlike matematical model around x, y, zaxes on a set point in a virtual space, by cutting it by a virtual knife wit relatively speedy operation. Te cutting moment was observed as given by Fig.9, wen te knife moves in a vertical direction of te arrow along te plane as illustrated by Fig.7. Te figure explains tat te moment around yaxis increases, if te knife is lopsidedly inclined toward yaxis, and tat te one around xaxis increases, if te knife is inclined toward xaxis. 8 Discussion Te matematical model consists of reconstructed differential equations wit different parameters at any time. Tus, te deformation and destruction of te ISBN:
8 virtual materials are effectively represented at real time. We tougt tat every plane represented every surface of section of te object, te proposed metod is useful for te construction of te objects, especially in acquisition of slice pictures on every equallydistant plane. Tus, it is possible to syntesize virtual organs based on te form of teir actual ones from medical image. However, it is impossible to acquire pysical properties suc as density, elasticity, viscosity and plasticity from teir image data, tus, tese parameters ave to be determined from te experimental process. We mentioned tat te deformation and destruction related to te velocity and distance between arbitral two masses on te apexes and tat tere occurred perfect elastic collision, if te distance became less tan definite lengt. Tereby, te concerning coefficients of restitution cange according to te dynamics of te properties on te element. Suc mutual reaction could substantially well describe touc and collision of te virtual objects, resulting in basic cutting operation in te present study. Hereby, all of te reactive force exerted on te masses and te distance are taken into account for calculating moment, and te operator obtains te aptic and force feeling due to te reaction in accordance wit pysical properties of materials. In te present study two kinds of simulation were performed for anticipating medical training in te next occasion As for te first case, it is rater difficult to know te state of needle inserted into subcutaneous blood vessel. Its tecnical progress is very dependent on tactile sense troug syringe by te skill of medical staff. Tus, it is effective to offer tem te visualized information for te training situation. Tat is, our system does not enoug simulate te blood sampling at present, but it is our first step in suc simulation. As for te second case, it is sometimes important to take out te brain tissue as laboratory testing to make tissue specimen from brain tumor. For tis purpose it is sometimes necessary to cut off brain tissue by using te so called brain knife considering tat te proposed system will be a training macine. However, te practical pysical properties are not actually reflected to our syntesized system because of complicated anatomy and various tissues of brain, so tat we stand only in te very beginning as well as te former example. 9 Conclusion Te tetraedron units are applied to te basic structure of virtual organs and virtual tools by teir continuous arrangement in order to make aptic and force display systems for medical training. However, it is still difficult to formulate well matematical model of organs because it requires sometimes bigger and complicated database form for large size viscoelastoplastic models. Te metod was proposed on te basis of te combination of apexes set on te planes, and it was confirmed by simulation to contribute to te easy formation of an arbitral object wit general versatility. Practically, very basic models of blood vessel and brain were constructed to do some experimental tests by puncturetype and knifetype edged tools. Tese tools are represented as visual information of teir position, attitude and forms and for te calculation of reactive force at te same time. In any case, te process of deformation and destruction was well represented by te proposed metod at a critical point of pysical properties. Furtermore, it is also ensured to make various kinds of internal organs from te MRI image and to syntesize various tools readily. In consequence, it is possibly expected to construct medical simulator for training of surgery by using virtual entire body including various virtual internal organs wit a elp of aptic and force display systems. Hereby, also te parameters of te pysical properties of practical materials will be our important subjects for our furter study, wic supplies as our useful software libraries of virtual objects. Acknowledgment Te autors would like to express appreciation to te staff of Biopysical system Engineering laboratory at Tokyo Medical and Dental University for valuable discussion. References: [1]P.A. Cundall, O.D.L. Strack: "A discrete numerical model for granular assemblies", Geotecnique, No.29, pp.47 65, (1979) [2]E.G.Pavia, B.C.Roisin : "Modeling of oceanic fronts using a particle metod", J. Geopysical Researc, Vol.93, No.C4, pp (1988) [3] H. Wakamatsu, T. Imai: "Stereoscopic display of te inside image of rat brain by tree dimensional ISBN:
