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We consider the spread of an infectious disease on a heterogeneous metapopulation defined by any (correlated or uncorrelated) network. The infection evolves under transmission, recovery and migration mechanisms. We study some spectral properties of a connectivity matrix arising from the continuous-time equations of the model. In particular we show that the classical sufficient condition of instability for the disease-free equilibrium, well known for the particular case of uncorrelated networks, works also for the general case. We give also an alternative condition that yields a more accurate estimation of the epidemic threshold for correlated (either assortative or dissortative) networks Supported by Ministry of Economy and Competitiveness of the Spanish Government grant numbers MTM2011-27739-C04-03 (first author) and DPI2011-25822 (second author). Also by Generalitat de Catalunya projects 2009-SGR-345 (first author) and 2009-SGR-1228 (second author).

We face the problem of characterizing the periodic cases in parametric families of (real or complex) rational diffeomorphisms having a fixed point. Our approach relies on the Normal Form Theory, to obtain necessary conditions for the existence of a formal linearization of the map, and on the introduction of a suitable rational parametrization of the parameters of the family. Using these tools we can find a finite set of values p for which the map can be p-periodic, reducing the problem of finding the parameters for which the periodic cases appear to simple computations. We apply our results to several two and three dimensional classes of polynomial or rational maps. In particular we find the global periodic cases for several Lyness type recurrences., Comment: 25 pages

El títol de la versió pre-print de l'article és: On two and three periodic Lyness difference equations Agraïments: GSD-UAB and CoDALab Groups are supported by the Government of Catalonia through the SGR program. They are also supported by through grants (first and second authors) and DPI2008-06699-C02-02 (third author). We describe the sequences {xn}n given by the non-autonomous second order Lyness difference equations xn+2 = (an + xn+1)/xn, where {an}n is either a 2-periodic or a 3-periodic sequence of positive values and the initial conditions x1, x2 are as well positive. We also show an interesting phenomenon of the discrete dynamical systems associated to some of these difference equations: the existence of one oscillation of their associated rotation number functions. This behavior does not appear for the autonomous Lyness difference equations.

We classify the set of central configurations lying on a common circle in the Newtonian four-body problem. Using mutual distances as coordinates, we show that the set of four-body co-circular central configurations with positive masses is a two-dimensional surface, a graph over two of the exterior side-lengths. Two symmetric families, the kite and isosceles trapezoid, are investigated extensively. We also prove that a co-circular central configuration requires a specific ordering of the masses and find explicit bounds on the mutual distances. In contrast to the general four-body case, we show that if any two masses of a four-body co-circular central configuration are equal, then the configuration has a line of symmetry.

We resort to non-linear viscoelasticity to develop a truss element able to model reversible softening in lung epithelial tissues undergoing transient stretch. Such a Maxwell truss element is built by resorting to a three-noded element whose mid-node is kinematically constrained to remain on the line connecting the end-nodes. The whole mechanical system undergoes an additive decomposition of the strains along the truss direction where the total contribution of the mid-node is accounted for by using a null-space projection and static condensation techniques. Assembling of such line-elements in 3D networks allows us to model extended regions of living tissues as well as their anisotropies.

A new finite element model is proposed for the analysis of the mechanical aspects of morphogenesis and tested on the biologically well studied gastrulation phenomenon, in particular ventral furrow invagination of the Drosophila melanogaster embryo. A set of mechanisms are introduced in the numerical model, which lead to the observed deformed shapes. We split the total deformation into two parts: an imposed active deformation, and an elastic deformation superimposed onto the latter. The active deformation simulates the effects of apical constriction and apico-basal elongation. These mechanisms are associated with known gene expressions and so in this way we attempt to bridge the well explored signalling pathways, and their associated phenotypes in a mechanical model. While the former have been studied in depth, much less can be said about the forces they produce and the mechanisms involved. From the numerical results, we are able to test different plausible mechanical hypotheses that generate the necessary folding observed in the invagination process. In particular, we conclude that only certain ratios between both modes (apical constriction and apico-basal elongation) can successfully reproduce the invagination process. The model also supports the idea that this invagination requires the contribution of several mechanisms, and that their redundancy provides the necessary robustness.

Solving the Helmholtz equation for a large number of input data in an heterogeneous media and unbounded domain still represents a challenge. This is due to the particular nature of the Helmholtz operator and the sensibility of the solution to small variations of the data. Here a reduced order model is used to determine the scattered solution everywhere in the domain for any incoming wave direction and frequency. Moreover, this is applied to a real engineering problem: water agitation inside real harbors for low to mid-high frequencies. The Proper Generalized Decomposition (PGD) model reduction approach is used to obtain a separable representation of the solution at any point and for any incoming wave direction and frequency. Here, its applicability to such a problem is discussed and demonstrated. More precisely, the contributions of the paper include the PGD implementation into a Perfectly Matched Layer framework to model the unbounded domain, and the separability of the operator which is addressed here using an efficient higher-order projection scheme. Then, the performance of the PGD in this framework is discussed and improved using the higher-order projection and a Petrov-Galerkin approach to construct the separated basis. Moreover, the efficiency of the higherorder projection scheme is demonstrated and compared with the higher-order singular value decomposition.

