Okan Üniversitesi / Okan University

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Browsing Okan Üniversitesi / Okan University by Author "Acar R."

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    Book Part
    Citation Count: 1
    Phase field topology constraints
    (Springer, 2018) Acar,R.; Sağırlı,N.; Bilgisayar Mühendisliği / Computer Engineering
    This paper presents a morphological approach to extract topologically critical regions in phase field models. There are a few studies regarding topological properties of phase fields. One line of work related to our problem addresses constrained phase field evolution. This approach is based on modifying the optimization problem to limit connectedness of the interface. However, this approach results in a complex optimization problem, and it provides nonlocal control. We adapted a non-simple point concept from digital topology to local regions using structuring masks. These regions can be used to constrain the evolution locally. Besides this approach is flexible as it allows the design of structuring elements. Such a study to define topological structures specific to phase field dynamics has not been done to our knowledge. © 2018, The Author(s) and the Association for Women in Mathematics.
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    Book Part
    Citation Count: 0
    Shape patterns in digital fabrication: A survey on negative poisson's ratio metamaterials
    (Springer, 2018) Yılmaz,B.; Adanova,V.; Acar,R.; Tari,S.; Bilgisayar Mühendisliği / Computer Engineering
    Poisson’s ratio for solid materials is defined as the ratio of the lateral length shrinkage to the longitudinal part extension on a simple tension test. While Poisson’s ratio for almost every material in nature is a positive number, materials having negative Poisson’s ratio may be engineered. We survey computational works toward design and fabrication of negative Poisson’s ratio materials focusing on shape patterns from macro to micro scale. Specifically, we cover folding, knitting, and repeatedly ordering geometric structures, i.e., symmetry. Both pattern design and the numerical aspects of the problem yield various future research possibilities. © 2018, The Author(s) and the Association for Women in Mathematics.
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    Article
    Citation Count: 0
    A topology constrained phase field model
    (Academic Press inc Elsevier Science, 2024) Acar, Rueyam; Bilgisayar Mühendisliği / Computer Engineering
    This paper presents a topology constrained phase field model based on a variable mobility Cahn-Hilliard equation. Mostly in the level set framework, this issue has been addressed using concepts from digital topology. However, point based specifications can not be effective in phase fields where the interface is represented by a diffuse region. In phase field models, topology constraints are included in the energy as a penalty term. However, there are no studies which provide topological constraints in the Cahn-Hilliard model to our knowledge. In this work, we use the mobility parameter to enforce topology constraints; this allows local, explicit control of topological events, unlike the optimization based solutions. We define topologically critical regions in phase fields based on a topological analysis of phase field evolution. This analysis shows that diffuse layers formed at topological encounters behave like a Morse function and the critical points of these transitional layers give topologically critical points in phase fields. Using this property, we first detect critical points using an efficient image analysis method. Then we detect the transitional region (critical region) around each critical point using a local morphological segmentation algorithm. We define a mobility function which both has a spatial and concentration dependence. This function is designed to reverse the effect of diffuse layers formed at topological encounters and prevent the further development of topological events. Being extracted from phase field values, the mobility map naturally aligns with phase field evolution. Together with the use of an unconditionally stable semi-implicit Fourier spectral method for the variable mobility Cahn -Hilliard equation, an efficient model is provided. Local, explicit control mechanism allows the design of free energy functional for modeling different materials; this extends the use of Cahn -Hilliard equation to applications which require topology control.