1,300 research outputs found

    Qualitative and quantitative properties of the dynamics of screw dislocations

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    This note collects some results on the behaviour of screw dislocation in an elastic medium. By using a semi-discrete model, we are able to investigate two specific aspects of the dynamics, namely (i) the interaction with free boundaries and collision events and (ii) the confinement inside the domain when a suitable Dirichlet-type boundary condition is imposed. In the first case, we analytically prove that free boundaries attract dislocations and we provide an expression for the Peach--Koehler force on a dislocation near the boundary. Moreover, we use this to prove an upper bound on the collision time of a dislocation with the boundary, provided certain geometric conditions are satisfied. An upper bound on the collision time for two dislocations with opposite Burgers vectors hitting each other is also obtained. In the second case, we turn to domains whose boundaries are subject to an external stress. In this situation, we prove that dislocations find it energetically favourable to stay confined inside the material instead of getting closer to the boundary. The result first proved for a single dislocation in the material is extended to a system of many dislocations, for which the analysis requires the careful treatments of the interaction terms.Comment: 12 pages, submitted for the Proceedings volume of the XXIII Conference AIMETA (The Italian Association of Theoretical and Applied Mechanics

    Renormalized Energy and Peach-K\"ohler Forces for Screw Dislocations with Antiplane Shear

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    We present a variational framework for studying screw dislocations subject to antiplane shear. Using a classical model developed by Cermelli and Gurtin, methods of Calculus of Variations are exploited to prove existence of solutions, and to derive a useful expression of the Peach-K\"ohler forces acting on a system of dislocation. This provides a setting for studying the dynamics of the dislocations, which is done in a forthcoming work.Comment: 22 page

    Properties of screw dislocation dynamics: time estimates on boundary and interior collisions

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    In this paper, the dynamics of a system of a finite number of screw dislocations is studied. Under the assumption of antiplane linear elasticity, the two-dimensional dynamics is determined by the renormalised energy. The interaction of one dislocation with the boundary and of two dislocations of opposite Burgers moduli are analysed in detail and estimates on the collision times are obtained. Some exactly solvable cases and numerical simulations show agreement with the estimates obtained.Comment: 25 pages, 4 figure

    Generation of Complex Quantum States Via Integrated Frequency Combs

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    The generation of optical quantum states on an integrated platform will enable low cost and accessible advances for quantum technologies such as secure communications and quantum computation. We demonstrate that integrated quantum frequency combs (based on high-Q microring resonators made from a CMOS-compatible, high refractive-index glass platform) can enable, among others, the generation of heralded single photons, cross-polarized photon pairs, as well as bi- and multi-photon entangled qubit states over a broad frequency comb covering the S, C, L telecommunications band, constituting an important cornerstone for future practical implementations of photonic quantum information processing

    Global minimizers for axisymmetric multiphase membranes

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    We consider a Canham-Helfrich-type variational problem defined over closed surfaces enclosing a fixed volume and having fixed surface area. The problem models the shape of multiphase biomembranes. It consists of minimizing the sum of the Canham-Helfrich energy, in which the bending rigidities and spontaneous curvatures are now phase-dependent, and a line tension penalization for the phase interfaces. By restricting attention to axisymmetric surfaces and phase distributions, we extend our previous results for a single phase (arXiv:1202.1979) and prove existence of a global minimizer.Comment: 20 pages, 3 figure
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