Volume integrals associated with the inhomogeneous Helmholtz equation. Part 1: Ellipsoidal region

Problems of wave phenomena in fields of acoustics, electromagnetics and elasticity are often reduced to an integration of the inhomogeneous Helmholtz equation. Results are presented for volume integrals associated with the Helmholtz operator, nabla(2) to alpha(2), for the case of an ellipsoidal region. By using appropriate Taylor series expansions and multinomial theorem, these volume integrals are obtained in series form for regions r 4' and r r', where r and r' are distances from the origin to the point of observation and source, respectively. Derivatives of these integrals are easily evaluated. When the wave number approaches zero, the results reduce directly to the potentials of variable densities

Local Spin Susceptibility of the S=1/2 Kagome Lattice in ZnCu3(OD)6Cl2

We report single-crystal 2-D NMR investigation of the nearly ideal spin S=1/2 kagome lattice ZnCu3(OD)6Cl2. We successfully identify 2-D NMR signals originating from the nearest-neighbors of Cu2+ defects occupying Zn sites. From the 2-D Knight shift measurements, we demonstrate that weakly interacting Cu2+ spins at these defects cause the large Curie-Weiss enhancement toward T=0 commonly observed in the bulk susceptibility data. We estimate the intrinsic spin susceptibility of the kagome planes by subtracting defect contributions, and explore several scenarios.Comment: 4 figures; published in PR-B Rapid Communication

Influence of rotational instability on the polarization structure of SrTiO3

The k-space polarization structure and its strain response in SrTiO3 with rotational instability are studied using a combination of first-principles density functional calculations, modern theory of polarization, and analytic Wannier-function formulation. (1) As one outcome of this study, we rigorously prove-both numerically and analytically-that folding effect exists in polarization structure. (2) After eliminating the folding effect, we find that the polarization structure for SrTiO3 with rotational instability is still considerably different from that for non-rotational SrTiO3, revealing that polarization structure is sensitive to structure distortion of oxygen-octahedra rotation and promises to be an effective tool for studying material properties. (3) Furthermore, from polarization structure we determine the microscopic Wannier-function interactions in SrTiO3. These interactions are found to vary significantly with and without oxygen-octahedra rotation.Comment: 25 pages, 7 figure

Transductive Multi-View Zero-Shot Learning

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Reflection high-energy electron diffraction studies of the growth of lnAs/Ga_(1-x)In_xSb strained-layer superlattices

We have used reflection high‐energy electron diffraction to study the surface periodicity of the growth front of InAs/GaInSb strained‐layer superlattices (SLSs). We found that the apparent surface lattice spacing reproducibly changed during layers which subsequent x‐ray measurements indicated were coherently strained. Abrupt changes in the measured streak spacings were found to be correlated to changes in the growth flux. The profile of the dynamic streak spacing was found to be reproducible when comparing consecutive periods of a SLSs or different SLSs employing the same shuttering scheme at the InAs/GaInSb interface. Finally, when the interface shuttering scheme was changed, it was found that the dynamic streak separation profile also changed. Large changes in the shuttering scheme led to dramatic differences in the streak separation profile, and small changes in the shuttering scheme led to minor changes in the profile. In both cases, the differences in the surface periodicity profile occurred during the parts of the growth where the incident fluxes differed