9 dissection metods", Int. Fed. Med. Biol. Eng., 29Suppl. Part1, p.123 (1991) [4] T. Imai, H. Wakamatsu: "Stereoscopic tree dimensional dissection of brain image by binocular parallax", Trans. IEE Jap., Vol.111C, No.6, pp (1991) [5]H. Wakamatsu, T. Imai, K. Okada: "Artificial realization of reactive force feeling on stereoscopic cutting of image of multilayer spere", Proc. 2nd Int. Conf. Image Process., pp (1992) [6] H. Wakamatsu, T.Imai: "Development of stereoscopic image cutting system wit reactive force feeling". Trans.IEE Jap., Vol.113C, No.9, pp (1993) [7] T. H. Massie, J. K. Salisbury: "Te PHANTOM Haptic Interface: A Device for Probing Virtual Objects", Symp. Haptic Interfaces (1994) [8] H.Wakamatsu: "Operational systems of stereoscopic cutting 3D virtual objects wit reactive feeling. Proc. IFAC 13t World Congr., Biomed. Control, ,(1996) [9] H. Wakamatsu, X. Zang, S. Honma: Teleoperational force display system in manipulation of virtual object using scissorstype cutting device", Proc. 3rd AsiaPacific Conf. Control & Meas., pp (1998) [1]K.Hirota, T.Kaneko: "A Study on te Model of an Elastic Virtual Object", Trans. Soc. Inst. Control Eng., Vol.34, No.3, pp (1998) [11]S. Honma, H. Wakamatsu, X. Zang: "Mecanics and Manipulation of Virtual Objects Represented by Viscoelastic Model", Trans. IEE Jap., Vol.119C, No.12, pp , (1999) [12]S.Honma, H. Wakamatsu: "Analysis of te Cutting Moment of Viscoelastic Material by a KnifeType Tool for Its Application to Force Display System", Trans. Soc. Instrum. Control Eng.", Vol.4, No.4, pp ,(24) [13]S. Honma, H. Wakamatsu: "Cutting Moment Analysis of Materials by te Saw for Force Display System", Trans. Virtual Reality Soc. Japan, Vol.9, No.3, pp (24) [14]S.Honma,H.Wakamatsu:"Realtime Representation of Destruction Process Considering Interaction between Two Virtual Objects", Trans. Soc. Inst. Control Eng., Vol.44, No.7, pp.668, (28) [15]S. Honma, H. Wakamatsu: "Cutting process of pysical models by a virtual knife based on an viscoelastoplastic model", National Convention Record IEE Japan, part 3, p.35 (326) (28) [16] S. Honma, H. Wakamatsu: "Unified Haptic System Using Tree Kinds of Cutting Devices for te Basic Use of Medical Application", Trans. IEE Jap., Vol.13C, No.1, (21) ISBN:
Research on the Antiperspective Correction Algorithm of QR Barcode
Researc on te Antiperspective Correction Algoritm of QR Barcode Jianua Li, YiWen Wang, YiJun Wang,Yi Cen, Guoceng Wang Key Laboratory of Electronic Tin Films and Integrated Devices University of Electronic
More informationThe EOQ Inventory Formula
Te EOQ Inventory Formula James M. Cargal Matematics Department Troy University Montgomery Campus A basic problem for businesses and manufacturers is, wen ordering supplies, to determine wat quantity of
More informationOptimized Data Indexing Algorithms for OLAP Systems
Database Systems Journal vol. I, no. 2/200 7 Optimized Data Indexing Algoritms for OLAP Systems Lucian BORNAZ Faculty of Cybernetics, Statistics and Economic Informatics Academy of Economic Studies, Bucarest
More informationVerifying Numerical Convergence Rates
1 Order of accuracy Verifying Numerical Convergence Rates We consider a numerical approximation of an exact value u. Te approximation depends on a small parameter, suc as te grid size or time step, and
More informationA LowTemperature Creep Experiment Using Common Solder
A LowTemperature Creep Experiment Using Common Solder L. Roy Bunnell, Materials Science Teacer Soutridge Hig Scool Kennewick, WA 99338 roy.bunnell@ksd.org Copyrigt: Edmonds Community College 2009 Abstract:
More informationModule 1: Introduction to Finite Element Analysis Lecture 1: Introduction
Module : Introduction to Finite Element Analysis Lecture : Introduction.. Introduction Te Finite Element Metod (FEM) is a numerical tecnique to find approximate solutions of partial differential equations.