This study extends the limit analysis techniques used for the computation of strict bounds of the load factors in solids to stability problems with interfaces, anchors and joints. The cases considered include the pull-out capacity of multibelled anchors and the stability of retaining walls for multiple conditions at the anchor/soil and wall/soil interfaces. Three types of wall supports are examined: free standing wall, simply supported wall and anchored wall. The results obtained are compared against available experimental and numerical data. The conclusion drawn confirms the validity of numerical limit analysis for the computation of accurate bounds on limit loads and capturing failure modes of structures with multiple inclusions of complex interface and support conditions.

Smooth Particle Hydrodynamics (SPH) are, in general, more robust than finite elements for large distortion problems. Nevertheless, updating the reference configuration may be necessary in some problems involving extremely large distortions. If a standard updated formulation is implemented in SPH zero energy modes are activated and spoil the solution. It is important to note that the updated Lagrangian does not present tension instability but only zero energy modes. Here an stabilization technique is incorporated to the updated formulation to obtain an improved method without mechanisms.

This is the pre-peer reviewed version of the following article: Sevilla, R.; Fernandez, S.; Huerta, A. NURBS-enhanced finite element method (NEFEM). "International journal for numerical methods in engineering", Octubre 2008, vol. 76, núm. 1, p. 56-83., which has been published in final form at http://www3.interscience.wiley.com/journal/117912616/abstract An improvement to the classical finite element (FE) method is proposed. It is able to exactly represent the geometry by means of the usual CAD description of the boundary with non-uniform rational B-splines (NURBS). Here, the 2D case is presented. For elements not intersecting the boundary, a standard FE interpolation and numerical integration are used. But elements intersecting the NURBS boundary need a specifically designed piecewise polynomial interpolation and numerical integration. A priori error estimates are also presented. Finally, some examples demonstrate the applicability and benefits of the proposed methodology. NURBS-enhanced finite element method (NEFEM) is at least one order of magnitude more precise than the corresponding isoparametric FE in every numerical example shown. This is the case for both continuous and discontinuous Galerkin formulations. Moreover, for a desired precision, NEFEM is also more computationally efficient, as shown in the numerical examples. The use of NEFEM is strongly recommended in the presence of curved boundaries and/or when the boundary of the domain has complex geometric details. The possibility of computing an accurate solution with coarse meshes and high-order interpolations makes NEFEM a more efficient strategy than classical isoparametric FE.

The treatment of (near-)incompressibility is a major concern for the simulation of rubber-like parts, or forming processes. The use of mixed finite element methods is known to prevent the locking of the F.E. approximation in the incompressible limit. However, the stability of these formulations is conditionned by the fullfilment of the inf-sup condition. Recently, finite elements method has evolved with the introduction of the partition of unity. The X-FEM uses it to remove the need to mesh (and remesh) physical surfaces. In this paper, a strategy is proposed for the treatment of holes within X-FEM in the incompressible setting. Numerical examples show that F.E. convergence rate is preserved and that the inf-sup condition is passed.

In this paper, a well-known numerical benchmark test which is usually solved with displacement control for low values of the load eccentricity is examined for a complete range of eccentricities of the ring load. For a certain range of the eccentricity the response shows either snap-through or snap-back, depending on the controlled variable. Thus, in this range of eccentricities, the test can be used to verify implementations of arc-length algorithms, using the displacement controlled solution as a reference. Moreover, results are presented for large eccentricities beyond the applicability of displacement-controlled strategies.

Two algorithms for the stress update (i.e., time integration of the constitutive equation) in large-strain solid mechanics are compared from an analytical point of view. The order of the truncation error associated to the numerical integration is deduced for each algorithm a priori, using standard numerical analysis. This accuracy analysis has been performed by means of a convected frame formalism, which also allows a unied derivation of both algorithms in spite of their inherent dierences. Then the two algorithms are adapted from convected frames to a xed Cartesian frame and implemented in a small-strain nite element code. The implementation is validated by means of a set of simple deformation paths (simple shear, extension, extension and compression, extension and rotation) and two benchmark tests in non-linear mechanics (the necking of a circular bar and a shell under ring loads). In these numerical tests, the observed order of convergence is in very good agreement with the theoretical order of convergence, thus corroborating the accuracy analysis. ? 1997 John Wiley & Sons, Ltd.

An arbitrary Lagrangian-Eulerian (ALE) Petrov-Galerkin finite element technique is developed to study nonlinear viscous fluids under large free surface wave motion. A review of the kinematics and field equations from an arbitrary reference is presented and since the major challenge of the ALE description lies in the mesh rezoning algorithm, various methods, including a new mixed formulation, are developed to update the mesh and map the moving domain in a more rational manner. Moreover, the streamline-upwind/Petrov-Galerkin formulation is implemented to accurately describe highly convective free surface flows. The effectiveness of the algorithm is demonstrated on a tsunami problem, the dam-break problem where the Reynolds number is taken as high as 3000, and a large-amplitude sloshing problem.

