Results 1 to 10 of about 93,045 (267)
Numerical Solution of Differential Equations of Elastic Curves in 3-dimensional Anti-de Sitter Space [PDF]
Sahand Communications in Mathematical Analysis, 2023 In this paper, we aim to extend the Darboux frame field into 3-dimensional Anti-de Sitter space and obtain two cases for this extension by considering a parameterized curve on a hypersurface; then we carry out the Euler-Lagrange equations and derive ...
Samira Latifi +2 more
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Geometric and topological approaches to shape variation in
Royal Society Open Science, 2021 Leaf shape is a key plant trait that varies enormously. The range of applications for data on this trait requires frequent methodological development so that researchers have an up-to-date toolkit with which to quantify leaf shape. We generated a dataset
Haibin Hang +3 more
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Rolling Geodesics, Mechanical Systems and Elastic Curves
Mathematics, 2022 This paper defines a large class of differentiable manifolds that house two distinct optimal problems called affine-quadratic and rolling problem.
Velimir Jurdjevic
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SIAM Journal on Applied Mathematics, 2011 We consider the problem of minimizing Euler's elastica energy for simple closed curves confined to the unit disk. We approximate a simple closed curve by the zero level set of a function with values +1 on the inside and -1 on the outside of the curve. The outer container now becomes just the domain of the phase field.
Dondl, Patrick +2 more
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Additive Manufacturing Letters, 2022 The near-net-shape manufacturing in additive manufactured and cast of Al-Si alloys results in a heterogeneous solidification and cooling of the parts, leading to significant gradients in microstructural and defect features as well as deformation behavior.
Jochen Tenkamp +3 more
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Weak elastic energy of irregular curves
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2023 A weak notion of elastic energy for (not necessarily regular) rectifiable curves in any space dimension is proposed. Ourp-energy is defined through a relaxation process, where a suitablep-rotation of inscribed polygons is adopted. The discretep-rotation we choose has a geometric flavour: a polygon is viewed as an approximation to a smooth curve, and ...
D. Mucci, A. Saracco
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Evolution characteristics of elastic energy storage of marble under creep loading
矿业科学学报, 2022 In order to study the energy absorption and transformation characteristics of marble, the release of strain energy and dissipation mechanism during creep process, this paper tested the stress-strain relationship of marble under uniaxial cyclic loading ...
Li Dongyang +4 more
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Black rubber and the non-linear elastic response of scale invariant solids
Journal of High Energy Physics, 2020 We discuss the nonlinear elastic response in scale invariant solids. Following previous work, we split the analysis into two basic options: according to whether scale invariance (SI) is a manifest or a spontaneously broken symmetry.
Matteo Baggioli +2 more
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Curves in the Lorentz-Minkowski plane with curvature depending on their position
Open Mathematics, 2020 Motivated by the classical Euler elastic curves, David A. Singer posed in 1999 the problem of determining a plane curve whose curvature is given in terms of its position. We propound the same question in the Lorentz-Minkowski plane, focusing on spacelike
Castro Ildefonso +2 more
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How a Curved Elastic Strip Opens [PDF]
Physical Review Letters, 2014 An elastic strip is transversely clamped in a curved frame. The induced curvature decreases as the strip opens and connects to its flat natural shape. Various ribbon profiles are measured and the scaling law for the opening length validates a description where the in-plane stretching gradually relaxes the bending stress.
Barois, Thomas +3 more
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