Inferring the structure of the solar corona and inner heliosphere during the Maunder minimum using global thermodynamic magnetohydrodynamic simulations

Observations of the Sun’s corona during the space era have led to a picture of relatively constant, but cyclically varying solar output and structure. Longer-term, more indirect measurements, such as from 10Be, coupled by other albeit less reliable contemporaneous reports, however, suggest periods of significant departure from this standard. The Maunder Minimum was one such epoch where: (1) sunspots effectively disappeared for long intervals during a 70 yr period; (2) eclipse observations suggested the distinct lack of a visible K-corona but possible appearance of the F-corona; (3) reports of aurora were notably reduced; and (4) cosmic ray intensities at Earth were inferred to be substantially higher. Using a global thermodynamic MHD model, we have constructed a range of possible coronal configurations for the Maunder Minimum period and compared their predictions with these limited observational constraints. We conclude that the most likely state of the corona during—at least—the later portion of the Maunder Minimum was not merely that of the 2008/2009 solar minimum, as has been suggested recently, but rather a state devoid of any large-scale structure, driven by a photospheric field composed of only ephemeral regions, and likely substantially reduced in strength. Moreover, we suggest that the Sun evolved from a 2008/2009-like configuration at the start of the Maunder Minimum toward an ephemeral-only configuration by the end of it, supporting a prediction that we may be on the cusp of a new grand solar minimum.

The Maunder minimum (1645-1715) was indeed a grand minimum: a reassessment of multiple datasets

Aims. Although the time of the Maunder minimum (1645–1715) is widely known as a period of extremely low solar activity, it is still being debated whether solar activity during that period might have been moderate or even higher than the current solar cycle (number 24). We have revisited all existing evidence and datasets, both direct and indirect, to assess the level of solar activity during the Maunder minimum. Methods. We discuss the East Asian naked-eye sunspot observations, the telescopic solar observations, the fraction of sunspot active days, the latitudinal extent of sunspot positions, auroral sightings at high latitudes, cosmogenic radionuclide data as well as solar eclipse observations for that period. We also consider peculiar features of the Sun (very strong hemispheric asymmetry of the sunspot location, unusual differential rotation and the lack of the K-corona) that imply a special mode of solar activity during the Maunder minimum. Results. The level of solar activity during the Maunder minimum is reassessed on the basis of all available datasets. Conclusions. We conclude that solar activity was indeed at an exceptionally low level during the Maunder minimum. Although the exact level is still unclear, it was definitely lower than during the Dalton minimum of around 1800 and significantly below that of the current solar cycle #24. Claims of a moderate-to-high level of solar activity during the Maunder minimum are rejected with a high confidence level.

Conditioning of the weak-constraint variational data assimilation problem for numerical weather prediction

4-Dimensional Variational Data Assimilation (4DVAR) assimilates observations through the minimisation of a least-squares objective function, which is constrained by the model flow. We refer to 4DVAR as strong-constraint 4DVAR (sc4DVAR) in this thesis as it assumes the model is perfect. Relaxing this assumption gives rise to weak-constraint 4DVAR (wc4DVAR), leading to a different minimisation problem with more degrees of freedom. We consider two wc4DVAR formulations in this thesis, the model error formulation and state estimation formulation. The 4DVAR objective function is traditionally solved using gradient-based iterative methods. The principle method used in Numerical Weather Prediction today is the Gauss-Newton approach. This method introduces a linearised `inner-loop' objective function, which upon convergence, updates the solution of the non-linear `outer-loop' objective function. This requires many evaluations of the objective function and its gradient, which emphasises the importance of the Hessian. The eigenvalues and eigenvectors of the Hessian provide insight into the degree of convexity of the objective function, while also indicating the difficulty one may encounter while iterative solving 4DVAR. The condition number of the Hessian is an appropriate measure for the sensitivity of the problem to input data. The condition number can also indicate the rate of convergence and solution accuracy of the minimisation algorithm. This thesis investigates the sensitivity of the solution process minimising both wc4DVAR objective functions to the internal assimilation parameters composing the problem. We gain insight into these sensitivities by bounding the condition number of the Hessians of both objective functions. We also precondition the model error objective function and show improved convergence. We show that both formulations' sensitivities are related to error variance balance, assimilation window length and correlation length-scales using the bounds. We further demonstrate this through numerical experiments on the condition number and data assimilation experiments using linear and non-linear chaotic toy models.

Data Assimilation and Inverse Methods in Terms of a Probabilistic Formulation

The weak-constraint inverse for nonlinear dynamical models is discussed and derived in terms of a probabilistic formulation. The well-known result that for Gaussian error statistics the minimum of the weak-constraint inverse is equal to the maximum-likelihood estimate is rederived. Then several methods based on ensemble statistics that can be used to find the smoother (as opposed to the filter) solution are introduced and compared to traditional methods. A strong point of the new methods is that they avoid the integration of adjoint equations, which is a complex task for real oceanographic or atmospheric applications. they also avoid iterative searches in a Hilbert space, and error estimates can be obtained without much additional computational effort. the feasibility of the new methods is illustrated in a two-layer quasigeostrophic model.

