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The moving boundary in arbitrary Lagrangian Eulerian (ALE) formulation is included in the variational equations by the mesh velocity obtained from a displacement-loaded pseudo-structural problem at a concurrent configuration, which eventually facilitates to derive shape design sensitivity.
A set of methods is described which can be used to efficiently derive shape information from natural biosonar antennas, to characterize their system properties using numerical methods and visualize the results in a way that gives access to salient features.
This suggests that the visual system tries to derive shape by connecting individual visual elements.
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In this perspective, we use a moment of inertia derived shape analysis to interrogate potential libraries for chemical synthesis.
This paper proposes a convenient and efficient method of combining these essential elements using analytically derived shape factors for bending modes.
Therefore, a mathematically derived shape factor which reflects the gravity drainage behavior into an exchange term using shape factor concept is essential.
The optimal free-boundary shapes are determined by applying the derived shape gradient function to the H1 gradient method for shells, which is a parameter-free shape optimization method proposed by one of the authors.
Then, the derived shape gradient functions are applied to a gradient method in the Hilbert space with a P.D.E (Partial Differential Equation) smoother, which is referred as the H1 gradient method for frame structures.
Each vibration problem is formulated as a distributed-parameter shape optimization problem, and the derived shape gradient function is applied to the H1 gradient method for the shells proposed by the authors, where the shape gradient function is used as a distributed force function to vary the surface.
This study was based on the anisotropic mechanical-mathematical model of inclining multilayer massif with a doubly periodic system of slots studied numerically, the patterns of distribution of elastic-creep stresses, displacements near two diagonal cavities of derived shape, and the depth of the Finite Element Method in generalized plane strain.
I then compared the geometric circularity metric to the empirically derived shape space and the standard metric, circularity shape factor.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com