| 1. |
- Aarao, J, et al.
(författare)
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Extended-domain-eigenfunction method (EDEM): a study of ill posedness and regularization
- 2013
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Ingår i: Journal of Physics A. - : Institute of Physics. - 1751-8113 .- 1751-8121. ; 46:8
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Tidskriftsartikel (refereegranskat)abstract
- The extended-domain-eigenfunction method (EDEM) proposed for solving elliptic boundary value problems on annular-like domains requires an inversion process. The procedure thus represents an ill-posed problem, whose numerical solution involves an ill-conditioned system of equations. In this paper, the ill-posed nature of EDEM is studied and numerical solutions based on regularization schemes are considered. It is shown that the EDEM solution methodology lends itself naturally to a formulation in terms of the well-known iterative Landweber method and the more general and faster converging semi-iterative regularization schemes. Theoretical details and numerical results of the regularization schemes are presented for the case of the two-dimensional Laplace operator on annular domains.
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| 2. |
- Aarao, J, et al.
(författare)
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Numerical implementation of the EDEM for modified Helmholtz BVPs on annular domains
- 2011
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Ingår i: JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS. - : Elsevier Science B.V., Amsterdam.. - 0377-0427. ; 235:5, s. 1342-1353
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Tidskriftsartikel (refereegranskat)abstract
- In a recent paper by the current authors a new methodology called the Extended-Domain-Eigenfunction-Method (EDEM) was proposed for solving elliptic boundary value problems on annular-like domains. In this paper we present and investigate one possible numerical algorithm to implement the EDEM. This algorithm is used to solve modified Helmholtz BVPs on annular-like domains. Two examples of annular-like domains are studied. The results and performance are compared with those of the well-known boundary element method (BEM). The high accuracy of the EDEM solutions and the superior efficiency of the EDEM over the BEM, make EDEM an excellent alternate candidate to use in the animation industry, where speed is a predominant requirement, and by the scientific community where accuracy is the paramount objective.
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| 3. |
- Aarao, J, et al.
(författare)
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The extended-domain-eigenfunction method for solving elliptic boundary value problems with annular domains
- 2010
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Ingår i: JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL. - : Iop. - 1751-8113 .- 1751-8121. ; 43:18, s. 185202-
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Tidskriftsartikel (refereegranskat)abstract
- Standard analytical solutions to elliptic boundary value problems on asymmetric domains are rarely, if ever, obtainable. In this paper, we propose a solution technique wherein we embed the original domain into one with simple boundaries where the classical eigenfunction solution approach can be used. The solution in the larger domain, when restricted to the original domain, is then the solution of the original boundary value problem. We call this the extended-domain-eigenfunction method. To illustrate the methods strength and scope, we apply it to Laplaces equation on an annular-like domain.
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| 4. |
- Ahualli, S., et al.
(författare)
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Dynamic electrophoretic mobility of concentrated dispersions of spherical colloidal particles. On the consistent use of the cell model
- 2006
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Ingår i: Langmuir. - : American Chemical Society (ACS). - 0743-7463 .- 1520-5827. ; 22:16, s. 7041-7051
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Tidskriftsartikel (refereegranskat)abstract
- This paper outlines a complete and self-consistent cell model theory of the electrokinetics of dense spherical colloidal suspensions for general electrolyte composition, frequency of applied field, ? potential, and particle size. The standard electrokinetic equations, first introduced for any given particle configuration, are made tractable to computation by averaging over particle configurations. The focus of this paper is on the systematic development of suitable boundary conditions at the outer cell boundary obtained from global constraints on the suspension. The approach is discussed in relation to previously published boundary conditions that have often been introduced in an ad hoc manner. Results of a robust numerical calculation of high-frequency colloidal transport properties, such as dynamic mobility, using the present model are presented and compared with some existing dense suspension models. © 2006 American Chemical Society.
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| 5. |
- Ahualli, S., et al.
(författare)
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Use of a cell model for the evaluation of the dynamic mobility of spherical silica suspensions
- 2007
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Ingår i: Journal of Colloid and Interface Science. - : Elsevier BV. - 0021-9797 .- 1095-7103. ; 309:2, s. 342-349
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we evaluate the validity of a cell model for the calculation of the dynamic mobility of concentrated suspensions of spheres. The key point is the consideration of the boundary conditions (electrical and hydrodynamic) at the boundary of the fluid cell surrounding a single probe particle. The model proposed is based on a universal criterion for the averages of fluid velocity, electric potential, pressure field or electrochemical properties in the cell. The calculations are checked against a wide set of experimental data on the dynamic mobility of silica suspensions with two different radii, several ionic strengths, and two particle concentrations. The comparison reveals an excellent agreement between theory and experiment, and the model appears to be extremely suitable for correctly predicting the behavior of the dynamic mobility, including the changes in the zeta potential, ?, with ionic strength, the frequency and amplitude of the Maxwell-Wagner-O'Konski relaxation, and the inertial relaxation occurring at the top of the frequency range accessible to our experimental device. © 2007 Elsevier Inc. All rights reserved.
