Mimetic Finite Difference methods for Hamiltonian wave equations in 2D

In this paper we consider the numerical solution of the Hamiltonian wave equation in two spatial dimension. We use the Mimetic Finite Difference (MFD) method to approximate the continuous problem combined with a symplectic integration in time to integrate the semi-discrete Hamiltonian system. The main characteristic of MFD methods, when applied to stationary problems, is to mimic important properties of the continuous system. This approach, associated with a symplectic method for the time integration yields a full numerical procedure suitable to integrate Hamiltonian problems. A complete theoretical analysis of the method and some numerical simulations are developed in the paper.Comment: 26 pages, 8 figure

Arbitrary order 2D virtual elements for polygonal meshes: Part II, inelastic problem

The present paper is the second part of a twofold work, whose first part is reported in [3], concerning a newly developed Virtual Element Method (VEM) for 2D continuum problems. The first part of the work proposed a study for linear elastic problem. The aim of this part is to explore the features of the VEM formulation when material nonlinearity is considered, showing that the accuracy and easiness of implementation discovered in the analysis inherent to the first part of the work are still retained. Three different nonlinear constitutive laws are considered in the VEM formulation. In particular, the generalized viscoplastic model, the classical Mises plasticity with isotropic/kinematic hardening and a shape memory alloy (SMA) constitutive law are implemented. The versatility with respect to all the considered nonlinear material constitutive laws is demonstrated through several numerical examples, also remarking that the proposed 2D VEM formulation can be straightforwardly implemented as in a standard nonlinear structural finite element method (FEM) framework

Numerical results for mimetic discretization of Reissner-Mindlin plate problems

A low-order mimetic finite difference (MFD) method for Reissner-Mindlin plate problems is considered. Together with the source problem, the free vibration and the buckling problems are investigated. Full details about the scheme implementation are provided, and the numerical results on several different types of meshes are reported

Stability Analysis for the Virtual Element Method

We analyse the Virtual Element Methods (VEM) on a simple elliptic model problem, allowing for more general meshes than the one typically considered in the VEM literature. For instance, meshes with arbitrarily small edges (with respect to the parent element diameter), can be dealt with. Our general approach applies to different choices of the stability form, including, for example, the "classical" one introduced in [L. Beirao da Veiga, F. Brezzi, A. Cangiani, G. Manzini, L. D. Marini, and A. Russo, Basic principles of virtual element methods, Math. Models Methods Appl. Sci. 23 (2013), no. 1, 199-214], and a recent one presented in [Wriggers, P., Rust, W.T., and Reddy, B.D., A virtual element method for contact, submitted for publication]. Finally, we show that the stabilization term can be simplified by dropping the contribution of the internal-to-the-element degrees of freedom. The resulting stabilization form, involving only the boundary degrees of freedom, can be used in the VEM scheme without affecting the stability and convergence properties. The numerical tests are in accordance with the theoretical predictions

Comparativa entre el sistema tradicional de alojamiento, hotel, y uno de los nuevos modelos de alojamiento, Airbnb. El desestimiento

En el presente trabajo hacemos una comparativa entre el sistema tradicional de alojamiento, hotel, y Airbnb. Vamos a presentar ambas empresas, cómo están formadas y, posteriormente, estudiaremos los medios para hacer una reserva en ambos modelos de estudio.Grado en Turism

Regulation of pluripotent states in human embryonic stem cells

A growing array of mouse and human pluripotent stem cell lines has been derived from the early embryo as well as from adult cells reprogrammed by ectopic expression of transcription factors – i.e. induced pluripotent stem (iPS) cells. These cell lines share the expression of key pluripotency markers and are able to self-renew and to generate differentiated progenies when induced. Their relationship to each other and whether they correspond to different pluripotent states with distinct developmental capacities and affiliations in vivo remains unclear, however. Profiling chromatin in a particular cell line has proven to be a valuable signature for cell identity and developmental stage. One approach has been to assay the timing of DNA replication across a panel of loci, as an indicator of chromatin accessibility. Of interest, this replication timing profiling was capable of discriminating pluripotent mouse ES (mES) cells from cells with a more restricted differentiation capacity. In this study, I have addressed whether distinct pluripotent states could be reliably discriminated at the chromatin level. In particular, I characterised the replication timing profile of a number of human ES (hES) cell lines alongside mES and mouse epiblast-derived stem (mEpiS) cell lines. I showed that mES cells have a steady and mostly early-replicating profile, regardless of their genetic background. In contrast, the profile of undifferentiated H1, H7 and H9 hES cell lines harboured an increased proportion of late-replicating loci during S-phase. Moreover, hES cell replication profile greatly varied between cultures and cell lines; a level of replication timing variability also observed among mEpiS cells, as opposed to mES cells. These results highlighted that hES and mEpiS cells share a common unstable or transitional state: primed on the verge of differentiation. This view was, however, further challenged by exploring how hES cell cultures could be modulated towards an ES-like versus epiblast-like state under different conditions. In particular, extensive and dynamic shifts of replication timing, from late to early, were consistently observed at many target loci in hES and hiPS cells upon increased Smad2/3 and p300 histone acetyltransferase activity. Importantly, these alterations were reversible and associated with differential gene expression profiles and functional properties of hES cells. Collectively, these data revealed the existence of distinct but interchangeable pluripotent hES cell states and proposed a key role for TGF-β/Activin signalling and the HAT p300 in modulating the balance between a naive versus primed state in hES cell cultures