Applied mathematical modelling of engineering problems
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Norwell, Mass. [u.a.]
Kluwer Acad. Publ.
2003
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| Schriftenreihe: | Applied optimization
81 |
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| 100 | 1 | |a Hritonenko, Natali |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Applied mathematical modelling of engineering problems |c by Natali Hritonenko ; Yuri Yatsenko |
| 264 | 1 | |a Norwell, Mass. [u.a.] |b Kluwer Acad. Publ. |c 2003 | |
| 300 | |a XXI, 286 S. |b Ill. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Applied optimization |v 81 | |
| 500 | |a Includes bibliographical references (p. 261-276) and index | ||
| 650 | 4 | |a Ingenieurwissenschaften | |
| 650 | 4 | |a Mathematisches Modell | |
| 650 | 4 | |a Engineering |x Mathematical models | |
| 650 | 0 | 7 | |a Mathematisches Modell |0 (DE-588)4114528-8 |2 gnd |9 rswk-swf |
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| 689 | 0 | 1 | |a Mathematisches Modell |0 (DE-588)4114528-8 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Jatsenko, Jurij |e Sonstige |4 oth | |
| 830 | 0 | |a Applied optimization |v 81 |w (DE-604)BV010841718 |9 81 | |
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Datensatz im Suchindex
| _version_ | 1819605453215105024 |
|---|---|
| adam_text | Contents
PREFACE xi
ACKNOWLEDGEMENTS xxi
CHAPTER 1. SOME BASIC MODELS OF PHYSICAL
SYSTEMS 1
1. BASIC MODELS OF PARTICLE DYNAMICS 2
1.1 Motion of a Particle in Gravitational Field 3
1.1.1 Vertical Projectile Problem. 4
1.1.2 Free Fall with Air Resistance 4
1.1.3 Plane Projectile Problem 5
1.1.4 More General Ballistic Problems 6
1.2 One Dimensional Mechanical Vibrations 6
1.2.1 Linear Oscillator 7
1.2.2 Forced Linear Vibrations and Resonance. 9
1.2.3 Nonlinear Oscillators 11
1.2.4 Nonlinear Vibrations and Resonance. 14
1.2.5 Nonlinear Electrical Mechanical Systems 16
2. INVERSE PROBLEMS AND INTEGRAL MODELS 19
2.1 Sliding Particle and Abel s Equation 20
2.2 Sliding Chain 22
2.3 Models of Computerized Tomography 24
2.3.1 Radon Transform 2 5
2.3.2 Inverse Scattering Problems 28
vi Applied Mathematical Modelling of Engineering Problems
CHAPTER 2. MODELS OF CONTINUUM
MECHANICAL SYSTEMS 29
1. CONSERVATION LAWS IN ONE DIMENSIONAL
MEDIUM 30
1.1 Eulerian and Lagrangian Coordinates 31
1.2 Mass Conservation 32
1.3 Momentum Conservation 33
1.4 Energy Conservation and Thermodynamics 36
2. MODELS OF ONE DIMENSIONAL CONTINUUM
DYNAMICS 39
2.1 Nonlinear Model of Solid Bar Dynamics 40
2.2 Linearized Model of Solid Bar Dynamics 41
2.3 Discontinuities in Linear Models 44
2.3.1 Analysis of Discontinuity Propagation 45
2.3.2 Analysis of Size of Discontinuity 47
2.3.3 Discontinuities Fixed in Space 49
2.4 Discontinuities in Nonlinear Models 50
2.4.1 Nonlinear Conservation Laws. 51
2.4.2 Impact of Diffusion and Dispersion. 53
2.5 Models of Viscoelasticity 54
3. THREE DIMENSIONAL CONSERVATION LAWS
AND MODELS 56
3.1 Mass Conservation and Continuity Equations 57
3.2 Momentum Conservation and Cauchy Equations 58
3.2.1 Conservation of Angular Momentum 59
3.2.2 Newtonian Viscous Fluids 60
3.2.3 Inviscid Fluids 61
3.2.4 Propagation of Sound in Space 62
3.2.5 Elastic Waves in Solids 63
3.3 Energy Balance and Thermodynamics 65
3.4 Heat Balance and Diffusion Processes 66
3.4.1 Diffusion Equation 68
3.4.2 Advection Diffusion Equation 69
4. APPLIED MODELLING OF WATER TRANSPORT
AND CONTAMINATION 70
4.1 Description of Physical Processes. 71
4.2 Classification of Models 72
4.3 Three Dimensional Model 74
Contents vii
4.3.1 Equation of Transport of the Ingredient in Solute 75
4.3.2 Equation of Transport of Suspended Particles 76
4.3.3 Equation of Ingredient Transport on Suspended Particles 77
4.3.4 Equations of Surface Water Dynamics 77
4.3.5 Equations of Adsorption and Sedimentation 78
4.4 Two Dimensional Horizontal Model and Stationary Flows 79
