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pt. 6 : us ISBN 9780387941578
内容説明
This is the sixth volume in the series "Mathematics in Industrial Prob- lems. " The motivation for these volumes is to foster interaction between Industry and Mathematics at the "grass roots level"; that is, at the level of specific problems. These problems come from Industry: they arise from models developed by the industrial scientists in ventures directed at the manufacture of new or improved products. At the same time, these prob- lems have the potential for mathematical challenge and novelty. To identify such problems, I have visited industries and had discussions with their scientists. Some of the scientists have subsequently presented their problems in the IMA Seminar on Industrial Problems. The book is based on the seminar presentations and on questions raised in subse- quent discussions. Each chapter is devoted to one of the talks and is self- contained. The chapters usually provide references to the mathematical literature and a list of open problems which are of interest to the industrial scientists. For some problems a partial solution is indicated briefly.
The last chapter of the book contains a short description of solutions to some of the problems raised in previous volumes, as well as references to papers in which such solutions have been published. The speakers in the seminar on Industrial Problems have given us at the IMA hours of delight and discovery. My thanks to Thomas Hoffend (3M), John Spence (Eastman Kodak Company), Marius Orlowski (Mo- torola, Inc. ), Robert J.
目次
1 Magnetization reversal in particulate recording media.- 1.1 The physical system.- 1.2 The model.- 1.3 Results and open problems.- 1.4 References.- 2 Variable forgetting factors in Kalman filtering.- 2.1 The dynamic Kalman filtering.- 2.2 Variable forgetting factor.- 2.3 Modification of VFF.- 2.4 Applications.- 2.5 References.- 3 Modeling of dopant diffusion networks.- 3.1 Diffusion on networks.- 3.2 Random walks.- 3.3 Effects of grains' boundaries.- 3.4 Solution of Problems.- 3.5 References.- 4 Statistical optics and effective medium theories of color.- 4.1 Color.- 4.2 Calculating reflectivity.- 4.3 Effective medium theory (EMT).- 4.4 Mathematical problems.- 4.5 References.- 5 Amorphous and polysilicon devices.- 5.1 Amorphous semiconductors.- 5.2 A mathematical model.- 5.3 Numerical results.- 5.4 Open problems and partial solution.- 5.5 References.- 6 Modeling the performance of a piezoelectric gyroscope.- 6.1 Vibrating gyroscope.- 6.2 Linear elasticity.- 6.3 Rotating disk.- 6.4 Rotating piezoelectric disk.- 6.5 Approximate solution.- 6.6 References.- 7 Particle simulations for xerographic development.- 7.1 The model.- 7.2 More on the particle motion.- 7.3 Open problems.- 7.4 References.- 8 A statistical dynamic theory of glassy polymers.- 8.1 Glassy state.- 8.2 Viscoelastic relaxation.- 8.3 Strain-stress behavior.- 8.4 Composite modulus.- 8.5 Open problems.- 8.6 References.- 9 Simulation of magnetic recording and playback processes.- 9.1 Magnetic tape and the recording process.- 9.2 Model of the record process.- 9.3 Record model implementation.- 9.4 The playback process.- 9.5 Open issues.- 9.6 References.- 10 Sunglitter in oceanic remote detection.- 10.1 Background noise.- 10.2 Signal processing.- 10.3 The model.- 10.4 Model/data comparison.- 11 Computer simulations of electrorheological fluids.- 11.1 Modeling ER fluids.- 11.2 Bulk polarization model.- 11.3 Numerical results.- 11.4 Optical probing.- 11.5 Areas for future work.- 11.6 References.- 12 Local flaws in permeation reducing barrier layers.- 12.1 Fluorinated fuel tanks.- 12.2 Mathematical model.- 12.3 Results for circular holes.- 12.4 Open problems.- 12.5 Partial results.- 12.6 References.- 13 Iterative solution methods on the Cray YMP/C90.- 13.1 Iterative schemes.- 13.2 Preconditioning strategies.- 13.3 Computational results.- 13.4 References.- 14 Track reconstruction and data fusion.- 14.1 Data fusion.- 14.2 Data sources and model selection.- 14.3 Extended Kalman filter and smoothing.- 14.4 References.- 15 Approximation to Boltzmann transport in semiconductor devices.- 15.1 The Boltzmann transport equation.- 15.2 Approximation to B.T.E..- 15.3 The f0-equation.- 15.4 References.- 16 Systematic data fusion using the theory of random conditional sets.- 16.1 Data fusion algorithms.- 16.2 Bayesian classification.- 16.3 The Dempster-Shafer approach.- 16.4 Fuzzy logic.- 16.5 Random sets.- 16.6 Conditional set theory.- 16.7 References.- 17 Micromagnetic simulation.- 17.1 The magnetic head.- 17.2 The magnetic energy in film.- 17.3 The pole tip.- 17.4 Swirl points.- 17.5 References.- 18 Dissolution kinetics with feedback.- 18.1 The model.- 18.2 Fast kinetic limit.- 18.3 Numerical solution.- 18.4 Remarks.- 18.5 References.- 19 Wetting and adsorption at chemically heterogeneous surfaces.- 19.1 Wettability.- 19.2 Wettability on self-assembled monolayers.- 19.3 Mathematical model.- 19.4 References.- 20 Fluid and kinetic modeling for micromechanical structures.- 20.1 Modeling micromechanical structures.- 20.2 Fluid description.- 20.3 Accelerometer.- 20.4 References.- 21 Modeling exhaust-gas oxygen sensors.- 21.1 The sensor.- 21.2 Mathematical model.- 21.3 Open problems.- 21.4 References.- 22 3D modeling of a smart power device.- 22.1 The device.- 22.2 Thermal modeling.- 22.3 Solution to problem (1).- 23 Solutions to problems from previous parts.- 23.1 Part 1.- 23.2 Part 3.- 23.3 Part 5.- 23.4 References.
