Statistical physics approach to dendritic computation: The excitable-wave mean-field approximation

We analytically study the input-output properties of a neuron whose active dendritic tree, modeled as a Cayley tree of excitable elements, is subjected to Poisson stimulus. Both single-site and two-site mean-field approximations incorrectly predict a nonequilibrium phase transition which is not allowed in the model. We propose an excitable-wave mean-field approximation which shows good agreement with previously published simulation results [Gollo et al., PLoS Comput. Biol. 5, e1000402 (2009)] and accounts for finite-size effects. We also discuss the relevance of our results to experiments in neuroscience, emphasizing the role of active dendrites in the enhancement of dynamic range and in gain control modulation.

GENERALIZED FINITE ELEMENT METHOD ON NONCONVENTIONAL HYBRID-MIXED FORMULATION

The generalized finite element method (GFEM) is applied to a nonconventional hybrid-mixed stress formulation (HMSF) for plane analysis. In the HMSF, three approximation fields are involved: stresses and displacements in the domain and displacement fields on the static boundary. The GFEM-HMSF shape functions are then generated by the product of a partition of unity associated to each field and the polynomials enrichment functions. In principle, the enrichment can be conducted independently over each of the HMSF approximation fields. However, stability and convergence features of the resulting numerical method can be affected mainly by spurious modes generated when enrichment is arbitrarily applied to the displacement fields. With the aim to efficiently explore the enrichment possibilities, an extension to GFEM-HMSF of the conventional Zienkiewicz-Patch-Test is proposed as a necessary condition to ensure numerical stability. Finally, once the extended Patch-Test is satisfied, some numerical analyses focusing on the selective enrichment over distorted meshes formed by bilinear quadrilateral finite elements are presented, thus showing the performance of the GFEM-HMSF combination.

Interpolation estimate for a finite-element space with embedded discontinuities

We consider a recently proposed finite-element space that consists of piecewise affine functions with discontinuities across a smooth given interface Γ (a curve in two dimensions, a surface in three dimensions). Contrary to existing extended finite element methodologies, the space is a variant of the standard conforming Formula space that can be implemented element by element. Further, it neither introduces new unknowns nor deteriorates the sparsity structure. It is proved that, for u arbitrary in Formula, the interpolant Formula defined by this new space satisfies Graphic where h is the mesh size, Formula is the domain, Formula, Formula, Formula and standard notation has been adopted for the function spaces. This result proves the good approximation properties of the finite-element space as compared to any space consisting of functions that are continuous across Γ, which would yield an error in the Formula-norm of order Graphic. These properties make this space especially attractive for approximating the pressure in problems with surface tension or other immersed interfaces that lead to discontinuities in the pressure field. Furthermore, the result still holds for interfaces that end within the domain, as happens for example in cracked domains.

delta-Superderivations of Semisimple Finite-Dimensional Jordan Superalgebras

In the paper, a complete description of the delta-derivations and the delta-superderivations of semisimple finite-dimensional Jordan superalgebras over an algebraically closed field of characteristic p not equal 2 is given. In particular, new examples of nontrivial (1/2)-derivations and odd (1/2)-superderivations are given that are not operators of right multiplication by an element of the superalgebra.

Numeric reconstruction of cytoskeleton with finite element method and topology optimization method

The importance of mechanical aspects related to cell activity and its environment is becoming more evident due to their influence in stem cell differentiation and in the development of diseases such as atherosclerosis. The mechanical tension homeostasis is related to normal tissue behavior and its lack may be related to the formation of cancer, which shows a higher mechanical tension. Due to the complexity of cellular activity, the application of simplified models may elucidate which factors are really essential and which have a marginal effect. The development of a systematic method to reconstruct the elements involved in the perception of mechanical aspects by the cell may accelerate substantially the validation of these models. This work proposes the development of a routine capable of reconstructing the topology of focal adhesions and the actomyosin portion of the cytoskeleton from the displacement field generated by the cell on a flexible substrate. Another way to think of this problem is to develop an algorithm to reconstruct the forces applied by the cell from the measurements of the substrate displacement, which would be characterized as an inverse problem. For these kind of problems, the Topology Optimization Method (TOM) is suitable to find a solution. TOM is consisted of an iterative application of an optimization method and an analysis method to obtain an optimal distribution of material in a fixed domain. One way to experimentally obtain the substrate displacement is through Traction Force Microscopy (TFM), which also provides the forces applied by the cell. Along with systematically generating the distributions of focal adhesion and actin-myosin for the validation of simplified models, the algorithm also represents a complementary and more phenomenological approach to TFM. As a first approximation, actin fibers and flexible substrate are represented through two-dimensional linear Finite Element Method. Actin contraction is modeled as an initial stress of the FEM elements. Focal adhesions connecting actin and substrate are represented by springs. The algorithm was applied to data obtained from experiments regarding cytoskeletal prestress and micropatterning, comparing the numerical results to the experimental ones

