Spatio-temporal Functional Regression on Paleo-ecological Data

The influence of climate on biodiversity is an important ecological question. Various theories try to link climate change to allelic richness and therefore to predict the impact of global warming on genetic diversity. We model the relationship between genetic diversity in the European beech forests and curves of temperature and precipitation reconstructed from pollen databases. Our model links the genetic measure to the climate curves through a linear functional regression. The interaction in climate variables is assumed to be bilinear. Since the data are georeferenced, our methodology accounts for the spatial dependence among the observations. The practical issues of these extensions are discussed

A new operator splitting algorithm for elastoviscoplastic flow problems

International audienceThis paper presents an efficient time-dependent decoupled approach for the numerical resolution of the highly nonlinear set of coupled partial differential equations appearing in elastoviscoplastic fluid flow problems. The two main nonlinear difficulties, the viscoplasticity and the viscoelasticity, are then solved separately. Numerical simulations suggest an optimal convergence rate with respect to the space discretization. Finally, numerical results compare well with experimental measurements on liquid foams in a complex geometry. Future works will explore flows of liquid foams for tridimensional geometries where experimental data are available and also compare to flows of others soft glassy materials such as carbopol solutions

Understanding and predicting viscous, elastic, plastic flows

International audienceFoams, gels, emulsions, polymer solutions, pastes and even cell assemblies display both liquid and solid mechanical properties. On a local scale, such "soft glassy" systems are disordered assemblies of deformable rearranging units, the complexity of which gives rise to their striking flow behavior. On a global scale, experiments show that their mechanical behavior depends on the orientation of their elastic deformation with respect to the flow direction, thus requiring a description by tensorial equations for continuous materials. However, due to their strong non-linearities, the numerous candidate models have not yet been solved in a general multidimensional geometry to provide stringent tests of their validity. We compute the first solutions of a continuous model for a discriminant benchmark, namely the flow around an obstacle. We compare it with experiments of a foam flow and find an excellent agreement with the spatial distribution of all important features: we accurately predict the experimental fields of velocity, elastic deformation, and plastic deformation rate in terms of magnitude, direction, and anisotropy. We analyze the role of each parameter, and demonstrate that the yield strain is the main dimensionless parameter required to characterize the materials. We evidence the dominant effect of elasticity, which explains why the stress does not depend simply on the shear rate. Our results demonstrate that the behavior of soft glassy materials cannot be reduced to an intermediate between that of a solid and that of a liquid: the viscous, the elastic and the plastic contributions to the flow, as well as their couplings, must be treated simultaneously. Our approach opens the way to the realistic multidimensional prediction of complex flows encountered in geophysical, industrial and biological applications, and to the understanding of the link between structure and rheology of soft glassy systems

Guaranteed and robust a posteriori error estimates for singularly perturbed reaction-diffusion problems

International audienceWe derive a posteriori error estimates for singularly perturbed reaction-diffusion problems which yield a guaranteed upper bound on the discretization error and are fully and easily computable. Moreover, they are also locally efficient and robust in the sense that they represent local lower bounds for the actual error, up to a generic constant independent in particular of the reaction coefficient. We present our results in the framework of the vertex-centered finite volume method but their nature is general for any conforming method, like the piecewise linear finite element one. Our estimates are based on a H(div)-conforming reconstruction of the diffusive flux in the lowest-order Raviart-Thomas space linked with mesh dual to the original simplicial one, previously introduced by the last author in the pure diffusion case. They also rely on elaborated Poincaré, Friedrichs, and trace inequalities-based auxiliary estimates designed to cope optimally with the reaction dominance. In order to bring down the ratio of the estimated and actual overall energy error as close as possible to the optimal value of one, independently of the size of the reaction coefficient, we finally develop the ideas of local minimizations of the estimators by local modifications of the reconstructed diffusive flux. The numerical experiments presented confirm the guaranteed upper bound, robustness, and excellent efficiency of the derived estimates

Temperature Range Shifts for Three European Tree Species over the Last 10,000 Years.

