La exhibición y el episodio de Estesilao en el prólogo de Laques y su referencialidad respecto del Agón dialéctico

Lisímaco y Melesias han invitado a los generales Nicias y Laques a presenciar una exhibición de lucha armada. Con motivo del espectáculo y ante la recomendación de esa disciplina para la educación de sus hijos, los padres deciden consultar la opinión de quienes son considerados especialistas en la materia. Esta especie de simulacro de pelea es el inicio de una conversación acerca de si es beneficioso, o no este aprendizaje. Al diálogo entre los padres y los generales se suma Sócrates. A partir de la discrepancia entre Laques y Nicias y el ingreso de Sócrates comienza a desplegarse una suerte de agón dialéctico. La presente comunicación intenta establecer una analogía entre el comportamiento de Estesilao, el luchador de la exhibición, en un determinado episodio relatado por Laques y el que sostiene Nicias frente a los embates del élenkhos socráticoLysimachus and Melesias have invited the Generals Nicias and Laches to witness a display of armed struggle. The parents decide to consult the opinion of those who are considered experts in the field on the occasion of the show and on the recommendation of the discipline for the education of their children. This kind of sham fight is the beginning of a conversation about whether it this learning is beneficial or not. Socrates joins the dialogue between the parents and the generals. A sort of dialectical agon begins due to the discrepancy between Laches and Nicias and Socrates. This paper seeks to draw an analogy between the behavior of Estesilao (the fighter of the exhibition in one episode told by Laches) and the one of Nicias against the attacks of the Socratic elenkho

Hierarchical X-FEM for n-phase flow (n>2)

The eXtended Finite Element Method (X-FEM) has been successfully used in two-phase flow problems involving a moving interface. In order to simulate problems involving more than two phases, the X-FEM has to be further eXtended. The proposed approach is presented in the case of a quasi-static Stokes n-phase flow and it is based on using an ordered collection of level set functions to describe the location of the phases. A level set hierarchy allows describing triple junctions avoiding overlapping or “voids” between materials. Moreover, an enriched solution accounting for several simultaneous phases inside one element is proposed. The interpolation functions corresponding to the enriched degrees of freedom require redefining the associated ridge function accounting for all the level sets. The computational implementation of this scheme involves calculating integrals in elements having several materials inside. An adaptive quadrature accounting for the interfaces locations is proposed to accurately compute these integrals. Examples of the hierarchical X-FEM approach are given for a n-phase Stokes problem in 2 and 3 dimensions

Computable bounds of functional outputs in linear visco-elastodynamics

This work presents a new technique yielding computable bounds of quantities of interest in the framework of linear visco-elastodynamics. A novel expression for the error representation is introduced, alternative to the previous ones using the Cauchy–Schwarz inequality. The proposed formulation utilizes symmetrized forms of the error equations to derive error bounds in terms of energy error measures. The practical implementation of the method is based on constructing admissible fields for both the original problem and the adjoint problem associated with the quantity of interest. Here, the flux-free technique is considered to compute the admissible stress fields. The proposed methodology yields estimates with better quality than the ones based on the Cauchy–Schwarz inequality. In the studied examples the bound gaps obtained are approximately halved, that is the estimated intervals of confidence are reduce

Fast r-adaptivity for multiple queries of heterogeneous stochastic material fields

We present an r-adaptivity approach for boundary value problems with randomly fluctuating material parameters solved through the Monte Carlo or stochastic collocation methods. This approach tailors a specific mesh for each sample of the problem. It only requires the computation of the solution of a single deterministic problem with the same geometry and the average parameter, whose numerical cost becomes marginal for large number of samples. Starting from the mesh used to solve that deterministic problem, the nodes are moved depending on the particular sample of mechanical parameter field. The reduction in the error is small for each sample but sums up to reduce the overall bias on the statistics estimated through the Monte Carlo scheme. Several numerical examples in 2D are presented