The microscopic stress field provides a unique connection between atomistic simulations and mechanics at the nanoscale. However, its definition remains ambiguous. Rather than a mere theoretical preoccupation, we show that this fact acutely manifests itself in local stress calculations of defective graphene, lipid bilayers, and fibrous proteins. We find that popular definitions of the microscopic stress violate the continuum statements of mechanical equilibrium, and we propose an unambiguous and physically sound definition. Award-winning

Crack propagation in brittle materials with anisotropic surface energy is important in applications involving single crystals, extruded polymers, or geological and organic materials. Furthermore, when this anisotropy is strong, the phenomenology of crack propagation becomes very rich, with forbidden crack propagation directions or complex sawtooth crack patterns. This problem interrogates fundamental issues in fracture mechanics, including the principles behind the selection of crack direction. Here, we propose a variational phase-field model for strongly anisotropic fracture, which resorts to the extended Cahn-Hilliard framework proposed in the context of crystal growth. Previous phase-field models for anisotropic fracture were formulated in a framework only allowing for weak anisotropy. We implement numerically our higher-order phase-field model with smooth local maximum entropy approximants in a direct Galerkin method. The numerical results exhibit all the features of strongly anisotropic fracture and reproduce strikingly well recent experimental observations. rack propagation in brittle materials with anisotropic surface energy is important in applications involving single crystals, extruded polymers, or geological and organic materials. Furthermore, when this anisotropy is strong, the phenomenology of crack propagation becomes very rich, with forbidden crack propagation directions or complex sawtooth crack patterns. This problem interrogates fundamental issues in fracture mechanics, including the principles behind the selection of crack direction. Here, we propose a variational phase-field model for strongly anisotropic fracture, which resorts to the extended Cahn-Hilliard framework proposed in the context of crystal growth. Previous phase-field models for anisotropic fracture were formulated in a framework only allowing for weak anisotropy. We implement numerically our higher-order phase-field model with smooth local maximum entropy approximants in a direct Galerkin method. The numerical results exhibit all the features of strongly anisotropic fracture and reproduce strikingly well recent experimental observations.

We present an adaptive meshfree method to approximate phase-field models of biomembranes. In such models, the Helfrich curvature elastic energy, the surface area, and the enclosed volume of a vesicle are written as functionals of a continuous phase-field, which describes the interface in a smeared manner. Such functionals involve up to second-order spatial derivatives of the phase-field, leading to fourth-order Euler–Lagrange partial differential equations (PDE). The solutions develop sharp internal layers in the vicinity of the putative interface, and are nearly constant elsewhere. Thanks to the smoothness of the local maximum-entropy (max-ent) meshfree basis functions, we approximate numerically this high-order phase-field model with a direct Ritz–Galerkin method. The flexibility of the meshfree method allows us to easily adapt the grid to resolve the sharp features of the solutions. Thus, the proposed approach is more efficient than common tensor product methods (e.g. finite differences or spectral methods), and simpler than unstructured Cº finite element methods, applicable by reformulating the model as a system of second-order PDE. The proposed method, implemented here under the assumption of axisymmetry, allows us to show numerical evidence of convergence of the phase-field solutions to the sharp interface limit as the regularization parameter approaches zero. In a companion paper, we present a Lagrangian method based on the approximants analyzed here to study the dynamics of vesicles embedded in a viscous fluid. We present an adaptive meshfree method to approximate phase-field models of biomembranes. In such models, the Helfrich curvature elastic energy, the surface area, and the enclosed volume of a vesicle are written as functionals of a continuous phase-field, which describes the interface in a smeared manner. Such functionals involve up to second-order spatial derivatives of the phase-field, leading to fourth-order Euler–Lagrange partial differential equations (PDE). The solutions develop sharp internal layers in the vicinity of the putative interface, and are nearly constant elsewhere. Thanks to the smoothness of the local maximum-entropy (max-ent) meshfree basis functions, we approximate numerically this high-order phase-field model with a direct Ritz–Galerkin method. The flexibility of the meshfree method allows us to easily adapt the grid to resolve the sharp features of the solutions. Thus, the proposed approach is more efficient than common tensor product methods (e.g. finite differences or spectral methods), and simpler than unstructured C0C0 finite element methods, applicable by reformulating the model as a system of second-order PDE. The proposed method, implemented here under the assumption of axisymmetry, allows us to show numerical evidence of convergence of the phase-field solutions to the sharp interface limit as the regularization parameter approaches zero. In a companion paper, we present a Lagrangian method based on the approximants analyzed here to study the dynamics of vesicles embedded in a viscous fluid.

Wrinkle networks are ubiquitous buckle-induced delaminations in supported graphene, which locally modify the electronic structure and degrade device performance. Although the strong property-deformation coupling of graphene can be potentially harnessed by strain engineering, it has not been possible to precisely control the geometry of wrinkle networks. Through numerical simulations based on an atomistically informed continuum theory, we understand how strain anisotropy, adhesion and friction govern spontaneous wrinkling. We then propose a strategy to control the location of wrinkles through patterns of weaker adhesion. This strategy is deceptively simple, and can in fact fail in several ways, particularly under biaxial compression. However, within bounds set by the physics of wrinkling, it is possible to robustly create by strain a variety of wrinkle network geometries and junction configurations. Graphene is nearly unstrained in the planar regions bounded by wrinkles, highly curved along wrinkles, and highly stretched and curved at junctions, which can either locally attenuate or amplify the applied strain depending on their configuration. These mechanically self-assembled networks are stable under the pressure produced by an enclosed fluid and form continuous channels, opening the door to nano-fluidic applications.

