DEVELOPMENT OF A BRAKING MODEL FOR SPEED SUPERVISION SYSTEMS

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "DEVELOPMENT OF A BRAKING MODEL FOR SPEED SUPERVISION SYSTEMS"

Transcription

1 DEVELOPMENT OF A BRAKING MODEL FOR SPEED SUPERVISION SYSTEMS Paolo Presciani*, Monica Malvezzi #, Giuseppe Luigi Bonacci +, Monica Balli + * FS Trenitalia Unità Tecnologie Materiale Rotabile Direzione Tecnica Sperimentazione Viale S. Lavagnini Firenze Italy # University of Florence - Department of Energetics "Sergio Stecco" + FS Trenitalia Unità Tecnologie Materiale Rotabile Summary The monitoring curves of a spee control system are generally implemente through a moel escribing the braking performances of trains in terms of initial elay an braking eceleration. The paper presents a braking moel evelope to be employe in a new ATP system for the Italian railways. Such moel, base on the brake weight percentage, was erive from the UIC regulation so as to be applicable to all kin of trains an braking systems. Taking also into account the variability of the major parameters affecting the braking performances of trains, a probabilistic analysis is presente with the purpose of etermining the proper safety margins to be applie to the basic braking moel. Abstract To improve safety an efficiency in the management of railway traffic, a new spee control system name SCMT is currently being carrie out at the Italian Railways. Other innovative spee supervision systems are being evelope in Europe, such as the ETCS/ERTMS, which will be also installe on the new high spee line Roma-Napoli. All traffic management systems are generally base on a set of supervision curves relating the permitte velocity of the train to the running istance, in orer to ensure the respect of spee restrictions on the line by intervention of an emergency braking in case of train velocity exceeing the permitte one. These supervision systems must apply to all trains: passenger an freight trains of ifferent lengths, with various braking equipment, for all ranges of velocity. To elaborate this set of supervision curves, the on-boar unit nees train eceleration epening on time an spee, as basic information about the braking behaviour of the train. For high spee trains the knowlege of a eceleration profile is currently available, because moern UIC regulation requires the experimental assessment of this parameter. But the braking performances of conventional trains are usually expresse by the brake weight percentage, calculate through the weights an the brake weights of the vehicles which make up the train. The brake weights are usually etermine on the basis of stopping istances obtaine in tests, accoring to UIC leaflet The brake weight percentage is therefore an effective way of

2 expressing the capacity of the train to stop over a certain istance, when running at a efinite initial spee. However, this parameter oes not provie any information about the actual eceleration characteristics, which can wiely vary epening on the brake equipment. Therefore the implementation of a spee supervision system requires the preliminary efinition of braking moels which allow to convert the general parameters affecting the braking performances of trains (such as brake weight percentage, goos/passenger brake position, brake equipment, train length etc.) into a basic eceleration profile as function of time, uring the eceleration rise phase, an of spee, uring fully evelope braking. But this basic eceleration profile is not yet sufficient to buil the emergency brake intervention curve, because this one nees a guarantee eceleration profile, which can be obtaine from the basic profile using appropriate safety coefficients. The paper presents the braking moel evelope for the SCMT system, base on the UIC evaluation metho an applying to all trains, which enables to transform the available information concerning train an brake features into the essential input ata for a spee supervision system. This moel takes also into account the scattering of the eceleration ue to the main factors involve in the braking, in orer to obtain the require safety level of the emergency brake intervention curve. To evaluate the safety margins, a complete analysis of parameters affecting the braking performance was carrie out. For the major parameters, the probability istribution was etermine on the basis of technical knowlege an experimental results, in orer to establish the combine probability istribution for ifferent types of trains, thus enabling the assessment of the safety egree as function of a reuction factor applie to the basic eceleration. Keywors Braking moel; spee supervision system; brake weight percentage; safety margins; probabilistic analysis.. DEVELOPMENT OF THE BRAKING MODEL. Introuction For all the conventional rolling stock an for spee until km/h the basic parameter currently use for national an international traffic in orer to etermine the braking performance of a train is the brake weight percentage as efine by the UIC regulation. For this reason the braking moel evelope for SCMT is base on this regulation. Nevertheless, the information about the eceleration uring a fully evelope braking cannot be irectly erive from the UIC brake weight percentage. The brake weight of vehicles is usually pre-etermine by calculations an verifie by tests in line carrie out either on a single vehicle or on a train-set, using the evaluation iagrams of the UIC leaflet Such iagrams establish a relationship, for ifferent initial spees, between the brake weight percentage an the average stopping istance obtaine in emergency braking on level track, with a train having a nominal length an a braking equipment in normal operating conitions. Incientally it is also important to consier the tolerance of the friction coefficient of the braking components. Therefore, the brake weight percentage only gives information about the average performance of the train in emergency braking an it oes not inclue any safety margin. This funamental consieration has to be taken into account for the efinition of a braking moel applicable to spee control systems. In aition, a braking moel that is evelope for this purpose has to be applicable both to stop braking an to spee reuction braking.

3 . Definition of the braking moel for SCMT In general a braking moel can be represente as follows (fig. ): an initial elay, a linear or step transient, a series of constant eceleration steps within establishe spee ranges. v v v a a 3 a s Figure General braking moel As a particular case of that general representation, a braking moel with a step transient an one level of eceleration was efine for SCMT (fig. ), for the spee range until km/h. a t e t Figure Basic braking moel for SCMT The basic parameters of this moel are the following: t e braking equivalent time, eceleration of fully evelope braking. The step transient variant, even if less accurate than the linear transient variant, is wiely an effectively use for braking moels because it allows simpler calculations. For reasons of simplicity this representation refers to the situation on level track. The complete moel must obviously take into account the effect of the graient on the eceleration. As a consequence of the ifferent brake systems use on the vehicles (isc brake; cast iron block brake with one pressure level; cast iron block brake with two pressure levels etc.), also consiering 3

