Solving Nonlinear Systems of Equations Via Spectral Residual Methods: Stepsize Selection and Applications

Spectral residual methods are derivative-free and low-cost per iteration procedures for solving nonlinear systems of equations. They are generally coupled with a nonmonotone linesearch strategy and compare well with Newton-based methods for large nonlinear systems and sequences of nonlinear systems. The residual vector is used as the search direction and choosing the steplength has a crucial impact on the performance. In this work we address both theoretically and experimentally the steplength selection and provide results on a real application such as a rolling contact problem

New updates of incomplete LU factorizations and applications to large nonlinear systems

Abstract In this paper, we address the problem of preconditioning sequences of large sparse nonsymmetric systems of linear equations and present two new strategies to construct approximate updates of factorized preconditioners. Both updates are based on the availability of an incomplete LU (ILU) factorization for one matrix of the sequence and differ in the approximation of the so-called ideal updates. The first strategy is an approximate diagonal update of the ILU factorization; the second strategy relies on banded approximations of the factors in the ideal update. The efficiency and reliability of the proposed preconditioners are shown in the solution of nonlinear systems of equations by preconditioned inexact Newton-Krylov methods. Matrix-free implementations of the updating strategy are provided and numerical experiments are carried out on application problems

Extremely high He isotope ratios in MORB-source mantle from the proto-Iceland plume

The high <sup>3</sup>He/<sup>4</sup>He ratio of volcanic rocks thought to be derived from mantle plumes is taken as evidence for the existence of a mantle reservoir that has remained largely undegassed since the Earth's accretion. The helium isotope composition of this reservoir places constraints on the origin of volatiles within the Earth and on the evolution and structure of the Earth's mantle. Here we show that olivine phenocrysts in picritic basalts presumably derived from the proto-Iceland plume at Baffin Island, Canada, have the highest magmatic <sup>3</sup>He/<sup>4</sup>He ratios yet recorded. A strong correlation between <sup>3</sup>He/<sup>4</sup>He and <sup>87</sup>Sr/<sup>86</sup>Sr, <sup>143</sup>Nd/<sup>144</sup>Nd and trace element ratios demonstrate that the <sup>3</sup>He-rich end-member is present in basalts that are derived from large-volume melts of depleted upper-mantle rocks. This reservoir is consistent with the recharging of depleted upper-mantle rocks by small volumes of primordial volatile-rich lower-mantle material at a thermal boundary layer between convectively isolated reservoirs. The highest <sup>3</sup>He/<sup>4</sup>He basalts from Hawaii and Iceland plot on the observed mixing trend. This indicates that a <sup>3</sup>He-recharged depleted mantle (HRDM) reservoir may be the principal source of high <sup>3</sup>He/<sup>4</sup>He in mantle plumes, and may explain why the helium concentration of the 'plume' component in ocean island basalts is lower than that predicted for a two-layer, steady-state model of mantle structure

The Effects of Acute Stress on Human Prefrontal Working Memory Systems

We examined the relationship between acute stress and prefrontal-cortex (PFC) based working memory (WM) systems using behavioral (Experiment 1) and functional magnetic resonance imaging (fMRI; Experiment 2) paradigms. Subjects performed a delayed-response item-recognition task, with alternating blocks of high and low WM demand trials. During scanning, participants performed this task under three stress conditions: cold stress (induced by cold-water hand-immersion), a room temperature water control (induced by tepid-water hand-immersion), and no-water control (no hand-immersion). Performance was affected by WM demand, but not stress. Cold stress elicited greater salivary cortisol readings in behavioral subjects, and greater PFC signal change in fMRI subjects, than control conditions. These results suggest that, under stress, increases in PFC activity may be necessary to mediate cognitive processes that maintain behavioral organization

Evidence for Multiple Manipulation Processes in Prefrontal Cortex

The prefrontal cortex (PFC) is known to subserve working memory (WM) processes. Brain imaging studies of WM using delayed response tasks (DRTs) have shown memory-load-dependent activation increases in dorsal prefrontal cortex (PFC) regions. These activation increases are believed to reflect manipulation of to-be-remembered information in the service of memory-consolidation. This speculation has been based on observations of similar activation increases in tasks that overtly require manipulation by instructing participants to reorder to-be-remembered list items. In this study, we tested the assumption of functional equivalence between these two types of WM tasks. Participants performed a DRT under two conditions with memory loads ranging from 3 to 6 letters. In an “item-order” condition, participants were required to remember letters in the order in which they were presented. In a “reordering” condition, participants were required to remember the letters in alphabetical order. Load-related activation increases were observed during the encoding and maintenance periods of the order maintenance condition, whereas load-related activation decreases were observed in the same periods of the reordering condition. These results suggest that (1) the neural substrates associated with long-list retention and those associated with reordering are not equivalent, (2) cognitive processes associated with long-list retention may be more closely approximated by item-order maintenance than by reordering, and (3) multiple forms of WM manipulation are dissociable on the basis of fMRI data

Gyrofluid simulations of collisionless reconnection in the presence of diamagnetic effects

The effects of the ion Larmor radius on magnetic reconnection are investigated by means of numerical simulations, with a Hamiltonian gyrofluid model. In the linear regime, it is found that ion diamagnetic effects decrease the growth rate of the dominant mode. Increasing ion temperature tends to make the magnetic islands propagate in the ion diamagnetic drift direction. In the nonlinear regime, diamagnetic effects reduce the final width of the island. Unlike the electron density, the guiding center density does not tend to distribute along separatrices and at high ion temperature, the electrostatic potential exhibits the superposition of a small scale structure, related to the electron density, and a large scale structure, related to the ion guiding-center density

Gyrofluid simulations of collisionless reconnection in the presence of diamagnetic effects

The effects of the ion Larmor radius on magnetic reconnection are investigated by means of numerical simulations, with a Hamiltonian gyrofluid model. In the linear regime, it is found that ion diamagnetic effects decrease the growth rate of the dominant mode. Increasing ion temperature tends to make the magnetic islands propagate in the ion diamagnetic drift direction. In the nonlinear regime, diamagnetic effects reduce the final width of the island. Unlike the electron density, the guiding center density does not tend to distribute along separatrices and at high ion temperature, the electrostatic potential exhibits the superposition of a small scale structure, related to the electron density, and a large scale structure, related to the ion guiding-center density

Gyrofluid simulations of collisionless reconnection in the presence of diamagnetic effects

The effects of the ion Larmor radius on magnetic reconnection are investigated by means of numerical simulations, with a Hamiltonian gyrofluid model. In the linear regime, it is found that ion diamagnetic effects decrease the growth rate of the dominant mode. Increasing ion temperature tends to make the magnetic islands propagate in the ion diamagnetic drift direction. In the nonlinear regime, diamagnetic effects reduce the final width of the island. Unlike the electron density, the guiding center density does not tend to distribute along separatrices and at high ion temperature, the electrostatic potential exhibits the superposition of a small scale structure, related to the electron density, and a large scale structure, related to the ion guiding-center density