COMPUTATIONAL INVESTIGATIONS OF THE BME MAPPING APPROACH
AND INCORPORATION OF PHYSICAL KNOWLEDGE BASES


by Alexander Kolovos

A dissertation submitted to the faculty of the University of North Carolina at Chapel Hill in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the Department of Environmental Sciences and Engineering, School of Public Health.
Chapel Hill, North Carolina, 2001

Approved by:
Dr. George Christakos (Adviser).
Dr. Harvey Jeffries, Dr. Stephen J. McGregor, Dr. David Adalsteinsson, Dr. Michael J. Symons, Dr. Marc L. Serre (Readers).


 
 
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Contents

COVER PAGE .....i (In section 1, 1.5 MB)

ABSTRACT .....ii (In section 1, 1.5 MB)

Acknowledgements, Table of Contents, Lists of Tables and Figures .....iv (In section 1, 1.5 MB)

INTRODUCTION .....1 (In section 1, 1.5 MB)

CHAPTER I. THE MAPPING PROBLEM AND BME .....4 (Section 2, 7.2 MB)

1.1 The need for a new mapping method4
1.2 Basic notions about spatiotemporal mapping8
1.3 The spatiotemporal random field10
1.4 The advantage of knowledge15
1.5 Representation of general knowledge bases16
1.6 Sources of specificatory knowledge19
1.7 The core of BME analysis21
1.8 A closer look at the BME processing stages22
1.9 Versatility and applications27

CHAPTER II. DEALING WITH PHYSICAL LAWS: A STOCHASTIC FLOWPATH ANALYSIS EXAMPLE .....28 (Section 3, 8.9 MB)

2.1 Steady-state two-phase flow31
2.2 Geometric description of flowpath trajectories34
2.3 Flowpath formulation of two-phase flow38
2.4 Two-phase flow in a layered heterogeneous medium41
2.5 Waterflooding of a heterogeneous oil reservoir42
2.6 Transient effects in multiphase flow59
2.7 A few remarks on the stochastic flowpaths method60

CHAPTER III. BME MAPPING IN HEALTH IMPACTS ASSESSMENT .....61 (Section 4, 8.4 MB)

3.1 Information about ozone exposure and health hazards62
3.2 BME exposure mapping66
3.3 Pollutokinetic or toxicokinetic modeling73
3.4 Assessment of health effect and population damage82
3.4.1 Burden-response curve
82
3.4.2 Mapping of Population Health Damage Indicators
84
3.5 Effectiveness and considerations of BME analysis in health effects studies89

CHAPTER IV. A FIRST VIEW ON MAKING THE MOST OF GENERAL KNOWLEDGE .....93 (Section 5, 10.3 MB)

4.1 Early developments94
4.2 Variations on a problem100
4.2.1 Univariate case with known first and second order moments
102
4.2.1.1 Explicit solutions for the Lagrangian coefficients
104
4.2.1.2 Numerical results
106
4.2.2 Univariate case with known up to fourth order moments
109
4.2.2.1 Explicit solutions for the Lagrangian coefficients
113
4.2.2.2 Numerical results
114

CHAPTER V. USING PHYSICAL LAWS WITH BME : A NUMERICAL GUIDE .....118 (Section 6, 13.5 MB)

5.1 Handling information with BME119
5.2 Explicit expressions for the Lagrange multipliers123
5.3 Solution of the numerical BME system127
5.4 Discretization and performance issues129
5.5 Monitoring the physical problem at the prior stage135
5.5.1 One datum point and a large grid of estimation points
136
5.5.2 Combined grids of data and estimation points
144
5.6 Processing at the posterior stage146
5.7 So many laws in nature151

CHAPTER VI. A CONCLUDING OVERVIEW .....154 (In section 7, 5.5 MB)

6.1 A world of applications155
6.2 Present status and some ideas for the future157

APPENDICES .....159 (In section 7, 5.5 MB)

APPENDIX A: CHANGE OF THE PRESSURE GRADIENT ALONG A STOCHASTIC FLOWPATH159
APPENDIX B: DERIVATION OF NUMERICAL EQUATION SYSTEM FROM A GIVEN PHYSICAL LAW AND STATISTICAL MOMENTS160
APPENDIX C: A FEW NUMERICAL INTEGRATION METHODS162
C.1 Simpson' s Rule
162
C.2 Trapezoidal Rule
163
C.3 Gaussian Quadrature
164
APPENDIX D: DISCRETIZATION OF NUMERICAL EQUATION SYSTEM AND ITS DERIVATIVES166
APPENDIX E: A SIMPLE ADAPTIVE INTEGRATION TECHNIQUE FOR NON-SYMMETRIC DISTRIBUTION FUNCTIONS172

REFERENCES .....175 (In section 7, 5.5 MB)