Conjugate Gradient Relaxation Research Articles

FeRh ground state and martensitic transformation

Cubic B2 FeRh exhibits a metamagnetic transition [(111) antiferromagnet (AFM) to ferromagnet (FM)] around 353 K and remains structurally stable at higher temperatures. However, the calculated zero-Kelvin phonons of AFM FeRh exhibit imaginary modes at M-points in the Brillouin zone, indicating a premartensitic instability, which is a precursor to a martensitic transformation at low temperatures. Combining electronic-structure calculations with ab initio molecular dynamics, conjugate gradient relaxation, and the solid-state nudged-elastic band (SSNEB) methods, we predict that AFM B2 FeRh becomes unstable at ambient pressure and transforms without a barrier to an AFM(111) orthorhombic (martensitic) groundstate below 90K. We also consider competing structures, in particular, a tetragonal AFM(100) phase that is not the global groundstate, as proposed [Phys. Rev. B 94, 180407(R) (2016)], but a constrained solution.

Research on Inversion Resolution for ERT Data and Applications for Mineral Exploration

This paper presents the effects of two factors on electrical resistivity tomography (ERT) resolution using numerical simulations. The results obtained from the first group of synthetic resistivity model numerical simulations with different electrode configurations illustrate that the inversion resolution can be improved if the current electrodes and potential electrodes are installed at a subsurface depth. The results obtained from the second group of synthetic resistivity models with different mesh densities illustrate that the inversion resolution can be improved if the mesh grid density is increased. The increased number of degrees of freedom necessary to fit the data to a prescribed target misfit leads to the inverted imagery deviating from the true resistivity model. Throughout the literature the inversion procedure is implemented in the conjugate gradient relaxation method and the model calculation speed is enhanced using the parallel processing mode. ERT surveys were employed for mineral exploration at Chifeng in Inner Mongolia, China. The inverted image clearly describes the vein behavior down to 200 m in depth in the prospect area and is consistent with the drilling data results.

Electronic and magnetic properties of bimetallicL10cuboctahedral clusters by means of fully relativistic density-functional-based calculations

By means of density functional theory (DFT) and the generalized gradient approximation (GGA) we present a structural, electronic and magnetic study of FePt, CoPt, FeAu and FePd based L1$_0$ ordered cuboctahedral nanoparticles, with total numbers of atoms, N$_{tot}$ = 13, 55, 147. After a conjugate gradient relaxation, the nanoparticles retain their L1$_0$ symmetry, but the small displacements of the atomic positions tune the electronic and magnetic properties. The value of the total magnetic moment stabilizes as the size increases. We also show that the Magnetic Anisotropy Energy (MAE) depends on the size as well as the position of the Fe-atomic planes in the clusters. We address the influence on the MAE of the surface shape, finding a small in-plane MAE for (Fe,Co)$_{24}$Pt$_{31}$ nanoparticles.

Two dimensional combined inversion of short- and long-normal dc resistivity well log data

Abstract A method is presented for the two-dimensional combined inversion of short- and long-normal tool direct current resistivity data with symmetry. The forward problem is solved using the finite element method in the cylindrical coordinates system. The inverse problem is solved using a conjugate gradient technique with the partial derivatives obtained using reciprocity. The parameters were obtained by means of both conjugate gradient relaxation and conventional conjugate gradient method. The solution of this highly underdetermined inverse problem is stabilized using Tikhonov regularization and the scheme yields a blurred image of the subsurface. The scheme is tested using synthetic data and field data. Tests using synthetic data suggest that traces of the horizontal boundaries are delineated in the range of the exploration distance while the resolution of vertical boundaries depends upon the solution regularization. Application to field data shows that additional information is necessary for resolving the resistivity structure when there are low resistivity contrasts between formation units.

Atomistic modeling of helium interacting with screw dislocations in α-Fe

Formation energies, binding energies, and migration energies of interstitial He atoms in and near the core of an a/2〈1 1 1〉 screw dislocation in α-Fe are determined in atomistic simulations using molecular statics employing conjugate gradient relaxation and the dimer method for determining saddle point energies. The set of interatomic potentials employed is the same as used in many recent static and dynamic He–Fe simulations. Interstitial He atoms have a maximum positive binding energy of about 1 eV to the screw dislocation core relative to interstitial He atoms in the perfect crystal, which is about half that of binding energies of He to the edge dislocation. However, interstitial He atoms diffuse along the screw dislocation core with a migration energy of 0.4–0.5 eV, which is the same range as migration energies of interstitial He atoms along the edge dislocation.

Interaction of helium atoms with edge dislocations in α-Fe

Formation energies, binding energies, and migration energies of interstitial He atoms in and near the core of an a/2〈1 1 1〉{1 1 0} edge dislocation in α-Fe are determined in atomistic simulations using conjugate gradient relaxation and the Dimer method for determining saddle point energies. Results are compared as a function of the proximity of the He to the dislocation core and the excess interstitial volume in regions around the dislocation. Interstitial He atoms have negative binding energy on the compression side of the dislocation and strong positive binding energy on the tension side. Even at low temperatures, interstitial He atoms in the vicinity of the dislocation easily migrate to the dislocation core, where they form crowdion interstitials oriented along the close-packed slip direction, with binding energies in excess of 2 eV. Crowdion interstitial He atoms diffuse along the dislocation core, transverse to the crowdion direction, with a migration energy of 0.4–0.5 eV.