More informationGeometric Stratification of Accounting Data
Stratification of Accounting Data Patricia Gunning * Jane Mary Horgan ** William Yancey *** Abstract: We suggest a new procedure for defining te boundaries of te strata in igly skewed populations, usual
More informationModule 2. The Science of Surface and Ground Water. Version 2 CE IIT, Kharagpur
Module Te Science of Surface and Ground Water Version CE IIT, Karagpur Lesson 6 Principles of Ground Water Flow Version CE IIT, Karagpur Instructional Objectives On completion of te lesson, te student
More informationOptimal Pricing Strategy for Second Degree Price Discrimination
Optimal Pricing Strategy for Second Degree Price Discrimination Alex O Brien May 5, 2005 Abstract Second Degree price discrimination is a coupon strategy tat allows all consumers access to te coupon. Purcases
More informationTrapezoid Rule. y 2. y L
Trapezoid Rule and Simpson s Rule c 2002, 2008, 200 Donald Kreider and Dwigt Lar Trapezoid Rule Many applications of calculus involve definite integrals. If we can find an antiderivative for te integrand,
More information7.6 Complex Fractions
Section 7.6 Comple Fractions 695 7.6 Comple Fractions In tis section we learn ow to simplify wat are called comple fractions, an eample of wic follows. 2 + 3 Note tat bot te numerator and denominator are
More information2 Limits and Derivatives
2 Limits and Derivatives 2.7 Tangent Lines, Velocity, and Derivatives A tangent line to a circle is a line tat intersects te circle at exactly one point. We would like to take tis idea of tangent line
More information2.28 EDGE Program. Introduction
Introduction Te Economic Diversification and Growt Enterprises Act became effective on 1 January 1995. Te creation of tis Act was to encourage new businesses to start or expand in Newfoundland and Labrador.
More informationME422 Mechanical Control Systems Modeling Fluid Systems
Cal Poly San Luis Obispo Mecanical Engineering ME422 Mecanical Control Systems Modeling Fluid Systems Owen/Ridgely, last update Mar 2003 Te dynamic euations for fluid flow are very similar to te dynamic
More information2.23 Gambling Rehabilitation Services. Introduction
2.23 Gambling Reabilitation Services Introduction Figure 1 Since 1995 provincial revenues from gambling activities ave increased over 56% from $69.2 million in 1995 to $108 million in 2004. Te majority
More informationTangent Lines and Rates of Change
Tangent Lines and Rates of Cange 922005 Given a function y = f(x), ow do you find te slope of te tangent line to te grap at te point P(a, f(a))? (I m tinking of te tangent line as a line tat just skims
More informationCan a LumpSum Transfer Make Everyone Enjoy the Gains. from Free Trade?
Can a LumpSum Transfer Make Everyone Enjoy te Gains from Free Trade? Yasukazu Icino Department of Economics, Konan University June 30, 2010 Abstract I examine lumpsum transfer rules to redistribute te
More informationWhat is Advanced Corporate Finance? What is finance? What is Corporate Finance? Deciding how to optimally manage a firm s assets and liabilities.
Wat is? Spring 2008 Note: Slides are on te web Wat is finance? Deciding ow to optimally manage a firm s assets and liabilities. Managing te costs and benefits associated wit te timing of cas in and outflows
More informationNotes: Most of the material in this chapter is taken from Young and Freedman, Chap. 12.
Capter 6. Fluid Mecanics Notes: Most of te material in tis capter is taken from Young and Freedman, Cap. 12. 6.1 Fluid Statics Fluids, i.e., substances tat can flow, are te subjects of tis capter. But
More informationM(0) = 1 M(1) = 2 M(h) = M(h 1) + M(h 2) + 1 (h > 1)
Insertion and Deletion in VL Trees Submitted in Partial Fulfillment of te Requirements for Dr. Eric Kaltofen s 66621: nalysis of lgoritms by Robert McCloskey December 14, 1984 1 ackground ccording to Knut
More informationLecture 10: What is a Function, definition, piecewise defined functions, difference quotient, domain of a function
Lecture 10: Wat is a Function, definition, piecewise defined functions, difference quotient, domain of a function A function arises wen one quantity depends on anoter. Many everyday relationsips between
More informationThis supplement is meant to be read after Venema s Section 9.2. Throughout this section, we assume all nine axioms of Euclidean geometry.
Mat 444/445 Geometry for Teacers Summer 2008 Supplement : Similar Triangles Tis supplement is meant to be read after Venema s Section 9.2. Trougout tis section, we assume all nine axioms of uclidean geometry.