Goal-oriented error estimation for transient parabolic problems

This work focuses on controlling the error and adapting the discretization in the context of parabolic problems. In order to obtain a sound mathematical framework, the time domain is discretized using a Discontinuous Galerkin (DG) approach. This allows to formulate the time stepping procedure in a variational format. The error is measured in the basis of an output of interest of the solution, defined by a linear functional. A dual problem, associated with this linear output is introduced. The dual problem has to be solved backward in time. An error representation is introduced, based on the weak residual of the primal error applied to the dual solution. Two different alternatives are studied to estimate the error in the dual solution: 1) recovery based error estimators and 2) implicit residual type estimators. Once the error assessment is performed implicitly in the dual problem, the obtained estimate is plugged into the primal residual to obtain the error in the quantity of interest. The implementation of the estimator is drastically simplified by using the weak version of the residual instead of the strong version used in previous works. Thus, the output error is assessed using a mixed technique, explicit for the primal problem and implicit for the dual. In the framework of adaptive computations of transient problems, this approach is very attractive because it allows using first the implicit scheme for the dual problem and then integrating the primal problem, estimating the error explicitly and eventually adapting the space-time grid. Thus, at every time step of the time marching scheme, the estimate of the dual error is injected into the primal residual (explicit estimate for the primal problem)

Remeshing criteria and proper error representations for goal oriented h-adaptivity

A key ingredient in h-adaptivity pertains to the transformation of output data from a given error estimator into input data, usually in the form of an element-size distribution, that needs to be supplied to a mesh generator. This paper analyzes the different possibilities of de¯ning remeshing criteria in the framework of goal oriented adaptivity. In standard energy norm driven adaptivity, the optimal mesh is clearly obtained if the local error distribution is uniform. The goal-oriented paradigm introduces new di±culties associated with the different possibilities for the spatial error representation and the signs of the local error contributions. A nodal error representation is introduced in order to improve the communication with the automatic mesh generation tool, precluding the transfer of information from elements to nodes. Numerical experiments demonstrate the ability of the introduced remeshing strategies to drive e±cient adaptive procedures and to control the error in quantities of interest. The results of the numerical tests fit the expected properties of the different remeshing strategies

Discovery of conserved epitopes through sequence variability analyses

Depto. de Inmunología, Oftalmología y ORLFac. de MedicinaTRUEpu

An algorithm for mesh refinement and un-refinement in fast transient dynamics

A procedure to locally refine and un-refine an unstructured computational grid of four-node quadrilaterals (in 2D) or of eight-node hexahedra (in 3D) is presented. The chosen refinement strategy generates only elements of the same type as their parents, but also produces so-called hanging nodes along non-conforming element-to-element interfaces. Continuity of the solution across such interfaces is enforced strongly by Lagrange multipliers. The element split and un-split algorithm is entirely integer-based. It relies only upon element connectivity and makes no use of nodal coordinates or other real-number quantities. The chosen data structure and the continuous tracking of the nature of each node facilitate the treatment of natural and essential boundary conditions in adaptivity. A generalization of the concept of neighbor elements allows transport calculations in adaptive fluid calculations. The proposed procedure is tested in structure and fluid wave propagation problems in explicit transient dynamics

Error assessment in structural transient dynamics

This paper presents in a unified framework the most representative state-of-the-art techniques on a posteriori error assessment for second order hyperbolic problems, i.e., structural transient dynamics. For the sake of presentation, the error estimates are grouped in four types: recovery-based estimates, the dual weighted residual method, the constitutive relation error method and error estimates for timeline-dependent quantities of interest. All these methodologies give a comprehensive overview on the available error assessment techniques in structural dynamics, both for energy-like and goal-oriented estimates

An efficient and general approach for implementing thermodynamic phase equilibria information in geophysical and geodynamic studies

We present a flexible, general, and efficient approach for implementing thermodynamic phase equilibria information (in the form of sets of physical parameters) into geophysical and geodynamic studies. The approach is based on Tensor Rank Decomposition methods, which transform the original multidimensional discrete information into a separated representation that contains significantly fewer terms, thus drastically reducing the amount of information to be stored in memory during a numerical simulation or geophysical inversion. Accordingly, the amount and resolution of the thermodynamic information that can be used in a simulation or inversion increases substantially. In addition, the method is independent of the actual software used to obtain the primary thermodynamic information, and therefore, it can be used in conjunction with any thermodynamic modeling program and/or database. Also, the errors associated with the decomposition procedure are readily controlled by the user, depending on her/his actual needs (e.g., preliminary runs versus full resolution runs). We illustrate the benefits, generality, and applicability of our approach with several examples of practical interest for both geodynamic modeling and geophysical inversion/modeling. Our results demonstrate that the proposed method is a competitive and attractive candidate for implementing thermodynamic constraints into a broad range of geophysical and geodynamic studies. MATLAB implementations of the method and examples are provided as supporting information and can be downloaded from the journal's website