4 the possibility of mixe train-sets, the typical curves of the instantaneous eceleration may be ifferent for the same brake weight percentage, as shown in figure 3. isc brake block brake pressure levels block brake pressure level a v nom v Figure 3 Instantaneous eceleration of various types of brakes Possible evolutions in braking systems must be consiere, such as the replacement of cast iron brake blocks with composite brake blocks on freight wagons for noise reuction. A braking moel that will be use for a spee control system must also be applicable in intermeiate ranges of spee. For that reason the constant eceleration profile chosen for SCMT has to prevent that real eceleration profiles are overestimate in significant spee areas. The equivalent time epens on the goos/passenger brake position an on the length of the train. The eceleration epens on the type of brake equipment (isc brake, block brake etc.) an on the brake force. For this parameter it is necessary to etermine a relation with the brake weight percentage..3 Braking equivalent time The braking equivalent time t e is obtaine by aing the absolute elay an a half of the eceleration buil up time. The absolute elay represents the elay with which the eceleration ue to pneumatic braking appears, from the moment in which the braking is activate. The time necessary in emergency braking to reach the maximum eceleration ue to the pneumatic brake has been obtaine from iagrams of the ERRI report B6 RP5, proviing the braking time at the en of the train epening on the train length. The following formulas aopte for the present braking moel give the braking equivalent time as function of the train length L (m), in emergency braking: Passenger position: t e = (L / ) (.) Goos position: t e = (L / ) (.) Over a certain train length the equivalent time calculate by means of the passenger position formula excees the value calculate by means of the goos position formula: in this case even for the goos position the first formula is to be use. The iagrams relating to these formulas are shown in fig. 4. 4

5 Braking equivalent time 6 Equivalent time (s) 8 4 P position G position Train length (m) Figure 4 Equivalent time use for the braking moel.4 Relation between the brake weight percentage an the eceleration uring fully evelope braking.4. General consierations The purpose of the proceure escribe in this section is to establish a relation between the brake weight percentage an the eceleration uring fully evelope braking, base on the UIC evaluation metho (UIC leaflet 544-) an applicable to all kin of trains an braking systems. Therefore such relation oes not supply an average eceleration value linke to a certain brake weight percentage, but the minimum common value among those potentially linke to the same brake weight percentage, for ifferent braking systems an ifferent initial spees. The main criteria on which the evaluation curves of the UIC leaflet 544- are base were taken into account: the evaluation curve for km/h is especially applicable to freight trains with braking in passenger position; the evaluation curves for spee between an 6 km/h are base on the braking performance of trains with cast iron block brake, but they have general application for all passenger trains; the evaluation curves for 8 an km/h are specifically applicable to passenger trains with isc brake. The knowlege of such characteristics prevents from following the UIC increasing eceleration at spee lower than km/h for trains with isc brake or composite block brake, to avoi an overestimation of their braking performances..4. Deceleration relate to the UIC brake weight percentage The general formula of the UIC evaluation curves is the following: 5

6 S C = λ + D () where S is the stopping istance, λ the brake weight percentage, C an D the coefficients epening on the initial spee. For practical reasons in this proceure such formula was expresse in the following way: S C' V = λ + D (3) where V is the initial spee of braking an C' a new coefficient having a tren that is easier to interpolate for initial spees ifferent from the nominal ones. The corresponing eceleration values uring steay braking were calculate by the formula: = V 3.6 V S te 3.6 (4) where the total stopping istance S, given by the basic UIC formula, is reuce by the istance covere uring the braking equivalent time t e. An example of the results obtaine from the evaluation curves of the UIC leaflet 544- an of the ERRI report B 6 RP 7 is shown in fig. 5. UIC eceleration on steay braking with eq. time 4.35 s eceleration [m/s ] brake weight perc. 6% 4% % % 8%.6 6% initial spee [km/h] Figure 5 Deceleration uring fully evelope braking, calculate on the basis of UIC/ERRI iagrams Consiering the basic criteria establishe for this proceure, the minimum value of equivalent time relate to a train of nominal length is to be use for the calculation. In this way, a shorter istance being covere uring the equivalent time an a longer istance being covere uring constant braking, the calculation prouces a eceleration value that is minimum within the possible range. 6

7 .4.3 Basic relation between eceleration an brake weight percentage Since ifferent eceleration values epening on the initial spee of braking correspon to the same UIC brake weight percentage, it is important to choose the most suitable nominal conition for which the two parameters must be relate to each other. Among all the possible solutions, the following two were taken into particular consieration: the evaluation spee of km/h, accoring to the latest UIC irectives that are vali in particular for isc brakes; the stopping istance of m, accoring to the current UIC regulation. In case of high braking performances the first solution has the isavantage of proucing higher eceleration values on shorter braking istance; passenger trains equippe with cast iron block brake are not able to prouce such ecelerations in the spee range between an 6 km/h. The secon solution has the following avantages: it correspons to the UIC irective officially applicable until now, accoring to which most of the vehicles that are in service have been evaluate; it is generally applicable to ifferent braking systems such as isc brakes an block brakes; it allows to etermine a relationship between eceleration an brake weight percentage vali for initial spees increasing in a coherent way with the braking performances. Due to these significant avantages the secon solution has been aopte for the following proceure. This proceure consists of four steps: evaluation of the brake weight percentage values proucing a stopping istance of m for initial spees between an 6 km/h, through the UIC formula an iagrams; calculation of the constant values of maximum eceleration from the above mentione initial spees, using the minimum braking equivalent time, as explaine in the previous paragraph; these eceleration values are associate to the previously etermine brake weight percentages, etermination of the linear regression representing the eceleration as function of the brake weight percentage; evelopment of a further stuy to calculate the reuction of such basic eceleration above a spee threshol for the constant value. As concerns the braking equivalent time two ifferent hypotheses have been mae: t e = 3.5 s, as minimum absolute value; t e = 4.35 s, as minimum value for a train having a nominal length of 3 m. The linear relations which link the eceleration to the brake weight percentage in these two hypotheses are: I hyp. b =,647 λ +,3 (5.) II hyp. b =,685 λ +,94 (5.) that are characterize by a goo correlation coefficient. The couples of values "initial spee - brake weight percentage" for which these relations have been etermine are shown in table (approximate values). 7

8 λ % V in km/h Table Relation between the nominal spee an the brake weight percentage The iagrams of the linear regressions (5.) an (5.) are shown in fig. 6 an 7..3 Relation between brake weight percentage an steay eceleration for a stopping istance of m with an equivalent time of 3.5 s 6 km/h eceleration (m/s ) y =.647x +.35 R = km/h km/h km/h 4 km/h 5 km/h km/h brake weight percentage Figure 6 Linear regression for t e = 3.5 s.3 Relation between brake weight percentage an steay eceleration for a stopping istance of m with an equivalent time of 4.35 s eceleration (m/s ) y =.685x R = km/h km/h km/h 4 km/h 5 km/h 6 km/h km/h brake weight percentage Figure 7 Linear regression for t e = 4.35 s 8

