SIAM Journal on Numerical Analysis, ISSN 0036-1429, 1/2012, Volume 50, Issue 6, pp. 3259 - 3279

When using standard deterministic particle methods, point values of the computed solutions have to be recovered from their singular particle approximations by...

Mathematical procedures | Approximation | Liouville equations | Numerical methods | Hyperplanes | Particle density | Poisson equation | Electric fields | Density | Vlasov-Poisson equation | Particle method | Schrödinger equation | MATHEMATICS, APPLIED | Schrodinger equation | SYSTEMS | TRANSPORT MODEL | WEAK SOLUTIONS | particle method

Mathematical procedures | Approximation | Liouville equations | Numerical methods | Hyperplanes | Particle density | Poisson equation | Electric fields | Density | Vlasov-Poisson equation | Particle method | Schrödinger equation | MATHEMATICS, APPLIED | Schrodinger equation | SYSTEMS | TRANSPORT MODEL | WEAK SOLUTIONS | particle method

Journal Article

2014, Volume 660

Partial differential equations -- Miscellaneous topics -- Inverse problems | Partial differential equations -- Elliptic equations and systems -- Laplacian operator, reduced wave equation (Helmholtz equation), Poisson equation | Partial differential equations -- Elliptic equations and systems -- Boundary value problems for second-order elliptic equations | Partial differential equations -- Qualitative properties of solutions -- Dependence of solutions on initial and boundary data, parameters | Partial differential equations -- Qualitative properties of solutions -- Periodic solutions | Signal processing | Differential equations, Partial | Numerical analysis -- Partial differential equations, boundary value problems -- Error bounds | Partial differential equations -- Miscellaneous topics -- Partial differential equations with randomness, stochastic partial differential equations | Geophysics -- Geophysics -- Seismology | Numerical analysis -- Numerical methods in Fourier analysis -- Wavelets

Conference Proceeding

3.
Full Text
Statistical shape analysis using 3D Poisson equation—A quantitatively validated approach

Medical Image Analysis, ISSN 1361-8415, 05/2016, Volume 30, pp. 72 - 84

Statistical shape analysis has been an important area of research with applications in biology, anatomy, neuroscience, agriculture, paleontology, etc....

Statistical shape analysis | Poisson equation | Reproducibility | Quantitative evaluation | ENGINEERING, BIOMEDICAL | VOLUME | REPRESENTATION | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MORPHOMETRY | SEGMENTATION | MANIFOLDS | RADIOLOGY, NUCLEAR MEDICINE & MEDICAL IMAGING | Reproducibility of Results | Humans | Image Interpretation, Computer-Assisted - methods | Imaging, Three-Dimensional - methods | Magnetic Resonance Imaging - methods | Hippocampus - pathology | Schizophrenia - pathology | Models, Statistical | Schizophrenia - diagnostic imaging | Hippocampus - diagnostic imaging | Computer Simulation | Sensitivity and Specificity | Poisson Distribution | Image Enhancement - methods | Pattern Recognition, Automated - methods | Computer science | Analysis | Neurosciences | Algorithms | Paleontology | Index Medicus

Statistical shape analysis | Poisson equation | Reproducibility | Quantitative evaluation | ENGINEERING, BIOMEDICAL | VOLUME | REPRESENTATION | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | MORPHOMETRY | SEGMENTATION | MANIFOLDS | RADIOLOGY, NUCLEAR MEDICINE & MEDICAL IMAGING | Reproducibility of Results | Humans | Image Interpretation, Computer-Assisted - methods | Imaging, Three-Dimensional - methods | Magnetic Resonance Imaging - methods | Hippocampus - pathology | Schizophrenia - pathology | Models, Statistical | Schizophrenia - diagnostic imaging | Hippocampus - diagnostic imaging | Computer Simulation | Sensitivity and Specificity | Poisson Distribution | Image Enhancement - methods | Pattern Recognition, Automated - methods | Computer science | Analysis | Neurosciences | Algorithms | Paleontology | Index Medicus

Journal Article

1992, Springer series in computational mathematics, ISBN 354054822X, Volume 18, xiv, 311

Book

1995, 4th ed., Universitext, ISBN 3540602437, xvi, 271

Book

2010, Volume 577

Conference Proceeding

Compositio Mathematica, ISSN 0010-437X, 11/2013, Volume 149, Issue 11, pp. 1856 - 1870

In this paper, we develop a method of solving the Poincare-Lelong equation, mainly via the study of the large time asymptotics of a global solution to the...

