The Effects of Manifold Design Changes on Charge Distribution and Engine Performance
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The Grassmann Manifold
The Grassmann Manifold 1. For vector spaces V and W denote by L(V; W ) the vector space of linear maps from V to W . Thus L(Rk; Rn) may be identified with the space Rk£n of k £ n matrices. An injective linear map u : Rk ! V is called a k-frame in V . The set k n GFk;n = fu 2 L(R ; R ): rank(u) = kg of k-frames in Rn is called the Stiefel manifold. Note that the special case k = n is the general linear group: k k GLk = fa 2 L(R ; R ) : det(a) 6= 0g: The set of all k-dimensional (vector) subspaces ¸ ½ Rn is called the Grassmann n manifold of k-planes in R and denoted by GRk;n or sometimes GRk;n(R) or n GRk(R ). Let k ¼ : GFk;n ! GRk;n; ¼(u) = u(R ) denote the map which assigns to each k-frame u the subspace u(Rk) it spans. ¡1 For ¸ 2 GRk;n the fiber (preimage) ¼ (¸) consists of those k-frames which form a basis for the subspace ¸, i.e. for any u 2 ¼¡1(¸) we have ¡1 ¼ (¸) = fu ± a : a 2 GLkg: Hence we can (and will) view GRk;n as the orbit space of the group action GFk;n £ GLk ! GFk;n :(u; a) 7! u ± a: The exercises below will prove the following n£k Theorem 2. The Stiefel manifold GFk;n is an open subset of the set R of all n £ k matrices. There is a unique differentiable structure on the Grassmann manifold GRk;n such that the map ¼ is a submersion. -
Mean Value Modelling of a Poppet Valve EGR-System
Mean value modelling of a poppet valve EGR-system Master’s thesis performed in Vehicular Systems by Claes Ericson Reg nr: LiTH-ISY-EX-3543-2004 14th June 2004 Mean value modelling of a poppet valve EGR-system Master’s thesis performed in Vehicular Systems, Dept. of Electrical Engineering at Linkopings¨ universitet by Claes Ericson Reg nr: LiTH-ISY-EX-3543-2004 Supervisor: Jesper Ritzen,´ M.Sc. Scania CV AB Mattias Nyberg, Ph.D. Scania CV AB Johan Wahlstrom,¨ M.Sc. Linkopings¨ universitet Examiner: Associate Professor Lars Eriksson Linkopings¨ universitet Linkoping,¨ 14th June 2004 Avdelning, Institution Datum Division, Department Date Vehicular Systems, Dept. of Electrical Engineering 14th June 2004 581 83 Linkoping¨ Sprak˚ Rapporttyp ISBN Language Report category — ¤ Svenska/Swedish ¤ Licentiatavhandling ISRN ¤ Engelska/English ££ ¤ Examensarbete LITH-ISY-EX-3543-2004 ¤ C-uppsats Serietitel och serienummer ISSN ¤ D-uppsats Title of series, numbering — ¤ ¤ Ovrig¨ rapport ¤ URL for¨ elektronisk version http://www.vehicular.isy.liu.se http://www.ep.liu.se/exjobb/isy/2004/3543/ Titel Medelvardesmodellering¨ av EGR-system med tallriksventil Title Mean value modelling of a poppet valve EGR-system Forfattare¨ Claes Ericson Author Sammanfattning Abstract Because of new emission and on board diagnostics legislations, heavy truck manufacturers are facing new challenges when it comes to improving the en- gines and the control software. Accurate and real time executable engine models are essential in this work. One successful way of lowering the NOx emissions is to use Exhaust Gas Recirculation (EGR). The objective of this thesis is to create a mean value model for Scania’s next generation EGR system consisting of a poppet valve and a two stage cooler. -
117001 Tiertwo Cp6 14.Pdf
This is what it takes to be a PRO. Performance enhancing features like a heavy-duty air cleaner, forged-steel crankshaft, electronic ignition and cast-iron cylinder liner. KOHLER® Command PRO® is the standard for professional-grade power and performance. COURAGE XT COMMAND PRO® DEPENDABLE OPERATI COURAGE SINGLE ON • Quad-Clean ™ all-season four-stage cyclonic air filter – effective COURAGE TWINS engine protection for tough-and-dirty conditions. COURAGE XT • Protects from airborne contaminants that can easily clog COURAGE PRO TWINS COMMAND PRO® traditional air filters. LoNGER RUN TIMES COURAGE SINGLE • Large-capacity fuel tank means more time working, less time filling. COURAGE XT COURAGE TWINS • Electronic ignition and an advanced combustion system design help COMMAND PRO® reduce fuel consumption. COURAGE PRO TWINS COURAGE XT EASIER REPOWERING COURAGE SINGLE COMMAND PRO® • Power or repower your equipment without expensive modifications. COURAGE TWINS ALL-WEATHER P COURAGE SINGLE ERFORMANCE COURAGE PRO TWINS • Quad-Clean air filter reconfigures in seconds to recycle engine heat. COURAGE XT COURAGE TWINS • Command PRO starts effortlessly in all weather conditions, from COMMAND PRO® 0 to 110 degrees. COURAGE PRO TWINS BUILT TO LAST COURAGE SINGLE • Forged-steel crankshafts and tough Stellite ®-faced exhaust valves with COURAGE TWINS Tufftride ®-coated stems and cast-iron cylinder bores. • Oil Sentry ™ automatically shuts engine down in low-oil conditions. COURAGE PRO TWINS 6-HP HORIZONTAL-SHAFT ENGINES 6-HP HORIZONTAL-SHAFT ENGINES TOP VIEW -
