343 Whilst this may be so it is also true that this in itself is not sufficient to deter­ mine it completely. In fact the extent of the dead air region and the behaviour of the shear layer are also of prime importance and in short a unified treatment comprising external flow, boundary layer, shear layer and dead air region becomes necessary to complete the investigation. This would take us outside the scope of the present article and for the substantial progress that has been made towards such a treatment the reader is referred to a paper by HOLDER and GADD 1 and its comprehensive list of references. v. Heat transfer in incompressible boundary layers. 25. Introduction. The term fluid includes gases and liquids. Both gases and liquids are to some extent compressible but in many problems of fluid flow the density changes occurring are small. When they are small enough to be negligible we can regard the flow as incompressible. In Chap. IV we have established the equations for compressible flow of gases and these can of course be used to deter­ mine when density changes in a gas flow are in fact negligible. Broadly speaking this will be so when the temperature changes as determined by the energy equation are small enough.

Stratification of computer tasks 94 Example I 94 Example 2 96 Controllevels and computer input/output hardware 104 Leveli 105 Level 2 118 Level 3 118 Level4 118 Level5 119 Characteristics of process control computer systems 119 A survey of process control computer hardware 120 Communication codes and circuits 138 Channe1 capacity 138 Types of connection and communication hardware 140 Practical suggestions and recommendations 152 Rcferences 153 Part II: The Role of Software in Process Control Systems 155 Chapter 4: The relative roles of software and hardware 157 In troduction 157 Data processing 158 Hardware 159 Computingpower 163 Software for process control data processing 169 Process software 170 Intercomputer communication software 173 Message switching software 173 Software for engineering ca1culations 173 Extcnded real-time software 173 Software versus hardware 174 Program loop 175 References 183 Chapter 5: System software 185 Introduction 185 Basic concepts of real-time operating systems 186 Structure and functions of real-time operating systems 190 Data and symbols for the operating system 200 System software 204 Cost, safety and reliability of operating system software 208 References 209 Chapter 6: Application pro grams and databases 211 Introduction 211 Application program tasks 211 Structure and timing requirement of application programs 220 Direct communication 227 Multiprogramming constraints 228 Database and basic process software 233 Access to database 235 Basic faciJities of an on-line database 236 Database organization 240 Contention resolution 243 Distributed database 244 Extended real-time software 247 Referenees 257 Part III: The Man-Machine Interface 259

Agriculture has benefited considerably from the wide-scale use of tractors and associated implements. Tractors have developed along two, at times contradictory, design paths. The first of these has resulted in functional improvements to the vehicle, making it capable of im­ proved performance in the often harsh environmental conditions in which it is required to operate. For example, agricultural tires have improved the versatility of tractors by allowing them to operate at relatively high speeds on a variety of terrains, and hydraulics have provided for flexibility in controlling and operating implements. It can also be seen that these particular functional design improvements have contributed significantly to the second design pathway, that of ergon­ omics, and the human-machine interface. Recent stress on the working environment for the tractor operator has led to design improvements relative to tractor cabs, the placement and labeling of controls, etc. This text discusses those factors relevant to the design, selection, and operation of tractor-implement systems. The audience for which it is intended is undergraduate and graduate students of agricultural engineering studying power and machinery. However, the text is suf­ ficiently applied to have relevance for those extension personnel in­ volved with advising farmers on the selection and operation of tractor­ implement combinations. The tractor cannot be regarded in isolation from the implement, nor from the environment in which both the tractor and implement are ix x Preface working.

Singularity theory is growing very fast and many new results have been discovered since the Russian edition appeared: for instance the relation of the icosahedron to the problem of by­ passing a generic obstacle. The reader can find more details about this in the articles "Singularities of ray systems" and "Singularities in the calculus of variations" listed in the bi­ bliography of the present edition. Moscow, September 1983 v. I. Arnold Preface to the Russian Edition "Experts discuss forecasting disasters" said a New York Times report on catastrophe theory in November 1977. The London Times declared Catastrophe Theory to be the "main intellectual movement of the century" while an article on catastrophe theory in Science was headed "The emperor has no clothes". This booklet explains what catastrophe theory is about and why it arouses such controversy. It also contains non-con­ troversial results from the mathematical theories of singulari­ ties and bifurcation. The author has tried to explain the essence of the fundamen­ tal results and applications to readers having minimal mathe­ matical background but the reader is assumed to have an in­ quiring mind. Moscow 1981 v. I. Arnold Contents Chapter 1. Singularities, Bifurcations, and Catastrophe Theories …………… 1 Chapter 2. Whitney's Singularity Theory … 3 Chapter 3. Applications of Whitney's Theory 7 Chapter 4. A Catastrophe Machine …… 10 Chapter 5. Bifurcations of Equilibrium States 14 Chapter 6. Loss of Stability of Equilibrium and the Generation of Auto-Oscillations . . . . . . 20 .

3. 2 Making capital and running costs commensurate 49 3. 3 Optimum speed of a tanker 50 3. 4 The optimisation of the sag:span ratio of a suspension bridge 52 3. 5 Optimisation with more than one degree of freedom: heat exchanger 55 3. 6 Putting a price on heat-exchanger performance 57 3. 7 Variation of costs with application 59 3. 8 Further aspects of heat-exchanger optimisation 59 3. 9 An elementary programming problem 60 3. 10 Classification of optimisation problems and methods of solution 62 3. 11 The design of rotating discs: an optimum structure 66 3. 12 Hubdesign 73 3. 13 Summary 73 Questions 73 Answers 74 4 Insight 4. 1 Introduction 76 4. 2 Rough calculations 76 4. 3 Optimisation of compressor shaft diameter 83 4. 4 The optimum virtual shaft: a digression 85 4. 5 Useful measures and concepts 87 4. 6 Bounds and limits 91 4. 7 Scale effects 94 4. 8 Dimensional analysis and scaling 98 4. 9 Proportion 99 100 4. 10 Change of viewpoint Questions 102 104 Answers 5 Matching 5. 1 Matching: the windlass 107 5. 2 An extended example of matching: ship propulsion 107 5. 3 Matching within a single machine III 5. 4 Further aspects of ship propulsion 112 5. 5 Specific speeds: degrees of freedom 113 5. 6 Matching of a spring to its task liS 5. 7 Matching in thermodynamic processes 117 5. 8 Two old cases of matching 121 5.