More informationAn inquiry into the multiplier process in ISLM model
An inquiry into te multiplier process in ISLM model Autor: Li ziran Address: Li ziran, Room 409, Building 38#, Peing University, Beijing 00.87,PRC. Pone: (86) 0062763074 Internet Address: jefferson@water.pu.edu.cn
More informationComputer Vision System for Tracking Players in Sports Games
Computer Vision System for Tracking Players in Sports Games Abstract Janez Perš, Stanislav Kovacic Faculty of Electrical Engineering, University of Lublana Tržaška 5, 000 Lublana anez.pers@kiss.unil.si,
More informationPressure. Pressure. Atmospheric pressure. Conceptual example 1: Blood pressure. Pressure is force per unit area:
Pressure Pressure is force per unit area: F P = A Pressure Te direction of te force exerted on an object by a fluid is toward te object and perpendicular to its surface. At a microscopic level, te force
More informationFINITE DIFFERENCE METHODS
FINITE DIFFERENCE METHODS LONG CHEN Te best known metods, finite difference, consists of replacing eac derivative by a difference quotient in te classic formulation. It is simple to code and economic to
More informationReinforced Concrete Beam
Mecanics of Materials Reinforced Concrete Beam Concrete Beam Concrete Beam We will examine a concrete eam in ending P P A concrete eam is wat we call a composite eam It is made of two materials: concrete
More informationCollege Planning Using Cash Value Life Insurance
College Planning Using Cas Value Life Insurance CAUTION: Te advisor is urged to be extremely cautious of anoter college funding veicle wic provides a guaranteed return of premium immediately if funded
More informationDerivatives Math 120 Calculus I D Joyce, Fall 2013
Derivatives Mat 20 Calculus I D Joyce, Fall 203 Since we ave a good understanding of its, we can develop derivatives very quickly. Recall tat we defined te derivative f x of a function f at x to be te
More informationNew Vocabulary volume
. Plan Objectives To find te volume of a prism To find te volume of a cylinder Examples Finding Volume of a Rectangular Prism Finding Volume of a Triangular Prism 3 Finding Volume of a Cylinder Finding
More informationA strong credit score can help you score a lower rate on a mortgage
NET GAIN Scoring points for your financial future AS SEEN IN USA TODAY S MONEY SECTION, JULY 3, 2007 A strong credit score can elp you score a lower rate on a mortgage By Sandra Block Sales of existing
More informationTheoretical calculation of the heat capacity
eoretical calculation of te eat capacity Principle of equipartition of energy Heat capacity of ideal and real gases Heat capacity of solids: DulongPetit, Einstein, Debye models Heat capacity of metals
More informationAn Intuitive Framework for RealTime Freeform Modeling
An Intuitive Framework for RealTime Freeform Modeling Mario Botsc Leif Kobbelt Computer Grapics Group RWTH Aacen University Abstract We present a freeform modeling framework for unstructured triangle
More information1.6. Analyse Optimum Volume and Surface Area. Maximum Volume for a Given Surface Area. Example 1. Solution
1.6 Analyse Optimum Volume and Surface Area Estimation and oter informal metods of optimizing measures suc as surface area and volume often lead to reasonable solutions suc as te design of te tent in tis
More informationInstantaneous Rate of Change:
Instantaneous Rate of Cange: Last section we discovered tat te average rate of cange in F(x) can also be interpreted as te slope of a scant line. Te average rate of cange involves te cange in F(x) over
More informationACTIVITY: Deriving the Area Formula of a Trapezoid
4.3 Areas of Trapezoids a trapezoid? How can you derive a formula for te area of ACTIVITY: Deriving te Area Formula of a Trapezoid Work wit a partner. Use a piece of centimeter grid paper. a. Draw any
More informationSurface Areas of Prisms and Cylinders
12.2 TEXAS ESSENTIAL KNOWLEDGE AND SKILLS G.10.B G.11.C Surface Areas of Prisms and Cylinders Essential Question How can you find te surface area of a prism or a cylinder? Recall tat te surface area of
More informationSchedulability Analysis under Graph Routing in WirelessHART Networks
Scedulability Analysis under Grap Routing in WirelessHART Networks Abusayeed Saifulla, Dolvara Gunatilaka, Paras Tiwari, Mo Sa, Cenyang Lu, Bo Li Cengjie Wu, and Yixin Cen Department of Computer Science,
More informationMATHEMATICS FOR ENGINEERING DIFFERENTIATION TUTORIAL 1  BASIC DIFFERENTIATION
MATHEMATICS FOR ENGINEERING DIFFERENTIATION TUTORIAL 1  BASIC DIFFERENTIATION Tis tutorial is essential prerequisite material for anyone stuing mecanical engineering. Tis tutorial uses te principle of
More informationSAT Subject Math Level 1 Facts & Formulas
Numbers, Sequences, Factors Integers:..., 3, 2, 1, 0, 1, 2, 3,... Reals: integers plus fractions, decimals, and irrationals ( 2, 3, π, etc.) Order Of Operations: Aritmetic Sequences: PEMDAS (Parenteses
More informationQuasistatic Multilayer Electrical Modeling of Human Limb for IBC
Quasistatic Multilayer Electrical Modeling of Human Limb for IBC S H Pun 1,2, Y M Gao 2,3, P U Mak 1,2, M I Vai 1,2,3, and M Du 2,3 1 Department of Electrical and Electronics Engineering, Faculty of Science
More informationOPTIMAL DISCONTINUOUS GALERKIN METHODS FOR THE ACOUSTIC WAVE EQUATION IN HIGHER DIMENSIONS
OPTIMAL DISCONTINUOUS GALERKIN METHODS FOR THE ACOUSTIC WAVE EQUATION IN HIGHER DIMENSIONS ERIC T. CHUNG AND BJÖRN ENGQUIST Abstract. In tis paper, we developed and analyzed a new class of discontinuous
More informationA system to monitor the quality of automated coding of textual answers to open questions
Researc in Official Statistics Number 2/2001 A system to monitor te quality of automated coding of textual answers to open questions Stefania Maccia * and Marcello D Orazio ** Italian National Statistical
More informationComparison between two approaches to overload control in a Real Server: local or hybrid solutions?