Hodge-Laplacian heat equation | Kähler manifolds | Poincaré-Lelong equation | Convex exhaustion | MATHEMATICS | Kahler manifolds | CURVATURE | COMPLETE KAHLER-MANIFOLDS | POISSON EQUATION | Poincare-Lelong equation | Studies | Theorems | Topological manifolds | Mathematical analysis | Asymptotic properties

Hodge-Laplacian heat equation | Kähler manifolds | Poincaré-Lelong equation | Convex exhaustion | MATHEMATICS | Kahler manifolds | CURVATURE | COMPLETE KAHLER-MANIFOLDS | POISSON EQUATION | Poincare-Lelong equation | Studies | Theorems | Topological manifolds | Mathematical analysis | Asymptotic properties

Journal Article

8.
Full Text
The Laplace Equation : Boundary Value Problems on Bounded and Unbounded Lipschitz Domains

03/2018, ISBN 9783319743066, 669

eBook

Engineering Analysis with Boundary Elements, ISSN 0955-7997, 04/2013, Volume 37, Issue 4, pp. 788 - 804

Various real-world processes usually can be described by mathematical models consisted of partial differential equations (PDEs) with nonlocal boundary...

Radial basis function | Collocation | Meshless method | Shape parameter | Condition number | Poisson equation | Nonlocal boundary condition | ERROR ESTIMATE | 2ND-ORDER PARABOLIC EQUATION | FUNCTION APPROXIMATION METHODS | NUMERICAL-SOLUTION | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | SCATTERED DATA | ENGINEERING, MULTIDISCIPLINARY | MULTIQUADRIC COLLOCATION METHOD | COMPUTATIONAL FLUID-DYNAMICS | BASIS FUNCTION INTERPOLATION | PRECISION COMPUTATION | Analysis | Methods | Differential equations

Radial basis function | Collocation | Meshless method | Shape parameter | Condition number | Poisson equation | Nonlocal boundary condition | ERROR ESTIMATE | 2ND-ORDER PARABOLIC EQUATION | FUNCTION APPROXIMATION METHODS | NUMERICAL-SOLUTION | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | SCATTERED DATA | ENGINEERING, MULTIDISCIPLINARY | MULTIQUADRIC COLLOCATION METHOD | COMPUTATIONAL FLUID-DYNAMICS | BASIS FUNCTION INTERPOLATION | PRECISION COMPUTATION | Analysis | Methods | Differential equations

Journal Article

Journal of Functional Analysis, ISSN 0022-1236, 2006, Volume 237, Issue 2, pp. 655 - 674

In this paper we study the problem where are positive radial functions, and . We give existence and nonexistence results, depending on the parameters and . It...

Schrödinger–Poisson equation | Pohozaev equality | Lagrange multiplier rule | Variational methods | Schrödinger-Poisson equation | HARTREE | STATES | MAXWELL EQUATIONS | Schrodinger-Poisson equation | MOLECULES | variational methods | MATHEMATICS | THOMAS-FERMI | SOLITARY WAVES | ATOMS | SYSTEMS

Schrödinger–Poisson equation | Pohozaev equality | Lagrange multiplier rule | Variational methods | Schrödinger-Poisson equation | HARTREE | STATES | MAXWELL EQUATIONS | Schrodinger-Poisson equation | MOLECULES | variational methods | MATHEMATICS | THOMAS-FERMI | SOLITARY WAVES | ATOMS | SYSTEMS

Journal Article

IEEE Transactions on Electron Devices, ISSN 0018-9383, 11/2007, Volume 54, Issue 11, pp. 2901 - 2909

We propose an efficient and fast algorithm to solve the coupled Poisson-Schrodinger and Boltzmann transport equations (BTE) in two dimensions. The BTE is...

