CARNEGIEMELLON UNIV PITTSBURGH PA Dept. of MATHEMATICS
Overview
Works:  46 works in 50 publications in 1 language and 50 library holdings 

Classifications:  QL628.N8, 510.7808 
Publication Timeline
.
Most widely held works by
CARNEGIEMELLON UNIV PITTSBURGH PA Dept. of MATHEMATICS
The AEMS (Analysis of Electrical and Mechanical Systems) Project in Applied Mathematics at CarnegieMellon University(
Book
)
2 editions published between 1971 and 1982 in English and held by 2 WorldCat member libraries worldwide
This is a record of a research project in applied mathematics at CarnegieMellon University. The project is called Analysis of Electrical and Mechanical Systems or AEMS for short. The goals of AEMS were threefold: (a) to apply mathematical analysis to treat new problems arising in science and technology; (b) to develop new mathematical concepts and structures using facets of science and technology as models; and (c) to help students start a career in the interesting area of applied mathematics
2 editions published between 1971 and 1982 in English and held by 2 WorldCat member libraries worldwide
This is a record of a research project in applied mathematics at CarnegieMellon University. The project is called Analysis of Electrical and Mechanical Systems or AEMS for short. The goals of AEMS were threefold: (a) to apply mathematical analysis to treat new problems arising in science and technology; (b) to develop new mathematical concepts and structures using facets of science and technology as models; and (c) to help students start a career in the interesting area of applied mathematics
Controlled Diffusion Approximations for Controlled Queueing Systems(
Book
)
2 editions published in 1998 in English and held by 1 WorldCat member library worldwide
Four problem areas were studied. These are: (1) controlled heavy traffic queueing systems, (2) queueing systems with due dates, (3) backwardforward stochastic differential equations, and (4) GinzburgLandau equations and evolving interfaces. In areas (1) and (2), diffusion approximations were obtained for queues in heavy traffic. In (3), connections were established between quasilinear partial differential equations and diffusion processes constructed via a new class of stochastic differential equations. Finally, (4) provides a study of the partial differential equation characterizing vortices in superconducting material in three dimensions
2 editions published in 1998 in English and held by 1 WorldCat member library worldwide
Four problem areas were studied. These are: (1) controlled heavy traffic queueing systems, (2) queueing systems with due dates, (3) backwardforward stochastic differential equations, and (4) GinzburgLandau equations and evolving interfaces. In areas (1) and (2), diffusion approximations were obtained for queues in heavy traffic. In (3), connections were established between quasilinear partial differential equations and diffusion processes constructed via a new class of stochastic differential equations. Finally, (4) provides a study of the partial differential equation characterizing vortices in superconducting material in three dimensions
The AEMs Project in Applied Mathematics at CarnegieMellon University. Comprehensive Report, Period 19701980(
Book
)
1 edition published in 1980 in English and held by 1 WorldCat member library worldwide
The aims of the Analysis of Electrical and Mechanical Systems Project are threefold: to apply mathematical analysis to new problems arising in science and technology; to develop new mathematical concepts and structures using facets of science and technology as models; and to help students start a career in the interesting area of applied mathematics. Included is a list of papers published since 1970. Abstracts are included
1 edition published in 1980 in English and held by 1 WorldCat member library worldwide
The aims of the Analysis of Electrical and Mechanical Systems Project are threefold: to apply mathematical analysis to new problems arising in science and technology; to develop new mathematical concepts and structures using facets of science and technology as models; and to help students start a career in the interesting area of applied mathematics. Included is a list of papers published since 1970. Abstracts are included
A Linear Programming Model for Design of Communications Networks with Time Varying Probabilistic Demands(
Book
)
1 edition published in 1980 in English and held by 1 WorldCat member library worldwide
1 edition published in 1980 in English and held by 1 WorldCat member library worldwide
On the Finite Element Approximation of the StreamfunctionVorticity Equations(
Book
)
1 edition published in 1984 in English and held by 1 WorldCat member library worldwide
Finite element algorithms are presented for the approximate solution of the streamfunctionvorticity equations of steady incompressible viscous flows. Both the linear Stokes and the nonlinear NavierStokes equations are considered. The methods discussed require low continuity finite element spaces and do not require any artificial specification of the vorticity at solid boundaries. Particular attention is paid to methods for multiply connected domains and to theoretical and computational estimates for the accuracy of the algorithms. Brief consideration is also given to three dimensional problems, to exterior problems, and to the recovery of the pressure field. (Author)
1 edition published in 1984 in English and held by 1 WorldCat member library worldwide