We quantified the degree to which the relationship between the geographic distribution of three major European tree species, Abies alba, Fagus sylvatica and Picea abies and January temperature (Tjan) has remained stable over the past 10,000 years. We used an extended data-set of fossil pollen records over Europe to reconstruct spatial variation in Tjan values for each 1000-year time slice between 10,000 and 3000 years BP (before present). We evaluated the relationships between the occurrences of the three species at each time slice and the spatially interpolated Tjan values, and compared these to their modern temperature ranges. Our results reveal that F. sylvatica and P. abies experienced Tjan ranges during the Holocene that differ from those of the present, while A. alba occurred over a Tjan range that is comparable to its modern one. Our data suggest the need for re-evaluation of the assumption of stable climate tolerances at a scale of several thousand years. The temperature range instability in our observed data independently validates similar results based exclusively on modeled Holocene temperatures. Our study complements previous studies that used modeled data by identifying variation in frequencies of occurrence of populations within the limits of suitable climate. However, substantial changes that were observed in the realized thermal niches over the Holocene tend to suggest that predicting future species distributions should not solely be based on modern realized niches, and needs to account for the past variation in the climate variables that drive species ranges

Power Flow Calculations by Deterministic Methods and Artificial Intelligence Method

In this paper, we will present different methods for Power Flow Calculations. First, we will describe the deterministic methods; which are Gauss-Seidel (GS) and Newton-Raphson (NR) methods, in addition to that, we will use also a Newton based method Fast Decoupled Load Flow (FDLF). Second, we have the Artificial intelligence method Neural Network (NN). Matlab programs were developed for solving Power Flow problem using GS and NR methods and regarding the ANN, we established and trained artificial neural networks models for computing voltage magnitudes and voltage phase angles. We used these methods to solve the Power Flow problem of the Institute of Electrical and Electronics Engineers (IEEE) 14 bus system. The results that we obtained were presented in graphs at the end of the paper

Colloquium: Mechanical formalisms for tissue dynamics

The understanding of morphogenesis in living organisms has been renewed by tremendous progressin experimental techniques that provide access to cell-scale, quantitative information both on theshapes of cells within tissues and on the genes being expressed. This information suggests that ourunderstanding of the respective contributions of gene expression and mechanics, and of their crucialentanglement, will soon leap forward. Biomechanics increasingly benefits from models, which assistthe design and interpretation of experiments, point out the main ingredients and assumptions, andultimately lead to predictions. The newly accessible local information thus calls for a reflectionon how to select suitable classes of mechanical models. We review both mechanical ingredientssuggested by the current knowledge of tissue behaviour, and modelling methods that can helpgenerate a rheological diagram or a constitutive equation. We distinguish cell scale ("intra-cell")and tissue scale ("inter-cell") contributions. We recall the mathematical framework developpedfor continuum materials and explain how to transform a constitutive equation into a set of partialdifferential equations amenable to numerical resolution. We show that when plastic behaviour isrelevant, the dissipation function formalism appears appropriate to generate constitutive equations;its variational nature facilitates numerical implementation, and we discuss adaptations needed in thecase of large deformations. The present article gathers theoretical methods that can readily enhancethe significance of the data to be extracted from recent or future high throughput biomechanicalexperiments.Comment: 33 pages, 20 figures. This version (26 Sept. 2015) contains a few corrections to the published version, all in Appendix D.2 devoted to large deformation

Mechanics of epithelial closure over non-adherent environments

International audienceThe closure of gaps within epithelia is crucial to maintain its integrity during biological processes such as wound healing and gastrulation. Depending on the distribution of extracellular matrix, gap closure occurs through assembly of multicellular actin-based contractile cables or protrusive activity of border cells into the gap. Here we show that the supracellular actomyosin contractility of cells near the gap edge exerts sufficient tension on the surrounding tissue to promote closure of non-adherent gaps. Using traction force microscopy, we observe that cell-generated forces on the substrate at the gap edge first point away from the centre of the gap and then increase in the radial direction pointing into the gap as closure proceeds. Combining with numerical simulations, we show that the increase in force relies less on localized purse-string contractility and more on large-scale remodelling of the suspended tissue around the gap. Our results provide a framework for understanding the assembly and the mechanics of cellular contractility at the tissue level