We study the effect of membrane viscosity in the dynamics of liquid membranes{possibly with free or internal boundaries{ driven by conservative forces (curvature elasticity and line tension) and dragged by the bulk dissipation of the ambient fluid and the friction occurring when the amphiphilic molecules move relative to each other. To this end, we formulate a continuum model which includes a new form of the governing equations for a two-dimensional viscous fluid moving on a curved, time-evolving surface. The effect of membrane viscosity has received very limited attention in previous continuum studies of the dynamics of fluid membranes, although recent coarse-grained discrete simulations suggest its importance. By applying our model to the study of vesiculation and membrane fusion in a simpli ed geometry, we conclude that membrane viscosity plays a dominant role in the relaxation dynamics of fluid membranes of sizes comparable to those found in eukaryotic cells, and is not negligible in many large synthetic systems of current interest.

This work is devoted to the description of an algorithm for automatic quadrilateral mesh generation. The technique is based on a recursive decomposition of the domain into quadrilateral elements. This automatically generates meshes composed entirely by quadrilaterals over complex geometries (there is no need for a previous step where triangles are generated). A background mesh with the desired element sizes allows to obtain the preferred sizes anywhere in the domain. The final mesh can be viewed as the optimal one given the objective function is defined. The recursive algorithm induces an efficient data structure which optimizes the computer cost. Several examples are presented to show the efficiency of this algorithm. Copyright © 2000 John Wiley & Sons, Ltd.

In this note a new procedure to represent the quality measure for triangles is proposed. The triangles are identified by their three angles and are represented in a bounded domain, called angle representation region, according to the area co-ordinates, which are common and well known by finite element users. The developed representation can also be used in order to visualize the characteristics of any quality measure. This new procedure is extended to graphically represent triangular meshes in the angle representation region.

A finite deformation hyper-elastic membrane theory based on inter-atomic potentials for crystalline films composed of a single atomic layer is developed. For this purpose, an extension of the standard Born rule that exploits the differential geometry concept of the exponential map is proposed to deal with the curvature of surfaces. The exponential map is approximated locally and strain measures based on the stretch and the curvature of the membrane arise. The methodology is first particularized to atomic chains in two dimensions, and then to graphene sheets. A reduced model for the transverse mechanics of carbon nanotubes is developed in detail. This model is a hyper-elastic constrained membrane which fully exploits the symmetry of the transverse deformation. Additionally, a continuum version of the non-bonded interactions is provided. The continuum model is discretized using finite elements and very good agreement with molecular mechanics simulations is obtained. Finally, several simulations illustrate the strong effect of the van der Waals interactions in the transverse deformation of carbon nanotubes.

We present a Lagrangian phase-field method to study the low Reynolds number dynamics of vesicles embedded in a viscous fluid. In contrast to previous approaches, where the field variables are the phase-field and the fluid velocity, here we exploit the fact that the phasefield tracks a material interface to reformulate the problem in terms of the Lagrangian motion of a background medium, containing both the biomembrane and the fluid. We discretize the equations in space with maximum-entropy approximants, carefully shown to perform well in phase-field models of biomembranes in a companion paper. The proposed formulation is variational, lending itself to implicit time-stepping algorithms based on minimization of a time-incremental energy, which are automatically nonlinearly stable. The proposed method deals with two of the major challenges in the numerical treatment of coupled fluid/phase-field models of biomembranes, namely the adaptivity of the grid to resolve the sharp features of the phase-field, and the stiffness of the equations, leading to very small time-steps. In our method, local refinement follows the features of the phasefield as both are advected by the Lagrangian motion, and large time-steps can be robustly chosen in the variational time-stepping algorithm, which also lends itself to time adaptivity. The method is presented in the axisymmetric setting, but it can be directly extended to 3D. We present a Lagrangian phase-field method to study the low Reynolds number dynamics of vesicles embedded in a viscous fluid. In contrast to previous approaches, where the field variables are the phase-field and the fluid velocity, here we exploit the fact that the phase-field tracks a material interface to reformulate the problem in terms of the Lagrangian motion of a background medium, containing both the biomembrane and the fluid. We discretize the equations in space with maximum-entropy approximants, carefully shown to perform well in phase-field models of biomembranes in a companion paper. The proposed formulation is variational, lending itself to implicit time-stepping algorithms based on minimization of a time-incremental energy, which are automatically nonlinearly stable. The proposed method deals with two of the major challenges in the numerical treatment of coupled fluid/phase-field models of biomembranes, namely the adaptivity of the grid to resolve the sharp features of the phase-field, and the stiffness of the equations, leading to very small time-steps. In our method, local refinement follows the features of the phase-field as both are advected by the Lagrangian motion, and large time-steps can be robustly chosen in the variational time-stepping algorithm, which also lends itself to time adaptivity. The method is presented in the axisymmetric setting, but it can be directly extended to 3D.

Plasticity models provide suitable tools to describe the so-called yield line pattern that occurs with the failure of plates. However, in a Lagrangian description a huge number of finite elements are needed for accurate solutions. Accuracy can be combined with low computer costs by means of the arbitrary Lagrangian–Eulerian (ALE) method. With the ALE method, the finite element mesh is automatically refined in the yield lines. A new remesh indicator is proposed that captures newly appearing yield lines as well as already formed yield lines. Numerical examples show the effectiveness of this approach.