On Manifolds of Tensors of Fixed Tt-Rank
ON MANIFOLDS OF TENSORS OF FIXED TT-RANK SEBASTIAN HOLTZ, THORSTEN ROHWEDDER, AND REINHOLD SCHNEIDER Abstract. Recently, the format of TT tensors [19, 38, 34, 39] has turned out to be a promising new format for the approximation of solutions of high dimensional problems. In this paper, we prove some new results for the TT representation of a tensor U ∈ Rn1×...×nd and for the manifold of tensors of TT-rank r. As a first result, we prove that the TT (or compression) ranks ri of a tensor U are unique and equal to the respective seperation ranks of U if the components of the TT decomposition are required to fulfil a certain maximal rank condition. We then show that d the set T of TT tensors of fixed rank r forms an embedded manifold in Rn , therefore preserving the essential theoretical properties of the Tucker format, but often showing an improved scaling behaviour. Extending a similar approach for matrices [7], we introduce certain gauge conditions to obtain a unique representation of the tangent space TU T of T and deduce a local parametrization of the TT manifold. The parametrisation of TU T is often crucial for an algorithmic treatment of high-dimensional time-dependent PDEs and minimisation problems [33]. We conclude with remarks on those applications and present some numerical examples. 1. Introduction The treatment of high-dimensional problems, typically of problems involving quantities from Rd for larger dimensions d, is still a challenging task for numerical approxima- tion. This is owed to the principal problem that classical approaches for their treatment normally scale exponentially in the dimension d in both needed storage and computa- tional time and thus quickly become computationally infeasable for sensible discretiza- tions of problems of interest. -
INTRODUCTION to ALGEBRAIC GEOMETRY 1. Preliminary Of
INTRODUCTION TO ALGEBRAIC GEOMETRY WEI-PING LI 1. Preliminary of Calculus on Manifolds 1.1. Tangent Vectors. What are tangent vectors we encounter in Calculus? 2 0 (1) Given a parametrised curve α(t) = x(t); y(t) in R , α (t) = x0(t); y0(t) is a tangent vector of the curve. (2) Given a surface given by a parameterisation x(u; v) = x(u; v); y(u; v); z(u; v); @x @x n = × is a normal vector of the surface. Any vector @u @v perpendicular to n is a tangent vector of the surface at the corresponding point. (3) Let v = (a; b; c) be a unit tangent vector of R3 at a point p 2 R3, f(x; y; z) be a differentiable function in an open neighbourhood of p, we can have the directional derivative of f in the direction v: @f @f @f D f = a (p) + b (p) + c (p): (1.1) v @x @y @z In fact, given any tangent vector v = (a; b; c), not necessarily a unit vector, we still can define an operator on the set of functions which are differentiable in open neighbourhood of p as in (1.1) Thus we can take the viewpoint that each tangent vector of R3 at p is an operator on the set of differential functions at p, i.e. @ @ @ v = (a; b; v) ! a + b + c j ; @x @y @z p or simply @ @ @ v = (a; b; c) ! a + b + c (1.2) @x @y @z 3 with the evaluation at p understood. -
Engine Cylinder Head Installation
Engine Cylinder Head Installation Important: Install the cylinder head without the camshafts. 1. Install the engine cylinder head to the engine block. 2. Install the AIR pump bolt and fir tree fastener from the back of the cylinder head. Refer to Service Bulletin 06-06-04-016A for further information. 3. Install new cylinder head bolts and tighten the bolts. Refer to Cylinder Head Replacement in SI. Camshaft Holding Tool Caution: The camshaft holding tools must be installed on the camshafts to prevent camshaft rotation. When performing service to the valve train and/or timing components, valve spring pressure can cause the camshafts to rotate unexpectedly and can cause personal injury. Important: Before installing the camshafts, refer to Camshafts Cleaning and Inspection in SI. 4. Install the camshafts with the flats up using the J 44221 - Camshaft Holding Tool. Refer to Camshaft Installation in SI. Notice: Tension must be always kept on the intake side of the timing chain to properly keep the engine in time. If the chain is loose the timing will be off, which may cause internal engine damage or set DTC P0017. Fastener Notice: Use the correct fastener in the correct location. Replacement fasteners must be the correct part number for that application. Fasteners requiring replacement or fasteners requiring the use of thread locking compound or sealant are identified in the service procedure. Do not use paints, lubricants, or corrosion inhibitors on fasteners or fastener joint surfaces unless specified. These coatings affect fastener torque and joint clamping force and may damage the fastener. Use the correct tightening sequence and specifications when installing fasteners in order to avoid damage to parts and systems. -