Sparse density estimation on multinomial manifold combining local component analysis

A new sparse kernel density estimator is introduced based on the minimum integrated square error criterion combining local component analysis for the finite mixture model. We start with a Parzen window estimator which has the Gaussian kernels with a common covariance matrix, the local component analysis is initially applied to find the covariance matrix using expectation maximization algorithm. Since the constraint on the mixing coefficients of a finite mixture model is on the multinomial manifold, we then use the well-known Riemannian trust-region algorithm to find the set of sparse mixing coefficients. The first and second order Riemannian geometry of the multinomial manifold are utilized in the Riemannian trust-region algorithm. Numerical examples are employed to demonstrate that the proposed approach is effective in constructing sparse kernel density estimators with competitive accuracy to existing kernel density estimators.

Skull Modularity in Neotropical Marsupials and Monkeys: Size Variation and Evolutionary Constraint and Flexibility

An organism is built through a series of contingent factors, yet it is determined by historical, physical, and developmental constraints. A constraint should not be understood as an absolute obstacle to evolution, as it may also generate new possibilities for evolutionary change. Modularity is, in this context, an important way of organizing biological information and has been recognized as a central concept in evolutionary biology bridging on developmental, genetics, morphological, biochemical, and physiological studies. In this article, we explore how modularity affects the evolution of a complex system in two mammalian lineages by analyzing correlation, variance/covariance, and residual matrices (without size variation). We use the multivariate response to selection equation to simulate the behavior of Eutheria and Metharia skulls in terms of their evolutionary flexibility and constraints. We relate these results to classical approaches based on morphological integration tests based on functional/developmental hypotheses. Eutherians (Neotropical primates) showed smaller magnitudes of integration compared with Metatheria (didelphids) and also skull modules more clearly delimited. Didelphids showed higher magnitudes of integration and their modularity is strongly influenced by within-groups size variation to a degree that evolutionary responses are basically aligned with size variation. Primates still have a good portion of the total variation based on size; however, their enhanced modularization allows a broader spectrum of responses, more similar to the selection gradients applied (enhanced flexibility). Without size variation, both groups become much more similar in terms of modularity patterns and magnitudes and, consequently, in their evolutionary flexibility. J. Exp. Zool. (Mol. Dev. Evol.) 314B:663-683, 2010. (C) 2010 Wiley-Liss, Inc.

Quantum States Allowing Minimum Uncertainty Product of phi and L(z)

We provide necessary and sufficient conditions for states to have an arbitrarily small uncertainty product of the azimuthal angle phi and its canonical moment L(z). We illustrate our results with analytical examples.

Minimum cycle cover and Chinese postman problems on mixed graphs with bounded tree-width

Let M = (V, E, A) be a mixed graph with vertex set V, edge set E and arc set A. A cycle cover of M is a family C = {C(1), ... , C(k)} of cycles of M such that each edge/arc of M belongs to at least one cycle in C. The weight of C is Sigma(k)(i=1) vertical bar C(i)vertical bar. The minimum cycle cover problem is the following: given a strongly connected mixed graph M without bridges, find a cycle cover of M with weight as small as possible. The Chinese postman problem is: given a strongly connected mixed graph M, find a minimum length closed walk using all edges and arcs of M. These problems are NP-hard. We show that they can be solved in polynomial time if M has bounded tree-width. (C) 2008 Elsevier B.V. All rights reserved.

Augmented Lagrangian methods under the constant positive linear dependence constraint qualification

Two Augmented Lagrangian algorithms for solving KKT systems are introduced. The algorithms differ in the way in which penalty parameters are updated. Possibly infeasible accumulation points are characterized. It is proved that feasible limit points that satisfy the Constant Positive Linear Dependence constraint qualification are KKT solutions. Boundedness of the penalty parameters is proved under suitable assumptions. Numerical experiments are presented.

New material for orthopedic implants: Electrochemical study of nickel free P558 stainless steel in minimum essential medium

Nickel, a component of stainless steels (SS) applied in orthopedic implants may cause allergic processes in human tissues P558 nickel free SS was studied to verify its viability as a substitute for stainless steel containing nickel Its performance is compared to ISO 5832-9 and F138 most used nowadays grades in implants fabrications, in minimum essential medium. MEM, at 37 degrees C. Potentiodynamic polarization curves, electrochemical impedance spectroscopy (EIS), scanning electron microscopy (SEM) and ""in vitro"" cytotoxicity were used as techniques. From the electrochemical point of view P558 SS is comparable to ISO 5832-9 SS in MEM It remains passivated until the transpassivation potential, above which generalized corrosion occurs F138 presents pitting corrosion at 370 mV/SCE. The cytotoxicity results showed that P558. ISO 5832-9 and F138 do not present cytotoxic character Therefore, these results suggest that P558 SS can be applied in orthopedic implants (C) 2010 Elsevier BV All rights reserved