4,802 research outputs found
Electronic structure of VO: charge ordering, metal-insulator transition and magnetism
The low and high-temperature phases of VO have been studied by
\textit{ab initio} calculations. At high temperature, all V atoms are
electronically equivalent and the material is metallic. Charge and orbital
ordering, associated with the distortions in the V pseudo-rutile chains, occur
below the metal-insulator transition. Orbital ordering in the low-temperature
phase, different in V and V chains, allows to explain the
distortion pattern in the insulating phase of VO. The in-chain magnetic
couplings in the low-temperature phase turn out to be antiferromagnetic, but
very different in the various V and V bonds. The V dimers
formed below the transition temperature form spin singlets, but V ions,
despite dimerization, apparently participate in magnetic ordering.Comment: 10 pages, 6 figures, 2 table
A Deep Fourier Residual Method for solving PDEs using Neural Networks
When using Neural Networks as trial functions to numerically solve PDEs, a key choice to be
made is the loss function to be minimised, which should ideally correspond to a norm of the error.
In multiple problems, this error norm coincides with–or is equivalent to–the H−1
-norm of the
residual; however, it is often difficult to accurately compute it. This work assumes rectangular
domains and proposes the use of a Discrete Sine/Cosine Transform to accurately and efficiently
compute the H−1 norm. The resulting Deep Fourier-based Residual (DFR) method efficiently
and accurately approximate solutions to PDEs. This is particularly useful when solutions lack
H2
regularity and methods involving strong formulations of the PDE fail. We observe that the
H1
-error is highly correlated with the discretised loss during training, which permits accurate
error estimation via the loss
A Quadrature-Free Method for Simulation and Inversion of 1.5D Direct Current (DC) Borehole Measurements
Resistivity inverse problems are routinely solved in order to characterize hydrocarbon bearing formations. They often require a large number of forward problems simulations. When considering a one dimensional (1D) planarly layered media, semi-analytical methods can be employed in order to solve a single forward problem in a fraction of a second. However, in some situations, a large number of (over one million) simulations is required, preventing this method to be used as a real time (logging) alternative. In this paper, we propose a novel semi-analytical method that dramatically reduces the total computational time, so it can be employed for real time inversion. In our proposed method, we select an ad hoc basis representation for the spectral solution such that its inverse Hankel transform can be computed analytically. The proposed method requires a pre-process that is expensive when compared with a single evaluation in classical semi-analytical methods. However, subsequent evaluations can be rapidly obtained, decreasing thus the total computational time by orders of magnitude when the number of required forward simulations is large.Marie Sklodowska-Curie grant agreement No 644602
MTM2013-40824-P
SEV-2013-0323
BERC 2014-201
Homopolar bond formation in ZnVO close to a metal-insulator transition
Electronic structure calculations for spinel vanadate ZnVO show that
partial electronic delocalization in this system leads to structural
instabilities. These are a consequence of the proximity to the
itinerant-electron boundary, not being related to orbital ordering. We discuss
how this mechanism naturally couples charge and lattice degrees of freedom in
magnetic insulators close to such a crossover. For the case of ZnVO,
this leads to the formation of V-V dimers along the [011] and [101] directions
that readily accounts for the intriguing magnetic structure of ZnVO.Comment: 5 pages, 3 figures, 1 tabl
Minimum disparity estimators for discrete and continuous models
summary:Disparities of discrete distributions are introduced as a natural and useful extension of the information-theoretic divergences. The minimum disparity point estimators are studied in regular discrete models with i.i.d. observations and their asymptotic efficiency of the first order, in the sense of Rao, is proved. These estimators are applied to continuous models with i.i.d. observations when the observation space is quantized by fixed points, or at random, by the sample quantiles of fixed orders. It is shown that the random quantization leads to estimators which are robust in the sense of Lindsay [9], and which can achieve the efficiency in the underlying continuous models provided these are regular enough
Semi-analytical response of acoustic logging measurements in frequency domain
This work proposes a semi-analytical method for simulation of the acoustic response of multipole eccentered sources in a fluid-filled borehole. Assuming a geometry that is invariant with respect to the azimuthal and vertical directions, the solution in frequency domain is expressed in terms of a Fourier series and a Fourier integral. The proposed semi-analytical method builds upon the idea of separating singularities from the smooth part of the integrand when performing the inverse Fourier transform. The singular part is treated analytically using existing inversion formulae, while the regular part is treated with a FFT technique. As a result, a simple and effective method that can be used for simulating and understanding the main physical principles occurring in borehole-eccentered sonic measurements is obtained. Numerical results verify the proposed method and illustrate its advantages
Goal-Oriented p-Adaptivity using Unconventional Error Representations for a 1D Steady State Convection-Diffusion Problem
This work proposes the use of an alternative error representation for Goal-Oriented Adaptivity (GOA) in context of steady state convection dominated diffusion problems. It introduces an arbitrary operator for the computation of the error of an alternative dual problem. From the new representation, we derive element-wise estimators to drive the adaptive algorithm. The method is applied to a one dimensional (1D) steady state convection dominated diffusion problem with homogeneous Dirichlet boundary conditions. This problem exhibits a boundary layer that produces a loss of numerical stability. The new error representation delivers sharper error bounds. When applied to a -GOA Finite Element Method (FEM), the alternative error representation captures earlier the boundary layer, despite the existing spurious numerical oscillations.Basque Government Consolidated Research Group Grant IT649-13
Spanish Ministry under Grant No. FPDI- 2013-17098
ICERMAR Project KK-2015/0000097
CYTED 2011 project 712RT0449
FONDECYT project 116077
A Deep Double Ritz Method (D2RM) for solving Partial Differential Equations using Neural Networks
Residual minimization is a widely used technique for solving Partial Differential Equations in variational form. It minimizes the dual norm of the residual, which naturally yields a saddle-point (min–max) problem over the so-called trial and test spaces. In the context of neural networks, we can address this min–max approach by employing one network to seek the trial minimum, while another network seeks the test maximizers. However, the resulting method is numerically unstable as we approach the trial solution. To overcome this, we reformulate the residual minimization as an equivalent minimization of a Ritz functional fed by optimal test functions computed from another Ritz functional minimization. We call the resulting scheme the Deep Double Ritz Method (DRM), which combines two neural networks for approximating trial functions and optimal test functions along a nested double Ritz minimization strategy. Numerical results on different diffusion and convection problems support the robustness of our method, up to the approximation properties of the networks and the training capacity of the optimizers
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