MODULE 11: GLOSSARY and CONVERSIONS Cell Engines
Hydrogen Fuel MODULE 11: GLOSSARY AND CONVERSIONS Cell Engines CONTENTS 11.1 GLOSSARY.......................................................................................................... 11-1 11.2 MEASUREMENT SYSTEMS .................................................................................. 11-31 11.3 CONVERSION TABLE .......................................................................................... 11-33 Hydrogen Fuel Cell Engines and Related Technologies: Rev 0, December 2001 Hydrogen Fuel MODULE 11: GLOSSARY AND CONVERSIONS Cell Engines OBJECTIVES This module is for reference only. Hydrogen Fuel Cell Engines and Related Technologies: Rev 0, December 2001 PAGE 11-1 Hydrogen Fuel Cell Engines MODULE 11: GLOSSARY AND CONVERSIONS 11.1 Glossary This glossary covers words, phrases, and acronyms that are used with fuel cell engines and hydrogen fueled vehicles. Some words may have different meanings when used in other contexts. There are variations in the use of periods and capitalization for abbrevia- tions, acronyms and standard measures. The terms in this glossary are pre- sented without periods. ABNORMAL COMBUSTION – Combustion in which knock, pre-ignition, run- on or surface ignition occurs; combustion that does not proceed in the nor- mal way (where the flame front is initiated by the spark and proceeds throughout the combustion chamber smoothly and without detonation). ABSOLUTE PRESSURE – Pressure shown on the pressure gauge plus at- mospheric pressure (psia). At sea level atmospheric pressure is 14.7 psia. Use absolute pressure in compressor calculations and when using the ideal gas law. See also psi and psig. ABSOLUTE TEMPERATURE – Temperature scale with absolute zero as the zero of the scale. In standard, the absolute temperature is the temperature in ºF plus 460, or in metric it is the temperature in ºC plus 273. Absolute zero is referred to as Rankine or r, and in metric as Kelvin or K. -
DIFFERENTIAL GEOMETRY COURSE NOTES 1.1. Review of Topology. Definition 1.1. a Topological Space Is a Pair (X,T ) Consisting of A
DIFFERENTIAL GEOMETRY COURSE NOTES KO HONDA 1. REVIEW OF TOPOLOGY AND LINEAR ALGEBRA 1.1. Review of topology. Definition 1.1. A topological space is a pair (X; T ) consisting of a set X and a collection T = fUαg of subsets of X, satisfying the following: (1) ;;X 2 T , (2) if Uα;Uβ 2 T , then Uα \ Uβ 2 T , (3) if Uα 2 T for all α 2 I, then [α2I Uα 2 T . (Here I is an indexing set, and is not necessarily finite.) T is called a topology for X and Uα 2 T is called an open set of X. n Example 1: R = R × R × · · · × R (n times) = f(x1; : : : ; xn) j xi 2 R; i = 1; : : : ; ng, called real n-dimensional space. How to define a topology T on Rn? We would at least like to include open balls of radius r about y 2 Rn: n Br(y) = fx 2 R j jx − yj < rg; where p 2 2 jx − yj = (x1 − y1) + ··· + (xn − yn) : n n Question: Is T0 = fBr(y) j y 2 R ; r 2 (0; 1)g a valid topology for R ? n No, so you must add more open sets to T0 to get a valid topology for R . T = fU j 8y 2 U; 9Br(y) ⊂ Ug: Example 2A: S1 = f(x; y) 2 R2 j x2 + y2 = 1g. A reasonable topology on S1 is the topology induced by the inclusion S1 ⊂ R2. Definition 1.2. Let (X; T ) be a topological space and let f : Y ! X. -
Manifold Reconstruction in Arbitrary Dimensions Using Witness Complexes Jean-Daniel Boissonnat, Leonidas J
Manifold Reconstruction in Arbitrary Dimensions using Witness Complexes Jean-Daniel Boissonnat, Leonidas J. Guibas, Steve Oudot To cite this version: Jean-Daniel Boissonnat, Leonidas J. Guibas, Steve Oudot. Manifold Reconstruction in Arbitrary Dimensions using Witness Complexes. Discrete and Computational Geometry, Springer Verlag, 2009, pp.37. hal-00488434 HAL Id: hal-00488434 https://hal.archives-ouvertes.fr/hal-00488434 Submitted on 2 Jun 2010 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Manifold Reconstruction in Arbitrary Dimensions using Witness Complexes Jean-Daniel Boissonnat Leonidas J. Guibas Steve Y. Oudot INRIA, G´eom´etrica Team Dept. Computer Science Dept. Computer Science 2004 route des lucioles Stanford University Stanford University 06902 Sophia-Antipolis, France Stanford, CA 94305 Stanford, CA 94305 [email protected] [email protected] [email protected]∗ Abstract It is a well-established fact that the witness complex is closely related to the restricted Delaunay triangulation in low dimensions. Specifically, it has been proved that the witness complex coincides with the restricted Delaunay triangulation on curves, and is still a subset of it on surfaces, under mild sampling conditions. In this paper, we prove that these results do not extend to higher-dimensional manifolds, even under strong sampling conditions such as uniform point density. -
