The TDNNS method for Reissner-Mindlin plates

A new family of locking-free finite elements for shear deformable Reissner-Mindlin plates is presented. The elements are based on the "tangential-displacement normal-normal-stress" formulation of elasticity. In this formulation, the bending moments are treated as separate unknowns. The degrees of freedom for the plate element are the nodal values of the deflection, tangential components of the rotations and normal-normal components of the bending strain. Contrary to other plate bending elements, no special treatment for the shear term such as reduced integration is necessary. The elements attain an optimal order of convergence

The polarization process of ferroelectric materials analyzed in the framework of variational inequalities

We are concerned with the mathematical modeling of the polarization process in ferroelectric media. We assume that this dissipative process is governed by two constitutive functions, which are the free energy function and the dissipation function. The dissipation function, which is closely connected to the dissipated energy, is usually non-differentiable. Thus, a minimization condition for the overall energy includes the subdifferential of the dissipation function. This condition can also be formulated by way of a variational inequality in the unknown fields strain, dielectric displacement, remanent polarization and remanent strain. We analyze the mathematical well-posedness of this problem. We provide an existence and uniqueness result for the time-discrete update equation. Under stronger assumptions, we can prove existence of a solution to the time-dependent variational inequality. To solve the discretized variational inequality, we use mixed finite elements, where mechanical displacement and dielectric displacement are unknowns, as well as polarization (and, if included in the model, remanent strain). It is then possible to satisfy Gauss' law of zero free charges exactly. We propose to regularize the dissipation function and solve for all unknowns at once in a single Newton iteration. We present numerical examples gained in the open source software package Netgen/NGSolve

Adaptive BDDC in Three Dimensions

The adaptive BDDC method is extended to the selection of face constraints in three dimensions. A new implementation of the BDDC method is presented based on a global formulation without an explicit coarse problem, with massive parallelism provided by a multifrontal solver. Constraints are implemented by a projection and sparsity of the projected operator is preserved by a generalized change of variables. The effectiveness of the method is illustrated on several engineering problems.Comment: 28 pages, 9 figures, 9 table

Optogenetics and electron microscopy reveal an ultrafast mode of synaptic vesicle recycling, adding a new twist to a 40-year-old controversy

Optogenetics and electron microscopy reveal an ultrafast mode of synaptic vesicle recycling, adding a new twist to a 40-year-old controversy. - See more at: http://elifesciences.org/content/2/e01233#sthash.K8kQedyo.dpu

Taking a Back Seat: Synaptic Vesicle Clustering in Presynaptic Terminals

Central inter-neuronal synapses employ various molecular mechanisms to sustain neurotransmitter release during phases of high-frequency synaptic activity. One of the features ensuring this property is the presence of a pool of synaptic vesicles (SVs) in the presynaptic terminal. At rest and low rates of stimulation, most of the vesicles composing this pool remain in a tight cluster. They are actively utilized when neurons fire action potentials at higher rates and the capability of the recycling machinery is limited. In addition, SV clusters are capable of migrating between release sites and reassemble into clusters at neighboring active zones (AZs). Within the cluster, thin “tethers” interconnect SVs. These dynamic filamentous structures are reorganized during stimulation thereby releasing SVs from the cluster. So far, one protein family, the synapsins, which bind actin filaments and vesicles in a phosphorylation-dependent manner, has been implicated in SV clustering in vertebrate synapses. As evident from recent studies, many endocytic proteins reside in the SV cluster in addition to synapsin. Here we discuss alternative possible mechanisms involved in the organization of this population of SVs. We propose a model in which synapsins together with other synaptic proteins, a large proportion of which is involved in SV recycling, form a dynamic proteinaceous “matrix” which limits the mobility of SVs. Actin filaments, however, do not seem to contribute to SV crosslinking within the SV cluster, but instead they are present peripherally to it, at sites of neurotransmitter release, and at sites of SV recycling

Abstract robust coarse spaces for systems of PDEs via generalized eigenproblems in the overlaps

Coarse spaces are instrumental in obtaining scalability for domain decomposition methods for partial differential equations (PDEs). However, it is known that most popular choices of coarse spaces perform rather weakly in the presence of heterogeneities in the PDE coefficients, especially for systems of PDEs. Here, we introduce in a variational setting a new coarse space that is robust even when there are such heterogeneities. We achieve this by solving local generalized eigenvalue problems in the overlaps of subdomains that isolate the terms responsible for slow convergence. We prove a general theoretical result that rigorously establishes the robustness of the new coarse space and give some numerical examples on two and three dimensional heterogeneous PDEs and systems of PDEs that confirm this property

Direct Coupling of Continuum and Shell Elements in Large Deformation Problems

In many applications, thin shell-like structures are integrated within or attached to volumetric bodies. This includes reinforcements placed in soft matrix material in lightweight structure design, or hollow structures that are partially or completely filled. Finite element simulations of such setups are highly challenging. A brute force discretization of structural as well as volumetric parts using well-shaped three-dimensional elements may be accurate, but leads to problems of enormous computational complexity even for simple models. One desired alternative is the use of shell elements for thin-walled parts, as such a discretization greatly alleviates size restrictions on the underlying finite element mesh. However, the coupling of different formulations within a single framework is often not straightforward and may lead to locking if not done carefully. Neunteufel and Schöberl proposed a mixed shell element where, apart from displacements of the center surface, bending moments are used as independent unknowns. These elements were not only shown to be locking free and highly accurate in large-deformation regime, but also do not require differentiability of the shell surface and can handle kinked and branched shell structures. They can directly be coupled to classical volume elements of arbitrary order by sharing displacement degrees of freedom at the center surface, thus achieving the desired coupled discretization. As the elements can be used on unstructured meshes, adaptive mesh refinement based on local stress and bending moments can be used. We present computational results that confirm exceptional accuracy for problems where thin-walled structures are embedded as reinforcements within soft matrix material