MINNESOTA UNIV MINNEAPOLIS SCHOOL OF MATHEMATICS
Overview
Works:  24 works in 28 publications in 1 language and 28 library holdings 

Classifications:  U394.M55, 
Publication Timeline
.
Most widely held works by
MINNESOTA UNIV MINNEAPOLIS SCHOOL OF MATHEMATICS
Ergodic theory of dynamical systems. volume i(
Book
)
1 edition published in 1966 in English and held by 1 WorldCat member library worldwide
1 edition published in 1966 in English and held by 1 WorldCat member library worldwide
QuasiLinear Elliptic and Parabolic Equations(
Book
)
1 edition published in 1971 in English and held by 1 WorldCat member library worldwide
In this report the authors give an outline of the work performed under the contract. For more detailed discussions the authors refer to the five technical reports which go with this terminal report. The titles of the technical reports are the following: Similarity profiles of flows through porous media; Asymptotic behaviour of solutions of the porous media equation; On the asymptotic behaviour of velocity profiles in laminar boundary layers; Limit conditions on the solutions of quasilinear elliptic and parabolic equations, and, On the stability of symmetric and asymmetric concentration profiles in catalyst particles
1 edition published in 1971 in English and held by 1 WorldCat member library worldwide
In this report the authors give an outline of the work performed under the contract. For more detailed discussions the authors refer to the five technical reports which go with this terminal report. The titles of the technical reports are the following: Similarity profiles of flows through porous media; Asymptotic behaviour of solutions of the porous media equation; On the asymptotic behaviour of velocity profiles in laminar boundary layers; Limit conditions on the solutions of quasilinear elliptic and parabolic equations, and, On the stability of symmetric and asymmetric concentration profiles in catalyst particles
Generalized Inverses of Linear Differential Operators(
Book
)
1 edition published in 1978 in English and held by 1 WorldCat member library worldwide
In recent years there has been much activity in the area of generalized inverses of linear operators. It is the purpose of this paper to discuss generalized inverses of linear operators generated by ordinary linear differential equations with a view to examination of an entire class of such inverses. The class of inverses considered includes as special cases the analogue of the MoorePenrose generalized inverse for matrices and the group inverse for square matrices. We also discuss the application of such inverses in problems of branching of solutions of nonlinear boundaryvalue problems. (Author)
1 edition published in 1978 in English and held by 1 WorldCat member library worldwide
In recent years there has been much activity in the area of generalized inverses of linear operators. It is the purpose of this paper to discuss generalized inverses of linear operators generated by ordinary linear differential equations with a view to examination of an entire class of such inverses. The class of inverses considered includes as special cases the analogue of the MoorePenrose generalized inverse for matrices and the group inverse for square matrices. We also discuss the application of such inverses in problems of branching of solutions of nonlinear boundaryvalue problems. (Author)
Sensor Management and Nonlinear Filtering Research(
Book
)
2 editions published in 1998 in English and held by 1 WorldCat member library worldwide
This grant is supporting development of mathematical foundations for sensor management and nonlinear filtering. The accomplishments so far are in two areas: (1) The use of Interactive Multiple Model Kalman Filters (IMMKF) with a metric called discrimination gain (DG); and (2) the use of nonlinear filtering, (NLF) in the tracking of target elevation for objects flying close to a reflecting surface. In the case of IMMKF, we demonstrate, using simulated data, that IMMKF can be used to compute the information gain when multiple sensors observe a collection of maneuvering airborne targets. In the case of NLF, we demonstrate the feasibility of using NLF methods for altitude tracking in multipath
2 editions published in 1998 in English and held by 1 WorldCat member library worldwide
This grant is supporting development of mathematical foundations for sensor management and nonlinear filtering. The accomplishments so far are in two areas: (1) The use of Interactive Multiple Model Kalman Filters (IMMKF) with a metric called discrimination gain (DG); and (2) the use of nonlinear filtering, (NLF) in the tracking of target elevation for objects flying close to a reflecting surface. In the case of IMMKF, we demonstrate, using simulated data, that IMMKF can be used to compute the information gain when multiple sensors observe a collection of maneuvering airborne targets. In the case of NLF, we demonstrate the feasibility of using NLF methods for altitude tracking in multipath
