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- Ackleh, Azmy S., et al.
(författare)
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High resolution finite difference schemes for a size structured coagulation-fragmentation model in the space of radon measures
- 2023
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Ingår i: Mathematical Biosciences and Engineering. - : American Institute of Mathematical Sciences. - 1547-1063 .- 1551-0018. ; 20:7, s. 11805-11820
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, we develop explicit and semi-implicit second-order high-resolution finite difference schemes for a structured coagulation-fragmentation model formulated on the space of Radon measures. We prove the convergence of each of the two schemes to the unique weak solution of the model. We perform numerical simulations to demonstrate that the second order accuracy in the Bounded-Lipschitz norm is achieved by both schemes.
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| 4. |
- Lyons, Rainey, et al.
(författare)
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A Continuum Model for Morphology Formation from Interacting Ternary Mixtures : Simulation Study of the Formation and Growth of Patterns
- 2023
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Ingår i: Physica D. - : Elsevier. - 0167-2789 .- 1872-8022. ; 453
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Tidskriftsartikel (refereegranskat)abstract
- Our interest lies in exploring the ability of a coupled nonlocal system of two quasilinear parabolic partial differential equations to produce phase separation patterns. The obtained patterns are referred here as morphologies. Our target system is derived in the literature as the rigorous hydrodynamic limit of a suitably scaled interacting particle system of Blume–Capel–type driven by Kawasaki dynamics. The system describes in a rather implicit way the interaction within a ternary mixture that is the macroscopic counterpart of a mix of two populations of interacting solutes in the presence of a background solvent. Our discussion is based on the qualitative behavior of numerical simulations of finite volume approximations of smooth solutions to our system and their quantitative postprocessing in terms of two indicators (correlation and structure factor calculations). Our results show many similar qualitative features (e.g. general shape and approximate coarsening rates) which have been observed in previous works on the stochastic Blume–Capel dynamics with three interacting species. The properties of the obtained morphologies (shape, connectivity, and so on) can play a key role in, e.g., the design of the active layer for efficient organic solar cells.
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| 5. |
- Lyons, Rainey, et al.
(författare)
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Phase separation and morphology formation in interacting ternarymixtures under evaporation : Well-posedness and numerical simulation of a non-local evolution system
- 2024
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Ingår i: Nonlinear Analysis. - : Elsevier. - 1468-1218. ; 77
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Tidskriftsartikel (refereegranskat)abstract
- We study a nonlinear coupled parabolic system with non-local drift terms modeling at the continuum level the inter-species interaction within a ternary mixture that allows the evaporation of one of the species. In the absence of evaporation, the proposed system coincides with the hydrodynamic limit of a stochastic interacting particle system of Blume–Capel-type driven by the Kawasaki dynamics. Similar governing dynamics are found in models used to study morphology formation in the design of organic solar cells, thin adhesive bands, and other applications. We investigate the well-posedness of the target system and present preliminary numerical simulations which incorporate ‘from the top’ evaporation into the model. We employ a finite volumes scheme to construct approximations of the weak solution and illustrate how the evaporation process can affect the shape and connectivity of the evolving-in-time morphologies
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