9 .4.4 Deceleration as function of the initial spee of braking To take into account the behaviour of isc brake an composite block brake, in this braking moel the basic eceleration etermine by the proceure inicate above is applie as a constant value from initial spees lower than the spee threshol. For initial spees higher than the spee threshol it is necessary to apply a graual reuction of the eceleration uring fully evelope braking; this reuction can be assume as linear with a goo approximation, in coherence with the UIC evaluation curves. Even in case of a braking carrie out from a spee higher than the threshol, the new value of eceleration is consiere as constant over instantaneous spee. This characteristic behaviour is shown in fig. 8. b a V nom V in V max V Figure 8 Deceleration for initial spee higher than the spee threshol The relations between the eceleration an the brake weight percentage for initial braking spees exceeing the spee threshol, in the two previous hypotheses, become respectively: I hyp. = (,647 λ +,3) * (,(V V thr )) (6.) II hyp. = (,685 λ +,94) * (,(V V thr )) (6.) if V > V thr where such spee threshol is obtaine from the formula: V thr = 6,7 λ,443 (7) Compare to the ecelerations calculate from the UIC / ERRI evaluation curves, the formulas of this braking moel present the tenency shown in fig. 9. 9

10 eceleration [m/s ] Comparison between UIC eceleration for a t e = 4.35 s an braking moel eceleration initial spee [km/h] brake weight perc. 4% UIC 4% br.mo. % UIC % br.mo. 8% UIC 8% br.mo. 5% UIC 5% br.mo. Figure 9 Comparison between UIC/ERRI eceleration an braking moel eceleration As an alternative to the constant eceleration moel, the possibility has been consiere of replacing the constant eceleration uring the fully evelope braking with an instantaneous eceleration profile ecreasing in a linear way. The total ecrease shoul be equal to a fixe percentage (e.g. %) of the eceleration value calculate by the basic formula, being equivalent to this one from the point of view of the total braking istance (example in fig. ). This behaviour can be more appropriate in case of a spee reuction, for braking systems having a lower performance in a higher spee range. % a V o V in V inst Figure Alternative moel with a ecreasing eceleration profile.5 Remarks With the basic eceleration an the braking equivalent time etermine by the proceure escribe above the basic braking moel is achieve. Moreover, in orer to reuce the possibility of interference in the normal behaviour of the river, a ynamic reuction of the braking transient was inclue in the complete moel for SCMT, taking into account the eceleration alreay evelope by the safe brakes of the train.

11 However the basic eceleration values o not inclue any estimation about the necessary safety margins, so they cannot be irectly use to calculate the braking curves of a spee control system. The assessment of such safety margins, to be carrie out on the basis of an appropriate probabilistic analysis, is the subject of the next section.. PROBABILISTIC ANALYSIS APPLIED TO THE BRAKING MODEL. Braking moel The braking moel use in this analysis is the basic moel escribe in section. an represente in fig. : ' t t t Figure Braking moel use in the probabilistic analysis t represents the initial elay time; t is the time necessary to obtain the maximum eceleration; is the nominal eceleration value; is the eceleration value obtaine applying a safety coefficient. In this analysis, t an t variability is neglecte an the ispersion of the braking performance is exclusively relate to the variability of eceleration, that is consiere the funamental parameter an is consequently reuce using a proper safety coefficient. In this paper the analysis was carrie out using information relative to a passenger train equippe with isc brake. Similar consierations can be mae for ifferent types of trains (e.g. freight trains equippe with cast iron or composite block brakes).. Moel use to calculate the eceleration During a braking, the train eceleration can be approximately calculate applying the first ynamic equation to the train (projecte on the horizontal irection of motion) an the secon ynamic equation to each axle. From these equations the following expression can be obtaine:

12 where: n F i= = M + bi r R + R J R n i i= is the train eceleration; Fbi is the braking force applie on the i-th axle; n is the number of axles; r is the istance between the rotation axes an the point where the braking force is applie; R is the wheel raius; Rm is the motion resistance (aeroynamics an internal resistance); M is the mass of the train; J is the moment of inertia of the i-th axles. i The braking force applie to each axle is given by: where: pi S i Fmi is the pressure in the brake cyliner; is the cyliner surface; is the brake cyliner spring force; τ is the brake rig ratio; η is the brake efficiency; µ is the brake friction coefficient; ρ is wheel-rail ahesion coefficient. Neglecting the following terms: R m ; F mi ; n J i = ; i R F bi m (8) = ( p S F )τηµρ (9) the eceleration can be expresse using the following simplifie expression: i i r psτηµρ = R. M () r In this stuy, besies the surface S an the ratio τ, also the ratio R was consiere constant, while the variability of pressure p, efficiency η, friction coefficient µ, mass M an ahesion coefficient ρ were taken into account. When each parameter assumes its nominal value p, η, µ, ρ, M, the eceleration is given by: mi

13 r psτηµ ρ = R. () M To guarantee the require safety level of the system, the eceleration value to be use in the braking moel for the calculation of the monitoring curves is given by: ' = k () where k is a safety coefficient ( k < ). The objective of this analysis is the evaluation of the probability that the real eceleration is smaller than ', i.e. the ratio is smaller than a given k. The ratio between real an nominal eceleration can be expresse as: p p η η = (3) M M µ µ ρ ρ The probability istribution of the ratio can be calculate as a combination of the probability of each parameter..3 Probability istribution of the parameters A probability ensity function was suppose for each of the ratios in the preceing formula. For the major parameters, the probability istribution was etermine on the basis of technical knowlege. p η The probability ensity of the ratios an is not known exactly, only the extremes of the p η ispersion fiels are known with goo approximation. In these cases, normal probability istributions were suppose, with mean m = an extremes given by the mean value ± 3σ, in particular ± 5% both for pressure an efficiency. µ The ratio can be expresse as: µ µ µ µ me = (4) µ µ me µ where µ, µ me an µ represent respectively the real, mean (for a given friction material) an nominal value of the friction coefficient. µ The probability istribution of the ratio was efine using a wie set of experimental ata: µ me from the experimental results, a probability istribution was evaluate, then the experimental istribution was approximate by a normal istribution. The mean an the variance of the normal istribution were tune to minimize the ifference between the experimental an the approximate cumulative curve (fig. ). 3