The behavior of two stress update algorithms for shear-free large deformation paths is analyzed. The first algorithm has a truncation error of order 1. The second algorithm has a truncation error of order 2. As a consequence, the global performance of the second algorithm is clearly superior. However, for the particular case of shear-free deformation paths, the first algorithm correctly predicts null shear stresses, while the second one does not. This behavior was reported in a previous paper for an extension-rotation test. In this note a general shear-free deformation path is considered in full detail.

In materials with a strain-softening characteristic behavior, classical continuum mechanics favors uncontrolled strain localization in numerical analyses. Several methods have been proposed to regularize the problem. Two such localization limiters developed to overcome spurious instabilities in computational failure analysis are examined and compared. A disturbance analysis, on both models, around an initially homogeneous state of strain is performed to obtain the closed-form solution of propagating wave velocities as well as the velocities at which the energy travels. It also shows that in spite of forcing the same stress-strain response on both models, the wave equation does not yield similar results. Both propagations of waves are dispersive, but the internal length of each model is different when equivalent behavior is desired. In fact, the previously suggested derivations of gradient models from nonlocal integral models were not completely rigorous. The localization modes and the influence of the internal length should be different in each limiter. The perturbation analysis is pursued in the discrete space where computations are done, and the closed form solutions for the dispersion equations are also obtained. The finite-element discretization introduces an added dispersion: the usual dispersion introduced by elliptic operators and another associated to the regularization technique. Therefore, the influence of the discretization on the localization limiters can be evaluated. The element size must be in the order of, or smaller than, the internal length of the models in order to obtain sufficient accuracy on the phase velocities of the propagating waves in transient analysis.

International audience; For particular structures like containment buildings of nuclear power plants, the study of the hydraulic behaviour is of great concern. These structures are indeed the third barrier used to protect the environment in case of accidents. The evolution of the leaking rate through the porous medium is closely related to the changes in the permeability during the ageing process of the structure. It is thus essential to know the relation between concrete degradation and the transfer property when the consequences of a mechanical loading on the hydraulic behaviour have to be evaluated. A chained approach is designed for this purpose. The mechanical behaviour is described by an elastic plastic damage formulation, where damage is responsible for the softening evolution while plasticity accounts for the development of irreversible strains. The drying process is evaluated according to a non-linear equation of diffusion. From the knowledge of the damage and the degree of saturation, a relation is proposed to calculate the permeability of concrete. Finally, the non-homogeneous distribution of the hydraulic conductivity is included in the hydraulic problem which is in fact the association of the mass balance equation for gas phase and Darcy law. From this methodology, it is shown how an indicator for the hydraulic flows can be deduced.

We develop a phenomenological model of electro-mechanical ferroelectric fatigue based on a ferroelectric cohesive law that couples mechanical displacement and electric-potential discontinuity to mechanical tractions and surface-charge density. The ferroelectric cohesive law exhibits a monotonic envelope and loading-unloading hysteresis. The model is applicable whenever the changes in properties leading to fatigue are localized in one or more planar-like regions, modelled by the cohesive surfaces. We validate the model against experimental data for a simple test configuration consisting of an infinite slab acted upon by an oscillatory voltage differential across the slab and otherwise stress free. The model captures salient features of the experimental record including: the existence of a threshold nominal field for the onset of fatigue; the dependence of the threshold on the applied-field frequency; the dependence of fatigue life on the amplitude of the nominal field; and the dependence of the coercive field on the size of the component, or size effect. Our results, although not conclusive, indicate that planar-like regions affected by cycling may lead to the observed fatigue in tetragonal PZT.

Isogeometric analysis (IGA) is emerging as a technology bridging computer aided geometric design (CAGD), most commonly based on Non-Uniform Rational B-Splines (NURBS) surfaces, and engineering analysis. In finite element and boundary element isogeometric methods (FE-IGA and IGA-BEM), the NURBS basis functions that describe the geometry define also the approximation spaces. In the FE-IGA approach, the surfaces generated by the CAGD tools need to be extended to volumetric descriptions, a major open problem in 3D. This additional passage can be avoided in principle when the partial differential equations to be solved admit a formulation in terms of boundary integral equations, leading to boundary element isogeometric analysis (IGA-BEM). The main advantages of such an approach are given by the dimensionality reduction of the problem (from volumetric-based to surface-based), by the fact that the interface with CAGD tools is direct, and by the possibility to treat exterior problems, where the computational domain is infinite. By contrast, these methods produce system matrices which are full, and require the integration of singular kernels. In this paper we address the second point and propose a nonsingular formulation of IGA-BEM for 3D Stokes flows, whose convergence is carefully tested numerically. Standard Gaussian quadrature rules suffice to integrate the boundary integral equations, and carefully chosen known exact solutions of the interior Stokes problem are used to correct the resulting matrices, extending the work by Klaseboer et al. (2012) [27] to IGA-BEM.