Sensor Management Research(
Book
)
3 editions published between 1996 and 1997 in English and held by 1 WorldCat member library worldwide
This grant is supporting development of mathematical foundations for sensor management systems. This year's accomplishments are in three areas: Extension of a Kalmanfilter based discrimination metric to interacting multiple model filters; extension of sensor management based on Joint Multitarget Probabilities to incorporate multiple sensor modes and target classification; and development of fast methods to solve the FokkerPlanck equation for realtime nonlinear filtering applications. To support sensor management representations of multitarget probability densities must be developed that model the uncertainty between quantities such as the number of targets, their locations and their class. To solve this problem and study it in a simple setting, the notion of Joint Multitarget Probabilities for detection, tracking, and target classification was developed and tested. In certain cases the timeevolution of these probabilities is characterized by a partial differential equation called the FokkerPlanck equation leading to a nonlinear filter. Several prototype nonlinear filters using the Alternating Direction Implicit scheme to solve the FokkerPlanck equation in realtime were formulated. In these applications it seems to offer significant improvement in estimation performance at a supportable cost in computational load
3 editions published between 1996 and 1997 in English and held by 1 WorldCat member library worldwide
This grant is supporting development of mathematical foundations for sensor management systems. This year's accomplishments are in three areas: Extension of a Kalmanfilter based discrimination metric to interacting multiple model filters; extension of sensor management based on Joint Multitarget Probabilities to incorporate multiple sensor modes and target classification; and development of fast methods to solve the FokkerPlanck equation for realtime nonlinear filtering applications. To support sensor management representations of multitarget probability densities must be developed that model the uncertainty between quantities such as the number of targets, their locations and their class. To solve this problem and study it in a simple setting, the notion of Joint Multitarget Probabilities for detection, tracking, and target classification was developed and tested. In certain cases the timeevolution of these probabilities is characterized by a partial differential equation called the FokkerPlanck equation leading to a nonlinear filter. Several prototype nonlinear filters using the Alternating Direction Implicit scheme to solve the FokkerPlanck equation in realtime were formulated. In these applications it seems to offer significant improvement in estimation performance at a supportable cost in computational load
Regularity Properties of Flows through Porous Media: The Interface(
Book
)
1 edition published in 1969 in English and held by 1 WorldCat member library worldwide
1 edition published in 1969 in English and held by 1 WorldCat member library worldwide
Gauge Theories and Spontaneous Symmetry Breaking(
Book
)
1 edition published in 1980 in English and held by 1 WorldCat member library worldwide
This report summarizes attempts to understand in what way spontaneous symmetry breaking arose in the context of guage field theories of elementary particles. The main interest was in knowing whether techniques of bifurcation theory could be applied to the problem of spontaneous symmetry breaking in gauge field theories. It was felt that the symmetry breaking used by the physicists (a procedure known as the Higgs mechanism) is not precisely a bifurcation problem in the usual sense of the term, but more a matter of fixing a guage and thereby reducing the amount of symmetry of the problem. In other words, it is not really a matter of 'spontaneous' symmetry breaking
1 edition published in 1980 in English and held by 1 WorldCat member library worldwide
This report summarizes attempts to understand in what way spontaneous symmetry breaking arose in the context of guage field theories of elementary particles. The main interest was in knowing whether techniques of bifurcation theory could be applied to the problem of spontaneous symmetry breaking in gauge field theories. It was felt that the symmetry breaking used by the physicists (a procedure known as the Higgs mechanism) is not precisely a bifurcation problem in the usual sense of the term, but more a matter of fixing a guage and thereby reducing the amount of symmetry of the problem. In other words, it is not really a matter of 'spontaneous' symmetry breaking
Asymptotic Behaviour of Solutions of the Porous Media Equation(
Book
)
1 edition published in 1971 in English and held by 1 WorldCat member library worldwide