Comparison between two approaces to overload control in a Real Server: local or ybrid solutions? S. Montagna and M. Pignolo Researc and Development Italtel S.p.A. Settimo Milanese, ITALY Abstract Tis wor
More informationUnderstanding the Derivative Backward and Forward by Dave Slomer
Understanding te Derivative Backward and Forward by Dave Slomer Slopes of lines are important, giving average rates of cange. Slopes of curves are even more important, giving instantaneous rates of cange.
More informationACT Math Facts & Formulas
Numbers, Sequences, Factors Integers:..., 3, 2, 1, 0, 1, 2, 3,... Rationals: fractions, tat is, anyting expressable as a ratio of integers Reals: integers plus rationals plus special numbers suc as
More informationSolution Derivations for Capa #7
Solution Derivations for Capa #7 1) Consider te beavior of te circuit, wen various values increase or decrease. (Select Iincreases, Ddecreases, If te first is I and te rest D, enter IDDDD). A) If R1
More information3D TOUCHLESS FINGERPRINTS: COMPATIBILITY WITH LEGACY ROLLED IMAGES. Department of Computer Science and Engineering East Lansing, Michigan, 48824
3D TOUCHLESS FINGERPRINTS: COMPATIBILITY WITH LEGACY ROLLED IMAGES Yi Cen 1, Geppy Parziale 2, Eva DiazSantana 2, and Anil K. Jain 1 1 Micigan State University Department of Computer Science and Engineering
More informationAreas and Centroids. Nothing. Straight Horizontal line. Straight Sloping Line. Parabola. Cubic
Constructing Sear and Moment Diagrams Areas and Centroids Curve Equation Sape Centroid (From Fat End of Figure) Area Noting Noting a x 0 Straigt Horizontal line /2 Straigt Sloping Line /3 /2 Paraola /4
More informationPerimeter, Area and Volume of Regular Shapes
Perimeter, Area and Volume of Regular Sapes Perimeter of Regular Polygons Perimeter means te total lengt of all sides, or distance around te edge of a polygon. For a polygon wit straigt sides tis is te
More informationA FLOW NETWORK ANALYSIS OF A LIQUID COOLING SYSTEM THAT INCORPORATES MICROCHANNEL HEAT SINKS
A FLOW NETWORK ANALYSIS OF A LIQUID COOLING SYSTEM THAT INCORPORATES MICROCHANNEL HEAT SINKS Amir Radmer and Suas V. Patankar Innovative Researc, Inc. 3025 Harbor Lane Nort, Suite 300 Plymout, MN 55447
More informationTAKEHOME EXP. # 2 A Calculation of the Circumference and Radius of the Earth
TAKEHOME EXP. # 2 A Calculation of te Circumference and Radius of te Eart On two dates during te year, te geometric relationsip of Eart to te Sun produces "equinox", a word literally meaning, "equal nigt"
More informationWe consider the problem of determining (for a short lifecycle) retail product initial and
Optimizing Inventory Replenisment of Retail Fasion Products Marsall Fiser Kumar Rajaram Anant Raman Te Warton Scool, University of Pennsylvania, 3620 Locust Walk, 3207 SHDH, Piladelpia, Pennsylvania 191046366
More informationh Understanding the safe operating principles and h Gaining maximum benefit and efficiency from your h Evaluating your testing system's performance
EXTRA TM Instron Services Revolve Around You It is everyting you expect from a global organization Te global training centers offer a complete educational service for users of advanced materials testing
More informationAreaSpecific Recreation Use Estimation Using the National Visitor Use Monitoring Program Data
United States Department of Agriculture Forest Service Pacific Nortwest Researc Station Researc Note PNWRN557 July 2007 AreaSpecific Recreation Use Estimation Using te National Visitor Use Monitoring
More informationMath 113 HW #5 Solutions
Mat 3 HW #5 Solutions. Exercise.5.6. Suppose f is continuous on [, 5] and te only solutions of te equation f(x) = 6 are x = and x =. If f() = 8, explain wy f(3) > 6. Answer: Suppose we ad tat f(3) 6. Ten
More informationIn other words the graph of the polynomial should pass through the points
Capter 3 Interpolation Interpolation is te problem of fitting a smoot curve troug a given set of points, generally as te grap of a function. It is useful at least in data analysis (interpolation is a form
More informationIs Gravity an Entropic Force?
