6,262 research outputs found
Special Lagrangians, stable bundles and mean curvature flow
We make a conjecture about mean curvature flow of Lagrangian submanifolds of
Calabi-Yau manifolds, expanding on \cite{Th}. We give new results about the
stability condition, and propose a Jordan-H\"older-type decomposition of
(special) Lagrangians. The main results are the uniqueness of special
Lagrangians in hamiltonian deformation classes of Lagrangians, under mild
conditions, and a proof of the conjecture in some cases with symmetry: mean
curvature flow converging to Shapere-Vafa's examples of SLags.Comment: 36 pages, 4 figures. Minor referee's correction
Analysis of interface cracks in adhesively bonded lap shear joints, part 4
Conservation laws of elasticity for nonhomogeneous materials were developed and were used to study the crack behavior in adhesively bonded lap shear joints. By using these laws and the fundamental relationships in fracture mechanics of interface cracks, the problem is reduced to a pair of linear algebraic equations, and stress intensity solutions can be determined directly by information extracted from the far field. The numerical results obtained show that: (1) in the lap-shear joint with a given adherend, the opening-mode stress intensity factor, (K sub 1) is always larger than that of the shearing-mode (K sub 2); (2) (K sub 1) is not sensitive to adherent thickness abut (K sub 2) increases rapidly with increasing thickness; and (3) (K sub 1) and (K sub 2) increase simultaneously as the interfacial crack length increases
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