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pt. 7 : us ISBN 9780387944449
内容説明
This is the seventh volume in the series "Mathematics in Industrial Prob lems. " The motivation for these volumes is to foster interaction between Industry and Mathematics at the "grass roots level;" that is, at the level of specific problems. These problems come from Industry: they arise from models developed by the industrial scientists in ventures directed at the manufacture of new or improved products. At the same time, these prob lems have the potential for mathematical challenge and novelty. To identify such problems, I have visited industries and had discussions with their scientists. Some of the scientists have subsequently presented their problems in the IMA Seminar on Industrial Problems. The book is based on the seminar presentations and on questions raised in subse quent discussions. Each chapter is devoted to one of the talks and is self contained. The chapters usually provide references to the mathematical literature and a list of open problems which are of interest to the industrial scientists. For some problems a partial solution is indicated briefly. The last chapter of the book contains a short description of solutions to some of the problems raised in previous volumes, as well as references to papers in which such solutions have been published. The speakers in the Seminar on Industrial Problems have given us at the IMA hours of delight and discovery. My thanks to David K. Lambert (Gen eral Motors Research and Development), David S.
目次
- 1 Mass flow sensing with heat waves.- 1.1 Air flow sensor.- 1.2 Steady-state heat transfer.- 1.3 Heat waves.- 1.4 Automotive air flow sensor model.- 1.5 Mathematical results.- 1.6 References.- 2 Mass transport in colloidal dispersions.- 2.1 Physical motivation.- 2.2 Modeling equilibrium.- 2.3 Kinetics: single component.- 2.4 Kinetics: multiple components.- 2.5 References.- 3 Crack propagation modeling.- 3.1 Crack propagation in a conductor.- 3.2 The hypersingular integrals.- 3.3 Open problems.- 3.4 References.- 4 Modeling of electrostatic bell sprayers.- 4.1 The coating process.- 4.2 Mathematical modeling.- 4.3 Numerical results.- 4.4 Future directions.- 4.5 References.- 5 Neural networks as controllers.- 5.1 Neural networks.- 5.2 Control of dynamical systems.- 5.3 Gradient methods for controller training.- 5.4 An example.- 5.5 The idle-speed control problem.- 5.6 Unresolved questions.- 5.7 References.- 6 Head-media interaction in magnetic recording.- 6.1 Head-tape interaction.- 6.2 The mathematical model.- 6.3 Test case.- 6.4 Open problems.- 6.5 References.- 7 Geometric path planning in rapid prototyping.- 7.1 Layered manufacturing.- 7.2 Offset curve representation.- 7.3 Pythagorean—hodograph (PH) curves.- 7.4 Bézier representation.- 7.5 References.- 8 Feature detection and tracking in three dimensional image analysis.- 8.1 Applications.- 8.2 Edge detection.- 8.3 Topographic classification.- 8.4 Image registration.- 8.5 Future research issues.- 8.6 References.- 9 Robot localization using landmarks.- 9.1 The position estimation problem.- 9.2 Linear position estimation.- 9.3 Open problems.- 9.4 References.- 10 Coordinates for mechanisms configuration spaces.- 10.1 Kinematics of closed-loop mechanisms.- 10.2 Mechanism coordinates
- an example.- 10.3 Mechanismcomplexity.- 10.4 Mathematical modeling.- 10.5 Open problems.- 10.6 References.- 11 Pulse optimization for multi-user data communications.- 11.1 Multiple access.- 11.2 The single user case.- 11.3 The multiple user case.- 11.4 Coupled base stations.- 11.5 Open problems.- 11.6 References.- 12 Propagation of highly scattered radiation in tissue.- 12.1 Maxwell’s equations.- 12.2 Radiation transport theory.- 12.3 Diffusion approximation.- 12.4 Imaging.- 12.5 References.- 13 Doping profiling by inverse device methods.- 13.1 Semiconductor devices.- 13.2 Measuring doping profile by direct measurements.- 13.3 PN junction.- 13.4 The inverse problem.- 13.5 References.- 14 Mathematical modeling in diffractive optics.- 14.1 The direct problem.- 14.2 Solution of the direct problem.- 14.3 Optimal design problem.- 14.4 Inverse problem.- 14.5 Diffractive optics in nonlinear media.- 14.6 Truncated periodic structure.- 14.7 References.- 15 Coping with complex boundaries.- 15.1 Capacity and translational friction.- 15.2 Flow through duct having arbitrary cross-section.- 15.3 Effective properties of inhomogeneous media.- 15.4 References.