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Hiroyuki Ohshima - One of the best experts on this subject based on the ideXlab platform.
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Approximate expressions for the surface charge density/surface Potential relationship and Double-Layer Potential distribution for a spherical or cylindrical colloidal particle based on the modified Poisson-Boltzmann equation
Colloid and Polymer Science, 2018Co-Authors: Hiroyuki OhshimaAbstract:Approximate expressions for the surface charge density/surface Potential relationship and Double-Layer Potential distribution are derived for a spherical or cylindrical colloidal particle in an electrolyte solution. The obtained expressions are based on an approximate form of the modified Poisson-Boltzmann equation taking into account the ion size effects through the Carnahan-Starling activity coefficients of electrolyte ions. We further derive approximate expression for the effective surface Potentials of a spherical or cylindrical particle and for the electrostatic interaction energy between two spherical or cylindrical particles on the basis of the linear superposition approximation.
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approximate expressions for the surface charge density surface Potential relationship and Double Layer Potential distribution for a spherical or cylindrical colloidal particle based on the modified poisson boltzmann equation
Colloid and Polymer Science, 2018Co-Authors: Hiroyuki OhshimaAbstract:Approximate expressions for the surface charge density/surface Potential relationship and Double-Layer Potential distribution are derived for a spherical or cylindrical colloidal particle in an electrolyte solution. The obtained expressions are based on an approximate form of the modified Poisson-Boltzmann equation taking into account the ion size effects through the Carnahan-Starling activity coefficients of electrolyte ions. We further derive approximate expression for the effective surface Potentials of a spherical or cylindrical particle and for the electrostatic interaction energy between two spherical or cylindrical particles on the basis of the linear superposition approximation.
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A simple algorithm for the calculation of the electric Double Layer Potential distribution in a charged cylindrical narrow pore
Colloid and Polymer Science, 2016Co-Authors: Hiroyuki OhshimaAbstract:A simple algorithm is presented for obtaining an approximate analytic solution to the cylindrical Poisson-Boltzmann equation for the electric Double Layer Potential distribution in a charged cylindrical narrow pore filled with an electrolyte solution. Agreement with the exact numerical solution is excellent for low-to-moderate values of the pore surface Potential when the pore radius is less than the Debye length. The obtained results are thus considerably better approximations than those previously obtained by Martynov and Avdeev (Colloid J 44: 626–632 (1983)). Approximate analytic expressions are also derived for the relationship between the pore surface charge density and the pore surface Potential.
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Double Layer Potential distribution and surface charge density surface Potential relationship for a nearly spherical spheroid in an electrolyte solution
Colloids and Surfaces A: Physicochemical and Engineering Aspects, 2000Co-Authors: Hiroyuki OhshimaAbstract:Abstract A simple approximation method is presented to derive the Double Layer Potential distribution and the surface charge density/surface Potential relationship for a nearly spherical spheroidal colloidal particle immersed in an electrolyte solution on the basis of the linearized Poisson–Boltzmann equation.
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Double-Layer Potential distribution and surface charge density/surface Potential relationship for a nearly spherical spheroid in an electrolyte solution
Colloids and Surfaces A: Physicochemical and Engineering Aspects, 2000Co-Authors: Hiroyuki OhshimaAbstract:Abstract A simple approximation method is presented to derive the Double Layer Potential distribution and the surface charge density/surface Potential relationship for a nearly spherical spheroidal colloidal particle immersed in an electrolyte solution on the basis of the linearized Poisson–Boltzmann equation.
A. Rathsfeld - One of the best experts on this subject based on the ideXlab platform.
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Nystro¨m's method and iterative solvers for the solution of the Double-Layer Potential equation over polyhedral boundaries
SIAM Journal on Numerical Analysis, 1995Co-Authors: A. RathsfeldAbstract:In this paper we consider a quadrature method for the solution of the Double-Layer Potential equation corresponding to Laplace’s equation in a three-dimensional polyhedron. We prove the stability for our method in the case of special triangulations over the boundary of the polyhedron. For the solution of the corresponding system of linear equations, we consider a two-grid iteration and a further simple iteration procedure. Finally, we establish the rates of convergence and complexity and discuss the effect of mesh refinement near the corners and edges of the polyhedron.
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The invetibility of the Double Layer Potential operator in the space of continuous functions defined over a polyhedron. the panel method. erratum
Applicable Analysis, 1995Co-Authors: A. RathsfeldAbstract:summary:For fairly general open sets it is shown that we can express a solution of the Neumann problem for the Laplace equation in the form of a single Layer Potential of a signed measure which is given by a concrete series. If the open set is simply connected and bounded then the solution of the Dirichlet problem is the Double Layer Potential with a density given by a similar series
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On quadrature methods for the Double Layer Potential equation over the boundary of a polyhedron
Numerische Mathematik, 1993Co-Authors: A. RathsfeldAbstract:In this paper we consider a quadrature method for the solution of the Double Layer Potential equation corresponding to Laplace's equation in a threedimensional polyhedron. We prove the stability for our method in case of special triangulations over the boundary of the polyhedron. The assumptions imposed on the triangulations are analogous to those appearing in the one-dimensional case. Finally, we establish the rates of convergence and discuss the effect of mesh refinement near the corners and edges of the polyhedron.
