The dependence of southern ocean meridional overturning on wind stress

An eddy-resolving numerical model of a zonal flow, meant to resemble the Antarctic Circumpolar Current, is described and analyzed using the framework of J. Marshall and T. Radko. In addition to wind and buoyancy forcing at the surface, the model contains a sponge layer at the northern boundary that permits a residual meridional overturning circulation (MOC) to exist at depth. The strength of the residual MOC is diagnosed for different strengths of surface wind stress. It is found that the eddy circulation largely compensates for the changes in Ekman circulation. The extent of the compensation and thus the sensitivity of the MOC to the winds depend on the surface boundary condition. A fixed-heat-flux surface boundary severely limits the ability of the MOC to change. An interactive heat flux leads to greater sensitivity. To explain the MOC sensitivity to the wind strength under the interactive heat flux, transformed Eulerian-mean theory is applied, in which the eddy diffusivity plays a central role in determining the eddy response. A scaling theory for the eddy diffusivity, based on the mechanical energy balance, is developed and tested; the average magnitude of the diffusivity is found to be proportional to the square root of the wind stress. The MOC sensitivity to the winds based on this scaling is compared with the true sensitivity diagnosed from the experiments.

First order k-th moment finite element analysis of nonlinear operator equations with stochastic data

We develop and analyze a class of efficient Galerkin approximation methods for uncertainty quantification of nonlinear operator equations. The algorithms are based on sparse Galerkin discretizations of tensorized linearizations at nominal parameters. Specifically, we consider abstract, nonlinear, parametric operator equations J(\alpha ,u)=0 for random input \alpha (\omega ) with almost sure realizations in a neighborhood of a nominal input parameter \alpha _0. Under some structural assumptions on the parameter dependence, we prove existence and uniqueness of a random solution, u(\omega ) = S(\alpha (\omega )). We derive a multilinear, tensorized operator equation for the deterministic computation of k-th order statistical moments of the random solution's fluctuations u(\omega ) - S(\alpha _0). We introduce and analyse sparse tensor Galerkin discretization schemes for the efficient, deterministic computation of the k-th statistical moment equation. We prove a shift theorem for the k-point correlation equation in anisotropic smoothness scales and deduce that sparse tensor Galerkin discretizations of this equation converge in accuracy vs. complexity which equals, up to logarithmic terms, that of the Galerkin discretization of a single instance of the mean field problem. We illustrate the abstract theory for nonstationary diffusion problems in random domains.

Spatial interaction among nontoxic phytoplankton, toxic phytoplankton and zooplankton: emergence in space and time

In homogeneous environments, by overturning the possibility of competitive exclusion among phytoplankton species, and by regulating the dynamics of overall plankton population, toxin-producing phytoplankton (TPP) potentially help in maintaining plankton diversity—a result shown recently. Here, I explore the competitive effects of TPP on phytoplankton and zooplankton species undergoing spatial movements in the subsurface water. The spatial interactions among the species are represented in the form of reaction-diffusion equations. Suitable parametric conditions under which Turing patterns may or may not evolve are investigated. Spatiotemporal distributions of species biomass are simulated using the diffusivity assumptions realistic for natural planktonic systems. The study demonstrates that spatial movements of planktonic systems in the presence of TPP generate and maintain inhomogeneous biomass distribution of competing phytoplankton, as well as grazer zooplankton, thereby ensuring the persistence of multiple species in space and time. The overall results may potentially explain the sustainability of biodiversity and the spatiotemporal emergence of phytoplankton and zooplankton species under the influence of TPP combined with their physical movement in the subsurface water.

Determination of orientations of aromatic groups in self-assembled peptide fibrils by polarised Raman spectroscopy

In this paper we describe a novel combination of Raman spectroscopy, isotope editing and X-ray scattering as a powerful approach to give detailed structural information on aromatic side chains in peptide fibrils. The orientation of the tyrosine residues in fibrils of the peptide YTIAALLSPYS with respect to the fibril axis has been determined from a combination of polarised Raman spectroscopy and X-ray diffraction measurements. The Raman intensity of selected tyrosine bands collected at different polarisation geometries is related to the values and orientation of the Raman tensor for those specific vibrations. Using published Raman tensor values we solved the relevant expressions for both of the two tyrosine residues present in this peptide. Ring deuteration in one of the two tyrosine side chains allowed for the calculation to be performed individually for both, by virtue of the isotopic shift that eliminates band overlapping. Sample disorder was taken into account by obtaining the distribution of orientations of the samples from X-ray diffraction experiments. The results provide previously unavailable details about the molecular conformation of this peptide, and demonstrate the value of this approach for the study of amyloid fibrils.

