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25
Path planning using Laplace’s equation
, 1990
"... A method for planning smooth robot paths is presented. The method relies on the use of Laplace’s Equation to constrain the generation of a potential function over regions of the configuration space of an effector. Once the function is computed, paths may be found very quickly. These functions do not ..."
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Cited by 96 (8 self)
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A method for planning smooth robot paths is presented. The method relies on the use of Laplace’s Equation to constrain the generation of a potential function over regions of the configuration space of an effector. Once the function is computed, paths may be found very quickly. These functions do not exhibit the local minima which plague the potential field method. Unlike decompositional and algebraic techniques, Laplace’s Equation is very well suited to computation on massively parallel architectures. 1
Weak and Measurevalued Solutions to Evolutionary PDEs
, 1996
"... L p estimates for the Cauchy problem with applications to the NavierStokes equations in exterior domains. J. Funct. Anal. 102, no. 1, 7294. Girault, V. and Raviart, P.A. (1986) Finite Element Methods for NavierStokes Equations. SCM 5, SpringerVerlag, Berlin. Giusti, E. (1984) Minimal Surfac ..."
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Cited by 51 (3 self)
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L p estimates for the Cauchy problem with applications to the NavierStokes equations in exterior domains. J. Funct. Anal. 102, no. 1, 7294. Girault, V. and Raviart, P.A. (1986) Finite Element Methods for NavierStokes Equations. SCM 5, SpringerVerlag, Berlin. Giusti, E. (1984) Minimal Surfaces and Functions of Bounded Variation. Monographs in Mathematics, Vol. 80, Birkhauser, BaselBoston Stuttgart. Gobert, J. (1962) Une in'equation fondamentale de la th'eorie de l"elasticit'e (A fundamental inequality in elasticity theory). Bull. Soc. Roy. Sci. Li`ege 34, 182191. Gobert, J. (1971) Sur une in'egalit'e de coercivit'e (On an inequality related to coercivity). J. Math. Anal. Appl. 36, 518528. Godlewski, E. and Raviart, P.A. (1991) Hyperbolic Systems of Conservation Laws. Mathematiques & Applications, S.M.A.I., Ellipses, Paris (in English). Goldstein, S. (1963) Modern Developments in Fluid Dynamics. Oxford University Press, Oxford. Guillop'e, C. and Saut, J.C. (1990) Glo...
The simulationtabulation method for classical diffusion Monte
 J. Comput. Phys
, 2001
"... Many important classes of problems in materials science and biotechnology require the solution of the Laplace or Poisson equation in disordered twophase domains in which the phase interface is extensive and convoluted. Green’s function firstpassage (GFFP) methods solve such problems efficiently by ..."
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Cited by 9 (4 self)
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Many important classes of problems in materials science and biotechnology require the solution of the Laplace or Poisson equation in disordered twophase domains in which the phase interface is extensive and convoluted. Green’s function firstpassage (GFFP) methods solve such problems efficiently by generalizing the “walk on spheres ” (WOS) method to allow firstpassage (FP) domains to be not just spheres but a wide variety of geometrical shapes. (In particular, this solves the difficulty of slow convergence with WOS by allowing FP domains that contain patches of the phase interface.) Previous studies accomplished this by using geometries for which the Green’s function was available in quasianalytic form. Here, we extend these studies by using the simulation–tabulation (ST) method. We simulate and then tabulate surface Green’s functions that cannot be obtained analytically. The ST method is applied to the Solc–Stockmayer model with zero potential, to the mean trapping rate of a diffusing particle in a domain of nonoverlapping spherical traps, and to the effective conductivity for perfectly insulating, nonoverlapping spherical inclusions in a matrix of finite conductivity. In all cases, this class of algorithms provides the most efficient methods known to solve these problems to high
Selforganizing maps in sequence processing
, 2002
"... Teknillinen korkeakoulu Sähkö ja tietoliikennetekniikan osasto Laskennallisen tekniikan laboratorio Distribution: ..."
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Cited by 3 (0 self)
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Teknillinen korkeakoulu Sähkö ja tietoliikennetekniikan osasto Laskennallisen tekniikan laboratorio Distribution:
Toward a Path CoProcessor for Automated Vehicle Control
 Presented at the 1995 IEEE Symposium on Intelligent Vehicles, 25–26 September
, 1995
"... The paper describes an embedded controller as the basis for high performance navigation tasks. The approach solves Laplace's equation on a discrete grid representing the roadway map. The resulting harmonic potential is free of local minima and a greedy descent minimizes the probability of collision ..."
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Cited by 1 (0 self)
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The paper describes an embedded controller as the basis for high performance navigation tasks. The approach solves Laplace's equation on a discrete grid representing the roadway map. The resulting harmonic potential is free of local minima and a greedy descent minimizes the probability of collision with posted obstacles. In this paper, we will (1) introduce the important properties of harmonic potential functions for vehicle control applications, (2) describe a numerical procedure to compute harmonic functions on a grid, (3) express nonholonomic constraints as connectivity in the grid, (4) formulate an energyreferenced control scheme to manage vehicle dynamics, and (5) provide estimates for the performance on a four processor DSP architecture. 1 Introduction Automated vehicle controllers for general road navigation tasks introduce technical problems beyond the scope of most path planning techniques designed for robot control. For instance, many robot navigation algorithms exploit sy...