- 16 A short random walk through polymer material behavior.- 16.1 Strain-stress relations.- 16.2 Molecular modeling.- 16.3 Open problems.- 16.4 References.- 17 Finite set statistics with applications to data fusion.- 17.1 Random sets.- 17.2 Single-sensor, single-target estimation.- 17.3 Multi-sensor, multi-target estimation.- 17.4 An example.- 17.5 References.- 18 Electromigration modeling for smart power applications.- 18.1 Universal Power Output Driver (UPOD).- 18.2 Previous work.- 18.3 Electromigration.- 18.4 References.- 19 Maxwell’s equations and the analysis of electromagnetic devices.- 19.1 Electromagnetic actuators.- 19.2 The Maxwell equations.-19.3 The numerical scheme.- 19.4 References.- 20 Engineering modeling of batteries.- 20.1 Description of the battery cell.- 20.2 Mathematical modeling.- 20.3 Numerical results and open problems.- 20.4 References.- 21 Solutions to problems from previous parts.- 21.1 Part 6.- 21.2 Part 5.- 21.3 Part 3.- 21.4 Part 1.- 21.5 References.
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pt. 8 : us ISBN 9780387948652
内容説明
This is the eighth volume in the series "Mathematics in Industrial Prob lems." The motivation for these volumes is to foster interaction between Industry and Mathematics at the "grass roots level"; that is, at the level of specific problems. These problems come from Industry: they arise from models developed by the industrial scientists in ventures directed at the manufacture of new or improved products. At the same time, these prob lems have the potential for mathematical challenge and novelty. To identify such problems, I have visited industries and had discussions with their scientists. Some of the scientists have subsequently presented their problems in the IMA Seminar on Industrial Problems. The book is based on the seminar presentations and on questions raised in subsequent discussions. Each chapter is devoted to one of the talks and is self-contained. The chapters usually provide references to the mathematical literature and a list of open problems that are of interest to industrial scientists. For some problems, a partial solution is indicated briefly. The last chapter of the book contains a short description of solutions to some of the problems raised in the previous volume, as well as references to papers in which such solutions have been published.
目次
1 Dealing with geometric variations in manufacturing.- 1.1 Tolerancing.- 1.2 Metrology.- 1.3 Mathematical issues.- 1.4 References.- 2 Interdisciplinary computational fluid dynamics.- 2.1 Industrial interdisciplinary CFD.- 2.2 Thermal flow and combustion model.- 2.3 References.- 3 A mathematical model of a crystallizer.- 3.1 The physical model.- 3.2 Mathematical model for CSTR mixer.- 3.3 Mathematical model for PFR mixer.- 3.4 Scaling.- 3.5 Numerical results.- 3.6 References.- 4 Randomized algorithms in industrial problems.- 4.1 Programmable logical array (PLA).- 4.2 Gate arrays.- 4.3 Printed circuit board (PCB).- 4.4 References.- 5 Global geodesic coordinates on aG0 continuous surface.- 5.1 Basic problems.- 5.2 Geodesics on a smooth surface.- 5.3 Geodesics on non-smooth surfaces.- 5.4 References.- 6 Micromechanics effects in creep metal-matrix composites.- 6.1 Metal-matrix composites.- 6.2 The unreinforced model.- 6.3 The composite problem.- 6.4 References.- 7 Seismic inversion for geophysical prospecting.- 7.1 Data acquisition.- 7.2 Some traditional data processing steps.- 7.3 Multiparameter inversion.- 7.4 Open problems.- 7.5 References.- 8 Simulations for etch/deposition profile evolution.- 8.1 The problem.- 8.2 Mathematical formulation.- 8.3 Numerical results.- 8.4 Open problems.- 8.5 References.- 9 Analysis of cellular mobile radio.- 9.1 A cellular mobile radio system.- 9.2 Traditional queueing networks.- 9.3 An interacting queue model.- 9.4 Open problems.- 9.5 References.- 10 A pseudo non-time-splitting scheme in air quality modeling.- 10.1 The model.- 10.2 The pseudo non-time-splitting method.- 10.3 Numerical results.- 10.4 References.- 11 Fluid flow in a porous medium.- 11.1 The problem.- 11.2 The quasi-stationary 2-d model.- 11.3 Numerical results.- 11.4 Need for another model.- 11.5 Open problems.- 11.6 References.- 12 Robots, mechanisms and polynomial continuation.- 12.1 Examples.- 12.2 Polynomial continuation.- 12.3 The Stewart platform.- 12.4 Open questions.- 12.5 References.- 13 Failure times in metal lines.- 13.1 Electromigration.- 13.2 A mathematical model.