Finite element algorithms are presented for the approximate solution of the streamfunctionvorticity equations of steady incompressible viscous flows. Both the linear Stokes and the nonlinear NavierStokes equations are considered. The methods discussed require low continuity finite element spaces and do not require any artificial specification of the vorticity at solid boundaries. Particular attention is paid to methods for multiply connected domains and to theoretical and computational estimates for the accuracy of the algorithms. Brief consideration is also given to three dimensional problems, to exterior problems, and to the recovery of the pressure field. (Author)
Final Report For Grant AFOSR820213(
Book
)
1 edition published in 1985 in English and held by 1 WorldCat member library worldwide
This effort was focused on basic work on the numerical solution of the NavierStokes equations for incompressible flows. A basic problem in this theory is the compatibility of the finite element space used to approximate the pressure field. The investigator was able to devise a simple test of the finite element space. An inspection of the solution to this linear system immediately reveals whether the proposed scheme is stable. A second area of activity was an investigation of the applicability of the stream function formulation of the NavierStokes equations. This effort resulted in a number of publications in the scientific literature. Author
1 edition published in 1985 in English and held by 1 WorldCat member library worldwide
This effort was focused on basic work on the numerical solution of the NavierStokes equations for incompressible flows. A basic problem in this theory is the compatibility of the finite element space used to approximate the pressure field. The investigator was able to devise a simple test of the finite element space. An inspection of the solution to this linear system immediately reveals whether the proposed scheme is stable. A second area of activity was an investigation of the applicability of the stream function formulation of the NavierStokes equations. This effort resulted in a number of publications in the scientific literature. Author
On Phase Transitions with Interfacial Energy(
Book
)
1 edition published in 1985 in English and held by 1 WorldCat member library worldwide
This article considers a fluid which has free energy psi(the), a prescribed function of density rho, and which occupies a fixed container omega, with omega a bounded region in R sub 3
1 edition published in 1985 in English and held by 1 WorldCat member library worldwide
This article considers a fluid which has free energy psi(the), a prescribed function of density rho, and which occupies a fixed container omega, with omega a bounded region in R sub 3
Fast Algorithms for the CMU Attached Processor System(
Book
)
1 edition published in 1986 in English and held by 1 WorldCat member library worldwide
This project concerned research on developing fast algorithms for implementation on a parallel processing system. Titles of research papers resulting from this effort include the following: Least squares methods for fourth order problems, Least squares methods for problems with corner singularities, Finite element methods for the streamfunctionvorticity equatious, and On substructuring algorithms, solution techniques for the numerical solution of partial differential equations, On central difference approximations to general second order elliptic equations, and A modified defect correction algorithm for the solution of singularly perturbed differential equations
1 edition published in 1986 in English and held by 1 WorldCat member library worldwide
This project concerned research on developing fast algorithms for implementation on a parallel processing system. Titles of research papers resulting from this effort include the following: Least squares methods for fourth order problems, Least squares methods for problems with corner singularities, Finite element methods for the streamfunctionvorticity equatious, and On substructuring algorithms, solution techniques for the numerical solution of partial differential equations, On central difference approximations to general second order elliptic equations, and A modified defect correction algorithm for the solution of singularly perturbed differential equations
On Irwin's and Achenbach's Expressions for the Energy Release Rate(
Book
)
1 edition published in 1979 in English and held by 1 WorldCat member library worldwide
Using a constitutive equation and antiplane shear field introduced by Knowles, we show that the expressions of Irwin and Achenback for the energy release rate are not generally valid for nonlinear elastic materials. (Author)
1 edition published in 1979 in English and held by 1 WorldCat member library worldwide
Using a constitutive equation and antiplane shear field introduced by Knowles, we show that the expressions of Irwin and Achenback for the energy release rate are not generally valid for nonlinear elastic materials. (Author)
Note on the Energy Release Rate for a Crack Starting from the Apex of a Wedge(
Book
)
1 edition published in 1980 in English and held by 1 WorldCat member library worldwide
