Thermal metamaterials and devices based on transformation thermodynamics often require materials with anisotropic and inhomogeneous thermal conductivities. In this study, still based on the concept of transformation thermodynamics, we designed a planar illusion thermal device, which can delocalize a heat source in the device such that the temperature profile outside the device appears to be produced by a virtual source at another position. This device can be constructed by only one kind of material with constant anisotropic thermal conductivity. The condition which should be satisfied by the device is provided, and the required anisotropic thermal conductivity is then deduced theoretically. This study may be useful for the designs of metamaterials or devices since materials with constant anisotropic parameters have great facility in fabrication. A prototype device has been fabricated based on a composite composed by two naturally occurring materials. The experimental results validate the effectiveness of the device.
Traditionally variational level set model for image segmentation is solved by using gradient descent method, which has low computational efficiency and needs complex re-initialization of level set functions as signed distance functions. In this paper, we first reformulate the variational model as a constrained optimization problem. Then we present an augmented Lagrangian projection method to preserve signed distance functions and accelerate the implementation. By introducing auxiliary variables, we convert derivative constraints to algebraic equations with simple projection. We apply the proposed algorithm to the two-phase/multiphase Chan-Vese models. Numerical results are provided to compare our algorithm with some others, which demonstrate effectiveness and efficiency of our approach
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