| 1. |
- 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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| 2. |
- 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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| 3. |
- 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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| 4. |
- Bradshaw-Hajek, B. H., et al.
(författare)
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Dynamic Dielectric Response of Concentrated Colloidal Dispersions: Comparison between Theory and Experiment
- 2009
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Ingår i: Langmuir. - : ACS American Chemical Society. - 0743-7463 .- 1520-5827. ; 25:4, s. 1961-1969
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Tidskriftsartikel (refereegranskat)abstract
- The cell-model electrokinetic theory of Ahualli et al. Langmuir 2006, 22, 704 1; Ahualli et al. J. Colloid Interface Sci. 2007, 309, 342; and Bradshaw-Hajek et al. Langmuir 2008, 24, 4512 is applied to a dense suspension of charged spherical particles, to exhibit the systems dielectric response to an applied electric field as a function of solids volume fraction. The models predictions of effective permittivity and complex conductivity are favorably compared with published theoretical calculations and experimental measurements on dense colloidal systems. Physical factors governing the volume fraction dependence of the dielectric response are discussed.
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| 5. |
- 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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| 6. |
- 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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