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Creators/Authors contains: "Witelski, Thomas"

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  1. ; ; ; (, Communications on Applied Mathematics and Computation)
    Free, publicly-accessible full text available June 1, 2026
  2. ; (, Computational Materials Science)
    We explore a class of splitting schemes employing implicit-explicit (IMEX) time-stepping to achieve accurate and energy-stable solutions for thin-film equations and Cahn-Hilliard models with variable mobility. This splitting method incorporates a linear, constant coefficient implicit step, facilitating efficient computational implementation. We investigate the influence of stabi- lizing splitting parameters on the numerical solution computationally, considering various initial conditions. Furthermore, we generate energy-stability plots for the proposed methods, examin- ing different choices of splitting parameter values and timestep sizes. These methods enhance the accuracy of the original bi-harmonic-modified (BHM) approach, while preserving its energy- decreasing property and achieving second-order accuracy. We present numerical experiments to illustrate the performance of the proposed methods. 
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  3. ; (, SIAM Journal on Applied Mathematics)
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  4. ; ; (, Discrete and Continuous Dynamical Systems)
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  5. ; (, IMA Journal of Applied Mathematics)
    null (Ed.)
    Abstract We study steady-state thin films on chemically heterogeneous substrates of finite size, subject to no-flux boundary conditions. Based on the structure of the bifurcation diagram, we classify the 1D steady-state solutions that exist on such substrates into six different branches and develop asymptotic estimates for the steady states on each branch. Using perturbation expansions, we show that leading-order solutions provide good predictions of the steady-state thin films on stepwise-patterned substrates. We show how the analysis in one dimension can be extended to axisymmetric solutions. We also examine the influence of the wettability contrast of the substrate pattern on the linear stability of droplets and the time evolution for dewetting on small domains. Results are also applied to describe 2D droplets on hydrophilic square patches and striped regions used in microfluidic applications. 
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  6. ; ; ; (, Discrete & Continuous Dynamical Systems - B)
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  7. ; ; ; ; ; ; ; ; ; ; et al (, Science Advances)
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