- 13.3 Another model.- 13.4 Analysis of the solution.- 13.5 References.- 14 Surface modeling: impacts of design and manufacturing.- 14.1 Patched surfaces.- 14.2 Feature-based approach.- 14.3 Free-form deformation.- 14.4 References.- 15 Chemical filtration modeling.- 15.1 The chemistry of absorption.- 15.2 The occurrence of absorption.- 15.3 A recirculation model.- 15.4 Open problems.- 15.5 References.- 16 The element-free Galerkin method in large deformations.- 16.1 Large deformations.- 16.2 Moving least square interpolants.- 16.3 Kinematics of large deformations of continua.- 16.4 The EFG method.- 16.5 Proposed further research.- 16.6 References.- 17 Aeroacoustic research in the automotive industry.- 17.1 Basic acoustics.- 17.2 Mathematical modeling of sound.- 17.3 Acoustic source models.- 17.4 The antenna model.- 17.5 Open problems.- 17.6 References.- 18 Synchronization for chaotic dynamical systems.- 18.1 Synchronization.- 18.2 General definition of synchronization.- 18.3 Conditional Lyapunov exponents.- 18.4 Chaotic signal masking.- 18.5 Controlling chaos.- 18.6 References.- 19 Solutions to problems from part 7.- 19.1 Chapter 2.- 19.2 Chapter 3.- 19.3 Chapter 4.- 19.4 Chapter 14.- 19.5 Chapter 20.- 19.6 References.
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pt. 9 : us ISBN 9780387949451
内容説明
The 9th volume in Avner Friedmans collection of Mathematics in Industrial problems. Fostering interaction between industry and mathematics at the "grass roots" level, the problems presented here arise from models developed by industrial scientists engaged in R&D of new or improved products. Topics explored in this volume include diffusion in porous media and in rubber/glass transition, coating flows, solvation of molecules, semiconductor processing, optoelectronics, photographic images, density-functional theory, sphere packing, performance evaluation, causal networks, electrical well logging, general positioning system, sensor management, pursuit-evasion algorithms, and nonlinear viscoelasticity. Open problems and references are incorporated throughout and the final chapter contains some solutions to problems raised in earlier volumes.
目次
Contents: Sphere packing problems: from the obvious to the puzzling.- The value of performance improvements at constant price/performance.- A diffusion model of droplet absorption.- Information theory and sensor management.- Problems and applications in density-functional theory.- Nonlinear diffusion in coating flows.- A mini-max pursuit evasion algorithm.- Formation of photographic images.- Convective-diffusive lattice-gas models for flow under shear.- Multi-scale problems in modelling semiconductor processing equipment.- Mathematical modeling needs in optoelectronics.- Modeling solvation properties of molecules.- Mathematical problems in high-precision interferometric GPS.- Questions about the Poisson equation in semiconductor problems.- Causal modeling in diagnosing complex industrial equipment.- Mathematical problems in electrical well logging.
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[pt. 1] : us ISBN 9780387968605
内容説明
The book is based on a seminar conducted by the author at the Institute for Mathematics and its Applications during 1987-88. In this seminar, scientists from industry presented industrial problems to mathematicians, including the mathematical formulation of the problems. The book consists of twenty-two chapters, each one being independent of the others. Each chapter is based on a presentation by one of the speakers; it includes the industrial background, relevant mathematical literature, a list of open mathematical problems and, in some cases, reference to a solution or a partial solution of the problem. Most of the problems, however, are still open and they are addressed to mathematicians. The topics of the book include scattering, control and coding, conservation laws, inverse problems, network optimization, fluid problems, and a variety of free boundary problems in fluid mechanics. The book will be of interest to mathematicians seeking to work on mathematical problems which arise in industry. It will also be of interest to mathematicians and scientists who would like to learn about the interaction between mathematics and industry, what type of problems arise, how they are modelled, etc. Scientists working in industry may also be interested in the book as they discover that some of the topics dealt with are connected to their own work.