4.4.1 Equation of Ingredient Transport in Dissolved Phase 80
4.4.2 Equation of Suspended Particles Transport 80
4.4.3 Equation of Ingredient Transport on Suspended Particles 81
4.4.4 Equations of Water Dynamics 81
4.4.5 Equation of Ground Deposit Contamination 82
4.4.6 Analysis of Stationary Flow Problem 82
4.4.7 About Simulation Techniques 84
CHAPTER 3. VARIATIONAL MODELS AND
STRUCTURAL STABILITY 85
1. VARIATIONAL PRINCIPLES AND MODELS 85
1.1 Basic Models of Continuum Mechanics 87
1.1.1 Vibrations of String 87
1.1.2 Transverse Vibrations of Bar 88
1.1.3 Vibrations of Membrane 88
1.1.4 Vibrations of Plate 89
1.2 Variational Models for Spectral Problems 90
1.2.1 Eigenvalues and Eigenfunctions: Simplest Case 90
1.2.2 Raleigh Quotient and Raleigh Method 91
1.2.3 Eigenvalues of Bar with Variable Shape 92
1.2.4 Extremal Eigenvalues of Bar with Sought For Shape 94
2. VARIATIONAL MODELS OF STRUCTURAL
STABILITY 96
2.1 Model of Buckling Rod. 97
2.2 Model of Anti Plane Shear Collapse in Plasticity 98
2.3 Model of Capillarity Stability. 101
CHAPTER 4. INTEGRAL MODELS OF PHYSICAL
SYSTEMS 105
1. CONSTRUCTION OF INTEGRAL MODELS 106
1.1 Converting Differential Models to Integral Models 106
1.1.1 Initial Value Problems 107
viii Applied Mathematical Modelling of Engineering Problems
1.1.2 Boundary Value Problems for Ordinary Differential
Equations: Green s Function 112
1.1.3 Boundary Value Problems for Partial Differential Equations:
Boundary Integral Equation Method 114
1.2 Integral Models Occurring in Physical Problems 120
1.2.1 Integral Model of Membrane Vibrations. 120
1.2.2 Integral Models of Nuclear Reactors Dynamics. 122
2. MODELLING OF TRAFFIC NOISE PROPAGATION 125
3. MODELLING OF MINE ROPE DYNAMICS 129
3.1 Description of Physical Process. 130
3.2 Differential Model 131
3.3 Integral Model 134
3.4 Some Generalizations. 137
CHAPTER 5. MODELING IN BIOENGINEERING 139
1. MODELS OF POPULATION DYNAMICS
AND CONTROL 141
1.1 Classic Models for One Species Population 142
1.1.1 Malthus Model 142
1.1.2 Verhulst Pearl Model 144
1.1.3 Population Control and Harvesting 146
1.2 Age Dependent Models for One Species Population 148
1.2.1 Linear Integral Model (Lotka Model) 149
1.2.2 Linear Differential Model (Lotka Von Foerster Model) 150
1.2.3 Equivalence of Integral and Differential Models 151
1.3 Nonlinear Age Dependent Models with Intra Species
Competition 152
1.4 Models with Delay 154
1.5 Difference Models 155
1.6 Spatial Diffusion Models of Population Dynamics 159
1.6.1 Random Walk Models 159
1.6.2 Diffusion Models 163
2. BIFURCATION ANALYSIS FOR NONLINEAR
INTEGRAL MODELS 166
2.1 Stationary Solutions 167
2.2 Stability Analysis 168
2.2 Connection with Difference Models 177
Contents ix
2.3.1 Single Seasonal Reproduction 177
2.3.2 Double Seasonal Reproduction. 178
2.3 Open Problems 180
CHAPTER 6. MODELS OF TECHNOLOGICAL RENOVATION
IN PRODUCTION SYSTEMS 183
1. TRADITIONAL MODELS OF TECHNOLOGICAL
RENOVATION 184
1.1 Aggregated Models of Optimal Investments 185
1.2 Age Specific Models of Equipment Replacement 186
1.3 Statistical Models of Equipment Renewal 188
2. MODELS OF EQUIPMENT REPLACEMENT
UNDER TECHNOLOGICAL CHANGE 189
2.1 Self Organizing Market Model of Enterprise Under
Technological Change 190
2.2 Aggregated Model with Endogenous Useful Life
of Equipment 194
2.2.1 Integral Macroeconomic Models of Technological
Renovation 195
2.2.2 Statement of Optimization Problem 197
2.3 Disaggregated Integral Model of Equipment Replacement 199
2.3.1 Description of Production System 199
2.3.2 Construction of Model 200
2.3.3 About Prediction Problems 202
2.3.4 Statement of Optimization Problem 204
3. QUALITATIVE ANALYSIS OF OPTIMAL
EQUIPMENT REPLACEMENT 206
3.1 About Optimal Control Problems in Integral Models 206
3.1.1 General Statement of Optimal Control Problem 207
3.1.2 Necessary Conditions of Extremum 208
3.1.3 Lagrange Mu ltipl iers Method 211
3.1.4 Novelty and Common Features 214