Is Gravity an Entropic Force? San Gao Unit for HPS & Centre for Time, SOPHI, University of Sydney, Sydney, NSW 006, Australia; EMail: sgao7319@uni.sydney.edu.au Abstract: Te remarkable connections between
More informationSAMPLE DESIGN FOR THE TERRORISM RISK INSURANCE PROGRAM SURVEY
ASA Section on Survey Researc Metods SAMPLE DESIG FOR TE TERRORISM RISK ISURACE PROGRAM SURVEY G. ussain Coudry, Westat; Mats yfjäll, Statisticon; and Marianne Winglee, Westat G. ussain Coudry, Westat,
More informationStrategic trading in a dynamic noisy market. Dimitri Vayanos
LSE Researc Online Article (refereed) Strategic trading in a dynamic noisy market Dimitri Vayanos LSE as developed LSE Researc Online so tat users may access researc output of te Scool. Copyrigt and Moral
More informationMATHEMATICAL MODELS OF LIFE SUPPORT SYSTEMS Vol. I  Mathematical Models for Prediction of Climate  Dymnikov V.P.
MATHEMATICAL MODELS FOR PREDICTION OF CLIMATE Institute of Numerical Matematics, Russian Academy of Sciences, Moscow, Russia. Keywords: Modeling, climate system, climate, dynamic system, attractor, dimension,
More informationHEXAGON FLOWERS CUTTING OUT 1 COVERING THE FLOWERS 2
YOU WILL NEED Small scraps of fabric to cover fourteen exagons (includes enoug for front and back) Ribbon 6½in lengt Fourteen paper exagon templates (I used a size, but any would be fine, as long as you
More informationON LOCAL LIKELIHOOD DENSITY ESTIMATION WHEN THE BANDWIDTH IS LARGE
ON LOCAL LIKELIHOOD DENSITY ESTIMATION WHEN THE BANDWIDTH IS LARGE Byeong U. Park 1 and Young Kyung Lee 2 Department of Statistics, Seoul National University, Seoul, Korea Tae Yoon Kim 3 and Ceolyong Park
More informationOPTIMAL FLEET SELECTION FOR EARTHMOVING OPERATIONS
New Developments in Structural Engineering and Construction Yazdani, S. and Sing, A. (eds.) ISEC7, Honolulu, June 1823, 2013 OPTIMAL FLEET SELECTION FOR EARTHMOVING OPERATIONS JIALI FU 1, ERIK JENELIUS
More informationUnemployment insurance/severance payments and informality in developing countries
Unemployment insurance/severance payments and informality in developing countries David Bardey y and Fernando Jaramillo z First version: September 2011. Tis version: November 2011. Abstract We analyze
More informationDistances in random graphs with infinite mean degrees
Distances in random graps wit infinite mean degrees Henri van den Esker, Remco van der Hofstad, Gerard Hoogiemstra and Dmitri Znamenski April 26, 2005 Abstract We study random graps wit an i.i.d. degree
More informationSHAPE: A NEW BUSINESS ANALYTICS WEB PLATFORM FOR GETTING INSIGHTS ON ELECTRICAL LOAD PATTERNS
CIRED Worksop  Rome, 1112 June 2014 SAPE: A NEW BUSINESS ANALYTICS WEB PLATFORM FOR GETTING INSIGTS ON ELECTRICAL LOAD PATTERNS Diego Labate Paolo Giubbini Gianfranco Cicco Mario Ettorre Enel DistribuzioneItaly
More informationShell and Tube Heat Exchanger
Sell and Tube Heat Excanger MECH595 Introduction to Heat Transfer Professor M. Zenouzi Prepared by: Andrew Demedeiros, Ryan Ferguson, Bradford Powers November 19, 2009 1 Abstract 2 Contents Discussion
More informationFinite Difference Approximations
Capter Finite Difference Approximations Our goal is to approximate solutions to differential equations, i.e., to find a function (or some discrete approximation to tis function) tat satisfies a given relationsip
More informationFree Shipping and Repeat Buying on the Internet: Theory and Evidence
Free Sipping and Repeat Buying on te Internet: eory and Evidence Yingui Yang, Skander Essegaier and David R. Bell 1 June 13, 2005 1 Graduate Scool of Management, University of California at Davis (yiyang@ucdavis.edu)
More informationImproved dynamic programs for some batcing problems involving te maximum lateness criterion A P M Wagelmans Econometric Institute Erasmus University Rotterdam PO Box 1738, 3000 DR Rotterdam Te Neterlands
More informationDetermine the perimeter of a triangle using algebra Find the area of a triangle using the formula