Finite element methods for the Stokes system based on a Zienkiewicz type N-simplex

Hermite interpolation is increasingly showing to be a powerful numerical solution tool, as applied to different kinds of second order boundary value problems. In this work we present two Hermite finite element methods to solve viscous incompressible flows problems, in both two- and three-dimension space. In the two-dimensional case we use the Zienkiewicz triangle to represent the velocity field, and in the three-dimensional case an extension of this element to tetrahedra, still called a Zienkiewicz element. Taking as a model the Stokes system, the pressure is approximated with continuous functions, either piecewise linear or piecewise quadratic, according to the version of the Zienkiewicz element in use, that is, with either incomplete or complete cubics. The methods employ both the standard Galerkin or the Petrov–Galerkin formulation first proposed in Hughes et al. (1986) [18], based on the addition of a balance of force term. A priori error analyses point to optimal convergence rates for the PG approach, and for the Galerkin formulation too, at least in some particular cases. From the point of view of both accuracy and the global number of degrees of freedom, the new methods are shown to have a favorable cost-benefit ratio, as compared to velocity Lagrange finite elements of the same order, especially if the Galerkin approach is employed.

Comparison between 2.5-D and 3-D realistic models for wind field adjustment

[EN]In previous works, many authors have widely used mass consistent models for wind field simulation by the finite element method. On one hand, we have developed a 3-D mass consistent model by using tetrahedral meshes which are simultaneously adapted to complex orography and to terrain roughness length. In addition, we have included a local refinement strategy around several measurement or control points, significant contours, as for example shorelines, or numerical solution singularities. On the other hand, we have developed a 2.5-D model for simulating the wind velocity in a 3-D domain in terms of the terrain elevation, the surface temperature and the meteorological wind, which is consider as an averaged wind on vertical boundaries...

Finite element simulation of a local scale air quality model over complex terrain

[EN]In this paper we propose a finite element method approach for modelling the air quality in a local scale over complex terrain. The area of interest is up to tens of kilometres and it includes pollutant sources. The proposed methodology involves the generation of an adaptive tetrahedral mesh, the computation of an ambient wind field, the inclusion of the plume rise effect in the wind field, and the simulation of transport and reaction of pollutants. We apply our methodology to simulate a fictitious pollution episode in La Palma island (Canary Island, Spain)...

Adaptive finite element simulation of stack pollutant emissions over complex terrains

[EN]A three-dimensional finite element model for the pollutant dispersion is presented. In these environmental processes over a complex terrain, a mesh generator capable of adapting itself to the topographic characteristics is essential. The first stage of the model consists on the construction of an adaptive tetrahedral mesh of a rectangular region bounded in its lower part by the terrain and in its upper part by a horizontal plane. Once the mesh is constructed, an adaptive local refinement of tetrahedra is used in order to capture the plume rise. Wind measurements are used to compute an interpolated wind field, that is modified by using a mass-consistent model and perturbing its vertical component to introduce the plume rise effect...

Three-dimensional finite element modelling of stack pollutant emissions

[EN]In this paper we propose a finite element method approach for modelling the air quality in a local scale over complex terrain. The area of interest is up to tens of kilometres and it includes pollutant sources. The proposed methodology involves the generation of an adaptive tetrahedral mesh, the computation of an ambient wind field, the inclusion of the plume rise effect in the wind field, and the simulation of transport and reaction of pollutants. The methodology is used to simulate a fictitious pollution episode in La Palma island (Canary Island, Spain)…

Calibration and validation of an air quality finite element model around an electric power plant in Gran Canaria island

[EN]This work presents the calibration and validation of an air quality finite element model applied to the surroundings of Jinamar electric power plant in Gran Canaria island (Spain). The model involves the generation of an adaptive tetrahedral mesh, the computation of an ambient wind field, the inclusion of the plume rise effect in the wind field, and the simulation of transport and reaction of pollutants. The main advantage of the model is the treatment of complex terrains that introduces an alternative to the standard implementation of current models. In addition, it improves the computational cost through the use of unstructured meshes...