Sparse polynomial approximation in positive order Sobolev spaces with bounded mixed derivatives and applications to elliptic problems with random loading

In the present paper we study the approximation of functions with bounded mixed derivatives by sparse tensor product polynomials in positive order tensor product Sobolev spaces. We introduce a new sparse polynomial approximation operator which exhibits optimal convergence properties in L2 and tensorized View the MathML source simultaneously on a standard k-dimensional cube. In the special case k=2 the suggested approximation operator is also optimal in L2 and tensorized H1 (without essential boundary conditions). This allows to construct an optimal sparse p-version FEM with sparse piecewise continuous polynomial splines, reducing the number of unknowns from O(p2), needed for the full tensor product computation, to View the MathML source, required for the suggested sparse technique, preserving the same optimal convergence rate in terms of p. We apply this result to an elliptic differential equation and an elliptic integral equation with random loading and compute the covariances of the solutions with View the MathML source unknowns. Several numerical examples support the theoretical estimates.

Modeling Coulombic failure of sea ice with leads

[1] Sea ice failure under low-confinement compression is modeled with a linear Coulombic criterion that can describe either fractural failure or frictional granular yield along slip lines. To study the effect of anisotropy we consider a simplified anisotropic sea ice model where the sea ice thickness depends on orientation. Accommodation of arbitrary deformation requires failure along at least two intersecting slip lines, which are determined by finding two maxima of the yield criterion. Due to the anisotropy these slip lines generally differ from the standard, Coulombic slip lines that are symmetrically positioned around the compression direction, and therefore different tractions along these slip lines give rise to a nonsymmetric stress tensor. We assume that the skewsymmetric part of this tensor is counterbalanced by an additional elastic stress in the sea ice field that suppresses floe spin. We consider the case of two leads initially formed in an isotropic ice cover under compression, and address the question of whether these leads will remain active or new slip lines will form under a rotation of the principal compression direction. Decoupled and coupled models of leads are considered and it is shown that for this particular case they both predict lead reactivation in almost the same way. The coupled model must, however, be used in determining the stress as the decoupled model does not resolve the stress asymmetry properly when failure occurs in one lead and at a new slip line.

Modelling the rheology of sea ice as a collection of diamond-shaped floes

In polar oceans, seawater freezes to form a layer of sea ice of several metres thickness that can cover up to 8% of the Earth’s surface. The modelled sea ice cover state is described by thickness and orientational distribution of interlocking, anisotropic diamond-shaped ice floes delineated by slip lines, as supported by observation. The purpose of this study is to develop a set of equations describing the mean-field sea ice stresses that result from interactions between the ice floes and the evolution of the ice floe orientation, which are simple enough to be incorporated into a climate model. The sea ice stress caused by a deformation of the ice cover is determined by employing an existing kinematic model of ice floe motion, which enables us to calculate the forces acting on the ice floes due to crushing into and sliding past each other, and then by averaging over all possible floe orientations. We describe the orientational floe distribution with a structure tensor and propose an evolution equation for this tensor that accounts for rigid body rotation of the floes, their apparent re-orientation due to new slip line formation, and change of shape of the floes due to freezing and melting. The form of the evolution equation proposed is motivated by laboratory observations of sea ice failure under controlled conditions. Finally, we present simulations of the evolution of sea ice stress and floe orientation for several imposed flow types. Although evidence to test the simulations against is lacking, the simulations seem physically reasonable.

A continuum anisotropic model of sea-ice dynamics

We develop the essential ingredients of a new, continuum and anisotropic model of sea-ice dynamics designed for eventual use in climate simulation. These ingredients are a constitutive law for sea-ice stress, relating stress to the material properties of sea ice and to internal variables describing the sea-ice state, and equations describing the evolution of these variables. The sea-ice cover is treated as a densely flawed two-dimensional continuum consisting of a uniform field of thick ice that is uniformly permeated with narrow linear regions of thinner ice called leads. Lead orientation, thickness and width distributions are described by second-rank tensor internal variables: the structure, thickness and width tensors, whose dynamics are governed by corresponding evolution equations accounting for processes such as new lead generation and rotation as the ice cover deforms. These evolution equations contain contractions of higher-order tensor expressions that require closures. We develop a sea-ice stress constitutive law that relates sea-ice stress to the structure tensor, thickness tensor and strain rate. For the special case of empty leads (containing no ice), linear closures are adopted and we present calculations for simple shear, convergence and divergence.