modeling | Computational modeling | Scattering | Boltzmann transport equation | SchrÖdinger equation | Ballistic transport | nanoscale MOSFET device | Mathematical model | Approximation methods | Equations | MOSFETs | Distribution functions | Nanoscale MOSFET device | Modeling | Schrödinger equation | PHYSICS, APPLIED | Schrodinger equation | ELECTRONS | SEMICONDUCTORS | DEVICES | MODEL | SIMULATION | ballistic transport | ENGINEERING, ELECTRICAL & ELECTRONIC | Metal oxide semiconductor field effect transistors | Analysis | Design and construction | Transport theory | Electrons

modeling | Computational modeling | Scattering | Boltzmann transport equation | SchrÖdinger equation | Ballistic transport | nanoscale MOSFET device | Mathematical model | Approximation methods | Equations | MOSFETs | Distribution functions | Nanoscale MOSFET device | Modeling | Schrödinger equation | PHYSICS, APPLIED | Schrodinger equation | ELECTRONS | SEMICONDUCTORS | DEVICES | MODEL | SIMULATION | ballistic transport | ENGINEERING, ELECTRICAL & ELECTRONIC | Metal oxide semiconductor field effect transistors | Analysis | Design and construction | Transport theory | Electrons

Journal Article

Fuzzy Sets and Systems, ISSN 0165-0114, 09/2018, Volume 347, pp. 105 - 128

The fuzzy-valued vector function is defined and then divergence, Laplace, and gradient operators are defined for fuzzy-valued vector functions and fuzzy-valued...

Fuzzy-valued vector function | Fuzzy Green's theorem | Fuzzy Green's identity | Fuzzy Poisson equation | Fuzzy partial differential equation | Fuzzy divergence theorem | INTERVAL | MATHEMATICS, APPLIED | STATISTICS & PROBABILITY | PARTIAL-DIFFERENTIAL-EQUATIONS | COMPUTER SCIENCE, THEORY & METHODS | VALUED FUNCTIONS | GENERALIZED HUKUHARA DIFFERENTIABILITY | Differential equations

Fuzzy-valued vector function | Fuzzy Green's theorem | Fuzzy Green's identity | Fuzzy Poisson equation | Fuzzy partial differential equation | Fuzzy divergence theorem | INTERVAL | MATHEMATICS, APPLIED | STATISTICS & PROBABILITY | PARTIAL-DIFFERENTIAL-EQUATIONS | COMPUTER SCIENCE, THEORY & METHODS | VALUED FUNCTIONS | GENERALIZED HUKUHARA DIFFERENTIABILITY | Differential equations

Journal Article

1996, Cambridge texts in applied mathematics., ISBN 0521553768, xvi, 378

Book

Journal of Algebra and its Applications, ISSN 0219-4988, 01/2018, Volume 17, Issue 1

In this work, we compute solutions of the Yang-Baxter associative equation in dimensions one and two. For these solutions, we describe the double constructions...

Yang-Baxter equation | Frobenius algebra | Connes cocycle | dendriform algebra | D -equation | Associative algebra | D-equation | MATHEMATICS, APPLIED | HOPF-ALGEBRAS | MATHEMATICS | TREES | POISSON ALGEBRAS | HOMOLOGY | BIALGEBRAS

Yang-Baxter equation | Frobenius algebra | Connes cocycle | dendriform algebra | D -equation | Associative algebra | D-equation | MATHEMATICS, APPLIED | HOPF-ALGEBRAS | MATHEMATICS | TREES | POISSON ALGEBRAS | HOMOLOGY | BIALGEBRAS

Journal Article

Journal of Differential Equations, ISSN 0022-0396, 09/2016, Volume 261, Issue 6, pp. 3220 - 3246

In this paper, we prove the existence and uniqueness of weak entropy solutions to the Burgers–Poisson equation for initial data in . In addition an Oleinik...

Burgers–Poisson equation | Existence | Uniqueness | Blow-up | MATHEMATICS | Burgers-Poisson equation

Burgers–Poisson equation | Existence | Uniqueness | Blow-up | MATHEMATICS | Burgers-Poisson equation

Journal Article

Communications in Mathematical Physics, ISSN 0010-3616, 9/2016, Volume 346, Issue 3, pp. 877 - 906

In this paper, we deal with the electrostatic Born–Infeld equation $$\left\{\begin{array}{ll}-\operatorname{div}...