14 ashe curve = experimental istribution.5. continue curve = approximate istribution µ/µ µ/µ me me a) b) Fig. Distribution of the ratio µ me.4 µ, a) istribution obtaine from experimental ata, b) comparison between the experimental an the approximate normal istribution. For the ratios µ me M an µ M only the extremes of the variability fiels were known with goo approximation. Also in this case normal probability istributions were suppose, with mean m = µ an extremes given by the mean value ± 3σ, in particular ± 5% for me M an ± 8% for. µ M ρ To take into account the ratio, two cases were separately analyze. The first one is relative to ρ normal ahesion conition; in this case the ratio ρ ρ is equal to an its variability was not taken ρ ρ. The two cases into account. The secon case is relative to egrae ahesion conition; in this case the ratio was suppose to belong to a normal istribution with mean m =. 95 an 3 σ =. 5 were combine together, supposing that in the 95% of the cases the ahesion conitions are normal, while in the remaining 5% are egrae..4 Distribution of the ratio between the real an the nominal eceleration The istributions of the parameters were then combine to fin the istribution of the ratio. Since the terms σ of each istribution were small, the calculation was quite simplifie. The fraction between the real an the nominal eceleration can be expresse as the ratio between two terms: the numerator of the fraction represents the ratio between the real an the nominal braking force: F F p η µ ρ = (5) b b p η µ ρ while the enominator is the ratio between the real an the nominal mass: M. M 4

15 The numerator is the prouct of four ranom variables; each of them is characterize by a normal probability istribution, with given mean an variance values. Given a series of ranom variables ( x, x,..., x n ), belonging to normal istributions with mean m, m,..., m n an variance σ, σ,..., σ n, the istribution of their prouct can be approximate with a normal istribution whose mean is the prouct of the means of each parameter an whose variance is given by: = = σ = σ i i. (6) j, j i The istribution of the ratio between the braking force an the mass can be evaluate using the Taylor series expansion arreste at the first orer term. In particular, given two ranom variables x num an x en, which belong to two normal istributions N( m num, σ num ) an N( m en, σ en ), the xnum istribution of the ratio can be approximate with a normal istribution characterize by mean xen mnum m = (7) men an variance: 4 4 ( m j ) ( ) m num σ = σ + num σ en. (8) men men The istribution of the numerator epens also on the number of vehicles in the train: in particular, if n is the number of vehicles an m an σ are the parameters relative to the istribution of the F b ratio, evaluate consiering only one vehicle, the resulting istribution has mean m n = m Fb an variance σ σ n =. (9) n M It was suppose moreover that the istribution of the enominator is not influence by the M number of vehicles..5 Results In table cumulative probability istribution values corresponing to various safety coefficients an various numbers of vehicles are shown. The results are a combination between the istribution obtaine neglecting the variability of the wheel-rail ahesion coefficient an the one obtaine taking into account the variability of ahesion. In fig. 3 the istribution of the ratio obtaine neglecting the variance of the ahesion coefficient is shown, while in fig. 4 the results are obtaine consiering the istribution of the ρ parameter. ρ 5

16 In fig. 5 the effect of the number of vehicles on the istribution of the parameter is shown. k vehicle vehicles 4 vehicles 8 vehicles 6 vehicles.6.5e-9 6.6E-5.83E- 3.3E E E-7 7.4E-.53E-7.8E-3 6.3E E-6 8.8E-9 8.7E E-7 9.4E E-4.36E-6.8E-9.38E- 6.5E-5.8.8E-3 9.3E-5.5E-6.8E-8 4.5E E-.69E-3.5E-4.5E-5.4E-6.9.E- 4.73E-.84E- 6.89E-3 3.E E-.36E-.85E-.45E-.9E- Table - Cumulative istribution values for various safety coefficients an various numbers of vehicles vehicles 8 vehicles 4 vehicles vehicles vehicle vehicle vehicles 4 vehicles 8 vehicles 6 vehicles k k a) b) obtaine without the parameter ρ, Figure 3 Distribution of the ratio a) probability ensity function, b) cumulative istribution function. 6 vehicles 8 vehicles vehicles vehicles vehicle vehicle vehicles 4 vehicles 8 vehicles.. 6 vehicles k Figure 4 Distribution of the ratio k a) b) obtaine consiering the istribution of the parameter ρ, a) probability ensity function, b) cumulative istribution function. 6

17 4 6 vehicles 8 vehicles vehicles vehicles vehicle vehicle vehicles vehicles 8 vehicles 6 vehicles k k obtaine after combination of the two istributions with an without parameter ρ ; effect of the number of vehicles on the istribution, a) probability ensity function, b) cumulative istribution function. Figure 5 Distribution of the ratio Besies the probability analysis relative to the passenger train equippe with isc brakes, other probability analysis were unertaken for freight trains equippe with cast iron block brakes or with composite block brakes, in empty an in loae conitions. 3 CONCLUSIONS The evelopment of the new spee control system SCMT for the Italian railways require the implementation of a braking moel that was able to escribe with sufficient precision an proper safety margins the braking performances of passenger an freight trains. With this purpose a braking moel having a general valiity has been erive from the UIC evaluation metho; such moel allows to convert the general input parameters (brake weight percentage, goos/passenger brake position, train length etc.) into a basic eceleration profile as function of time an spee. In aition a complete analysis of parameters affecting the braking performance was carrie out. For the major parameters, the probability istribution was etermine on the basis of technical knowlege an experimental results, in orer to establish the combine probability istribution, thus enabling the assessment of the safety egree as function of a reuction factor applie to the basic eceleration. Following the same proceure, further analysis coul be unertaken in orer to choose the proper safety factors on the basis of a complete evaluation of the risks, also taking into account external factors. BIBLIOGRAPHY [ ] A. Singer: "Neue LZB/FZB-Bremskurven", (New LZB/FZB braking curves), Universität Hannover, Institut für Schienenfahrzeuge un maschinelle Bahnanlagen, Report No. 4/997. [ ] D. Jaenichen, R. Jaensch: "Neue LZB/FZB für Neubaustrecke Köln-Frankfurt/M.", (New LZB/FZB for the new line Cologne - Frankfurt am Main), Technische Universität Dresen, Institut für Schienenfahrzeugtechnik, Final report,

18 [ 3 ] P. Presciani: "Stuio i un moello i frenatura per sistemi i controllo ella velocità" (Research on a braking moel for spee control systems), Ingegneria Ferroviaria No. 8/. [ 4 ] ERRI B 6 RP 3 "Existing an future train control an comman systems on the European railways Moels for eceleration curves", April. [ 5 ] "Description of the brake curve calculation", Ref. EEIG-ERTMS: 97E88 version 5D, /7/. [ 6 ] P. J. Bickel, K. A. Doksum: "Mathematical statistics. Basic ieas an selecte topics", vol. I, Prentice Hall,. [ 7 ] M. Biloeau, D. Brenner: "Theory of multivariate statistics", Springer,

Hardness Evaluation of Polytetrafluoroethylene Products

Hardness Evaluation of Polytetrafluoroethylene Products ECNDT 2006 - Poster 111 Harness Evaluation of Polytetrafluoroethylene Proucts T.A.KODINTSEVA, A.M.KASHKAROV, V.A.KALOSHIN NPO Energomash Khimky, Russia A.P.KREN, V.A.RUDNITSKY, Institute of Applie Physics