Ensemble wind forecasting based on the HARMONIE model and adaptive finite elements in complex orography

[EN]Ensemble forecasting is a methodology to deal with uncertainties in the numerical wind prediction. In this work we propose to apply ensemble methods to the adaptive wind forecasting model presented in. The wind field forecasting is based on a mass-consistent model and a log-linear wind profile using as input data the resulting forecast wind from Harmonie, a Non-Hydrostatic Dynamic model used experimentally at AEMET with promising results. The mass-consistent model parameters are estimated by using genetic algorithms. The mesh is generated using the meccano method and adapted to the geometry…

3-D wind field simulation over complex terrain

[EN]A new methodology for wind field simulation or forecasting over complex terrain is introduced. The idea is to use wind measurements or predictions of the HARMONIE mesoscale model as the input data for an adaptive finite element mass consistent wind model. The method has been recently implemented in the freely-available Wind3D code. A description of the HARMONIE Non-Hydrostatic Dynamics can be found in. HARMONIE provides wind prediction with a maximum resolution about 1 Km that is refined by the finite element model in a local scale (about a few meters). An interface between both models is implemented such that the initial wind field approximation is obtained by a suitable interpolation of the HARMONIE results…

Analysis of optimal control problems for the incompressible MHD equations and implementation in a finite element multiphysics code

This thesis deals with the study of optimal control problems for the incompressible Magnetohydrodynamics (MHD) equations. Particular attention to these problems arises from several applications in science and engineering, such as fission nuclear reactors with liquid metal coolant and aluminum casting in metallurgy. In such applications it is of great interest to achieve the control on the fluid state variables through the action of the magnetic Lorentz force. In this thesis we investigate a class of boundary optimal control problems, in which the flow is controlled through the boundary conditions of the magnetic field. Due to their complexity, these problems present various challenges in the definition of an adequate solution approach, both from a theoretical and from a computational point of view. In this thesis we propose a new boundary control approach, based on lifting functions of the boundary conditions, which yields both theoretical and numerical advantages. With the introduction of lifting functions, boundary control problems can be formulated as extended distributed problems. We consider a systematic mathematical formulation of these problems in terms of the minimization of a cost functional constrained by the MHD equations. The existence of a solution to the flow equations and to the optimal control problem are shown. The Lagrange multiplier technique is used to derive an optimality system from which candidate solutions for the control problem can be obtained. In order to achieve the numerical solution of this system, a finite element approximation is considered for the discretization together with an appropriate gradient-type algorithm. A finite element object-oriented library has been developed to obtain a parallel and multigrid computational implementation of the optimality system based on a multiphysics approach. Numerical results of two- and three-dimensional computations show that a possible minimum for the control problem can be computed in a robust and accurate manner.

The contribution of the Finite Volume Point Dilution Method to the determination of solute mass flux in an alluvial aquifer.

Groundwater represents one of the most important resources of the world and it is essential to prevent its pollution and to consider remediation intervention in case of contamination. According to the scientific community the characterization and the management of the contaminated sites have to be performed in terms of contaminant fluxes and considering their spatial and temporal evolution. One of the most suitable approach to determine the spatial distribution of pollutant and to quantify contaminant fluxes in groundwater is using control panels. The determination of contaminant mass flux, requires measurement of contaminant concentration in the moving phase (water) and velocity/flux of the groundwater. In this Master Thesis a new solute flux mass measurement approach, based on an integrated control panel type methodology combined with the Finite Volume Point Dilution Method (FVPDM), for the monitoring of transient groundwater fluxes, is proposed. Moreover a new adsorption passive sampler, which allow to capture the variation of solute concentration with time, is designed. The present work contributes to the development of this approach on three key points. First, the ability of the FVPDM to monitor transient groundwater fluxes was verified during a step drawdown test at the experimental site of Hermalle Sous Argentau (Belgium). The results showed that this method can be used, with optimal results, to follow transient groundwater fluxes. Moreover, it resulted that performing FVPDM, in several piezometers, during a pumping test allows to determine the different flow rates and flow regimes that can occurs in the various parts of an aquifer. The second field test aiming to determine the representativity of a control panel for measuring mass flus in groundwater underlined that wrong evaluations of Darcy fluxes and discharge surfaces can determine an incorrect estimation of mass fluxes and that this technique has to be used with precaution. Thus, a detailed geological and hydrogeological characterization must be conducted, before applying this technique. Finally, the third outcome of this work concerned laboratory experiments. The test conducted on several type of adsorption material (Oasis HLB cartridge, TDS-ORGANOSORB 10 and TDS-ORGANOSORB 10-AA), in order to determine the optimum medium to dimension the passive sampler, highlighted the necessity to find a material with a reversible adsorption tendency to completely satisfy the request of the new passive sampling technique.