A degenerate quasilinear parabolic equation, which arises in the study of fluid flow through porous media is investigated. It is shown that the solutions of a class of mixed initialboundary value problems in the domain x> 0, t> 0 converge upon a suitably chosen similarity solution as t approaches infinity. The rate of convergence is discussed. (Author)
1 edition published in 1971 in English and held by 1 WorldCat member library worldwide
A degenerate quasilinear parabolic equation, which arises in the study of fluid flow through porous media is investigated. It is shown that the solutions of a class of mixed initialboundary value problems in the domain x> 0, t> 0 converge upon a suitably chosen similarity solution as t approaches infinity. The rate of convergence is discussed. (Author)
The Computation of Crystalline Microstructure(
Book
)
1 edition published in 1992 in English and held by 1 WorldCat member library worldwide
We describe a twodimensional model of crystalline martensitic microstructure, and we present a new visualization of computational results for the finite element approximation of solutions to the variational problem with microstructure on a sequence of refined meshes
1 edition published in 1992 in English and held by 1 WorldCat member library worldwide
We describe a twodimensional model of crystalline martensitic microstructure, and we present a new visualization of computational results for the finite element approximation of solutions to the variational problem with microstructure on a sequence of refined meshes
Functional analysis and stochastic processes(
Book
)
1 edition published in 1969 in English and held by 1 WorldCat member library worldwide
Research was continued in the areas of Wiener and Feynman integrals, analytic functions of several complex variables, ergodic theory, and Markov and other stochastic processes. (Author)
1 edition published in 1969 in English and held by 1 WorldCat member library worldwide
Research was continued in the areas of Wiener and Feynman integrals, analytic functions of several complex variables, ergodic theory, and Markov and other stochastic processes. (Author)
Similarity Profiles of Flows through Porous Media(
Book
)
1 edition published in 1971 in English and held by 1 WorldCat member library worldwide
The authors investigate the existence and uniqueness of a class of similarity solutions of an equation which arises in the study of fluid flow through porous media
1 edition published in 1971 in English and held by 1 WorldCat member library worldwide
The authors investigate the existence and uniqueness of a class of similarity solutions of an equation which arises in the study of fluid flow through porous media
Inertial Manifolds for NavierStokes Equations and Related Dynamical Systems(
Book
)
1 edition published in 1991 in English and held by 1 WorldCat member library worldwide
1 edition published in 1991 in English and held by 1 WorldCat member library worldwide
Dynamics of HomogeneousHeterogeneous Reactors(
)
1 edition published in 1992 in English and held by 0 WorldCat member libraries worldwide
In many industrial processes both heterogeneous and homogeneous reactions can occur, and these reactions are strongly coupled through heat and mass transfer and reactive intermediates. Surface reactions can heat the boundary layer sufficiently to ignite homogeneous reaction, can deplete the boundary layer of a limiting reactant, and can act as a source or sink of free radicals. We have studied combustion reactions over catalytic foils and in catalytic monoliths for simple oxidations such as CH4 + O2, NH3 + O2, CH4 + NO and NH3 + NO. For most reactions and geometries, we observe heterogeneous and homogeneous ignitions and extinctions and selfsustaining autothermal steady states. The range of compositions for which an autothermal state exists depends sensitively on the inlet gas velocity. For stagnation point flow, reaction over a catalytic foil can be modeled by a onedimensional boundary value problem in which saddlenode bifurcations correspond to ignitions and extinctions. Computations for a model with simplified kinetics reproduce the experimental dependence on input power to the foil and inlet gas composition. Calculations also show that the dynamics are affected strongly by the inlet gas velocity
1 edition published in 1992 in English and held by 0 WorldCat member libraries worldwide
In many industrial processes both heterogeneous and homogeneous reactions can occur, and these reactions are strongly coupled through heat and mass transfer and reactive intermediates. Surface reactions can heat the boundary layer sufficiently to ignite homogeneous reaction, can deplete the boundary layer of a limiting reactant, and can act as a source or sink of free radicals. We have studied combustion reactions over catalytic foils and in catalytic monoliths for simple oxidations such as CH4 + O2, NH3 + O2, CH4 + NO and NH3 + NO. For most reactions and geometries, we observe heterogeneous and homogeneous ignitions and extinctions and selfsustaining autothermal steady states. The range of compositions for which an autothermal state exists depends sensitively on the inlet gas velocity. For stagnation point flow, reaction over a catalytic foil can be modeled by a onedimensional boundary value problem in which saddlenode bifurcations correspond to ignitions and extinctions. Computations for a model with simplified kinetics reproduce the experimental dependence on input power to the foil and inlet gas composition. Calculations also show that the dynamics are affected strongly by the inlet gas velocity