Student Name: Date: Contact Person Name: Pone Number: Lesson 0 Perimeter, Area, and Similarity of Triangles Objectives Determine te perimeter of a triangle using algebra Find te area of a triangle using
More informationThe modelling of business rules for dashboard reporting using mutual information
8 t World IMACS / MODSIM Congress, Cairns, Australia 37 July 2009 ttp://mssanz.org.au/modsim09 Te modelling of business rules for dasboard reporting using mutual information Gregory Calbert Command, Control,
More informationThe finite element immersed boundary method: model, stability, and numerical results
Te finite element immersed boundary metod: model, stability, and numerical results Lucia Gastaldi Università di Brescia ttp://dm.ing.unibs.it/gastaldi/ INdAM Worksop, Cortona, September 18, 2006 Joint
More informationProjective Geometry. Projective Geometry
Euclidean versus Euclidean geometry describes sapes as tey are Properties of objects tat are uncanged by rigid motions» Lengts» Angles» Parallelism Projective geometry describes objects as tey appear Lengts,
More information2.15 Water Quality Management. Introduction
Introduction In May 2001, Government released a report entitled Source to Tap  Water Supplies in Newfoundland and Labrador (Source to Tap report). Te report was prepared in response to drinking water
More information 1  Handout #22 May 23, 2012 Huffman Encoding and Data Compression. CS106B Spring 2012. Handout by Julie Zelenski with minor edits by Keith Schwarz
CS106B Spring 01 Handout # May 3, 01 Huffman Encoding and Data Compression Handout by Julie Zelenski wit minor edits by Keit Scwarz In te early 1980s, personal computers ad ard disks tat were no larger
More informationMath Test Sections. The College Board: Expanding College Opportunity
Taking te SAT I: Reasoning Test Mat Test Sections Te materials in tese files are intended for individual use by students getting ready to take an SAT Program test; permission for any oter use must be sougt
More informationSecond Law Analysis of Parallel Plate Ducts with Span Wise Periodic Triangular Corrugations at one Wall
INTERNATIONAL JOURNAL OF MULTIDISCILINARY SCIENCES AND ENGINEERING, VOL., NO. 7, OCTOBER 011 Second La Analysis of arallel late Ducts it Span Wise eriodic Triangular Corrugations at one Wall Alireza Falaat
More informationCatalogue no. 12001XIE. Survey Methodology. December 2004
Catalogue no. 1001XIE Survey Metodology December 004 How to obtain more information Specific inquiries about tis product and related statistics or services sould be directed to: Business Survey Metods
More informationOn a Satellite Coverage
I. INTRODUCTION On a Satellite Coverage Problem DANNY T. CHI Kodak Berkeley Researc Yu T. su National Ciao Tbng University Te eart coverage area for a satellite in an Eart syncronous orbit wit a nonzero
More informationThe differential amplifier
DiffAmp.doc 1 Te differential amplifier Te emitter coupled differential amplifier output is V o = A d V d + A c V C Were V d = V 1 V 2 and V C = (V 1 + V 2 ) / 2 In te ideal differential amplifier A c
More informationTo motivate the notion of a variogram for a covariance stationary process, { Ys ( ): s R}
4. Variograms Te covariogram and its normalized form, te correlogram, are by far te most intuitive metods for summarizing te structure of spatial dependencies in a covariance stationary process. However,
More informationOverview of Component Search System SPARSJ
Overview of omponent Searc System Tetsuo Yamamoto*,Makoto Matsusita**, Katsuro Inoue** *Japan Science and Tecnology gency **Osaka University ac part nalysis part xperiment onclusion and Future work Motivation
More informationA NOVEL PASSIVE ENERGY DISSIPATION SYSTEM FOR FRAMECORE TUBE STRUCTURE
Te Sevent AsiaPacific Conference on Wind Engineering, November 8, 009, Taipei, Taiwan A NOVEL PASSIVE ENERGY DISSIPATION SYSTEM FOR FRAMECORE TUBE STRUCTURE Zengqing Cen and Ziao Wang Director, Wind
More informationELECTROMAGNETIC AND THERMAL PHENOMENA IN THE CONTROLLED PHASE TRANSFORMATION MELTING PROCESS