Enlarging Exhaust Ports
1.3mm/0.050in wide and a normal three angle valve seat is very suitable (45 degree seat/30 degree top cut/60 degree inner cut). The inner cut blends the 45 degree valve seat into the port throat and the top cut blends the 45 degree valve seat into the combustion chamber. The whole exhaust port passage- way must be enlarged throughout. The valve throat is ground or bored out to 34.5mm/1.358in and the original valve seat machined to suit the new valve size. The port outlet is taken out to the size of the exhaust manifold gasket aperture (oversize - lmm more height and width - exhaust manifold gaskets are available). The passage- way is ground out quite extensively, but note that while the floor of the port should be cleaned up it should not have any serious amount of material The areas of the combustion chamber to be reworked are shown here (see text for key). removed from it, especially where the The amount of material that is removed does vary depending on the proximity of the port runs into the valve throat area. gasket and bore wall. The sides of the exhaust ports and the to the full size of the standard gasket of gasket is used). This modification roof certainly have plenty of material using the gasket as a template. Over- gives a considerable increase in which can be removed and, once sized gaskets which allow an even exhaust port area because the stand- modified, bear little resemblance to the larger port exit cross-sectional area are ard 'as-cast' dimensions at this same originals. -
Jennings: Two-Stroke Tuner's Handbook
Two-Stroke TUNER’S HANDBOOK By Gordon Jennings Illustrations by the author Copyright © 1973 by Gordon Jennings Compiled for reprint © 2007 by Ken i PREFACE Many years have passed since Gordon Jennings first published this manual. Its 2007 and although there have been huge technological changes the basics are still the basics. There is a huge interest in vintage snowmobiles and their “simple” two stroke power plants of yesteryear. There is a wealth of knowledge contained in this manual. Let’s journey back to 1973 and read the book that was the two stroke bible of that era. Decades have passed since I hung around with John and Jim. John and I worked for the same corporation and I found a 500 triple Kawasaki for him at a reasonable price. He converted it into a drag bike, modified the engine completely and added mikuni carbs and tuned pipes. John borrowed Jim’s copy of the ‘Two Stoke Tuner’s Handbook” and used it and tips from “Fast by Gast” to create one fast bike. John kept his 500 until he retired and moved to the coast in 2005. The whereabouts of Wild Jim, his 750 Kawasaki drag bike and the only copy of ‘Two Stoke Tuner’s Handbook” that I have ever seen is a complete mystery. I recently acquired a 1980 Polaris TXL and am digging into the inner workings of the engine. I wanted a copy of this manual but wasn’t willing to wait for a copy to show up on EBay. Happily, a search of the internet finally hit on a Word version of the manual. -
Section 2.3 – Linear and Angular Velocities
Section 2.3 – Linear and Angular Velocities The most intuitive measure of the rate at which the rider is traveling around the wheel is what we call linear velocity. Another way to specify how fast the rider is traveling around the wheel is with what we call angular velocity. Linear Speed Definition If P is a point on a circle of radius r, and P moves a distance s on the circumference of the circle in an amount of time t, then the linear velocity, v, of P is given by the formula speed distance time v s t Example A point on a circle travels 5 cm in 2 sec. Find the linear velocity of the point. Solution Given: s = 5cm t = 2 sec v s 5 cm t 2 sec 2.5 cm/ sec 21 Angular Speed Definition If P is a point moving with uniform circular motion on a circle of radius r, and the line from the center of the circle through P sweeps out a central angle in an amount of time t, then the angular velocity, (omega), of P is given by the formula where is measured in radians t Example A point on a circle rotates through 3 radians in 3 sec. Give the angular velocity of the point. 4 Solution Given: = rad t = 3sec 3 rad 4 3 sec rad/ sec 4 Example A bicycle wheel with a radius of 13.0 in. turns with an angular velocity of 3 radians per seconds. Find the distance traveled by a point on the bicycle tire in 1 minute.