StateSelected Chemical Reaction Dynamics at the S Matrix Level: Final State Specificities of NearThreshold Processes at
Low and High Energies(
)
1 edition published in 1992 in English and held by 0 WorldCat member libraries worldwide
Statetostate reaction probabilities are found to be highly final state specific at stateselected threshold energies for the reactions 0 + H2 OH + H and H + H2  H2 + H. The study includes initial rotational states with quantum numbers 015, and the specificity is especially dramatic for the more highly rotationally excited reactants. The analysis is based on accurate quantum mechanical reactive scattering calculations. Finalstate specificity is shown in general to increase with the rotational quantum number of the reactant diatom, and the trends are confirmed for both zero and nonzero values of the total angular momentum
1 edition published in 1992 in English and held by 0 WorldCat member libraries worldwide
Statetostate reaction probabilities are found to be highly final state specific at stateselected threshold energies for the reactions 0 + H2 OH + H and H + H2  H2 + H. The study includes initial rotational states with quantum numbers 015, and the specificity is especially dramatic for the more highly rotationally excited reactants. The analysis is based on accurate quantum mechanical reactive scattering calculations. Finalstate specificity is shown in general to increase with the rotational quantum number of the reactant diatom, and the trends are confirmed for both zero and nonzero values of the total angular momentum
Stabilized Interior Penalty Methods for the TimeHarmonic Maxwell Equations(
)
1 edition published in 2001 in English and held by 0 WorldCat member libraries worldwide
We propose stabilized interior penalty discontinuous Galerkin methods for the indefinite timeharmonic Maxwell system. The methods are based on a mixed formulation of the boundary value problem chosen to provide control on the divergence of the electric field. We prove optimal error estimates for the methods in the special case of smooth coefficients and perfectly conducting boundary using a duality approach
1 edition published in 2001 in English and held by 0 WorldCat member libraries worldwide
We propose stabilized interior penalty discontinuous Galerkin methods for the indefinite timeharmonic Maxwell system. The methods are based on a mixed formulation of the boundary value problem chosen to provide control on the divergence of the electric field. We prove optimal error estimates for the methods in the special case of smooth coefficients and perfectly conducting boundary using a duality approach
The Conformation of Fluid Membranes: Monte Carlo Simulations by D. M Kroll(
)
1 edition published in 1992 in English and held by 0 WorldCat member libraries worldwide
The conformation and scaling properties of selfavoiding fluid membranes with an extrinsic bending rigidity K were studied with the use of Monte Carlo methods. For K = 0, the results are consistent with branched polymer behavior at large length scales. There is a smooth crossover from a crumpled to an extended state with increasing K, with a peak in the specific heat when the persistence length reaches the system size. The scaledependent effective bending rigidity is a decreasing function of system size for all bare rigidities. These results indicate that fluid membranes are always crumpled at sufficiently long length scales
1 edition published in 1992 in English and held by 0 WorldCat member libraries worldwide
The conformation and scaling properties of selfavoiding fluid membranes with an extrinsic bending rigidity K were studied with the use of Monte Carlo methods. For K = 0, the results are consistent with branched polymer behavior at large length scales. There is a smooth crossover from a crumpled to an extended state with increasing K, with a peak in the specific heat when the persistence length reaches the system size. The scaledependent effective bending rigidity is a decreasing function of system size for all bare rigidities. These results indicate that fluid membranes are always crumpled at sufficiently long length scales
CharacteristicGalerkin and Galerkin/LeastSquares SpaceTime Formulations for the AdvectionDiffusion Equation with TimeDependent
Domains by
Olivier Pironneau(
)
1 edition published in 1992 in English and held by 0 WorldCat member libraries worldwide