More information

Applications of Global Positioning System in Traffic Studies. Yi Jiang 1

Applications of Global Positioning System in Traffic Studies. Yi Jiang 1 Applications of Global Positioning System in Traffic Stuies Yi Jiang 1 Introuction A Global Positioning System (GPS) evice was use in this stuy to measure traffic characteristics at highway intersections

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

CHAPTER 5 : CALCULUS

CHAPTER 5 : CALCULUS Dr Roger Ni (Queen Mary, University of Lonon) - 5. CHAPTER 5 : CALCULUS Differentiation Introuction to Differentiation Calculus is a branch of mathematics which concerns itself with change. Irrespective

More information

Traffic Delay Studies at Signalized Intersections with Global Positioning System Devices

Traffic Delay Studies at Signalized Intersections with Global Positioning System Devices Traffic Delay Stuies at Signalize Intersections with Global Positioning System Devices THIS FEATURE PRESENTS METHODS FOR APPLYING GPS DEVICES TO STUDY TRAFFIC DELAYS AT SIGNALIZED INTERSECTIONS. MOST OF

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

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

9.3. Diffraction and Interference of Water Waves

9.3. Diffraction and Interference of Water Waves Diffraction an Interference of Water Waves 9.3 Have you ever notice how people relaxing at the seashore spen so much of their time watching the ocean waves moving over the water, as they break repeately

More information

Studying the Behavior of Active Mass Drivers during an Earthquake Using Discrete Instantaneous Optimal Control Method

Studying the Behavior of Active Mass Drivers during an Earthquake Using Discrete Instantaneous Optimal Control Method Stuying the Behavior of Active Mass Drivers uring an Earthquae Using Discrete Instantaneous Optimal Control Metho O. Bahar 1, M. R. Banan 2, an M. Mahzoon 3 1. Structural Engineering Research Center, International

More information

Springs, Shocks and your Suspension

Springs, Shocks and your Suspension rings, Shocks an your Suspension y Doc Hathaway, H&S Prototype an Design, C. Unerstaning how your springs an shocks move as your race car moves through its range of motions is one of the basics you must

More information

Nonlinear Frame Analysis Methods in Eurocode 8

Nonlinear Frame Analysis Methods in Eurocode 8 Seismic Evaluation of Constructions: Nonlinear rame Analysis Proceures in Z_SOIL Enrico Spacone, Moura Belgasmia, Aleksaner Urbanski PRICOS Dept. University G. D Annunzio of Chieti-Pescara viale Pinaro

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

INFLUENCE OF GPS TECHNOLOGY ON COST CONTROL AND MAINTENANCE OF VEHICLES

INFLUENCE OF GPS TECHNOLOGY ON COST CONTROL AND MAINTENANCE OF VEHICLES 1 st Logistics International Conference Belgrae, Serbia 28-30 November 2013 INFLUENCE OF GPS TECHNOLOGY ON COST CONTROL AND MAINTENANCE OF VEHICLES Goran N. Raoičić * University of Niš, Faculty of Mechanical

More information

n-parameter families of curves

n-parameter families of curves 1 n-parameter families of curves For purposes of this iscussion, a curve will mean any equation involving x, y, an no other variables. Some examples of curves are x 2 + (y 3) 2 = 9 circle with raius 3,

More information

Flow coefficient measurements for an engine cylinder head under transient flow conditions with continuous valve lift change

Flow coefficient measurements for an engine cylinder head under transient flow conditions with continuous valve lift change Flow coefficient measurements for an engine cyliner hea uner transient flow conitions with continuous valve lift change Daesan Oh, Choong Hoon Lee 2* Researcher, 2n Seoul Team, Defense Agency for Technology

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

6.3 Microbial growth in a chemostat

6.3 Microbial growth in a chemostat 6.3 Microbial growth in a chemostat The chemostat is a wiely-use apparatus use in the stuy of microbial physiology an ecology. In such a chemostat also known as continuous-flow culture), microbes such

More information

CURVES: VELOCITY, ACCELERATION, AND LENGTH

CURVES: VELOCITY, ACCELERATION, AND LENGTH CURVES: VELOCITY, ACCELERATION, AND LENGTH As examples of curves, consier the situation where the amounts of n-commoities varies with time t, qt = q 1 t,..., q n t. Thus, the amount of the commoities are

More information

LECTURE 15: LINEAR ARRAY THEORY - PART I

LECTURE 15: LINEAR ARRAY THEORY - PART I LECTURE 5: LINEAR ARRAY THEORY - PART I (Linear arrays: the two-element array; the N-element array with uniform amplitue an spacing; broa - sie array; en-fire array; phase array). Introuction Usually the

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

Capacitive mtouch Sensing Solutions

Capacitive mtouch Sensing Solutions Capacitive mtouch Sensing Solutions Design Guielines 2008 Microchip Technology Incorporate. ll Rights Reserve. Slie 1 Hello, my name is Marc McComb, Technical Training Engineer in the Security Microcontroller

More information

Dynamic Torque Control for Switched Reluctances Drives based on a new

Dynamic Torque Control for Switched Reluctances Drives based on a new Dynamic Torue Control for Switche Reluctances Drives base on a new Online Machine Moel Marc Hiller Universität er Buneswehr München Leistungselektronik un Steuerungen EIT6. Werner-Heisenberg-Weg 39 85577

More information

Digital barrier option contract with exponential random time

Digital barrier option contract with exponential random time IMA Journal of Applie Mathematics Avance Access publishe June 9, IMA Journal of Applie Mathematics ) Page of 9 oi:.93/imamat/hxs3 Digital barrier option contract with exponential ranom time Doobae Jun

More information

A New Evaluation Measure for Information Retrieval Systems

A New Evaluation Measure for Information Retrieval Systems A New Evaluation Measure for Information Retrieval Systems Martin Mehlitz martin.mehlitz@ai-labor.e Christian Bauckhage Deutsche Telekom Laboratories christian.bauckhage@telekom.e Jérôme Kunegis jerome.kunegis@ai-labor.e

More information

Chapter 2 Review of Classical Action Principles

Chapter 2 Review of Classical Action Principles Chapter Review of Classical Action Principles This section grew out of lectures given by Schwinger at UCLA aroun 1974, which were substantially transforme into Chap. 8 of Classical Electroynamics (Schwinger

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

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

Comparative study regarding the methods of interpolation

Comparative study regarding the methods of interpolation Recent Avances in Geoesy an Geomatics Engineering Comparative stuy regaring the methos of interpolation PAUL DANIEL DUMITRU, MARIN PLOPEANU, DRAGOS BADEA Department of Geoesy an Photogrammetry Faculty