This is the pre-peer reviewed version of the following article: Montlaur, A.; Fernandez, S.; Huerta, A. Discontinuous Galerkin methods for the Stokes equations using divergence-free approximations. "International journal for numerical methods in fluids", Juliol 2008, vol. 57, núm. 9, p. 1071-1092., which has been published in final form at http://www3.interscience.wiley.com/journal/117953707/abstract?CRETRY=1&SRETRY=0 A discontinuous Galerkin (DG) method with solenoidal approximation for the simulation of incompressible flow is proposed. It is applied to the solution of the Stokes equations. The interior penalty method is employed to construct the DG weak form. For every element, the approximation space for the velocity field is decomposed as the direct sum of a solenoidal space and an irrotational space. This allows to split the DG weak form into two uncoupled problems: the first one solves for the velocity and the hybrid pressure (pressure along the mesh edges) and the second one allows the computation of the pressure in the element interior. Furthermore, the introduction of an extra penalty term leads to an alternative DG formulation for the computation of solenoidal velocities with no presence of pressure terms. Pressure can then be computed as a post-process of the velocity solution. Numerical examples demonstrate the applicability of the proposed methodologies.

A simple numerical treatment of the infinite boundary in the BEM analysis of two-dimensional wave propagation problems in elastic half-spaces is proposed to avoid the spurious reflections of non-decaying Rayleigh waves introduced by the truncation of the boundary. The proposed method exploits the knowledge of the far-field asymptotic behavior of the solution to adequately correct the BEM displacement system matrix for the truncated problem to account for the contribution of the omitted part of the boundary. The reciprocal theorem of elastodynamics is used for a convenient computation of this contribution exclusively in terms of the boundary integrals of the original BEM system. The method is applied to the study of the acoustic emission from nucleating and propagating surface-breaking and buried cracks in a two-dimensional elastic half-space. It is shown to be particularly advantageous since it allows for an accurate calculation of the generated signal even when the observation point is located far from the acoustic emission source.

Graphene deposited on planar surfaces often exhibits sharp and localized folds delimiting seemingly planar regions, as a result of compressive stresses transmitted by the substrate. Such folds alter the electronic and chemical properties of graphene, and therefore, it is important to understand their emergence, to either suppress them or control their morphology. Here, we study the emergence of out-of-plane deformations in supported and laterally strained graphene with high-fidelity simulations and a simpler theoretical model. We characterize the onset of buckling and the nonlinear behavior after the instability in terms of the adhesion and frictional material parameters of the graphene-substrate interface. We find that localized folds evolve from a distributed wrinkling linear instability due to the nonlinearity in the van der Waals graphene-substrate interactions. We identify friction as a selection mechanism for the separation between folds, as the formation of far apart folds is penalized by the work of friction. Our systematic analysis is a first step towards strain engineering of supported graphene, and is applicable to other compressed thin elastic films weakly coupled to a substrate.

The paper introduces a methodology to compute strict upper and lower bounds for linear-functional outputs of the exact solutions of the advection-reaction-diffusion equation. The bounds are computed using implicit a-posteriori error estimators from stabilized finite element approximations of the exact solution. A new methodology is introduced, based in the ideas presented in [1] for the Galerkin formulation, that allows obtaining bounds also for stabilized formulations. This methodology is combined with both hybrid-flux and flux-free techniques for error assessment. The application to stabilized formulations provides sharper estimates than when applied to Galerkin methods. The best results are found in combination with the fluxfree technique.

This article presents a space-time adaptive strategy for transient elastodynamics. The method aims at computing an optimal space-time discretization such that the computed solution has an error in the quantity of interest below a user-defined tolerance. The methodology is based on a goal-oriented error estimate that requires accounting for an auxiliary adjoint problem. The major novelty of this paper is using modal analysis to obtain a proper approximation of the adjoint solution. The idea of using a modal-based description was introduced in a previous work for error estimation purposes. Here this approach is used for the first time in the context of adaptivity. With respect to the standard direct time-integration methods, the modal solution of the adjoint problem is highly competitive in terms of computational effort and memory requirements. The performance of the proposed strategy is tested in two numerical examples. The two examples are selected to be representative of different wave propagation phenomena, one being a 2D bulky continuum and the second a 2D domain representing a structural frame.

The assembly of sparse matrices is a key operation in finite element methods. In this study we analyze several factors that may have an influence on the efficiency of the assembly procedure. Different insertion strategies are compared using two metrics: a Cost function (the number of memory movements) and actual computing time. An improved algorithm implemented in MATLAB is proposed. It reduces both memory operations and computing time for all tested cases. The efficiency of the assembly process is found to be highly dependent on node and element numbering. The effect of the classic reverse Cuthill–McKee algorithm is, in most cases, positive and reduces computation costs. Finally, the case where a sparse matrix has to be re-assembled at each time step is studied. The efficiency of the assembly is improved if the matrix pattern is entirely or partially inherited from previous steps.

Classical implicit residual type error estimators require using an underlying spatial finer mesh to compute bounds for some quantity of interest. Consequently, the bounds obtained are only guaranteed asymptotically that is with respect to the reference solution computed with the fine mesh. Exact bounds, that is bounds guaranteed with respect to the exact solution, are needed to properly certify the accuracy of the results, especially if the meshes are coarse. The paper introduces a procedure to compute strict upper and lower bounds of the error in linear functional outputs of parabolic problems. In this first part, the bounds account for the error associated with the spatial discretization. The error coming from the time marching scheme is therefore assumed to be negligible in front of the spatial error. The time discretization is performed using the discontinuous Galerkin method, both for the primal and adjoint problems. In the error estimation procedure, equilibrated fluxes at interelement edges are calculated using hybridization techniques.