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Iterative solution of linear systems arising from the Nyström method for the Double-Layer Potential equation over curves with corners
Mathematical Methods in the Applied Sciences, 1993Co-Authors: A. RathsfeldAbstract:In this paper we consider a quadrature method for the solution of the Double-Layer Potential equation corresponding to Laplace's equation in a polygonal domain. We prove the stability for our method in case of special triangulations over the boundary of the polygon. For the solution of the corresponding system of linear equations, we consider a two-grid iteration and establish the rates of convergence and complexity. Finally, we discuss the effect of mesh refinement near the corners of the polygon.
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Finite Section Method for the Double Layer Potential Operator over Polyhedral Boundaries
Mathematische Nachrichten, 1992Co-Authors: A. RathsfeldAbstract:In this paper we consider the finite section method for the solution of the Double Layer Potential equation corresponding to Laplace's equation in a three-dimensional polyhedron. We prove the stability of our method in case of special polyhedrons.
Ivan B Bazhlekov - One of the best experts on this subject based on the ideXlab platform.
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contour integral representation of single and Double Layer Potentials for axisymmetric problems
Lecture Notes in Computer Science, 2003Co-Authors: Emilia Bazhlekova, Ivan B BazhlekovAbstract:Based on recently proposed non-singular contour-integral representations of single and Double Layer Potentials for 3D surfaces, formulas in the axisymmetric case are derived. They express explicitly the singular Layer Potentials in terms of elliptic integrals. The presented expressions are non-singular, satisfy exactly very important conservation principles and directly take into account the multivaluedness of the Double Layer Potential. The results are compared with another method for calculating the single and Double Layer Potentials. The comparison demonstrates higher accuracy and better performance of the presented formulas.
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Numerical Methods and Application - Contour-Integral Representation of Single and Double Layer Potentials for Axisymmetric Problems
Numerical Methods and Applications, 2002Co-Authors: Emilia Bazhlekova, Ivan B BazhlekovAbstract:Based on recently proposed non-singular contour-integral representations of single and Double Layer Potentials for 3D surfaces, formulas in the axisymmetric case are derived. They express explicitly the singular Layer Potentials in terms of elliptic integrals. The presented expressions are non-singular, satisfy exactly very important conservation principles and directly take into account the multivaluedness of the Double Layer Potential. The results are compared with another method for calculating the single and Double Layer Potentials. The comparison demonstrates higher accuracy and better performance of the presented formulas.
Y.v. Kasyanyuk - One of the best experts on this subject based on the ideXlab platform.
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Calculation of singular and hypersingular integrals in scalar diffraction problem
DIPED - 2000. Proceedings of 5th International Seminar Workshop on Direct and Inverse Problems of Electromagnetic and Acoustic Wave Theory (IEEE Cat. , 2000Co-Authors: O.i. Ovsyannikov, Y.v. KasyanyukAbstract:The axisymmetric scalar diffraction problem is presented. The singular and hypersingular integrals with normal derivative of Double Layer Potential are considered. The methods of singular and hypersingular integrals calculation are proposed.
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Calculation of singular integrals in scalar diffraction problems
Conference Proceedings 2000 International Conference on Mathematical Methods in Electromagnetic Theory (Cat. No.00EX413), 1Co-Authors: O.i. Ovsyannikov, Y.v. KasyanyukAbstract:The axisymmetric scalar diffraction problem is presented. The singular and hypersingular integrals with normal derivative of Double Layer Potential are considered. The methods of singular and hypersingular integrals calculation are proposed.
Johannes Elschner - One of the best experts on this subject based on the ideXlab platform.
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The Double-Layer Potential operator over polyhedral domains II: Spline Galerkin methods
Mathematical Methods in the Applied Sciences, 1992Co-Authors: Johannes ElschnerAbstract:We examine the numerical approximation of the integral equation (λ − K)u =f, where K is the Double Layer (harmonic) Potential operator on a closed polyhedral surface in ℝ3 and λ, ∣λ∣≥1, is a complex constant. The solution is approximated by Galerkin's method, which is based on piecewise polynomials of arbitrary degree on graded triangulations. By utilizing spline spaces which are modified in that the trial functions vanish on some of the triangles closest to the vertices and edges, we investigate the stability of this method in L2. Furthermore, the use of suitably graded meshes leads to the same quasioptimal error estimates as in the case of a smooth surface.
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The Double Layer Potential operator over polyhedral domains i: solvability in weighted sobolev spaces
Applicable Analysis, 1992Co-Authors: Johannes ElschnerAbstract:We consider the integral equation, (λ-K)u=f, where K is the Double Layer (harmonic) Potential operator on the boundary of a bounded polyhedron in R3 and λ∣λ∣≥1 is a complex constant. We study the mapping properties of λ - K in weighted Sobolev spaces, applying Mellin transformation techniques directly to the integral equation.