863 research outputs found
A wavelet-based Projector Augmented-Wave (PAW) method: reaching frozen-core all-electron precision with a systematic, adaptive and localized wavelet basis set
We present a Projector Augmented-Wave~(PAW) method based on a wavelet basis
set. We implemented our wavelet-PAW method as a PAW library in the ABINIT
package [http://www.abinit.org] and into BigDFT [http://www.bigdft.org]. We
test our implementation in prototypical systems to illustrate the potential
usage of our code. By using the wavelet-PAW method, we can simulate charged and
special boundary condition systems with frozen-core all-electron precision.
Furthermore, our work paves the way to large-scale and potentially order-N
simulations within a PAW method
Dynamical Mean-Field Theory within the Full-Potential Methods: Electronic structure of Ce-115 materials
We implemented the charge self-consistent combination of Density Functional
Theory and Dynamical Mean Field Theory (DMFT) in two full-potential methods,
the Augmented Plane Wave and the Linear Muffin-Tin Orbital methods. We
categorize the commonly used projection methods in terms of the causality of
the resulting DMFT equations and the amount of partial spectral weight
retained. The detailed flow of the Dynamical Mean Field algorithm is described,
including the computation of response functions such as transport coefficients.
We discuss the implementation of the impurity solvers based on hybridization
expansion and an analytic continuation method for self-energy. We also derive
the formalism for the bold continuous time quantum Monte Carlo method. We test
our method on a classic problem in strongly correlated physics, the
isostructural transition in Ce metal. We apply our method to the class of heavy
fermion materials CeIrIn_5, CeCoIn_5 and CeRhIn_5 and show that the Ce 4f
electrons are more localized in CeRhIn_5 than in the other two, a result
corroborated by experiment. We show that CeIrIn_5 is the most itinerant and has
a very anisotropic hybridization, pointing mostly towards the out-of-plane In
atoms. In CeRhIn_5 we stabilized the antiferromagnetic DMFT solution below 3K,
in close agreement with the experimental N\'eel temperature.Comment: The implementation of Bold-CTQMC added and some test of the method
adde
A real-space grid implementation of the Projector Augmented Wave method
A grid-based real-space implementation of the Projector Augmented Wave (PAW)
method of P. E. Blochl [Phys. Rev. B 50, 17953 (1994)] for Density Functional
Theory (DFT) calculations is presented. The use of uniform 3D real-space grids
for representing wave functions, densities and potentials allows for flexible
boundary conditions, efficient multigrid algorithms for solving Poisson and
Kohn-Sham equations, and efficient parallelization using simple real-space
domain-decomposition. We use the PAW method to perform all-electron
calculations in the frozen core approximation, with smooth valence wave
functions that can be represented on relatively coarse grids. We demonstrate
the accuracy of the method by calculating the atomization energies of twenty
small molecules, and the bulk modulus and lattice constants of bulk aluminum.
We show that the approach in terms of computational efficiency is comparable to
standard plane-wave methods, but the memory requirements are higher.Comment: 13 pages, 3 figures, accepted for publication in Physical Review
Nonrigid Registration of Brain Tumor Resection MR Images Based on Joint Saliency Map and Keypoint Clustering
This paper proposes a novel global-to-local nonrigid brain MR image registration to compensate for the brain shift and the unmatchable outliers caused by the tumor resection. The mutual information between the corresponding salient structures, which are enhanced by the joint saliency map (JSM), is maximized to achieve a global rigid registration of the two images. Being detected and clustered at the paired contiguous matching areas in the globally registered images, the paired pools of DoG keypoints in combination with the JSM provide a useful cluster-to-cluster correspondence to guide the local control-point correspondence detection and the outlier keypoint rejection. Lastly, a quasi-inverse consistent deformation is smoothly approximated to locally register brain images through the mapping the clustered control points by compact support radial basis functions. The 2D implementation of the method can model the brain shift in brain tumor resection MR images, though the theory holds for the 3D case
Curvelets and Ridgelets
International audienceDespite the fact that wavelets have had a wide impact in image processing, they fail to efficiently represent objects with highly anisotropic elements such as lines or curvilinear structures (e.g. edges). The reason is that wavelets are non-geometrical and do not exploit the regularity of the edge curve. The Ridgelet and the Curvelet [3, 4] transforms were developed as an answer to the weakness of the separable wavelet transform in sparsely representing what appears to be simple building atoms in an image, that is lines, curves and edges. Curvelets and ridgelets take the form of basis elements which exhibit high directional sensitivity and are highly anisotropic [5, 6, 7, 8]. These very recent geometric image representations are built upon ideas of multiscale analysis and geometry. They have had an important success in a wide range of image processing applications including denoising [8, 9, 10], deconvolution [11, 12], contrast enhancement [13], texture analysis [14, 15], detection [16], watermarking [17], component separation [18], inpainting [19, 20] or blind source separation[21, 22]. Curvelets have also proven useful in diverse fields beyond the traditional image processing application. Let’s cite for example seismic imaging [10, 23, 24], astronomical imaging [25, 26, 27], scientific computing and analysis of partial differential equations [28, 29]. Another reason for the success of ridgelets and curvelets is the availability of fast transform algorithms which are available in non-commercial software packages following the philosophy of reproducible research, see [30, 31]
TVL<sub>1</sub> Planarity Regularization for 3D Shape Approximation
The modern emergence of automation in many industries has given impetus to extensive research into mobile robotics. Novel perception technologies now enable cars to drive autonomously, tractors to till a field automatically and underwater robots to construct pipelines. An essential requirement to facilitate both perception and autonomous navigation is the analysis of the 3D environment using sensors like laser scanners or stereo cameras. 3D sensors generate a very large number of 3D data points when sampling object shapes within an environment, but crucially do not provide any intrinsic information about the environment which the robots operate within.
This work focuses on the fundamental task of 3D shape reconstruction and modelling from 3D point clouds. The novelty lies in the representation of surfaces by algebraic functions having limited support, which enables the extraction of smooth consistent implicit shapes from noisy samples with a heterogeneous density. The minimization of total variation of second differential degree makes it possible to enforce planar surfaces which often occur in man-made environments. Applying the new technique means that less accurate, low-cost 3D sensors can be employed without sacrificing the 3D shape reconstruction accuracy
- …