A non-standard new code to solve multiphase viscous thermo–mechanical problems applied to geophysics is presented. Two numerical methodologies employed in the code are described: A level set technique to track the position of the materials and an enrichment of the solution to allow the strain rate to be discontinuous across the interface. These techniques have low computational cost and can be used in standard desktop PCs. Examples of phase tracking with level set are presented in two and three dimensions to study slab detachment in subduction processes and Rayleigh–Taylor instabilities, respectively. The modelling of slab detachment processes includes realistic rheology with viscosity depending on temperature, pressure and strain rate; shear and adiabatic heating mechanisms; density including mineral phase changes and varying thermal conductivity. Detachment models show a first prolonged period of thermal diffusion until a fast necking of the subducting slab results in the break–off. The influence of several numerical and physical parameters on the detachment process is analyzed: The shear heating exerts a major influence accelerating the detachment process, reducing the onset time to one half and lubricating the sinking of the detached slab. The adiabatic heating term acts as a thermal stabilizer. If the mantle temperature follows an adiabatic gradient, neglecting this heating term must be included, otherwise all temperature contrasts are overestimated. As expected, the phase change at 410 km depth (olivine–spinel transition) facilitates the detachment process due to the increase in negative buoyancy. Finally, simple plume simulations are used to show how the presented numerical methodologies can be extended to three dimensions., This research has been supported by Ministerio de Educacio´n y Ciencia, Grants DPI2007-62395, SAGAS CTM2005-08071-C03-03/MAR and the Spanish Team η1/η2 = 0.01, h = 1/3 η1/η2 = 100, h = 1/3 η1/η2 = 1, h = 0. 1 η1/η2 = 1, h = 0.05 (a) (b) (c) (d) Figure 8 Two snapshots of the evolution of four different Rayleigh–Taylor instabilities. The viscosity ratios and thickness h of the lower layer determines the shape of the plume. 1508 Sergio Zlotnik et al. Pure appl. geophys., Consolider-Ingenio 2010 nrCSD2006-00041. We thank Vlad Manea and an anonymous reviewer for discussion and comments

A new residual type flux-free error estimator is presented. It estimates upper and lower bounds of the error in energy norm. The proposed approach precludes the main drawbacks of standard residual type estimators, circumvents the need of flux-equilibration and results in a simple implementation that uses standard resources available in finite element codes. This is specially interesting for 3D applications where the implementation of this technique is as simple as in 2D. Recall that on the contrary, the complexity of the flux-equilibration techniques increases drastically in the 3D case. The bounds for the energy norm of the error are used to produce upper and lower bounds of linear functional outputs, representing quantities of engineering interest. The presented estimators demonstrate their efficiency in numerical tests producing sharp estimates both for the energy and the quantities of interest.

In h-adaptivity, a remeshing strategy is needed to compute the distribution of required element size using the estimated error distribution. Several authors have introduced different remeshing strategies yielding very different results. In this work these methods are included in a unified framework, emphasizing the role of the underlying hypotheses. Moreover, an objective tool to evaluate the accuracy of the resulting finite element solution is presented. Thus, a new remeshing strategy is introduced to optimize the accuracy of the adapted solutions. The different remeshing strategies are compared with well-known numerical examples.

SUMMARY An implicit fractional-step method for the numerical solution of the time-dependent incompressible Navier–Stokes equations in primitive variables is studied in this paper. The method, which is first-orderaccurate in the time step, is shown to converge to an exact solution of the equations. By adequately splitting the viscous term, it allows the enforcement of full Dirichlet boundary conditions on the velocity in all substeps of the scheme, unlike standard projection methods. The consideration of this method was actually motivated by the study of a well-known predictor–multicorrector algorithm, when this is applied to the incompressible Navier–Stokes equations. A new derivation of the algorithm in a general setting is provided, showing in what sense it can also be understood as a fractional-step method; this justifies, in particular, why the original boundary conditions of the problem can be enforced in this algorithm. Two different finite element interpolations are considered for the space discretization, and numerical results obtained with them for standard benchmark cases are presented. © 1998 John Wiley & Sons, Ltd.

We present an efficient and reliable approach for the numerical modelling of failure with nonlocal damage models. The two major numerical challenges––the strongly nonlinear, highly localized and parameter-dependent structural response of quasi-brittle materials, and the interaction between nonadjacent finite elements associated to nonlocality––are addressed in detail. Reliability of the numerical results is ensured by an h-adaptive strategy based on error estimation. We use a residual-type error estimator for nonlinear FE analysis based on local computations, which, at the same time, accounts for the nonlocality of the damage model. Efficiency is achieved by a proper combination of load-stepping control technique and iterative solver for the nonlinear equilibrium equations. A major issue is the computation of the consistent tangent matrix, which is nontrivial due to nonlocal interaction between Gauss points. With computational efficiency in mind, we also present a new nonlocal damage model based on the nonlocal average of displacements. For this new model, the consistent tangent matrix is considerably simpler to compute than for current models. The various ideas discussed in the paper are illustrated by means of three application examples: the uniaxial tension test, the three-point bending test and the single-edge notched beam test.