Griffith was apparently the first to employ the energy release rate 'G' as a critical condition of crack extension. In this note we will show, however, that if a crack starts from the apex of a wedge, the initial value of 'G' is zero, although the stresses at the crack tip are unbounded. This example suggests that you cannot use the initial energy release rate as a critical condition of crack extension unless the openingangle of the crack faces in the reference is precisely zero. Since the order of the singularity of the strain energy density is less than one, this result may be predicted mathematically but it is not trivial physically. We confine our problem to a simple mode II crack; the given solutions are then simple and of closedform so that we can examine the precise dependence of 'G' on the crack length a. To the author's knowledge, no such closedform solutions for an arbitrary crack length a have been presented. (Author)
1 edition published in 1980 in English and held by 1 WorldCat member library worldwide
Griffith was apparently the first to employ the energy release rate 'G' as a critical condition of crack extension. In this note we will show, however, that if a crack starts from the apex of a wedge, the initial value of 'G' is zero, although the stresses at the crack tip are unbounded. This example suggests that you cannot use the initial energy release rate as a critical condition of crack extension unless the openingangle of the crack faces in the reference is precisely zero. Since the order of the singularity of the strain energy density is less than one, this result may be predicted mathematically but it is not trivial physically. We confine our problem to a simple mode II crack; the given solutions are then simple and of closedform so that we can examine the precise dependence of 'G' on the crack length a. To the author's knowledge, no such closedform solutions for an arbitrary crack length a have been presented. (Author)
Computational Methods for Electromagnetic Scattering and Structural Phase Transitions(
Book
)
2 editions published in 1997 in English and held by 1 WorldCat member library worldwide
Computational algorithms for electromagnetic scattering and structured phase transitions are investigated. For scattering, three contributions are presented: (1) Analysis of spurious offset fields, (2) the use of divergence boundary conditions, (3) analysis of covolume (unstructured FDTD) algorithms with estimates of convergence rates. For structural phase transitions adaptive mesh techniques are combined with finite dimensional optimization algorithms to compute new global minimizers for martensitic phase transformations
2 editions published in 1997 in English and held by 1 WorldCat member library worldwide
Computational algorithms for electromagnetic scattering and structured phase transitions are investigated. For scattering, three contributions are presented: (1) Analysis of spurious offset fields, (2) the use of divergence boundary conditions, (3) analysis of covolume (unstructured FDTD) algorithms with estimates of convergence rates. For structural phase transitions adaptive mesh techniques are combined with finite dimensional optimization algorithms to compute new global minimizers for martensitic phase transformations
Some Questions and Open Problems in Continuum Mechanics and Population Dynamics(
Book
)
1 edition published in 1983 in English and held by 1 WorldCat member library worldwide
1 edition published in 1983 in English and held by 1 WorldCat member library worldwide
Interim Technical Report, 1 June 198231 May 1983, Grant AFOSR820213(
Book
)
1 edition published in 1983 in English and held by 1 WorldCat member library worldwide
During this period, research continued in the area of numerical solution of the incompressible NavierStokes equations. In particular, the following topics have been addressed: (1) The question of achieving stable discretizations of the imcompressibility constraint; (2) The problem of obtaining accurate solutions in the limit of large Reynolds numbers; and (3) Devising efficient numerical solution algorithms for solving the nonlinear algebraic systems of equations arisings from the discretization step. A necessary condition for convergence of the discrete approximation was obtained. A major result achieved has been to show that many often used low order element pairs are, in fact, unstable in the sense of this criterion. In addition, new simple low order element pairs were introduced and proved to be stable. Concerning the second topic noted above, the investigator has taken an approach based on the idea that h (the discretization parameter) needs to be small only in certain locations, namely in boundary layers. Finally, solving the algebraic systems which arise from the discretization remains a major difficulty. Two new approaches have been developed, one dependent on time marching to the steady state limit, and the other based on an adaptation of a method used in structural mechanics to the fluids case. Four new scientific papers have been generated in the report period, to be published in the referred literature. (Author)
1 edition published in 1983 in English and held by 1 WorldCat member library worldwide
During this period, research continued in the area of numerical solution of the incompressible NavierStokes equations. In particular, the following topics have been addressed: (1) The question of achieving stable discretizations of the imcompressibility constraint; (2) The problem of obtaining accurate solutions in the limit of large Reynolds numbers; and (3) Devising efficient numerical solution algorithms for solving the nonlinear algebraic systems of equations arisings from the discretization step. A necessary condition for convergence of the discrete approximation was obtained. A major result achieved has been to show that many often used low order element pairs are, in fact, unstable in the sense of this criterion. In addition, new simple low order element pairs were introduced and proved to be stable. Concerning the second topic noted above, the investigator has taken an approach based on the idea that h (the discretization parameter) needs to be small only in certain locations, namely in boundary layers. Finally, solving the algebraic systems which arise from the discretization remains a major difficulty. Two new approaches have been developed, one dependent on time marching to the steady state limit, and the other based on an adaptation of a method used in structural mechanics to the fluids case. Four new scientific papers have been generated in the report period, to be published in the referred literature. (Author)