For the advectiondiffusion equation, the characteristicGalerkin formulations are obtained by temporal discretization of the total derivative. These formulations, by construction, are EulerianLagrangian, and therefore can handle timedependent domains without difficulty. The Galerkin/leastsquares spacetime formulation, on the other hand, is written over the spacetime domain of a problem, and therefore can handle timedependent domains with no implementational difficulty. The purpose of this paper is to compare these two formulations based on error estimates and numerical performance, in the context of the advectiondiffusion equation
1 edition published in 1992 in English and held by 0 WorldCat member libraries worldwide
For the advectiondiffusion equation, the characteristicGalerkin formulations are obtained by temporal discretization of the total derivative. These formulations, by construction, are EulerianLagrangian, and therefore can handle timedependent domains without difficulty. The Galerkin/leastsquares spacetime formulation, on the other hand, is written over the spacetime domain of a problem, and therefore can handle timedependent domains with no implementational difficulty. The purpose of this paper is to compare these two formulations based on error estimates and numerical performance, in the context of the advectiondiffusion equation
Computational Electromagnetics(
)
2 editions published between 2004 and 2007 in English and held by 0 WorldCat member libraries worldwide
Progress in the development of fast, errorcontrollable algorithms for the simulation of electromagnetic scattering throughout the frequency spectrum is reported. Advances are described in the development of (1) accelerated, highorder methods for the solution of general, penetrable scattering problems in the lowtomoderate frequency regime; (2) spectral methods for the solution of approximate highfrequency models (geometrical optics GO ); and (3) general errorcontrollable highfrequency scattering solvers. Major accomplishments include the completion of work on (1) in relation with scalar scattering models and the extension of the algorithms to vector models and composite backgrounds; the design, implementation and refinement of a spectral/discontinuous Galerkin method to resolve the GO model in phase space; the advancement of a spectral inverse raytracing approach; the development of methods for the evaluation of highfrequency scattering off composite rough surfaces; the derivation of general highfrequency scattering solvers applicable to both single and multiplescattering configurations consisting of bounded obstacles in two and three dimensions; and the analysis and implementation of strategies to account for and accelerate the evaluation of multiplescattering effects
2 editions published between 2004 and 2007 in English and held by 0 WorldCat member libraries worldwide
Progress in the development of fast, errorcontrollable algorithms for the simulation of electromagnetic scattering throughout the frequency spectrum is reported. Advances are described in the development of (1) accelerated, highorder methods for the solution of general, penetrable scattering problems in the lowtomoderate frequency regime; (2) spectral methods for the solution of approximate highfrequency models (geometrical optics GO ); and (3) general errorcontrollable highfrequency scattering solvers. Major accomplishments include the completion of work on (1) in relation with scalar scattering models and the extension of the algorithms to vector models and composite backgrounds; the design, implementation and refinement of a spectral/discontinuous Galerkin method to resolve the GO model in phase space; the advancement of a spectral inverse raytracing approach; the development of methods for the evaluation of highfrequency scattering off composite rough surfaces; the derivation of general highfrequency scattering solvers applicable to both single and multiplescattering configurations consisting of bounded obstacles in two and three dimensions; and the analysis and implementation of strategies to account for and accelerate the evaluation of multiplescattering effects
Electromagnetic Scattering(
)
1 edition published in 2001 in English and held by 0 WorldCat member libraries worldwide
The problems and techniques addressed under the present contract deal with issues of analysis and computation in electromagnetics. The primary goal consists of the development of efficient numerical tools for the prediction of scattered fields in a number of practical configurations. For this, substantial effort will be devoted to the extension and enhancement 0 the Method of Variation of Boundaries (MVB). Specific objectives in connection with MVB include: (1) advancement and implementation of algorithmic improvements for very highorder calculations; (2) application to the solution of eigenvalue problems (related to cavities, resonators and waveguides); to the calculation of electromagnetic scattering from damaged objects and rough terrain; and to inverse scattering problems. (3) Concurrent with these endeavors the program will pursue the incorporation of the boundaryvariation approach in more classical computational techniques, such as the finiteelement methods (FEM). A first instance of such interactions will be sought through the implementation of highorder boundary perturbation approximations to computational radiation conditions (typically imposed on separable geometries). To enable and enhance such applications, the plan includes the development of new (highorder) discontinuous Galerkin (DG) finite element approach to electromagnetic scattering calculations which is expected to provide an advantageous setting for adaptivity and parallelization. Alternative highorder methods (e.g., based on integral equation formulations) will also be considered