Este proyecto trata sobre la puesta a punto del prototipo de una torre eólica offshore para, posteriormente, realizar los tests pertinentes para la detección de algún tipo de daño en la estructura. En primer lugar se describe el marco teórico de la energía eólica, en concreto los parques offshore. Posteriormente se detalla paso a paso el montaje y puesta a punto de todo el instrumental necesario a la hora de recabar los datos, los cuales usaremos a la hora de crear el modelo de PCA –Análisis de componentes principales-. En definitiva, se equipa la torre prototipo con todo el materialnecesario para recopilar -de forma experimental-el comportamiento dinámico de la estructura ante las vibraciones producidas por el movimiento de las aspas, las cuales son accionadas por la energía cinética del viento.

Simulación numérica de un aerogenerador de eje vertical y validación con datos experimentales

A reparametrization of the Generalized Pareto Distribution is here proposed. It is suitable to parsimoniously check trend assumptions within a Point-Over-Threshold model of hazardous events. This is based on considerations about the scale of both the excesses of the event magnitudes and the distribution parameters. The usefulness of this approach is illustrated with a data set from two buoys, where hypotheses about the homogeneity of climate conditions and lack of trends are assessed.

The paper discusses the formulation of high-order accurate time-stepping schemes for transient convection–diffusion problems to be combined with finite element methods of the least-squares type for a stable discretization of highly convective problems. Padé approximations of the exponential function are considered for deriving multi-stage time integration schemes involving first time derivatives only, thus easier to implement in conjunction with C0 finite elements than standard time-stepping schemes which incorporate higher-order time derivatives. After a brief discussion of the stability and accuracy properties of the multi-stage Padé schemes and having underlined the similarity between Padé and Runge–Kutta methods, the paper closes with the presentation of illustrative examples which indicate the effectiveness of the proposed methods.

El presente trabajo se basa en el estudio de un diseño de rotor autorrotante que genere empuje empleando el mismo principio de funcionamiento del autogiro, introducido por el ingeniero Juan de la Cierva, en 1920. Para la concepción del diseño se define un modelo aerodinámico, teniendo en cuenta los parámetros de diseño del mecanismo rotor, posicionamiento sobre la embarcación propuesta y funcionamiento. Posteriormente, se atestigua el paradigma elaborado con una herramienta de software matemático, MATLAB, cotejando de esta forma los fundamentos teóricos tratados con un cálculo preciso. Incoming

During the embryonic development, it has been observed the prior to drastic shape changes of the organism, tissues deformations oscillate in a manner that resembles a fluid. Strikingly though, inertial terms are negligible in such systems, which renders the governing mechanical PDEs as elliptical or parabolic, with no apparent oscillatory solution. This work aims to investigate the coupling between mechanical equilibrium and biochemical coupling as a epossible source of this oscillations.

Soil organic matter dynamics are essential for terrestrial ecosystem functions as they affect biogeochemical cycles and, thus, the provision of plant nutrients or the release of greenhouse gases to the atmosphere. Most of the involved processes are driven by microorganisms. To investigate and understand these processes, individual-based models allow analyzing complex microbial systems' behavior based on rules and conditions for individual entities within these systems, taking into account local interactions and individual variations. Here, we present a streamlined, user-friendly and open version of the individual-based model INDISIM-SOM, which describes the mineralization of soil carbon and nitrogen. It was implemented in NetLogo, a widely used and easily accessible software platform especially designed for individual-based simulation models. Including powerful means to observe the model behavior and a standardized documentation, this increases INDISIM-SOM's range of potential uses and users, and facilitates the exchange among soil scientists as well as between different modeling approaches. We present a NetLogo version of an established IBM of SOM dynamics driven by microbes.The model was made simpler and less specific to increase its application potential.Users may easily access, explore and also modify the computational model.We provide the first complete standardized model description of INDISIM-SOM.The overall aim is an improved understanding of carbon and nitrogen dynamics in soils.

n this paper we present a method for decomposing a class of convex nonlinear programmes which are frequently encountered in engineering plastic analysis. These problems have second-order conic memberships constraints and a single complicating variable in the objective function. The method is based on finding the distance between the feasible sets of the decomposed problems, and updating the global optimal value according to the value of this distance. The latter is found by exploiting the method of averaged alternating reflections, which is here adapted to the optimisation problem at hand. The method is specially suited for non-linear problems and as our numerical results show, its convergence is independent of the number of variables of each sub-domain. We have tested the method with an illustrative example and with problems that have more than 10,000 variables.

This is a post-peer-review, pre-copyedit version of an article published in Journal of the Operational Research Society. The definitive publisher-authenticated version Freixas, J.; Pons, M. An axiomatic characterization of the potential decisiveness index. Journal of the Operational Research Society, 2015, vol. 66, no. 3, p. 353-359 is available online at: http://www.palgrave-journals.com/jors/journal/v66/n3/full/jors20145a.html Let us consider that somebody is extremely interested in increasing the probability of a proposal to be approved by a certain committee and that to achieve this goal he/she is prepared to pay off one member of the committee. In a situation like this one, and assuming that vote-buying is allowed and free of stigma, which voter should be offered a bribe? The potential decisiveness index for simple games, which measures the effect that ensuring one positive vote produces for the probability of passing the issue at hand, is a good tool with which to acquire the answer. An axiomatic characterization of this index is given in this paper, and its relation to other classical power indices is shown.