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pt. 2 : us ISBN 9780387971391
内容説明
This is the second volume in the series "Mathematics in Industrial Prob- lems." The motivation for both volumes is to foster inter action between Industry and Mathematics at the "grass roots"; that is at the level of spe- cific problems. These problems come from Industry: they arise from models developed by the industrial scientists in venture directed at the manufac- ture of new or improved products. At the same time, these problems have the potential for mathematical challenge and novelty. To identify such problems, I have visited industries and had discussions with their scientists. Some of the scientists have subsequently presented their problems in the IMA seminar on Industrial Problems. The book is based on questions raised in the seminar and subsequent discussions. Each chapter is devoted to one of the talks and is self-contained. The chap- ters usually provide references to the mathematical literat ure and a list of open problems which are of interest to the industrial scientists. For some problems partial solution is indicated briessy.
The last chapter of the book contains a short description of solutions to some of the problems raised in the first volume, as weIl as references to papers in which such solutions have been published. The experience of the last two years demonstrates a growing fruitful interaction between Industry and Mathematics. This interaction benefits Industry by increasing the mathematical knowledge and ideas brought to bear upon its concern, and benefits Mathematics through the infusion of exciting new problems.
目次
- 1 Signal design problems in multi-channel data communication.- 1.1 General problems.- 1.2 A lower bound on MCT(d).- 1.3 Pulse amplitude modulation (PAM).- 1.4 References.- 2 Solitons in non-homogeneous medium.- 2.1 Optical fiber sensor
- linear theory.- 2.2 Fiber optic sensor
- nonlinear theory.- 2.3 Known recent results.- 2.4 Back to the open questions.- 2.5 References.- 3 Foam rheology.- 3.1 Equilibrium Structure.- 3.2 Future directions.- 3.3 References.- 4 Applications of large deviations to communications.- 4.1 Examples.- 4.2 Theory of large deviations.- 4.3 Applications.- 4.4 Open problems.- 4.5 References.- 5 Phase modulation in nonlinear optical medium.- 5.1 The model and the problem.- 5.2 Two numerical approaches.- 5.3 The full problem.- 5.4 References.- 6 Multiple solutions in semiconductor device modeling.- 6.1 The basic equations.- 6.2 Ohm's law.- 6.3 A p - n diode.- 6.4 The p - n - p and n - p - n transistors.- 6.5 Flip-flop and p - n - p - n junction.- 6.6 Open problems.- 6.7 References.- 7 Mathematical models for thermal imaging-an heuristic approach.- 7.1 The problem.- 7.2 Linear diffusion approach.- 7.3 An alternative approach.- 7.4 References.- 8 Graph spectra, connectivity, and spin glass models of associative memory.- 8.1 Evolution of neural network.- 8.2 Spin glasses.- 8.3 Results for neural networks.- 8.4 Open problems.- 8.5 References.- 9 Mathematical problems in electron beam lithography.- 9.1 The lithography steps.- 9.2 Mathematical issues.- 9.3 The proximity equation.- 9.4 Suggestions.- 9.5 References.- 10 A reaction-diffusion model of color negative film development.- 10.1 The development process.- 10.2 Homogenization problems.- 10.3 Edge enhancement.- 10.4 Solution of Problem (1).- 10.5 Solution of Problem (2).- 10.6 Partial solution to problem (3).- 10.7 References.- 11 An inverse problem arising in the evolution of combustion aerosols.- 11.1 The model.- 11.2 Small coagulation.- 11.3 Partial solutions.- 11.4 References.- 12 Adaptive focused beamforming.- 12.1 The basic equations.- 12.2 The methods of AFB.- 12.3 Future directions.- 12.4 References.- 13 Optimal switching between a pair of Brownian motions.- 13.1 Optimal switching within a class of diffusion processes.- 13.2 Switching a pair of Brownian motions.- 13.3 Open problems.- 13.4 Solution of some of the problems.- 13.5 References.- 14 Mathematical models of latent image formation.- 14.1 The Hamilton-Bayer theory [1].- 14.2 The Monte Carlo Method.- 14.3 An alternate approach.- 14.4 References.- 15 Modeling problems in magneto-optic recording.- 15.1 An outline.- 15.2 Absorption of laser radiation.- 15.3 The heat generation.- 15.4 The magnetic energy effect.- 15.5 References.- 16 Shaped charge jets and subsonic free-surface flow theory.- 16.1 The model.- 16.2 The Chaplygin method.- 16.3 A variational approach.- 16.4 References.- 17 Electrophotographic system models.- 17.1 General description.- 17.2 Mathematical issues.- 17.3 References.- 18 Fluid models and other asymptotic limits with data and teletraffic applications.- 18.1 Asymptotics of closed product-form queueing networks.- 18.2 A fluid approximation.- 18.3 Stochastic fluid models.- 18.4 References.- 19 Solutions to problems from volume 1.- 19.1 References.