More information

Lecture 13: Differentiation Derivatives of Trigonometric Functions

Lecture 13: Differentiation Derivatives of Trigonometric Functions Lecture 13: Differentiation Derivatives of Trigonometric Functions Derivatives of the Basic Trigonometric Functions Derivative of sin Derivative of cos Using the Chain Rule Derivative of tan Using the

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

The Elastic Capacitor and its Unusual Properties

The Elastic Capacitor and its Unusual Properties 1 The Elastic Capacitor an its Unusual Properties Michael B. Partensky, Department of Chemistry, Braneis University, Waltham, MA 453 partensky@attbi.com The elastic capacitor (EC) moel was first introuce

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

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

Study on the Price Elasticity of Demand of Beijing Subway

Study on the Price Elasticity of Demand of Beijing Subway Journal of Traffic an Logistics Engineering, Vol, 1, No. 1 June 2013 Stuy on the Price Elasticity of Deman of Beijing Subway Yanan Miao an Liang Gao MOE Key Laboratory for Urban Transportation Complex

More information

Mean-Value Theorem (Several Variables)

Mean-Value Theorem (Several Variables) Mean-Value Theorem (Several Variables) 1 Mean-Value Theorem (Several Variables) THEOREM THE MEAN-VALUE THEOREM (SEVERAL VARIABLES) If f is ifferentiable at each point of the line segment ab, then there

More information

Stochastic Modeling of MEMS Inertial Sensors

Stochastic Modeling of MEMS Inertial Sensors BULGARIAN ACADEMY OF SCIENCES CYBERNETICS AND INFORMATION TECHNOLOGIES Volume 10, No Sofia 010 Stochastic Moeling of MEMS Inertial Sensors Petko Petkov, Tsonyo Slavov Department of Automatics, Technical

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

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

Estimating the drilling rate in Ahvaz oil field

Estimating the drilling rate in Ahvaz oil field J Petrol Explor Pro Technol (2013) 3:169 173 DOI 10.1007/s13202-013-0060-3 ORIGINAL PAPER - PRODUCTION ENGINEERING Estimating the rilling rate in Ahvaz oil fiel Masou Cheraghi Seifaba Peyman Ehteshami

More information

If you have ever spoken with your grandparents about what their lives were like

If you have ever spoken with your grandparents about what their lives were like CHAPTER 7 Economic Growth I: Capital Accumulation an Population Growth The question of growth is nothing new but a new isguise for an age-ol issue, one which has always intrigue an preoccupie economics:

More information

Chapter 10 Market Power: Monopoly and Monosony Monopoly: market with only one seller. Demand function, TR, AR, and MR

Chapter 10 Market Power: Monopoly and Monosony Monopoly: market with only one seller. Demand function, TR, AR, and MR ECON191 (Spring 2011) 27 & 29.4.2011 (Tutorial 9) Chapter 10 Market Power: Monopoly an Monosony Monopoly: market with only one seller a Deman function, TR, AR, an P p=a bq ( q) AR( q) for all q except

More information

Practical Lab 2 The Diffraction Grating

Practical Lab 2 The Diffraction Grating Practical Lab 2 The Diffraction Grating OBJECTIVES: 1) Observe the interference pattern prouce when laser light passes through multiple-slit grating (a iffraction grating). 2) Graphically verify the wavelength

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

MSc. Econ: MATHEMATICAL STATISTICS, 1995 MAXIMUM-LIKELIHOOD ESTIMATION

MSc. Econ: MATHEMATICAL STATISTICS, 1995 MAXIMUM-LIKELIHOOD ESTIMATION MAXIMUM-LIKELIHOOD ESTIMATION The General Theory of M-L Estimation In orer to erive an M-L estimator, we are boun to make an assumption about the functional form of the istribution which generates the

More information

Investigation on a Free-Piston Stirling Engine and Pneumatic Output

Investigation on a Free-Piston Stirling Engine and Pneumatic Output Investigation on a Free-Piston Stirling Engine an Pneumatic Output Kwankaomeng S, * an Promvonge P Department of Mechanical Engineering, Faculty of Engineering, King Mongkut's Institute of Technology Lakrabang,

More information

Week 4 - Linear Demand and Supply Curves

Week 4 - Linear Demand and Supply Curves Week 4 - Linear Deman an Supply Curves November 26, 2007 1 Suppose that we have a linear eman curve efine by the expression X D = A bp X an a linear supply curve given by X S = C + P X, where b > 0 an

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

A G R E A T E R M E A S U R E O F C O N F I D E N C E

A G R E A T E R M E A S U R E O F C O N F I D E N C E Achieving Quality Auio Tests for Mobile Phones System Characterization Basics for through-the-air Auio Test Joey Tun, Applications Engineer Keithley Instruments, Inc. Mobile phone prouction testing has

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

Robust Reading of Ambiguous Writing

Robust Reading of Ambiguous Writing In submission; please o not istribute. Abstract A given entity, representing a person, a location or an organization, may be mentione in text in multiple, ambiguous ways. Unerstaning natural language requires

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

Higher turbulent mixing due to UnoDuct - air supply system

Higher turbulent mixing due to UnoDuct - air supply system Higher turbulent mixing ue to UnoDuct - air supply system Christian Heschl, Anrea Kelz, Fachhochschulstuiengänge Burgenlan GmbH Abstract Previous investigations of free jet propagation are usually limite

More information

Calibration of the broad band UV Radiometer

Calibration of the broad band UV Radiometer Calibration of the broa ban UV Raiometer Marian Morys an Daniel Berger Solar Light Co., Philaelphia, PA 19126 ABSTRACT Mounting concern about the ozone layer epletion an the potential ultraviolet exposure

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

Optimal Control Policy of a Production and Inventory System for multi-product in Segmented Market

Optimal Control Policy of a Production and Inventory System for multi-product in Segmented Market RATIO MATHEMATICA 25 (2013), 29 46 ISSN:1592-7415 Optimal Control Policy of a Prouction an Inventory System for multi-prouct in Segmente Market Kuleep Chauhary, Yogener Singh, P. C. Jha Department of Operational

More information

_Mankiw7e_CH07.qxp 3/2/09 9:40 PM Page 189 PART III. Growth Theory: The Economy in the Very Long Run

_Mankiw7e_CH07.qxp 3/2/09 9:40 PM Page 189 PART III. Growth Theory: The Economy in the Very Long Run 189-220_Mankiw7e_CH07.qxp 3/2/09 9:40 PM Page 189 PART III Growth Theory: The Economy in the Very Long Run 189-220_Mankiw7e_CH07.qxp 3/2/09 9:40 PM Page 190 189-220_Mankiw7e_CH07.qxp 3/2/09 9:40 PM Page