Finite Element Analysis of Transonic Flows(
Book
)
1 edition published in 1980 in English and held by 1 WorldCat member library worldwide
Finite element algorithms were developed for the following class of problems: (1) Transonic flow problems governed by the potential equations; (2) Moving boundary problems; and (3) Incompressible flow problems governed by the NavierStokes equations
1 edition published in 1980 in English and held by 1 WorldCat member library worldwide
Finite element algorithms were developed for the following class of problems: (1) Transonic flow problems governed by the potential equations; (2) Moving boundary problems; and (3) Incompressible flow problems governed by the NavierStokes equations
Some Remarks on the Stefan Problem with Surface Structure. Stability and Thermal Influences in Nonlinear Continuum Mechanics(
)
2 editions published in 1990 in English and held by 0 WorldCat member libraries worldwide
This paper discusses a generalized Stefan problem which allows for supercooling and superheating and for capillarity in the interface between phases. Simple solutions are obtained indicating the chief differences between this problem and the classical Stefan problem. A weak formulation of the general problem is given
2 editions published in 1990 in English and held by 0 WorldCat member libraries worldwide
This paper discusses a generalized Stefan problem which allows for supercooling and superheating and for capillarity in the interface between phases. Simple solutions are obtained indicating the chief differences between this problem and the classical Stefan problem. A weak formulation of the general problem is given
New Techniques in Computational Fluid Dynamics: Algorithms, Analysis, Applications(
)
1 edition published in 1991 in English and held by 0 WorldCat member libraries worldwide
The overall goal of this research was the development and application of covolume methodology in CFD and related areas. The main framework of the covolume approach is now in place and its major characteristics are reasonably well understood. The research shows the algorithm to be a stable and accurate approach to computing viscous fluids on unstructured meshes. The covolume approach has several unique features, including an associated discrete vector field theory, which in turn permits covolume discretizations to exhibit important physical characteristics, for example being free of artificial vorticity creation. There is still need for work in compressible and three dimensional flows
1 edition published in 1991 in English and held by 0 WorldCat member libraries worldwide
The overall goal of this research was the development and application of covolume methodology in CFD and related areas. The main framework of the covolume approach is now in place and its major characteristics are reasonably well understood. The research shows the algorithm to be a stable and accurate approach to computing viscous fluids on unstructured meshes. The covolume approach has several unique features, including an associated discrete vector field theory, which in turn permits covolume discretizations to exhibit important physical characteristics, for example being free of artificial vorticity creation. There is still need for work in compressible and three dimensional flows
Behaviorbased language generation for believable agents by B Loyall(
)
1 edition published in 1995 in English and held by 0 WorldCat member libraries worldwide
We are studying how to create believable agents that perform actions and use natural language in interactive, animated, realtime worlds. We have extended Hap, our behaviorbased architecture for believable nonlinguistic agents, to better support natural language text generation. These extensions allow us to tightly integrate generation with other aspects of the agent, including action, perception, inference and emotion. We describe our approach, and show how it leads to agents with properties we believe important for believability, such as: using language and action together to accomplish communication goals; using perception to help make linguistic choices; varying generated text according to emotional state; and issuing the text in realtime with pauses, restarts and other breakdowns visible. Besides being useful in constructing believable agents, we feel these extensions may interest researchers seeking to generate language in other action architectures
1 edition published in 1995 in English and held by 0 WorldCat member libraries worldwide