3.2 Optimal Equipment Replacement in Aggregate Model 215
3.2.1 Structure of Aggregated Optimization Problem 216
3.2.2 Equation for Turnpike Regimes of Equipment
Replacement 218
3.2.3 Infinite Horizon Discounted Optimization 220
3.2.4 Finite Horizon Optimization 221
3.2.5 Discussion of Results 223
x Applied Mathematical Modelling of Engineering Problems
3.3 Optimal Equipment Replacement in Disaggregated Models225
3.3.1 Model with Different Lifetimes of Equipment 229
3.4 Open Problems 230
4. MATHEMATICAL DETAILS AND PROOFS 232
CHAPTER 7. APPENDIX 241
1. MISCELLANEOUS FACTS OF ANALYSIS 241
1.1 Vector and Integral Calculus 241
1.1.1 Gradient, Divergence and Rotation 241
1.1.2 Gauss Divergence Theorem. 242
1.1.3 Dubois Reymond s Lemma. 243
1.1.4 Leibniz s Formula for Derivatives 243
1.2 Functional Spaces 243
1.3 Calculus of Variations and Euler Equations 244
2. MATHEMATICAL MODELS AND EQUATIONS 245
2.1 Classification of Mathematical Models 245
2.1.1 Deterministic and Stochastic Models 245
2.1.2 Continuous and Discrete Models 246
2.1.3 Linear and Nonlinear Models 247
2.1.4 Difference, Differential and Integral Models 248
2.2 Integral Dynamical Models and Volterra
Integral Equations 254
2.2.1 Solvability of Volterra Integral Equations 254
2.2.2 Correctness and Stability of Volterra Integral Equations 256
2.2.3 Stability of Volterra Integral Equations 258
2.2.4 Integral Inequalities 258
REFERENCES 261
INDEX 277
|
| any_adam_object | 1 |
| author | Hritonenko, Natali |
| author_facet | Hritonenko, Natali |
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| dewey-ones | 620 - Engineering and allied operations |
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| dewey-search | 620/.001/5118 |
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| dewey-tens | 620 - Engineering and allied operations |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV017154136 |
| illustrated | Illustrated |
| indexdate | 2024-12-23T16:17:31Z |
| institution | BVB |
| isbn | 1402074840 |
| language | English |
| lccn | 2003051641 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-010341207 |
| oclc_num | 52208363 |
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| owner_facet | DE-703 DE-20 DE-634 |
| physical | XXI, 286 S. Ill. |
| publishDate | 2003 |
| publishDateSearch | 2003 |
| publishDateSort | 2003 |
| publisher | Kluwer Acad. Publ. |
| record_format | marc |
| series | Applied optimization |
| series2 | Applied optimization |
| spellingShingle | Hritonenko, Natali Applied mathematical modelling of engineering problems Applied optimization Ingenieurwissenschaften Mathematisches Modell Engineering Mathematical models Mathematisches Modell (DE-588)4114528-8 gnd Angewandte Mathematik (DE-588)4142443-8 gnd |
| subject_GND | (DE-588)4114528-8 (DE-588)4142443-8 |
| title | Applied mathematical modelling of engineering problems |
| title_auth | Applied mathematical modelling of engineering problems |
| title_exact_search | Applied mathematical modelling of engineering problems |
| title_full | Applied mathematical modelling of engineering problems by Natali Hritonenko ; Yuri Yatsenko |
| title_fullStr | Applied mathematical modelling of engineering problems by Natali Hritonenko ; Yuri Yatsenko |
| title_full_unstemmed | Applied mathematical modelling of engineering problems by Natali Hritonenko ; Yuri Yatsenko |
| title_short | Applied mathematical modelling of engineering problems |
| title_sort | applied mathematical modelling of engineering problems |
| topic | Ingenieurwissenschaften Mathematisches Modell Engineering Mathematical models Mathematisches Modell (DE-588)4114528-8 gnd Angewandte Mathematik (DE-588)4142443-8 gnd |
| topic_facet | Ingenieurwissenschaften Mathematisches Modell Engineering Mathematical models Angewandte Mathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010341207&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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