1 edition published in 2001 in English and held by 0 WorldCat member libraries worldwide
The problems and techniques addressed under the present contract deal with issues of analysis and computation in electromagnetics. The primary goal consists of the development of efficient numerical tools for the prediction of scattered fields in a number of practical configurations. For this, substantial effort will be devoted to the extension and enhancement 0 the Method of Variation of Boundaries (MVB). Specific objectives in connection with MVB include: (1) advancement and implementation of algorithmic improvements for very highorder calculations; (2) application to the solution of eigenvalue problems (related to cavities, resonators and waveguides); to the calculation of electromagnetic scattering from damaged objects and rough terrain; and to inverse scattering problems. (3) Concurrent with these endeavors the program will pursue the incorporation of the boundaryvariation approach in more classical computational techniques, such as the finiteelement methods (FEM). A first instance of such interactions will be sought through the implementation of highorder boundary perturbation approximations to computational radiation conditions (typically imposed on separable geometries). To enable and enhance such applications, the plan includes the development of new (highorder) discontinuous Galerkin (DG) finite element approach to electromagnetic scattering calculations which is expected to provide an advantageous setting for adaptivity and parallelization. Alternative highorder methods (e.g., based on integral equation formulations) will also be considered
Partial Differential Equations from the Materials Sciences: Analysis and Computation(
)
1 edition published in 1998 in English and held by 0 WorldCat member libraries worldwide
This report describes accomplishments in the areas of electromagnetic scattering and smart materials achieved under Grant No. F496209510113. With regards to problems of wave propagation, advances in the development of highorder perturbation methods are reported. These include the derivation and coding of algorithms for the numerical solution of the scalar and vector forward scattering problems for two and threedimensional configurations and the formulation of corresponding approaches to inverse scattering calculations and to the estimation of normal and quasinormal cavity modes. Concurrent achievements in the study of smart materials are also recounted here. They include the development of nonlinear homogenization theories intended to capture overall elastic behaviors (e.g., of shapememory alloys, SMA), or magnetic and rheological responses (such as those of magnetorheological fluids, MRF). The latter project was undertaken in collaboration with scientists at the Lord Corporation, the worldwide leader in MRF technology, and was geared towards the incorporation of advanced mathematical modeling and simulations into the design of MRF
1 edition published in 1998 in English and held by 0 WorldCat member libraries worldwide
This report describes accomplishments in the areas of electromagnetic scattering and smart materials achieved under Grant No. F496209510113. With regards to problems of wave propagation, advances in the development of highorder perturbation methods are reported. These include the derivation and coding of algorithms for the numerical solution of the scalar and vector forward scattering problems for two and threedimensional configurations and the formulation of corresponding approaches to inverse scattering calculations and to the estimation of normal and quasinormal cavity modes. Concurrent achievements in the study of smart materials are also recounted here. They include the development of nonlinear homogenization theories intended to capture overall elastic behaviors (e.g., of shapememory alloys, SMA), or magnetic and rheological responses (such as those of magnetorheological fluids, MRF). The latter project was undertaken in collaboration with scientists at the Lord Corporation, the worldwide leader in MRF technology, and was geared towards the incorporation of advanced mathematical modeling and simulations into the design of MRF
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