Influence of mass diffusion in sea ice dynamical models

The mixing of floes of different thickness caused by repeated deformation of the ice cover is modeled as diffusion, and the mass balance equation for sea ice accounting for mass diffusion is developed. The effect of deformational diffusion on the ice thickness balance is shown to reach 1% of the divergence effect, which describes ridging and lead formation. This means that with the same accuracy the mass balance equation can be written in terms of mean velocity rather than mean mass-weighted velocity, which one should correctly use for a multicomponent fluid such as sea ice with components identified by floe thickness. Mixing (diffusion) of sea ice also occurs because of turbulent variations in wind and ocean drags that are unresolved in models. Estimates of the importance of turbulent mass diffusion on the dynamic redistribution of ice thickness are determined using empirical data for the turbulent diffusivity. For long-time-scale prediction (≫5 days), where unresolved atmospheric motion may have a length scale on the order of the Arctic basin and the time scale is larger than the synoptic time scale of atmospheric events, turbulent mass diffusion can exceed 10% of the divergence effect. However, for short-time-scale prediction, for example, 5 days, the unresolved scales are on the order of 100 km, and turbulent diffusion is about 0.1% of the divergence effect. Because inertial effects are small in the dynamics of the sea ice pack, diffusive momentum transfer can be disregarded.

Corticospinal tract integrity and lesion volume play different roles in chronic hemiparesis and its improvement through motor practice

Background. Initial evidence suggests that the integrity of the ipsilesional corticospinal tract (CST) after stroke is strongly related to motor function in the chronic state but not the treatment gain induced by motor rehabilitation. Objective. We examined the association of motor status and treatment benefit by testing patients with a wide range of severity of hemiparesis of the left and right upper extremity. Method. Diffusion tensor imaging was performed in 22 patients beyond 12 months after onset of stroke with severe to moderate hemiparesis. Motor function was tested before and after 2 weeks of modified constraint-induced movement therapy. Results. CST integrity, but not lesion volume, correlated with the motor ability measures of the Wolf Motor Function Test and the Motor Activity Log. No differences were found between left and right hemiparesis. Motor performance improved significantly with the treatment regime, and did so equally for patients with left and right arm paresis. However, treatment benefit was not associated with either CST integrity or lesion volume. Conclusion. CST integrity correlated best in this small trial with chronic long-term status but not treatment-induced improvements. The CST may play a different role in the mechanisms mediating long-term outcome compared to those underlying practice-induced gains after a chronic plateau in motor function.

On the role of specific interactions in the diffusion of nanoparticles in aqueous polymer solutions

Understanding nanoparticle diffusion within non-Newtonian biological and synthetic fluids is essential in designing novel formulations (e.g., nanomedicines for drug delivery, shampoos, lotions, coatings, paints, etc.), but is presently poorly defined. This study reports the diffusion of thiolated and PEGylated silica nanoparticles, characterized by small-angle neutron scattering, in solutions of various water-soluble polymers such as poly(acrylic acid) (PAA), poly(Nvinylpyrrolidone) (PVP), poly(ethylene oxide) (PEO), and hydroxyethylcellulose (HEC) probed using NanoSight nanoparticle tracking analysis. Results show that the diffusivity of nanoparticles is affected by their dimensions, medium viscosity, and, in particular, the specific interactions between nanoparticles and the macromolecules in solution; strong attractive interactions such as hydrogen bonding hamper diffusion. The water-soluble polymers retarded the diffusion of thiolated particles in the order PEO > PVP > PAA > HEC whereas for PEGylated silica particles retardation followed the order PAA > PVP = HEC > PEO. In the absence of specific interactions with the medium, PEGylated nanoparticles exhibit enhanced mobility compared to their thiolated counterparts despite some increase in their dimensions.