Electrical conductivity structures estimated by thin sheet inversion, with special attention to the Beppu-Shimabara graben in central Kyushu, Japan

Abstract It is proposed that the Beppu-Shimabara graben (BSG), characterized by the continuous negative Bouguer anomaly, runs NE to SW in central Kyushu. In order to clarify the BSG, the shallow electrical conductivity structure in central Kyushu is obtained by thin sheet modeling using the inversion of a conjugate gradient relaxation method and also using the forward method. The data used are the single-site transfer functions at 75 sites for the periods of 77, 97 and 122 sec. The inverted model indicates three highly conductive areas: these are the Saga-Chikugo plain covered with thick alluvium and the eastern and the western parts of central Kyushu including the BSG. Both end zones of this BSG are highly conductive in our model, which is closely related to conductive layers shallower than about 1 km. In contrast, the central part of the BSG is rather highly resistive. The BSG, thus, is not revealed as a continuous high-conductive belt and seems to be separated into three parts; the eastern and the western high-conductive zones and the central resistive area in our geoelectrical model of the shallow crust.

Inversion of magnetometer array data by thin-sheet modelling

Summary A conjugate gradient relaxation method is employed in seeking an iterative solution to a particular 3-D electromagnetic inverse problem. The problem, which is non-linear, is that of modelling observed magnetic fluctuation response functions by a thin-sheet earth structure. The method optimizes data misfit and model roughness, and starting from a base model designed on known geology produces a series of improved models. Established thin-sheet algorithms are employed to compute the model responses and sensitivity, and utilization of a parallel computing system enables reasonable execution times. The method is demonstrated by inverting data generated for a synthetic example. Gaussian noise is added to the synthetic data. The inversion scheme has been applied to geomagnetic induction data which have been recorded widely on the Australian continent. Highly conductive structures in models given by the inversion method confirm regional conductivity anomalies indicated by induction arrow patterns, and give more quantitative information about them. The method appears to work well in areas of strong conductivity contrast such as coastlines.

Atomistic Features of the Amorphous-Crystal Interface in Silicon

We simulate the amorphous–crystal interface in silicon using a combination of interatomic potential molecular-dynamics and tight- binding conjugate-gradient relaxation. The samples we create have high quality crystalline and amorphous portions. We develop some localized measures of order to characterize the interface, including a missing neighbor vector and the bond angle deviation. We find that the measures of order interpolate smoothly from a bulk crystal value to a bulk amorphous value across a 7 A thick interface region. The interface structures exhibit a number of interesting features. The crystal planes near the interface are nearly perfect, with a few dimer defects similar to the Si(100) 2×1 reconstruction. Interfaces produced with one constant temperature simulation method are rough, with several layers of atoms forming chains and (111) facets. A different simulation method produces more planar interfaces with only a few chains.

Structure formation in low-energy methyl radical collisions onto diamond (100): an MD study

This work presents a molecular dynamics study of low-energy methyl radical deposition onto diamond (100). The total energy and interatomic forces are calculated within a density-functional based tight-binding scheme. Varying target temperatures and impact energies between 10 and 100 eV at normal incidence lead to a range of penetration depths and threshold energies for penetration or displacements. During the collision regions of local stress and disorder are formed in the surface and subsurface layers. Using a simulated cooling technique the model systems are equilibrated, and the generated structures after a final conjugate gradient relaxation are analyzed. As a main outcome a favourable range of ion energies between 20 and 40 eV for low-energy homoepitaxial diamond growth in [100] direction could be determined. This range is shifted to higher energies with increasing substrate temperatures.

3-D resistivity forward modeling and inversion using conjugate gradients

We have developed rapid 3-D dc resistivity forward modeling and inversion algorithms that use conjugate gradient relaxation techniques. In the forward network modeling calculation, an incomplete Cholesky decomposition for preconditioning and sparse matrix routines combine to produce a fast and efficient algorithm (approximately 2 minutes CPU time on a Sun SPARC‐station 2 for 50 × 50 × 20 blocks). The side and bottom boundary conditions are scaled impedance conditions that take into account the local current flow at the boundaries as a result of any configuration of current sources. For the inversion, conjugate gradient relaxation is used to solve the maximum likelihood inverse equations. Since conjugate gradient techniques only require the results of the sensitivity matrix [Formula: see text] or its transpose [Formula: see text] multiplying a vector, we are able to bypass the actual computation of the sensitivity matrix and the inversion of [Formula: see text], thus greatly decreasing the time needed to do 3-D inversions. We demonstrate 3-D resistivity tomographic imaging using pole‐pole resistivity data collected during an experiment for a leakage monitoring system near evaporation ponds at the Mojave Generating Station in Laughlin, Nevada.

Three-dimensional magnetotelluric inversion using conjugate gradients

SUMMARY We have developed an inversion procedure that uses conjugate gradient relaxation methods. Although one can generalize the method to all inverse problems, we demonstrate its use to invert magnetotelluric data for 3-D earth models. This procedure allows us to bypass the actual computation of the sensitivity matrix A or the inversion of the ATA term. In fact, with the relaxation approach, one only needs to compute the effect of the sensitivity matrix or its transpose multiplying an arbitrary vector. We show that each of these requires one forward problem with a distributed set of sources either in the volume (for A multiplying a vector) or on the surface (for AT multiplying a vector). This significantly reduces the computational requirements needed to do a 3-D inversion. For this paper, we have simplified the boundary conditions by assuming the model is repeated in the horizontal directions, but this is not a necessary constraint of the method. The algorithm reduces data errors to the 2 per cent level for noise-free synthetic 3-D magnetotelluric data.

Partitioning and preconditioning of finite element matrices on the DAP

A method for solving linear finite element equations is proposed for highly parallel SIMD architectures with limited local memory. The method is based on a fine domain decomposition that can be conveniently mapped onto the processor array. Then the equations are structured using a form of one-way dissection and the equations solved by an iteration that combines conjugate gradient relaxation with coarse grid smoothing. Numerical experiments using the 64 × 64 DAP are presented.