Journal of ELECTRICAL ENGINEERING, VOL. 57, NO., 2006, 36 4 ELECTROMAGNETIC AND THERMAL PHENOMENA IN THE CONTROLLED PHASE TRANSFORMATION MELTING PROCESS Ştefan Nagy Mojmír Kollár Tis paper presents te
More informationCharacterization of researchers in condensed matter physics using simple quantity based on h index. M. A. Pustovoit
Caracterization of researcers in condensed matter pysics using simple quantity based on index M. A. Pustovoit Petersburg Nuclear Pysics Institute, Gatcina Leningrad district 188300 Russia Analysis of
More informationComputer Science and Engineering, UCSD October 7, 1999 GoldreicLevin Teorem Autor: Bellare Te GoldreicLevin Teorem 1 Te problem We æx a an integer n for te lengt of te strings involved. If a is an nbit
More informationInverted pendulum systems: rotary and armdriven  a mechatronic system design case study
Mecatronics 12 2002) 357±370 Inverted pendulum systems: rotary and armdriven  a mecatronic system design case study S. Awtar, N. King, T. Allen, I. Bang, M. Hagan, D. Skidmore, K. Craig * Department
More informationWorking Capital 2013 UK plc s unproductive 69 billion
2013 Executive summary 2. Te level of excess working capital increased 3. UK sectors acieve a mixed performance 4. Size matters in te supply cain 6. Not all companies are overflowing wit cas 8. Excess
More informationCHAPTER TWO. f(x) Slope = f (3) = Rate of change of f at 3. x 3. f(1.001) f(1) Average velocity = 1.1 1 1.01 1. s(0.8) s(0) 0.8 0
CHAPTER TWO 2.1 SOLUTIONS 99 Solutions for Section 2.1 1. (a) Te average rate of cange is te slope of te secant line in Figure 2.1, wic sows tat tis slope is positive. (b) Te instantaneous rate of cange
More informationHeat Exchangers. Heat Exchanger Types. Heat Exchanger Types. Applied Heat Transfer Part Two. Topics of This chapter
Applied Heat Transfer Part Two Heat Excangers Dr. Amad RAMAZANI S.A. Associate Professor Sarif University of Tecnology انتقال حرارت کاربردی احمد رمضانی سعادت ا بادی Autumn, 1385 (2006) Ramazani, Heat Excangers
More informationPretrial Settlement with Imperfect Private Monitoring
Pretrial Settlement wit Imperfect Private Monitoring Mostafa Beskar University of New Hampsire JeeHyeong Park y Seoul National University July 2011 Incomplete, Do Not Circulate Abstract We model pretrial
More informationChapter 6 Tail Design
apter 6 Tail Design Moammad Sadraey Daniel Webster ollege Table of ontents apter 6... 74 Tail Design... 74 6.1. Introduction... 74 6.. Aircraft Trim Requirements... 78 6..1. Longitudinal Trim... 79 6...
More informationSpiral Physics. Modern Physics ... The Schrödinger Equation
.......... Spiral Pysics Modern Pysics.......... Te Scrödinger quation Copyrigt 3 Paul D Alessandris Spiral Pysics Rocester, NY 1463 All rigts reserved. No part of tis book may be reproduced or transmitted
More information1. Fluids Mechanics and Fluid Properties. 1.1 Objectives of this section. 1.2 Fluids
1. Fluids Mechanics and Fluid Properties What is fluid mechanics? As its name suggests it is the branch of applied mechanics concerned with the statics and dynamics of fluids  both liquids and gases.
More informationTorchmark Corporation 2001 Third Avenue South Birmingham, Alabama 35233 Contact: Joyce Lane 9725693627 NYSE Symbol: TMK
News Release Torcmark Corporation 2001 Tird Avenue Sout Birmingam, Alabama 35233 Contact: Joyce Lane 9725693627 NYSE Symbol: TMK TORCHMARK CORPORATION REPORTS FOURTH QUARTER AND YEAREND 2004 RESULTS
More informationAn Orientation to the Public Health System for Participants and Spectators
An Orientation to te Public Healt System for Participants and Spectators Presented by TEAM ORANGE CRUSH Pallisa Curtis, Illinois Department of Public Healt Lynn Galloway, Vermillion County Healt Department
More informationMultigrid computational methods are
M ULTIGRID C OMPUTING Wy Multigrid Metods Are So Efficient Originally introduced as a way to numerically solve elliptic boundaryvalue problems, multigrid metods, and teir various multiscale descendants,
More information