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pt. 3 : us ISBN 9780387974361
内容説明
This is the third volume in the series "Mathematics in Industrial Prob lems." The motivation for these volumes is to foster interaction between Industry and Mathematics at the "grass roots"; that is, at the level of spe cific problems. These problems come from Industry: they arise from models developed by the industrial scientists in ventures directed at the manufac ture of new or improved products. At the same time, these problems have the potential for mathematical challenge and novelty. To identify such problems, I have visited industries and had discussions with their scientists. Some of the scientists have subsequently presented their problems in the IMA seminar on Industrial Problems. The book is based on questions raised in the seminar and subsequent discussions. Each chapter is devoted to one of the talks and is self-contained. The chap ters usually provide references to the mathematical literature and a list of open problems which are of interest to the industrial scientists. For some problems partial solution is indicated briefly. The last chapter of the book contains a short description of solutions to some of the problems raised in the second volume, as well as references to papers in which such solutions have been published."
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pt. 4 : us ISBN 9780387976808
内容説明
This is the fourth volume in the series "Mathematics in Industrial Prob- lems." The motivation for these volumes is to foster interaction between Industry and Mathematics at the "grass roots"; that is, at the level of spe- cific problems. These problems come from Industry: they arise from models developed by the industrial scientists in ventures directed at the manufac- ture of new or improved products. At the same time, these problems have the potential for mathematical challenge and novelty. To identify such problems, I have visited industries and had discussions with their scientists. Some of the scientists have subsequently presented their problems in the IMA Seminar on Industrial Problems. The book is based on questions raised in the seminar and subsequent discussions. Each chapter is devoted to one of the talks and is self-contained. The chap- ters usually provide references to the mathematical literature and a list of open problems which are of interest to the industrial scientists. For some problems partial solution is indicated briefly.
The last chapter of the book contains a short description of solutions to some of the problems raised in the third volume, as well as references to papers in which such solutions have been published.
目次
1 Real-world free boundary problems.- 1.1 Hypersonic flow.- 1.2 Problems with free boundaries close to fixed boundaries.- 1.3 Free boundary problems in superconductors.- 1.4 Elastic contact.- 1.5 Partial solution.- 1.6 References.- 2 Terminally attached polymer chains.- 2.1 Experiments and the MWC model.- 2.2 The SCF theory.- 2.3 Numerical results.- 2.4 Mathematical problems.- 2.5 References.- 3 Orientation of colloidal magnetically switchable particles.- 3.1 Ferrohydrodynamics.- 3.2 A statistical mechanics approach.- 3.3 References.- 4 Information, probability and learning from examples.- 4.1 Learning from examples.- 4.2 Simple geometric examples.- 4.3 The Vapnik and Chervonenkis theory.- 4.4 References.- 5 An augmented drift-diffusion formulation in semiconductor devices.- 5.1 Semiconductor device modeling.- 5.2 The augmented drift-diffusion model.- 5.3 Mathematical issues.- 5.4 Partial solution.- 5.5 References.- 6 Analytical and heuristic modeling of distributed algorithms.- 6.1 Examples and terminology.- 6.2 Analytic results.- 6.3 Markov mode for search tree.- 6.4 Search with multiprocessor.- 6.5 References.- 7 Modeling catalytic converter performance.- 7.1 Chemical reactions.- 7.2 The differential equations.- 7.3 Numerical approach.- 7.4 Control problems.- 7.5 References.- 8 A model for titanium silicide film growth.- 8.1 Description of the process.- 8.2 A model with interfaces.- 8.3 A two-dimensional model.- 8.4 References.- 9 A three-state model for gel electrophoresis.- 9.1 Polymer reptation and the repton model.- 9.2 A biased repton model.- 9.3 Mapping into a discrete pseudospin model.- 9.4 Mean field approximation.- 9.5 Open problems.- 9.6 References.- 10 A limited coalescence problem.- 10.1 The model.- 10.2 Asymptotic distribution.- 10.3 The Monte Carlo method.- 10.4 Mathematical results.- 10.5 References.- 11 High field semiconductor equations.- 11.1 Motivation.- 11.2 Scaling.- 11.3 Moderate force.- 11.4 Strong force.- 11.5 The semiconductor case.- 11.6 Open problems.- 11.7 References.- 12 Structured singular values and invariant theory.- 12.1 FDLTI systems.- 12.2 Feedback under parametric uncertainty.- 12.3 Structured singular value.- 12.4 A new approach.- 12.5 Open problems.- 12.6 References.- 13 Signal design with an amplitude constraint.- 13.1 Lp/Lq signal design.- 13.2 Necessary optimality condition.- 13.3 The fixed-point problem.- 13.4 Open problems.- 13.5 References.- 14 Head-disk interface in magnetic storage device.- 14.1 Modified Reynolds equation.- 14.2 Free molecular flow.- 14.3 The limiting process as h?0.- 14.4 References.- 15 Parameter identification in a reaction diffusion model.- 15.1 The direct problem.- 15.2 The inverse problem.- 15.3 Modification of the model.- 15.4 A related problem.- 15.5 Existence and uniqueness.- 15.6 References.- 16 Linear analysis of megastructures.- 16.1 The three bar truss.- 16.2 The hypercircle method.- 16.3 References.- 17 Aerodynamic design with cfd.- 17.1 Vehicle drag.- 17.2 Governing equations.- 17.3 Simplifications.- 17.4 Research areas.- 17.5 References.- 18 Experimental design and quality loss function.- 18.1 Experimental design.- 18.2 Motivation.- 18.3 Sampling.- 18.4 The quality loss function.- 18.5 References.- 19 Numerical simulations for industrial chemical research.- 19.1 Computational approach to chemical research.- 19.2 Theoretical concepts.- 19.3 Requirements for atomistic computations.- 19.4 References.- 20 An adaptive feedforward approach to robot control.- 20.1 Mathematical model.- 20.2 Nonlinear feedforward.- 20.3 Path planning.- 20.4 Mathematical issues.- 20.5 References.- 21 Solutions to problems from part 3.- 21.1 References.
