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113
Some Large Scale Matrix Computation Problems
 J. Comput. Appl. Math
"... The central mathematical problem of this report is to bound the quantity u T f(A)v, where A is a given n \Theta n real matrix, u and v are given nvectors, and f is a given smooth function. Estimating the entries and the trace of the inverse of a matrix and the determinant of a matrix can be clas ..."
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Cited by 22 (6 self)
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The central mathematical problem of this report is to bound the quantity u T f(A)v, where A is a given n \Theta n real matrix, u and v are given nvectors, and f is a given smooth function. Estimating the entries and the trace of the inverse of a matrix and the determinant of a matrix can be classified as such problems. There are a number of interesting applications for such matrix computation problems. The applications in fractal and lattice Quantum Chromodynamics (QCD) are our new motivation for studying such problems. In these applications, the matrices involved are sparse and could be up to the order of millions. It is still a challenging problem to efficiently solve such large matrix computation problems on today's supercomputers. 1 Introduction The central problem studied in this chapter is to estimate a lower bound L and/or an upper bound U , such that L u T f(A)v U; (1) where A is an n \Theta n given real matrix, u and v are given nvectors, and f is a given smooth fun...
Thickrestart Lanczos method for electronic structure calculations
 J. Comput. Phys
, 1999
"... This paper describes two recent innovations related to the classic Lanczos method for eigenvalue problems, namely the thickrestart technique and dynamic restarting schemes. Combining these two new techniques we are able to implement an ecient eigenvalue problem solver. This paper will demonstrat ..."
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Cited by 5 (1 self)
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This paper describes two recent innovations related to the classic Lanczos method for eigenvalue problems, namely the thickrestart technique and dynamic restarting schemes. Combining these two new techniques we are able to implement an ecient eigenvalue problem solver. This paper will demonstrate its eectiveness on one particular class of problems for which this method is well suited: linear eigenvalue problems generated from nonselfconsistent electronic structure calculations. 1 Introduction The Lanczos method is a very simple and yet eective algorithm for nding extreme eigenvalues of large matrices. Since it only needs to access the matrix through matrixvector multiplications, the user has the exibility of choosing the most appropriate matrixvector multiplication scheme to reduce computer memory usage and the computation time. There is never any need to explicitly store the full matrix which can be prohibitively large in many electronic structure calculations. There ar...
On the interpretation of Michelson–Morley experiments
, 2001
"... Recent proposals for improved optical tests of Special Relativity have renewed interest in the interpretation of such tests. In this paper we discuss the interpretation of modern realizations of the Michelson–Morley experiment in the context of a new model of electrodynamics featuring a vector–value ..."
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Cited by 5 (2 self)
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Recent proposals for improved optical tests of Special Relativity have renewed interest in the interpretation of such tests. In this paper we discuss the interpretation of modern realizations of the Michelson–Morley experiment in the context of a new model of electrodynamics featuring a vector–valued photon mass. This model is gauge invariant, unlike massive–photon theories based on the Proca equation, and it predicts anisotropy of both the speed of light and the electric field of a point charge. The latter leads to an orientation dependence of the length of solid bodies which must be accounted for when interpreting the results of a Michelson–Morley experiment. Using a simple model of ionic solids we show that, in principle, the effect of orientation dependent length can conspire to cancel the effect of an anisotropic speed of light in a Michelson–Morley experiment, thus, complicating the interpretation of the results.
Integration Of Nanotechnology Into The Undergraduate Engineering Curriculum
, 2001
"... Today's advances and rapid growth in the fields of nanotechnology provide challenges to our academic communities to prepare engineering students with an ability to apply knowledge of mathematics, science and engineering to design, analysis and manufacture of nanocomponents, nanodevices and nanosyst ..."
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Cited by 5 (0 self)
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Today's advances and rapid growth in the fields of nanotechnology provide challenges to our academic communities to prepare engineering students with an ability to apply knowledge of mathematics, science and engineering to design, analysis and manufacture of nanocomponents, nanodevices and nanosystems. Nanotechnology is truly interdisciplinary; it involves manipulating and controlling individual atoms and molecules to design and create new materials, nanomachines, and nanodevices for application in all aspects of our lives. Our challenge is to provide an interdisciplinary education to students with a broad understanding of basic sciences (atomic physics, molecular chemistry, microbiology, genetics, etc.), engineering sciences (mechanical, electrical, chemical, biochemical, computer etc.), and information sciences (molecular coding, data analysis, imaging and visualization, biocomputation, molecular modeling and simulation of complex structures, etc.), and their application to nanotechnology. A methodology is proposed to integrate nanotechnology education into mainstream undergraduate engineering curricula. Strategies for teaching nanotechnology are also presented.
Emergence of particles from bosonic quantum field theory
, 2001
"... An examination is made of the way in which particles emerge from linear, bosonic, massive quantum field theories. Two different constructions of the oneparticle subspace of such theories are given, both illustrating the importance of the interplay between the quantummechanical linear structure and ..."
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Cited by 5 (2 self)
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An examination is made of the way in which particles emerge from linear, bosonic, massive quantum field theories. Two different constructions of the oneparticle subspace of such theories are given, both illustrating the importance of the interplay between the quantummechanical linear structure and the classical one. Some comments are made on the NewtonWigner representation of oneparticle states, and on the relationship between the approach of this paper and those of Segal, and of Haag and Ruelle.