We are studying how to create believable agents that perform actions and use natural language in interactive, animated, realtime worlds. We have extended Hap, our behaviorbased architecture for believable nonlinguistic agents, to better support natural language text generation. These extensions allow us to tightly integrate generation with other aspects of the agent, including action, perception, inference and emotion. We describe our approach, and show how it leads to agents with properties we believe important for believability, such as: using language and action together to accomplish communication goals; using perception to help make linguistic choices; varying generated text according to emotional state; and issuing the text in realtime with pauses, restarts and other breakdowns visible. Besides being useful in constructing believable agents, we feel these extensions may interest researchers seeking to generate language in other action architectures
Singular and BangBang Stochastic Control(
)
1 edition published in 1990 in English and held by 0 WorldCat member libraries worldwide
Research supported by this grant focussed on the regularity of the value function for multidimensional singular stochastic control problems. In addition, a multidimensional finitefuel problem has been studied, and known results for one dimensional problems have been extended to higher dimensions
1 edition published in 1990 in English and held by 0 WorldCat member libraries worldwide
Research supported by this grant focussed on the regularity of the value function for multidimensional singular stochastic control problems. In addition, a multidimensional finitefuel problem has been studied, and known results for one dimensional problems have been extended to higher dimensions
INFERENCE IN STOCHASTIC PROCESSES(
)
1 edition published in 1970 in English and held by 0 WorldCat member libraries worldwide
The investigation was designed to prepare a monograph on certain mathematical aspects of the inference theory of stochastic processes, the principal components of which are substantially completed. These include substantive treatments of the foundations of inference theory, i.e., the projective limits of probability spaces, of conditional probability distributions and expectations, which occupy a central position in the analysis of essentially all the problems of inference, some new or simplified proofs of the standard theory of martingales together with a demonstration of the equivalence of the martingale convergence and the AndersenJessen theory, of stochastic difference and differential equations in both the physical and social sciences, of Gaussian processes, and of hypothesis testing, parametric estimation, and prediction, as the latter three topics relate to inference theory
1 edition published in 1970 in English and held by 0 WorldCat member libraries worldwide
The investigation was designed to prepare a monograph on certain mathematical aspects of the inference theory of stochastic processes, the principal components of which are substantially completed. These include substantive treatments of the foundations of inference theory, i.e., the projective limits of probability spaces, of conditional probability distributions and expectations, which occupy a central position in the analysis of essentially all the problems of inference, some new or simplified proofs of the standard theory of martingales together with a demonstration of the equivalence of the martingale convergence and the AndersenJessen theory, of stochastic difference and differential equations in both the physical and social sciences, of Gaussian processes, and of hypothesis testing, parametric estimation, and prediction, as the latter three topics relate to inference theory
Nonlinear analysis, scientific computation, and continuum mechanics applied to the science of materials by
Morton E Gurtin(
)
1 edition published in 1993 in English and held by 0 WorldCat member libraries worldwide
This grant enabled the department to form the Research Group in Mathematical Materials Science in 1990, a group that formed the nucleus of the Center for Nonlinear Analysis, established in 1991, by the ARO. The Center has created a vigorous environment for collaboration among mathematicians and allied scientists. Within the international mathematics community the Center has assumed a leadership role, especially for questions related to materials science. The major research effort has focused toward developing, analyzing, and unifying mathematical models that characterize material behavior at a phenomenological level. The main thrust is applied nonlinear analysis, nonlinear continuum physics, and scientific computation. The educational goals have been to train young scientists, and to train and involve female and minority students in the sciences. Applied analysis, Continuum mechanics, Materials sciences
1 edition published in 1993 in English and held by 0 WorldCat member libraries worldwide
This grant enabled the department to form the Research Group in Mathematical Materials Science in 1990, a group that formed the nucleus of the Center for Nonlinear Analysis, established in 1991, by the ARO. The Center has created a vigorous environment for collaboration among mathematicians and allied scientists. Within the international mathematics community the Center has assumed a leadership role, especially for questions related to materials science. The major research effort has focused toward developing, analyzing, and unifying mathematical models that characterize material behavior at a phenomenological level. The main thrust is applied nonlinear analysis, nonlinear continuum physics, and scientific computation. The educational goals have been to train young scientists, and to train and involve female and minority students in the sciences. Applied analysis, Continuum mechanics, Materials sciences
more
fewer
Audience Level
0 

1  
Kids  General  Special 
Related Identities
Associated Subjects
Languages