More information

LABORATORY COMPACTION TEST Application

LABORATORY COMPACTION TEST Application 1 LABORATORY COMPACTION TEST Application Compaction of soil is probably one of the largest contributors to the site ork economy; in other ors-it is important. Large sums of money are spent on it every

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 Monte Carlo Simulation of Multivariate General

A Monte Carlo Simulation of Multivariate General A Monte Carlo Simulation of Multivariate General Pareto Distribution an its Application 1 1 1 1 1 1 1 1 0 1 Luo Yao 1, Sui Danan, Wang Dongxiao,*, Zhou Zhenwei, He Weihong 1, Shi Hui 1 South China Sea

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

Lecture 17: Implicit differentiation

Lecture 17: Implicit differentiation Lecture 7: Implicit ifferentiation Nathan Pflueger 8 October 203 Introuction Toay we iscuss a technique calle implicit ifferentiation, which provies a quicker an easier way to compute many erivatives we

More information

19.2. First Order Differential Equations. Introduction. Prerequisites. Learning Outcomes

19.2. First Order Differential Equations. Introduction. Prerequisites. Learning Outcomes First Orer Differential Equations 19.2 Introuction Separation of variables is a technique commonly use to solve first orer orinary ifferential equations. It is so-calle because we rearrange the equation

More information

UCLA STAT 13 Introduction to Statistical Methods for the Life and Health Sciences. Chapter 9 Paired Data. Paired data. Paired data

UCLA STAT 13 Introduction to Statistical Methods for the Life and Health Sciences. Chapter 9 Paired Data. Paired data. Paired data UCLA STAT 3 Introuction to Statistical Methos for the Life an Health Sciences Instructor: Ivo Dinov, Asst. Prof. of Statistics an Neurology Chapter 9 Paire Data Teaching Assistants: Jacquelina Dacosta

More information

ISSN: 2277-3754 ISO 9001:2008 Certified International Journal of Engineering and Innovative Technology (IJEIT) Volume 3, Issue 12, June 2014

ISSN: 2277-3754 ISO 9001:2008 Certified International Journal of Engineering and Innovative Technology (IJEIT) Volume 3, Issue 12, June 2014 ISSN: 77-754 ISO 900:008 Certifie International Journal of Engineering an Innovative echnology (IJEI) Volume, Issue, June 04 Manufacturing process with isruption uner Quaratic Deman for Deteriorating Inventory

More information

The Range of Alpha Particles in Air. Lennon Ó Náraigh, Date of Submission: 5 th April Abstract:

The Range of Alpha Particles in Air. Lennon Ó Náraigh, Date of Submission: 5 th April Abstract: The ange of lpha Particles in ir Lennon Ó Náraigh, Date of Submission: 5 th pril 4 bstract: This eperiment assumes that the notion of ange is applicable to alpha particles an sets out to calculate sai

More information

Sensor Network Localization from Local Connectivity : Performance Analysis for the MDS-MAP Algorithm

Sensor Network Localization from Local Connectivity : Performance Analysis for the MDS-MAP Algorithm Sensor Network Localization from Local Connectivity : Performance Analysis for the MDS-MAP Algorithm Sewoong Oh an Anrea Montanari Electrical Engineering an Statistics Department Stanfor University, Stanfor,

More information

5. DEPOSITION PROCESSES. 5.1 Dry deposition

5. DEPOSITION PROCESSES. 5.1 Dry deposition 1 5. DEPOSITION PROCESSES 5.1 Dry eposition Dry eposition escribes the uptake of atmospheric species (gases or aerosol particles) at the surface of the Earth. It provies a surface bounary conition for

More information

Cheng, N. S. (1997). "A simplified settling velocity formula for sediment particle." Journal of Hydraulic Engineering, ASCE, 123(2), 149-152.

Cheng, N. S. (1997). A simplified settling velocity formula for sediment particle. Journal of Hydraulic Engineering, ASCE, 123(2), 149-152. THIS PAPER IS CITED AS Cheng, N. S. (1997). "A simplifie settling velocity formula for seiment particle." Journal of Hyraulic Engineering, ASCE, 13(), 149-15. A SIMPLIFIED SETTLING VELOCITY FORMULA FOR

More information

Effects of Process Parameters & Depth of Cut Model for Abrasive Waterjet Cutting of Ceramics

Effects of Process Parameters & Depth of Cut Model for Abrasive Waterjet Cutting of Ceramics Effects of Process Parameters & Depth of Cut Moel for Abrasive Waterjet Cutting of Ceramics M. Chithirai Pon Selvan*, Dr. N. Mohana Sunara Raju** *PhD Research Scholar, Karpagam University, Coiambatore,

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

Standard Gears. Enquiry CD Contents. Power Transmission Solutions. Catalogue Selection INDEX CROSS+MORSE

Standard Gears. Enquiry CD Contents. Power Transmission Solutions. Catalogue Selection INDEX CROSS+MORSE Stanar Gears Inex Gear Proucts Overview 2 evel an Mitre Gear Selection -.P. evel an Mitre Gears Metric evel Gears 7- Metric Mitre Gear 6 Straight Racks Spur Gears - Spur Gear Selection 9 atalogue Selection

More information

Unbalanced Power Flow Analysis in a Micro Grid

Unbalanced Power Flow Analysis in a Micro Grid International Journal of Emerging Technology an Avance Engineering Unbalance Power Flow Analysis in a Micro Gri Thai Hau Vo 1, Mingyu Liao 2, Tianhui Liu 3, Anushree 4, Jayashri Ravishankar 5, Toan Phung

More information

A Universal Sensor Control Architecture Considering Robot Dynamics

A Universal Sensor Control Architecture Considering Robot Dynamics International Conference on Multisensor Fusion an Integration for Intelligent Systems (MFI2001) Baen-Baen, Germany, August 2001 A Universal Sensor Control Architecture Consiering Robot Dynamics Frierich

More information

M147 Practice Problems for Exam 2

M147 Practice Problems for Exam 2 M47 Practice Problems for Exam Exam will cover sections 4., 4.4, 4.5, 4.6, 4.7, 4.8, 5., an 5.. Calculators will not be allowe on the exam. The first ten problems on the exam will be multiple choice. Work

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

Universal Gravity Based on the Electric Universe Model

Universal Gravity Based on the Electric Universe Model Universal Gravity Base on the Electric Universe Moel By Frerik Nygaar frerik_nygaar@hotmail.com Nov 015, Porto Portugal. Introuction While most people are aware of both Newton's Universal Law of Gravity