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pt. 5 : us ISBN 9780387979373
内容説明
Developed from the cooperation between mathematicians and industrial scientists on the "grass roots" level of specific problems, this book is the most recent in a collection of self-contained volumes which present industrial problems to mathematicians. Topics include: imaging and visualization, diffusion in glassy and swelling polymers, composite materials, plastic flows, coating of fiber optics, communications, colloidal dispersion, stress in semiconductors, micromagnetics, photobleaching, and machine vision. Many chapters offer open problems and references, while the last chapter contains solutions to problems raised in previous volumes of Mathematics in Industrial Problems, Parts 2, 3, and 4, published in the IMA series as Volumes 24, 31, and 38 respectively.
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pt. 10 : us ISBN 9780387985183
内容説明
This is the tenth volume in the series "Mathematics in Industrial Prob lems. " The motivation for these volumes is to foster interaction between Industry and Mathematics at the "grass roots level;" that is, at the level of specific problems. These problems come from Industry: they arise from models developed by the industrial scientists in ventures directed at the manufacture of new or improved products. At the same time, these prob lems have the potential for mathematical challenge and novelty. To identify such problems, I have visited industries and had discussions with their scientists. Some of the scientists have subsequently presented their problems in the IMA Seminar on Industrial Problems. The book is based on the seminar presentations and on questions raised in subse quent discussions. Each chapter is devoted to one of the talks and is self contained. The chapters usually provide references to the mathematical literature and a list of open problems which are of interest to the industrial scientists. For some problems a partial solution is indicated briefly. The last chapter of the book contains a short description of solutions to some of the problems raised in the previous volume, as well as references to papers in which such solutions have been published. The speakers in the Seminar on Industrial Problems have given us at the IMA hours of delight and discovery.
目次
1 Simulation and modeling of updrain TMOS devices.- 1.1 Applications.- 1.2 Structure of a smart power device.- 1.3 Mathematical models.- 1.4 Solution to problem (1).- 1.5 Partial solution to problem (3).- 1.6 References.- 2 Strategic risk management using stochastic programming.- 2.1 Dynamic programming.- 2.2 Stochastic programming.- 2.3 Bundling.- 2.4 Epiconsistency.- 2.5 Future directions.- 2.6 References.- 3 Discrete fluids using lattice gas methods.- 3.1 Computational aeroacoustics.- 3.2 Lattice gas methods.- 3.3 Hypercubic lattice.- 3.3.1 Aerodynamic studies.- 3.3.2 Acoustic study.- 3.4 Open opportunities.- 3.5 References.- 4 Computer-aided design of developable surfaces.- 4.1 Developable surfaces.- 4.2 Properties of developable surfaces.- 4.3 Developable Bezier surfaces.- 4.4 Open problems.- 4.5 References.- 5 Modeling techniques for computation of coating flows.- 5.1 Coating configuration.- 5.2 The governing equations.- 5.3 Fluid flow in a slot.- 5.4 Inclined boundary.- 5.5 References.- 6 Measuring coalescence rates.- 6.1 The coalescence problem.- 6.2 Introducing chemiluminescent species.- 6.3 Results and open problems.- 6.4 Partial solutions.- 6.5 References.- 7 The light field for diffusely scattering media.- 7.1 The problem.- 7.2 Radiation transfer.- 7.3 Modulation transfer function.- 7.4 Solving for I.- 7.5 Further questions.- 7.6 References.- 8 The changing nature of network traffic analysis and modeling.- 8.1 Motivation.- 8.2 Changes and challenges.- 8.3 Self-similar processes.- 8.4 An example.- 8.5 Open problems.- 8.6 References.- 9 Stress-induced warpage in micro-accelerometers.- 9.1 Micro-accelerometers.- 9.2 Warping in micro-accelerometers.- 9.3 Buckling of micromachined structure.- 9.4 Solution to problem (1).- 9.5 References.- 10 Exchange energy representations in computational micromagnetics.- 10.1 Micromagnetic structure.- 10.2 The Landau-Lifshitz-Gilbert equation.- 10.3 Numerical methods.- 10.4 Open problem.- 10.5 References.- 11 Nonlinear effects in electrorheological fluids.- 11.1 Elect rorheological fluids.- 11.2 An integral equation approach.- 11.3 A time dependent model.- 11.4 Open problems.- 11.5 Solution to problems (1)(2).- 11.6 References.- 12 Modeling of a building cooling system.- 12.1 Cooling systems terminology.- 12.2 A cooling system diagram.- 12.3 Statement of the problem.- 12.4 Dynamic equations.- 12.5 Open problems.- 12.6 References.- 13 Mass transport and adsorption in particle-loaded beds.- 13.1 Adsorption measurements.- 13.2 A mathematical model.- 13.3 A simplified model.- 13.4 Numerical and experimental results.- 13.5 References.- 14 Growth instability in metal electrodeposition.- 14.1 The Hull cell.- 14.2 Model equations.- 14.3 Open problems.- 14.4 References.- 15 Simulation of production metal cutting processes.- 15.1 Metal cutting process.- 15.2 Model equations.- 15.3 Numerical results.- 15.4 References.- 16 Application of inverse scattering to oil field evaluation problems.- 16.1 Extended Born approximation.- 16.2 An inversion approach.- 16.3 Imaging pits in corroded steel casings.- 16.4 References.- 17 Solutions to problems from previous parts.- 17.1 Part 5.- 17.2 Part 7.- 17.3 Part 9.- 17.4 References.