A Hybrid Variational Front TrackingLevel Set Mesh Generator For Problems Exhibiting Large Deformations and Topological Changes
"... We present a method for generating 2D unstructured triangular meshes that undergo large deformations and topological changes in an automatic way. We employ a method for detecting when topological changes are imminent via distance functions and shape skeletons. When a change occurs, we use a level s ..."
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We present a method for generating 2D unstructured triangular meshes that undergo large deformations and topological changes in an automatic way. We employ a method for detecting when topological changes are imminent via distance functions and shape skeletons. When a change occurs, we use a level set method to guide the change of topology of the domain mesh. This is followed by an optimization procedure, using a variational formulation of active contours, that seeks to improve boundary mesh conformity to the zero level contour of the level set function. Our method is advantageous for ArbitraryLagrangianEulerian (ALE) type methods and directly allows for using a variational formulation of the physics being modeled and simulated, including the ability to account for important geometric information in the model (such as for surface tension driven flow). Furthermore, the meshing procedure is not required at every timestep and the level set update is only needed during a topological change. Hence, our method does not significantly affect computational cost. Key words:
Nonlinear Transport Processes in Tokamak Plasmas Part I: The Collisional Regimes
, 802
"... An application of the thermodynamic field theory (TFT) to transport processes in Lmode tokamak plasmas is presented. The nonlinear corrections to the linear (”Onsager”) transport coefficients in the collisional regimes are derived. A quite encouraging result is the appearance of an asymmetry betwee ..."
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Cited by 1 (1 self)
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An application of the thermodynamic field theory (TFT) to transport processes in Lmode tokamak plasmas is presented. The nonlinear corrections to the linear (”Onsager”) transport coefficients in the collisional regimes are derived. A quite encouraging result is the appearance of an asymmetry between the PfirschSchlüter (PS) ion and electron transport coefficients: the latter presents a nonlinear correction, which is absent for the ions, and makes the radial electron coefficients much larger than the former. Explicit calculations and comparisons between the neoclassical results and the TFT predictions for JET plasmas are also reported. We found that the nonlinear electron PS transport coefficients exceed the values provided by neoclassical theory by a factor, which may be of the order 10 2. The nonlinear classical coefficients exceed the neoclassical ones by a factor, which may be of order 2. The expressions of the ion transport coefficients, determined by the neoclassical theory in these two regimes, remain unaltered. The lowcollisional regimes i.e., the plateau and the banana regimes, are analyzed in the second part of this work. 1
/08/25 16:31
"... the fact that a collection of chapters can never be as homogeneous as a book conceived by a single person. We have tried to compensate for this by the selection and refereeing process of the submissions. In addition, we have written an introductory chapter describing the SV algorithm in some detail ..."
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the fact that a collection of chapters can never be as homogeneous as a book conceived by a single person. We have tried to compensate for this by the selection and refereeing process of the submissions. In addition, we have written an introductory chapter describing the SV algorithm in some detail (chapter 1), and added a roadmap (chapter 2) which describes the actual contributions which are to follow in chapters 3 through 20. Bernhard Scholkopf, Christopher J.C. Burges, Alexander J. Smola Berlin, Holmdel, July 1998/08/25 16:31 1 Introduction to Support Vector Learning The goal of this chapter, which describes the central ideas of SV learning, is twofold. First, we want to provide an introduction for readers unfamiliar with this field. Second, this introduction serves as a source of the basic equations for the chapters of this book. For more exhaustive treatments, we refer the interested reader to Vapnik (1995); Scholkopf (1997); Burges (1998). 1.1
Chapter 7 Hyperbolic Equations 7.1 The One Dimensional Wave Equation
"... We consider the one dimensional wave equation utt(x, t) =c 2 uxx(x, t), (x, t) ∈ R 2. (7.1.1) Here c is a positive constant that has the physical interpretation of wave speed. For example if u(x, t) corresponds to the displacement of a an infinite string then c = T/ρ where T is the tension in the s ..."
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We consider the one dimensional wave equation utt(x, t) =c 2 uxx(x, t), (x, t) ∈ R 2. (7.1.1) Here c is a positive constant that has the physical interpretation of wave speed. For example if u(x, t) corresponds to the displacement of a an infinite string then c = T/ρ where T is the tension in the string and ρ is the density. If u(x, t) is the longitudinal displacement of the crosssection of a bar, then c = E/ρ where E is Young’s modulus. We know that the characteristics are determined by or dt dx = ±1 c, x ± ct = constant. With the new coordinates α = x − ct, β = x + ct (7.1.1) becomes uαβ =0 which gives us the socalled D’Alembert’s solution u(x, t) =F (x + ct)+G(x − ct). (7.1.2) Usually we are interested in solving (7.1.1) subject to the initial consitions u(x, 0) = u0(x), ut(x, 0) = u1(x). 1 2