More information

Guidelines for the use of UHPLC Instruments

Guidelines for the use of UHPLC Instruments Guielines for the use of UHPLC Instruments Requirements for UHPLC instruments, metho evelopment in UHPLC an metho transfer from regular HPLC to UHPLC Authors: Dr. Davy Guillarme, Prof. Jean-Luc Veuthey

More information

A Data Placement Strategy in Scientific Cloud Workflows

A Data Placement Strategy in Scientific Cloud Workflows A Data Placement Strategy in Scientific Clou Workflows Dong Yuan, Yun Yang, Xiao Liu, Jinjun Chen Faculty of Information an Communication Technologies, Swinburne University of Technology Hawthorn, Melbourne,

More information

Rules for Finding Derivatives

Rules for Finding Derivatives 3 Rules for Fining Derivatives It is teious to compute a limit every time we nee to know the erivative of a function. Fortunately, we can evelop a small collection of examples an rules that allow us to

More information

Assignment 5 Solutions [Revision : 1.3]

Assignment 5 Solutions [Revision : 1.3] Assignment 5 Solutions Revision : 1.3] Q1.1 The equation of hyrostatic equilibrium is P r = gρ. Recalling that the efinition of optical epth is we can rewrite the HE equation as τ = κρ r, Rearranging,

More information

HIGH PRECISION IMAGING FOR NON-CONTACT MODE ATOMIC FORCE MICROSCOPE USING AN ADAPTIVE NONLINEAR OBSERVER AND OUTPUT STATE FEEDBACK CONTROLLER

HIGH PRECISION IMAGING FOR NON-CONTACT MODE ATOMIC FORCE MICROSCOPE USING AN ADAPTIVE NONLINEAR OBSERVER AND OUTPUT STATE FEEDBACK CONTROLLER Digest Journal of Nanomaterials an Biostructures Vol., No.3, September 9, p. 9- HIGH PRECISION IMAGING FOR NON-CONTACT MODE ATOMIC FORCE MICROSCOPE USING AN ADAPTIVE NONLINEAR OBSERVER AND OUTPUT STATE

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

Stress Concentration Factors of Various Adjacent Holes Configurations in a Spherical Pressure Vessel

Stress Concentration Factors of Various Adjacent Holes Configurations in a Spherical Pressure Vessel 5 th Australasian Congress on Applie Mechanics, ACAM 2007 10-12 December 2007, Brisbane, Australia Stress Concentration Factors of Various Ajacent Holes Configurations in a Spherical Pressure Vessel Kh.

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

Average-Case Analysis of a Nearest Neighbor Algorithm. Moett Field, CA USA. in accuracy. neighbor.

Average-Case Analysis of a Nearest Neighbor Algorithm. Moett Field, CA USA. in accuracy. neighbor. From Proceeings of the Thirteenth International Joint Conference on Articial Intelligence (1993). Chambery, France: Morgan Kaufmann Average-Case Analysis of a Nearest Neighbor Algorithm Pat Langley Learning

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

FOURIER TRANSFORM TERENCE TAO

FOURIER TRANSFORM TERENCE TAO FOURIER TRANSFORM TERENCE TAO Very broaly speaking, the Fourier transform is a systematic way to ecompose generic functions into a superposition of symmetric functions. These symmetric functions are usually

More information

CALCULATION INSTRUCTIONS

CALCULATION INSTRUCTIONS Energy Saving Guarantee Contract ppenix 8 CLCULTION INSTRUCTIONS Calculation Instructions for the Determination of the Energy Costs aseline, the nnual mounts of Savings an the Remuneration 1 asics ll prices

More information

CAPACITANCE 1. Since charge is conserved, the charge on the bigger drop is C. q V = = = 27 V = 9. = 9 cm = 0.

CAPACITANCE 1. Since charge is conserved, the charge on the bigger drop is C. q V = = = 27 V = 9. = 9 cm = 0. PITNE SOLVED EXMPLE Example : ssuming earth to be an isolate conucting sphere of raius 6400 km, what is the capacitance of earth? Solution: apacitance of earth, 4π ε 0 r Here, 4πε 0 ; r 6400 km 6.4 0 6

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

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

INTRODUCTION TO BEAMS

INTRODUCTION TO BEAMS CHAPTER Structural Steel Design LRFD etho INTRODUCTION TO BEAS Thir Eition A. J. Clark School of Engineering Department of Civil an Environmental Engineering Part II Structural Steel Design an Analsis

More information

SOME NOTES ON THE HYPERBOLIC TRIG FUNCTIONS SINH AND COSH

SOME NOTES ON THE HYPERBOLIC TRIG FUNCTIONS SINH AND COSH SOME NOTES ON THE HYPERBOLIC TRIG FUNCTIONS SINH AND COSH Basic Definitions In homework set # one of the questions involves basic unerstaning of the hyperbolic functions sinh an cosh. We will use this

More information

Chapter 11: Feedback and PID Control Theory

Chapter 11: Feedback and PID Control Theory Chapter 11: Feeback an ID Control Theory Chapter 11: Feeback an ID Control Theory I. Introuction Feeback is a mechanism for regulating a physical system so that it maintains a certain state. Feeback works

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

Jackson 1.9 Homework Problem Solution Dr. Christopher S. Baird University of Massachusetts Lowell

Jackson 1.9 Homework Problem Solution Dr. Christopher S. Baird University of Massachusetts Lowell Jackson 1.9 Homework Problem Solution Dr. Christopher S. Bair University of Massachusetts Lowell PROBLEM: Calculate the attractive force between conuctors in the parallel plate capacitor (Problem 1.6a:

More information

Robust Reading: Identification and Tracing of Ambiguous Names

Robust Reading: Identification and Tracing of Ambiguous Names Robust Reaing: Ientification an Tracing of Ambiguous Names Xin Li Paul Morie Dan Roth Department of Computer Science University of Illinois, Urbana, IL 61801 {xli1,morie,anr}@uiuc.eu Abstract A given entity,

More information

Wave Interference: Young s Double-Slit Experiment

Wave Interference: Young s Double-Slit Experiment Wave Interference: Young s Double-Slit Experiment 9.5 If light has wave properties, then two light sources oscillating in phase shoul prouce a result similar to the interference pattern in a ripple tank

More information

Open World Face Recognition with Credibility and Confidence Measures

Open World Face Recognition with Credibility and Confidence Measures Open Worl Face Recognition with Creibility an Confience Measures Fayin Li an Harry Wechsler Department of Computer Science George Mason University Fairfax, VA 22030 {fli, wechsler}@cs.gmu.eu Abstract.

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