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pt. 6 : gw ISBN 9783540941576
内容説明
This is the sixth volume in Avner Friedman's collection of "Mathematics in Industrial Problems". These books aim to foster interaction between industry and mathematics at the "grass root" level of specific problems. The problems presented in this book arise from models developed by industrial scientists engaged in research and development of new or improved products. The author's sources are affiliated with a variety of industrial enterprises including Eastman Kodak Company, Ford Motor Company, 3M, General Motors, Paramax, IBM/T.J. Watson Research Center, Xerox Corporation/Webster Research Center, Cray Research Inc., and Motorola. The topics explored in this volume include: magnetisation in recording media; effective medium theory for colour, particle simulation in xerography; amorphous semiconductors, small device semiconductor, and smart power device; dopant diffusion in network; reaction-diffusion and dissolution of crystals in solution; permeation through flawed surfaces; statistical quality control; glassy polymers; wettability for heterogeneous surfaces; electrorheological fluids; remote sensing and data fusion; micromechanical structures, and sensors.
Open problems and references to mathematical literature are incorporated into many chapters. The final chapter contains solutions to problems raised in parts of the preceding volumes of "Mathematics in Industrial Problems", published in the "IMA Volumes in Mathematics and its Applications" series.
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pt. 3 : gw ISBN 9783540974369
内容説明
This volume is based on a seminar conducted by the author, during which scientists from industry presented industrial problems to mathematicians, including the mathematical formulation of the problems. Each of the first 17 chapters is based on a presentation by one of the speakers, and includes the industrial background, relevant mathematical literature, open mathematical problems and, in some cases, references to a solution or partial solution of the problem. The last chapter of the book contains references to solutions of problems presented in the previous volume, "Mathematics in Industrial Problems, Part 2". The topics discussed in this book include electro-chemical processes, polymers, waveguides, diffractive optics, semiconductors and optimization. The book aims to be of interest to mathematicians seeking to work on mathematical problems which arise in industry. It should also be of interest to mathematicians and scientists who would like to learn about the interaction between mathematics and industry, what type of problems arise, and how they are modelled.
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pt. 4 : gw ISBN 9783540976806
内容説明
This text presents industrial problems for mathematicians and offers their mathematical formulations, although not the solutions in every case, as most of the problems described are still open. The last chapter refers back to solutions to problems dealt with in a prior volume (part 3, published in the IMA series as volume 31). Among the topics tackled are semiconductor devices and processing, particles dynamics, polymer chains and electrophoresis, catalytic converter, robotics and CFD in the automobile industry, superconductivity, magnetic storage devices, signal processing and experimental design.
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pt. 5 : gw ISBN 9783540979371
内容説明
Developed from the cooperation between mathematicians and industrial scientists on the "grass roots" level of specific problems, this book is the most recent in a collection of self-contained volumes which present industrial problems to mathematicians. Topics include: imaging and visualization, diffusion in glassy and swelling polymers, composite materials, plastic flows, coating of fibre optics, communications, colloidal dispersion, stress in semiconductors, micromagnetics, photobleaching, and machine vision. Many chapters offer open problems and references, while the last chapter contains solutions to problems raised in previous volumes of "Mathematics in Industrial Problems, Parts 2, 3, and 4", published in the "IMA" series as "Volumes 24, 31, and 38 respectively.
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