Origin of Low- and High-Energy Monopole Collectivity in 132Sn

Beginning with the Skyrme interaction, we study the properties of the isoscalar giant monopole resonances (ISGMR) of 132Sn. Using the finite-rank separable approximation for the particle-hole interaction, the coupling between one- and two-phonon terms in the wave functions of excited states is taken into account in very large configurational spaces. The inclusion of the phonon–phonon coupling (PPC) results in the formation of a low-energy 0+ state. The PPC inclusion leads to a fragmentation of the ISGMR strength to lower energy states and also to a higher energy tail. Using the same set of parameters, we describe the available experimental data for the ISGMR characteristics of 118,120,122,124Sn and give a prediction for 126,128,130,132Sn.

A Logarithmic Function-Based Novel Representation Algorithm for Image Classification

Salient feature extraction is an important task in image classification and recognition. Although classification techniques focus on the bright part of an image, many pixels of the image are of similar saliency. To address the issue, this paper proposes the logarithmic function-based novel representation algorithm (LFNR) to apply a novel representation for each image. The original and novel representations were fused to improve the classification accuracy. Experimental results show that, thanks to the simultaneous use of original and novel representations, the test samples could be better classified. The classification algorithms coupled with the LFNR all witnessed lower error rates than the original algorithms. In particular, the collaboration representation-based classification coupled with the LFNR significantly outperformed the other sparse representation algorithms, such as homotopy, primal augmented Lagrangian method (PALM), and sparse reconstruction by separable approximation algorithm (SpaRSA). The no-parameter property of the LFNR is also noteworthy.

Tensor-structured algorithm for reduced-order scaling large-scale Kohn–Sham density functional theory calculations

We present a tensor-structured algorithm for efficient large-scale density functional theory (DFT) calculations by constructing a Tucker tensor basis that is adapted to the Kohn–Sham Hamiltonian and localized in real-space. The proposed approach uses an additive separable approximation to the Kohn–Sham Hamiltonian and an L1 localization technique to generate the 1-D localized functions that constitute the Tucker tensor basis. Numerical results show that the resulting Tucker tensor basis exhibits exponential convergence in the ground-state energy with increasing Tucker rank. Further, the proposed tensor-structured algorithm demonstrated sub-quadratic scaling with system-size for both systems with and without a gap, and involving many thousands of atoms. This reduced-order scaling has also resulted in the proposed approach outperforming plane-wave DFT implementation for systems beyond 2000 electrons.

An efficient Helmholtz solver for acoustic transversely isotropic media

The acoustic approximation, even for anisotropic media, is widely used in current industry imaging and inversion algorithms mainly because P-waves constitute most of the energy recorded in seismic exploration. The resulting acoustic formulas tend to be simpler, resulting in more efficient implementations, and they depend on fewer medium parameters. However, conventional solutions of the acoustic-wave equation with higher-order derivatives suffer from S-wave artifacts. Thus, we separate the quasi-P-wave propagation in anisotropic media into the elliptic anisotropic operator (free of the artifacts) and the nonelliptic anisotropic components, which form a pseudodifferential operator. We then develop a separable approximation of the dispersion relation of nonelliptic-anisotropic components, specifically for transversely isotropic media. Finally, we iteratively solve the simpler lower-order elliptical wave equation for a modified source function that includes the nonelliptical terms represented in the Fourier domain. A frequency-domain Helmholtz formulation of the approach renders the iterative implementation efficient because the cost is dominated by the lower-upper decomposition of the impedance matrix for the simpler elliptical anisotropic model. In addition, the resulting wavefield is free of S-wave artifacts and has a balanced amplitude. Numerical examples indicate that the method is reasonably accurate and efficient.

Inversion gradients for acoustic VTI wavefield tomography

Wavefield tomography can handle complex subsurface geology better than ray-based techniques and, ultimately, provide a higher resolution. Here, we implement forward and adjoint wavefield extrapolation for VTI (transversely isotropic with a vertical symmetry axis) media using a generalized pseudospectral operator based on a separable approximation for the P-wave dispersion relation. This operator is employed to derive the gradients of the differential semblance optimization (DSO) and modified image-power objective functions. We also obtain the gradient expressions for a data-domain objective function that can more easily incorporate borehole information necessary for stable VTI velocity analysis. These gradients are similar to the ones obtained with a space-time finite-difference (FD) scheme for a system of coupled wave equations but the pseudospectral method is not hampered by the imprint of the shear-wave artifact. Numerical examples also show the potential advantages of the modified image-power objective function in estimating the anellipticity parameter [Formula: see text].