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| 6. |
- Attard, P, et al.
(författare)
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Effective spring constant of bubbles and droplets
- 2001
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Ingår i: Langmuir. - : American Chemical Society (ACS). - 0743-7463 .- 1520-5827. ; 17:26, s. 8217-8223
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Tidskriftsartikel (refereegranskat)abstract
- It is shown that gas bubbles and liquid droplets respond as hookean springs to applied loads in the experimental weak force regime. An analytic expression is obtained for the spring constant that is identical for both, linear in the surface tension gamma, and logarithmically dependent on the lengths (the decay length of the interaction, the radius of the bubble or droplet, and the radius of the particle or probe). For acute interior contact angles greater than about 20 degrees, it is typically in the range 0.8-1.2 gamma, in agreement with published atomic force microscopy data, and it increases logarithmically for smaller contact angles. Analytic expressions are also obtained for the deformed profile, the extent of the dimple and of the interaction region, the wrapping radius, and the rupture force.
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| 7. |
- Attard, Phil, et al.
(författare)
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Effective spring description of a bubble or a droplet interacting with a particle
- 2002
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Ingår i: Journal of Colloid and Interface Science. - : Elsevier. - 0021-9797 .- 1095-7103. ; 247:1, s. 255-257
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Tidskriftsartikel (övrigt vetenskapligt/konstnärligt)abstract
- It is shown that the interaction of a particle with a liquid drop or a gas bubble may be quantitatively described over the whole distance regime by treating the fluid interface as a Hookean spring. An algorithm suitable for analyzing atomic force microscopy data suitable for a calculator or a spread-sheet is given and applied to data for oil drops. (C) 2002 Elsevier Science (USA).
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| 8. |
- Bradshaw-Hajek, B H, et al.
(författare)
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A composite Level Set and Extended-Domain-Eigenfunction Method for simulating 2D Stokes flow involving a free surface
- 2013
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Ingår i: Journal of Computational and Applied Mathematics. - : Elsevier. - 0377-0427 .- 1879-1778. ; 237:1, s. 389-402
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, the Extended-Domain-Eigenfunction-Method (EDEM) is combined with the Level Set Method in a composite numerical scheme for simulating a moving boundary problem. The liquid velocity is obtained by formulating the problem in terms of the EDEM methodology and solved using a least square approach. The propagation of the free surface is effected by a narrow band Level Set Method. The two methods both pass information to each other via a bridging process, which allows the position of the interface to be updated. The numerical scheme is applied to a series of problems involving a gas bubble submerged in a viscous liquid moving subject to both an externally generated flow and the influence of surface tension.
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| 9. |
- Bradshaw-Hajek, B.H., et al.
(författare)
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Frequency-dependent electrical conductivity of concentrated dispersions of spherical colloidal particles
- 2008
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Ingår i: Langmuir. - : American Chemical Society (ACS). - 0743-7463 .- 1520-5827. ; 24:9, s. 4512-4522
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Tidskriftsartikel (refereegranskat)abstract
- This paper outlines the application of a self-consistent cell-model theory of electrokinetics to the problem of determining the electrical conductivity of a dense suspension of spherical colloidal particles. Numerical solutions of the standard electrokinetic equations, subject to self-consistent boundary conditions, are implemented in formulas for the electrical conductivity appropriate to the particle-averaged cell model of the suspension. Results of calculations as a function of frequency, zeta potential, volume fraction, and electrolyte composition, are presented and discussed. © 2008 American Chemical Society.
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| 10. |
- Bradshaw-Hajek, B H, et al.
(författare)
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The Actual Dielectric Response Function for a Colloidal Suspension of Spherical Particles
- 2010
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Ingår i: LANGMUIR. - : ACS American Chemical Society. - 0743-7463 .- 1520-5827. ; 26:11, s. 7875-7884
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, we present a theoretical analysis of the dielectric response of a dense suspension of spherical colloidal particles based on a self-consistent cell model. Particular attention is paid to (a) the relationship between the dielectric response and the conductivity response and (b) the connection between the real and imaginary parts of these responses based on the Kramers-Kronig relations. We have thus clarified the analysis of Carrique et al. (Carrique, F. Criado, C.; Delgado, A. V. J. Colloid Interface Sci. 1993, 156, 117). We have shown that both the conduction and displacement current components are complex quantities with both real and imaginary parts being frequency dependent. The dielectric response exhibits characteristics of two relaxation phenomena: the Maxwell-Wagner and the a-relaxations, with the imaginary part being the more sensitive instrument. The inverse Fourier transform of the simulated dielectric response is compared with a phenomenological, two-exponential response function with good agreement obtained. The two fitted decay times also compare well with times extracted from the explicit simulations.
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