Papers by Keyword: GLSL

Abstract: Circulant matrix is a special case of Toeplitz matrix, which is widely used in many domains of specialization, especially in image and digital signal processing. Calculating the inverse of this category of matrices consists of the following three steps: (1) transform the first row vector to frequency space by using DFT; (2) calculate the inverse of each amplitude in the spectrum; (3) apply IDFT to the adjusted spectrum and reconstruct the inverse of the original circulant matrix. This paper implements such a fast algorithm on the GPU, which is proved around five to ten times faster than is executed on the CPU.

Abstract: The effect of oxygen vacancies and their migrations on the dielectric responses of BaTiO₃ (BT) ceramics and (Ba, Ca)(Ti, Zr)O₃ (BCTZ) ceramics was studied using wideband dielectric spectroscopy. Both dipole and ionic polarization of BT ceramics after annealing in a reducing atmosphere markedly decreased. To elucidate the decrease of dipole and ionic polarization, we observed the domain width and the crystal structure of BT ceramics annealed in different PO₂. The mass fractions of constituted phases in 90^o domain were calculated using the refinement of XRD patterns to explain the degradation of ionic polarization by oxygen vacancies. From the results above, we judged that the decrease of dipole polarization was due to the domain wall clamping by oxygen vacancies, while that of ionic polarization was attributable to the lattice hardening by the incorporation of oxygen vacancies into the BT lattice. In the case of BCTZ ceramics, dipole polarization showed the same way as BT ceramics with annealing conditions but the ionic polarization was independent of PO₂ in annealing because of anti-reducing behavior of BCTZ ceramics. On the basis of the effect of oxygen vacancy in BT ceramics and BCTZ ceramics, we could clarify the oxygen vacancy migration in BCTZ ceramics under high direct-current voltage (DCV).