Quantum Physics | Statistical Physics, Dynamical Systems and Complexity | Mathematical Physics | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Physics | NONLINEAR KLEIN-GORDON | SOLITARY WAVES | FIELD-THEORY | HYPERSURFACES | MEAN-CURVATURE | MAXIMAL SURFACE EQUATION | MINKOWSKI SPACE | FOUNDATIONS | PHYSICS, MATHEMATICAL | Electric fields | Analysis | Charge density | Poisson equation | Smoothness | Calculus of variations | Uniqueness | Mathematics - Analysis of PDEs | Analysis of PDEs | Mathematics

Quantum Physics | Statistical Physics, Dynamical Systems and Complexity | Mathematical Physics | Classical and Quantum Gravitation, Relativity Theory | Theoretical, Mathematical and Computational Physics | Physics | NONLINEAR KLEIN-GORDON | SOLITARY WAVES | FIELD-THEORY | HYPERSURFACES | MEAN-CURVATURE | MAXIMAL SURFACE EQUATION | MINKOWSKI SPACE | FOUNDATIONS | PHYSICS, MATHEMATICAL | Electric fields | Analysis | Charge density | Poisson equation | Smoothness | Calculus of variations | Uniqueness | Mathematics - Analysis of PDEs | Analysis of PDEs | Mathematics

Journal Article

1996, ISBN 0521567386, xvi, 538

Book

2009, 2ND ED., Cambridge texts in applied mathematics, ISBN 9780511506376, 481

Numerical analysis presents different faces to the world. For mathematicians it is a bona fide mathematical theory with an applicable flavour. For scientists...

Differential equations - Numerical solutions | Differential equations

Differential equations - Numerical solutions | Differential equations

Book

19.
Full Text
Standing waves for the nonlinear Schrödinger equation coupled with the Maxwell equation

Nonlinearity, ISSN 0951-7715, 04/2017, Volume 30, Issue 5, pp. 1920 - 1947

In this paper, we are interested in standing waves of the nonlinear Schrodinger equation coupled with the Maxwell equation. Firstly we describe conditions for...

ground states | constraint minimization problem | orbital stability of standing waves | Schrödinger-Maxwell system | EXISTENCE | MATHEMATICS, APPLIED | GROUND-STATE | STATIONARY STATES | POSITIVE SOLUTIONS | STABILITY | CONCENTRATION-COMPACTNESS PRINCIPLE | PHYSICS, MATHEMATICAL | UNIQUENESS | EXTERNAL MAGNETIC-FIELD | CONSTRAINED MINIMIZERS | Schrodinger-Maxwell system | POISSON EQUATIONS | Analysis of PDEs | Mathematics

ground states | constraint minimization problem | orbital stability of standing waves | Schrödinger-Maxwell system | EXISTENCE | MATHEMATICS, APPLIED | GROUND-STATE | STATIONARY STATES | POSITIVE SOLUTIONS | STABILITY | CONCENTRATION-COMPACTNESS PRINCIPLE | PHYSICS, MATHEMATICAL | UNIQUENESS | EXTERNAL MAGNETIC-FIELD | CONSTRAINED MINIMIZERS | Schrodinger-Maxwell system | POISSON EQUATIONS | Analysis of PDEs | Mathematics

Journal Article

JOURNAL OF PHYSICS-CONDENSED MATTER, ISSN 0953-8984, 09/2019, Volume 31, Issue 37, pp. 375101 - 375101

The classical Poisson-Boltzmann equation (CPBE), which is a mean field theory by averaging the ion fluctuation, has been widely used to study ion distributions...

INTERACTION FREE-ENERGY | PHYSICS, CONDENSED MATTER | path integral | stochastic process | IONS | FORCES | DOUBLE-LAYER | Poisson-Boltzmann equation | monte carlo | charged fluids | field theory | SURFACES

INTERACTION FREE-ENERGY | PHYSICS, CONDENSED MATTER | path integral | stochastic process | IONS | FORCES | DOUBLE-LAYER | Poisson-Boltzmann equation | monte carlo | charged fluids | field theory | SURFACES

Journal Article

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