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The boundary element method is regarded as an efficient method for solving problems with complex domains. However most successful applications of the BEM have been thus far limited to linear analyses. A major difficulty with the BEM solution of a nonlinear problem is the handling of the volume integral resulting from the nonlinear terms. In this work, a grid-based direct-volume integration BEM has been developed for 3D geometrically nonlinear elastic problems. The volume integrals are evaluated using a regular Cartesian grid, and thus only the boundary discretization of the problem domain is required. The efficiency of the method is enhanced by using acceleration schemes for both surface and volume integration. Several 3-D example calculations have been performed to demonstrate the effectiveness of the three-dimensional formulas and the numerical implementation.

The surface response to the 11-yr solar cycle is assessed in ensemble simulations of the 20th century climate performed in the framework of the 5th phase of the Coupled Model Inter-Comparison Project (CMIP5). A lead/lag multiple linear regression analysis identifies a multi-model mean (MMM) global mean surface warming of about 0.07 K lagging the solar cycle by one to two years on average. The anomalous warming penetrates to approximately the first 80–100 m depth in the ocean. Solar signals in the troposphere show a similar time lag of one to two years and the strongest MMM warming is simulated in the tropics above 300 hPa. At the surface, the MMM response in a subset of models that show statistically significant global mean warming (CMIP5-SIG95) is characterized by an anomalous warming in the west equatorial Pacific Ocean and the Arctic, at one to two years after solar maximum. The Arctic warming is twice as strong as the global mean response and appears in winter months only. The surface warming in the equatorial Pacific Ocean is related to dynamical/thermodynamical processes. Different increase rates of global mean precipitation and atmospheric water vapor in response to a warmer surface lead to a weaker Walker circulation and anomalous westerly winds over the equatorial Pacific in years following solar maximum. Owing to atmosphere–ocean coupling, the anomalous westerly winds cool the subsurface and warm the surface in the western equatorial Pacific by ∼ 0.14 K. The CMIP5-SIG95 MMM surface warming in the equatorial Pacific and Arctic is weak but qualitatively similar compared to solar signals in the HadCRUT4 dataset.

A regular grid direct volume integral method has recently been proposed for domain integrals stemming from Poisson or nonlinear Laplace problems. The volume integral is exactly decomposed into a non-singular boundary integral, plus a remainder volume integral that can be accurately evaluated using a regular grid overlaying the problem domain. For elasticity, achieving the analogous decomposition requires the 'Galerkin vector' H that satisfies E(H)=U, where E is the elasticity equation and U the Kelvin fundamental solution. Herein, Fourier transforms are employed to derive formulas for H and the corresponding traction kernel TH, for both two and three dimensional isotropic elasticity. The three dimensional formulas, and their numerical implementation, are validated by solving relatively simple body force elasticity problems with known solutions. Results for a fast (P-FFT) boundary integral formulation are also presented.

Huntington's disease (HD) is a neurodegenerative disorder, involving psychiatric, cognitive and motor symptoms, caused by a CAG-repeat expansion encoding an extended polyglutamine tract in the huntingtin protein. Oxidative stress and excitotoxicity have previously been implicated in the pathogenesis of HD. We hypothesized that N-acetylcysteine (NAC) may reduce both excitotoxicity and oxidative stress through its actions on glutamate reuptake and antioxidant capacity. The R6/1 transgenic mouse model of HD was used to investigate the effects of NAC on HD pathology. It was found that chronic NAC administration delayed the onset and progression of motor deficits in R6/1 mice, while having an antidepressant-like effect on both R6/1 and wild-type mice. A deficit in the astrocytic glutamate transporter protein, GLT-1, was found in R6/1 mice. However, this deficit was not ameliorated by NAC, implying that the therapeutic effect of NAC is not due to rescue of the GLT-1 deficit and associated glutamate-induced excitotoxicity. Assessment of mitochondrial function in the striatum and cortex revealed that R6/1 mice show reduced mitochondrial respiratory capacity specific to the striatum. This deficit was rescued by chronic treatment with NAC. There was a selective increase in markers of oxidative damage in mitochondria, which was rescued by NAC. In conclusion, NAC is able to delay the onset of motor deficits in the R6/1 model of Huntington's disease and it may do so by ameliorating mitochondrial dysfunction. Thus, NAC shows promise as a potential therapeutic agent in HD. Furthermore, our data suggest that NAC may also have broader antidepressant efficacy.

A multiple linear regression statistical method is applied to model data taken from the Coupled Model Intercomparison Project, phase 5 (CMIP-5) to estimate the 11-yr solar cycle responses of stratospheric ozone, temperature, and zonal wind during the 1979-2005 period. The analysis is limited to the six CMIP-5 models that resolve the stratosphere (high-top models) and that include interactive ozone chemistry. All simulations assumed a conservative 11-yr solar spectral irradiance (SSI) variation based on the NRL model. These model responses are then compared to corresponding observational estimates derived from two independent satellite ozone profile data sets and from ERA Interim Reanalysis meteorological data. The models exhibit a range of 11-yr responses with three models (CESM1-WACCM, MIROC-ESM-CHEM, and MRI-ESM1) yielding substantial solar-induced ozone changes in the upper stratosphere that compare favorably with available observations. The remaining three models do not, apparently because of differences in the details of their radiation and photolysis rate codes. During winter in both hemispheres, the three models with stronger upper stratospheric ozone responses produce relatively strong latitudinal gradients of ozone and temperature in the upper stratosphere that are associated with accelerations of the polar night jet under solar maximum conditions. This behavior is similar to that found in the satellite ozone and ERA Interim data except that the latitudinal gradients tend to occur at somewhat higher latitudes in the models. The sharp ozone gradients are dynamical in origin and assist in radiatively enhancing the temperature gradients, leading to a stronger zonal wind response. These results suggest that simulation of a realistic solar-induced variation of upper stratospheric ozone, temperature and zonal wind in winter is possible for at least some coupled climate models even if a conservative SSI variation is adopted.

The 11-year solar cycle component of climate variability is assessed in the historical simulations of models taken from the Coupled Model Inter-comparison Project, phase 5 (CMIP-5). Multiple linear regression is applied to estimate the zonal-temperature, −wind and annular mode responses to a typical solar cycle, with a focus on both the stratosphere and the stratospheric influence on the surface over the period ∼1850-2005. The analysis is performed on all CMIP-5 models, but focuses on the 13 CMIP-5 models that resolve the stratosphere (high-top models), and compares the simulated solar cycle signature with reanalyses data. The 11-year solar cycle component of climate variability is found to be weaker in terms of magnitude and latitudinal gradient around the stratopause in the models than in reanalysis. The peak in temperature in the lower equatorial stratosphere (∼70 hPa) reported in some studies is found in the models to depend on the length of the analysis period, with the last 30 years yielding the strongest response. A modification of the Polar Jet Oscillation (PJO) in response to the 11-year solar cycle is not robust across all models, but is more apparent in models with high spectral resolution in the shortwave. The PJO evolution is slower in the models, leading to a stronger response during February, whereas observations indicate it to be weaker. In early winter, the magnitudes of the modelled response is more consistent with observations when only data from 1979–2005 is considered. The observed North Pacific high-pressure surface response during solar maximum is only simulated in some models, of which there are no distinguishing model characteristics. The lagged North Atlantic surface response is reproduced in both high- and low-top models, but is more prevalent in the former. In both cases, the magnitude of the response is generally lower than in observations.