application of differential geometry

To decline or learn more, visit our Cookies page. The solution yields non-parametric distributions for the objects of interest, thus providing most probable estimates and uncertainty bounds on latent structures at coarse and fine scales. Later on, a stress concentration manifold is built and used online for decision-making. Automation is conquering new fields on a daily basis. Using this q-difference equation, some multilinear generating functions for Hn are discussed. The procedure is based on determining two Muskhelishvili complex potentials in terms of complex Fourier series, and applying the Schwartz alternating method repeatedly until the boundary conditions on the contour of every hole are satisfied. The following main areas are covered: differential equations on manifolds, global analysis, Lie groups, local and global differential geometry, the calculus of variations on manifolds, topology of manifolds, and mathematical physics. List of the recent articles made freely available as part of this journal’s. The technique is tested using synthetic data. 262-277, Nonlinear Analysis: Real World Applications, Volume 21, 2015, pp. Numerical examples of this smoothing methodology, demonstrating the efficiency of the proposed approach, are presented. The thermoviscoelastic constitutive law includes a temperature effect described by the parabolic equation with the subdifferential boundary condition and a damage effect described by the parabolic inclusion with the homogeneous Neumann boundary condition. [4,6,7]. The existence of a unique weak solution is proved by using recent results from the theory of hemivariational inequalities, variational inequalities, and a fixed point argument. By forming a Dirichlet boundary value problem, the proposed method is applicable to both structured and unstructured grids. For instance in [27] a simple modification of the shape functions of an 8-node element has been proved to give similar performance of a 9-node element or in [28] a criterion is proposed to quantitatively check the interpolation precision of quadrilateral elements and the necessary geometry constraints are derived for 8-node element to exactly attain quadratic interpolation precision.Moreover the properties of geodesic curves have been used in defining distortion measures [29] and a corresponding 8-node isoparametric element with curved boundaries with normal (geodesic) co-ordinates and natural (isoparametric) co-ordinates has been developed showing less sensitivity to distortions [30].In [31] the authors present an analytic method to evaluate the effects of element distortions on the performance of displacement-based isoparametric quadrilateral finite elements. In fact, decisions with minimum allowable error are sought in real-time when facing any potential defect. Its advantage in defining geometry of elements [13–15] or modeling mechanical features of engineering problems under consideration [4–7] is its global character which includes also insight into a local behavior. A spectral coarse-scale representation is proposed to capture the salient transient wave phenomena, such as wave dispersion and band gaps that occur in the short wavelength regime. The binary medium of interest consists of spatially varying proportions of low and high permeability material with an isotropic structure. Transient elastic wave propagation in two-dimensional periodic structures is investigated. If you require any further information or help, please visit our Support Center. Once production of your article has started, you can track the status of your article via Track Your Accepted Article. The question of both indicial and constitutive symmetries of different crack density tensors is addressed: for instance the standard fourth order crack density tensor Dc is rari-constant (totally symmetric) and the fourth order closed cracks density tensor by which closed cracks are acting is found to have the square symmetry. Examples of structured and unstructured meshes are used to illustrate the applicability of the proposed approach. By representing the target metric of the mesh as a sum of a coarse-grained component and a component quadratic in surface gradients, an improved surface mesh may be obtained. In this paper we study this problem and prove that, while the answer to the previous question is negative in the general case, the approach by continuous functions is not restrictive with respect to the other, provided that some natural stability and completeness assumptions are made. [13–15], in defining distortion measures and inverse mappings for isoparametric quadrilateral hybrid stress four- and eight-node elements in R2. The tensorial nature of crack density of an initially isotropic 2D medium with open and closed cracks is studied by means of polar decomposition rewriting of standard micro-mechanics results. Special attention is focused on quadrilateral hybrid stress membrane elements with curved boundaries which belong to a series of isoparametric elements developed by Yuan et al. Differential Geometry and its Applications publishes original research papers and survey papers in differential geometry and in all interdisciplinary areas in mathematics which use differential geometric methods and investigate geometrical structures. Discover how our open access options can help you maximize reach and impact. Source Normalized Impact per Paper (SNIP). The mechanical basis of such a nonlinear model can be found in the mathematical foundation of elasticity [18]. The individual contributions of the static and dynamic data to the inference are also analyzed. This fact comes from the nature of a manifold and its bundle structure, which is the main element of the differential geometry. The notion of plane or space curves is one of the elementary ones in the theory of differential geometry, because the concept of a manifold comes from the generalization of a curve or a surface in R3. Differential geometry has encountered numerous applications in physics. In this paper a short survey of applications of differential geometry to engineering problems in the domain of the finite element method is presented together with a few new ideas. More and more physical concepts can be understood as a direct consequence of geometric principles. The real-time decision is based on multidimensional parametric simulation, performed offline, using the Proper Generalized Decomposition (PGD). 550-561, Advances in Water Resources, Volume 44, 2012, pp. Further, the real global nature of differential geometry, has been used by Simo et al. The metric tensor, through the underlying differential equations, controls the character of the grid.In the context of the finite element method, the local structure of the manifold was discussed in the article of Lautersztajn and Samuelsson [5].The goal of this paper is to apply the finite element method to grid smoothing. Common examples are employed to test the accuracy of the information provided by the method. The properties of a differential manifold M are independent of a chosen coordinate system. Trust. We present a Bayesian technique to estimate the fine-scale properties of a binary medium from multiscale observations. 不论您是正在查找出版流程的信息还是忙于撰写下一篇稿件,我们都随时待命。下面我们将重点介绍一些可以在您的科研旅程中对您提供支持的工具。, Ricci flat metrics with bidimensional null orbits and non-integrable orthogonal distribution, On higher order analogues of de Rham cohomology, The navigation problems on a class of conic Finsler manifolds, Nijenhuis geometry II: Left-symmetric algebras and linearization problem for Nijenhuis operators, Coverings and multivector pseudosymmetries of differential equations, Tensor decomposition and homotopy continuation, Laplacian solitons: Questions and homogeneous examples, The holonomy group of locally projectively flat Randers two-manifolds of constant curvature, A variational characterization of profile curves of invariant linear Weingarten surfaces, A note on twisted Dirac operators on closed surfaces, In support of equality, inclusion & diversity, Visibility.

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