Complex-valued B-spline neural networks for modeling and inverting Hammerstein systems

Many communication signal processing applications involve modelling and inverting complex-valued (CV) Hammerstein systems. We develops a new CV B-spline neural network approach for efficient identification of the CV Hammerstein system and effective inversion of the estimated CV Hammerstein model. Specifically, the CV nonlinear static function in the Hammerstein system is represented using the tensor product from two univariate B-spline neural networks. An efficient alternating least squares estimation method is adopted for identifying the CV linear dynamic model’s coefficients and the CV B-spline neural network’s weights, which yields the closed-form solutions for both the linear dynamic model’s coefficients and the B-spline neural network’s weights, and this estimation process is guaranteed to converge very fast to a unique minimum solution. Furthermore, an accurate inversion of the CV Hammerstein system can readily be obtained using the estimated model. In particular, the inversion of the CV nonlinear static function in the Hammerstein system can be calculated effectively using a Gaussian-Newton algorithm, which naturally incorporates the efficient De Boor algorithm with both the B-spline curve and first order derivative recursions. The effectiveness of our approach is demonstrated using the application to equalisation of Hammerstein channels.

Formulation and implementation of a residual-mean ocean circulation model

A parameterization of mesoscale eddies in coarse-resolution ocean general circulation models (GCM) is formulated and implemented using a residual-mean formalism. In that framework, mean buoyancy is advected by the residual velocity (the sum of the Eulerian and eddy-induced velocities) and modified by a residual flux which accounts for the diabatic effects of mesoscale eddies. The residual velocity is obtained by stepping forward a residual-mean momentum equation in which eddy stresses appear as forcing terms. Study of the spatial distribution of eddy stresses, derived by using them as control parameters to ‘‘fit’’ the residual-mean model to observations, supports the idea that eddy stresses can be likened to a vertical down-gradient flux of momentum with a coefficient which is constant in the vertical. The residual eddy flux is set to zero in the ocean interior, where mesoscale eddies are assumed to be quasi-adiabatic, but is parameterized by a horizontal down-gradient diffusivity near the surface where eddies develop a diabatic component as they stir properties horizontally across steep isopycnals. The residual-mean model is implemented and tested in the MIT general circulation model. It is shown that the resulting model (1) has a climatology that is superior to that obtained using the Gent and McWilliams parameterization scheme with a spatially uniform diffusivity and (2) allows one to significantly reduce the (spurious) horizontal viscosity used in coarse resolution GCMs.

Mixed layer lateral eddy fluxes mediated by air-sea interaction

The modulation of air–sea heat fluxes by geostrophic eddies due to the stirring of temperature at the sea surface is discussed and quantified. It is argued that the damping of eddy temperature variance by such air–sea fluxes enhances the dissipation of surface temperature fields. Depending on the time scale of damping relative to that of the eddying motions, surface eddy diffusivities can be significantly enhanced over interior values. The issues are explored and quantified in a controlled setting by driving a tracer field, a proxy for sea surface temperature, with surface altimetric observations in the Antarctic Circumpolar Current (ACC) of the Southern Ocean. A new, tracer-based diagnostic of eddy diffusivity is introduced, which is related to the Nakamura effective diffusivity. Using this, the mixed layer lateral eddy diffusivities associated with (i) eddy stirring and small-scale mixing and (ii) surface damping by air–sea interaction is quantified. In the ACC, a diffusivity associated with surface damping of a comparable magnitude to that associated with eddy stirring (;500 m2 s21) is found. In frontal regions prevalent in the ACC, an augmentation of surface lateral eddy diffusivities of this magnitude is equivalent to an air–sea flux of 100 W m22 acting over a mixed layer depth of 100 m, a very significant effect. Finally, the implications for other tracer fields such as salinity, dissolved gases, and chlorophyll are discussed. Different tracers are found to have surface eddy diffusivities that differ significantly in magnitude.

Centennial changes in solar activity and the response of galactic cosmic rays

There is a growing consensus that the eleven year modulation of galactic cosmic rays (GCRs) resulting from solar activity is related to interplanetary propagating diffusive barriers (PDBs). The source of these PDBs is not well understood and numerical models describing GCR modulation simulate their effect by scaling the diffusion tensor to the interplanetary magnetic field strength (IMF). The implications of a century-scale change in solar wind speed and open solar flux, for numerical modelling of GCR modulation and the reconstruction of GCR variations over the last hundred years are discussed. The dominant role of the solar non-axisymmetric magnetic field in both forcing longitudinal solar wind speed fluctuations at solar maximum and in increasing the IMF is discussed in the context of a long-term rise in the open solar magnetic flux.