本文以傳導的物理行為設計適當的材料係數來包覆曲線異向性材料中任意形狀以及性質的物體，藉由此設計適當的材料能夠控制能量(例如熱通量)前進的方向，並且會循著某特定之軌跡繞過物體回到原本行進的方向而不受到任何的干擾，對於外界的觀察者而言此被包覆的物體就像是隱形一樣，而這層包覆物體的裝置稱為「屏蔽裝置」。 本文設計出在圓柱型以及球型異向性材料中的屏蔽裝置，此類型的材料主要特徵在於材料係數在某些極座標特定方向為常數，以圓柱型異向性材料為例，其材料係數在徑向、切線方向以及軸向的數值都不同，因此在屏蔽裝置的設計方面與均向性材料或者直角異向性材料的情況不同在於屏蔽裝置的中心位置與材料的中心位置通常並不會一致。 本文證實如果將平移過後屏蔽裝置中心與曲線異向性材料中心使用一致的座標系統，則先前的座標轉換方式仍然適用，而且轉換後的材料係數會同時與屏蔽裝置中心位置以及背景材料有關。 本文同時以數值模擬的方法來展示此裝置的效果，藉由模擬的結果證實了在曲線異向性材料中的屏蔽裝置確實能夠達到屏蔽物體的效果。

Based on the form-invariant of the conductivity equation under coordinate transformation, we design the transformed material properties to control and direct the fields traveling around an arbitrary object, in which the background material is curvilinearly anisotropic. The layer that to make the object invisible is called “cloaking”. Specific results are derived for cylindrically orthotropic and spherically transversely isotropic media. Materials with curvilinear anisotropy possess constants properties in specific curvilinear coordinate systems. For example, cylindrically orthotropic material is characterized by that the material properties in the radial, tangential, and axial directions are distinct. In contrast to the isotropic or rectilinearly anisotropic media, the position of cloaking center and the material origin may not be the same. We show that, by incorporation of these two positions, the previous coordinate transformation procedure remains applicable and the transformed material specifications now depends on the position of cloaking center and the background material properties. We also use the numerical simulation to perform the properties of the cloak. The results of the simulation show that the cloak with the proposed parameters performs well in these curvilinear anisotropic media.

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