Diffusion limit of a semiconductor BoltzmannPoisson system
 SIAM J. Math. Anal
"... Abstract. The paper deals with the diffusion limit of the initialboundary value problem for the multidimensional semiconductor BoltzmannPoisson system. Here, we generalize the one dimensional results obtained in [6] to the case of several dimensions using global renormalized solutions. The method ..."
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Cited by 4 (2 self)
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Abstract. The paper deals with the diffusion limit of the initialboundary value problem for the multidimensional semiconductor BoltzmannPoisson system. Here, we generalize the one dimensional results obtained in [6] to the case of several dimensions using global renormalized solutions. The method of moments and a velocity averaging lemma are used to prove the convergence of the renormalized solutions to the semiconductor BoltzmannPoisson system towards a global weak solution of the DriftDiffusionPoisson model. Key words. Kinetic transport equations, semiconductor BoltzmannPoisson system, DriftDiffusion model, Entropy dissipation, moment method, velocity averaging lemma, renormalized solution,... 1 1 Introduction and Main results In this paper, we study the diffusion limit of the initialboundary value problem for the semiconductor BoltzmannPoisson system (see [27, 31]). The model we consider here is associated with a linear low density approximation of the electronphonon collisions. In other words it is a low density approximation of the physically correct
Preconditioned Techniques For Large Eigenvalue Problems
, 1997
"... This research focuses on finding a large number of eigenvalues and eigenvectors of a sparse symmetric or Hermitian matrix, for example, finding 1000 eigenpairs of a 100,000 \Theta 100,000 matrix. These eigenvalue problems are challenging because the matrix size is too large for traditional QR based ..."
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Cited by 4 (3 self)
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This research focuses on finding a large number of eigenvalues and eigenvectors of a sparse symmetric or Hermitian matrix, for example, finding 1000 eigenpairs of a 100,000 \Theta 100,000 matrix. These eigenvalue problems are challenging because the matrix size is too large for traditional QR based algorithms and the number of desired eigenpairs is too large for most common sparse eigenvalue algorithms. In this thesis, we approach this problem in two steps. First, we identify a sound preconditioned eigenvalue procedure for computing multiple eigenpairs. Second, we improve the basic algorithm through new preconditioning schemes and spectrum transformations. Through careful analysis, we see that both the Arnoldi and Davidson methods have an appropriate structure for computing a large number of eigenpairs with preconditioning. We also study three variations of these two basic algorithms. Without preconditioning, these methods are mathematically equivalent but they differ in numerical stab...
Dynamic classification of defect structures in molecular dynamics simulation data
 In SIAM Data Mining Conference
, 2005
"... In this application paper we explore techniques to classify anomalous structures (defects) in data generated from abinitio Molecular Dynamics (MD) simulations of Silicon (Si) atom systems. These systems are studied to understand the processes behind the formation of various defects as they have a pr ..."
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Cited by 4 (0 self)
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In this application paper we explore techniques to classify anomalous structures (defects) in data generated from abinitio Molecular Dynamics (MD) simulations of Silicon (Si) atom systems. These systems are studied to understand the processes behind the formation of various defects as they have a profound impact on the electrical and mechanical properties of Silicon. In our prior work we presented techniques for defect detection [11, 12, 14]. Here, we present a twostep dynamic classifier to classify the defects. The first step uses up to thirdorder shape moments to provide a smaller set of candidate defect classes. The second step assigns the correct class to the defect structure by considering the actual spatial positions of the individual atoms. The dynamic classifier is robust and scalable in the size of the atom systems. Each phase is immune to noise, which is characterized after a study of the simulation data. We also validate the proposed solutions by using a physical model and properties of lattices. We demonstrate the efficacy and correctness of our approach on several large datasets. Our approach is able to recognize previously seen defects and also identify new defects in real time. 1
Kinetics, statistics, and energetics of lipid membrane electroporation studied by molecular dynamics simulations
 Biophysical Journal
, 2008
"... ABSTRACT Membrane electroporation is the method to directly transfer bioactive substances such as drugs and genes into living cells, as well as preceding electrofusion. Although much information on the microscopic mechanism has been obtained both from experiment and simulation, the existence and nat ..."
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Cited by 4 (1 self)
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ABSTRACT Membrane electroporation is the method to directly transfer bioactive substances such as drugs and genes into living cells, as well as preceding electrofusion. Although much information on the microscopic mechanism has been obtained both from experiment and simulation, the existence and nature of possible intermediates is still unclear. To elucidate intermediates of electropore formation by direct comparison with measured prepore formation kinetics, we have carried out 49 atomistic electroporation simulations on a palmitoyloleoylphosphatidylcholine bilayer for electric field strengths between 0.04 and 0.7 V/nm. A statistical theory is developed to facilitate direct comparison of experimental (macroscopic) prepore formation kinetics with the (single event) preporation times derived from the simulations, which also allows us to extract an effective number of lipids involved in each pore formation event. A linear dependency of the activation energy for prepore formation on the applied field is seen, with quantitative agreement between experiment and simulation. The distribution of preporation times suggests a fourstate pore formation model. The model involves a first intermediate characterized by a differential tilt of the polar lipid headgroups on both leaflets, and a second intermediate (prepore), where a polar chain across the bilayer is formed by 3–4 lipid headgroups and several water molecules, thereby providing a microscopic explanation for the polarizable volume derived previously from the measured kinetics. An average pore radius of 0.47 6 0.15 nm is seen, in favorable agreement with conductance measurements and electrooptical experiments of lipid vesicles.