The signed Varchenko Determinant for Complexes of Oriented Matroids

We generalize the (signed) Varchenko matrix of a hyperplane arrangement to complexes of oriented matroids and show that it has a nice factorization.Comment: 19 Pages, 3 figure

Swelling-Induced Instabilities of Polymeric Hydrogels with Periodic Microstructures

Hydrogels are soft, hydrophilic materials which can absorb a large volume of solvent and undergo finite volumetric deformations known as swelling. The swelling of a hydrogel can be a driving mechanism for complex material responses such as pattern transformation which lead to change of periodicity as a result of a microscopic instability in periodic materials. In the present contribution, we deal with the computational analysis of swelling-induced instabilities in periodic hydrogels. The stability analysis based on the Bloch-Floquet theory is carried out within a transient two-field minimization-type variational principle. The presented formulation and methodology for the stability analysis are computationally efficient, since the computations are carried out on the smallest representative volume element of the microstructure. Within this framework, we study swelling-induced microscopic instabilities for various perforated hydrogels. Our findings are consistent with experimental observations and show that the so-called diamond plate patterns are the critical buckling mode for voided microstructures. Moreover, we observe long-wavelength instabilities for certain volume fractions of voids

A Simple Quantitative Model of Neuromodulation. Part I: Ion Flow Through Neural Ion Channels

We develop a simple model of ionic current through neuronal membranes as a function of membrane potential and extracellular ion concentration. The model combines a simplified Poisson-Nernst-Planck (PNP) model of ion transport through individual mechanosensitive ion channels with channel activation functions calibrated from ad hoc in-house experimental data. The simplified PNP model is validated against bacterial Gramicidin A ion channel data. The calibrated model accounts for the transport of calcium, sodium, potassium, and chloride and exhibits remarkable agreement with the experimentally measured current-voltage curves for the differentiated human neural cells. All relevant data and code related to the ion flow models are available at DaRUS.Comment: 17 pages, 8 figure

On the Influence of Ferroelectric Polarization States on the Magneto-electric Coupling in Two-phase Composites

Of particular attention in a variety of novel technical applications is the coupling between magnetic and electric field quantities. Materials that show magneto-electric (ME) coupling could enable new smart devices in the area of electric-field-controlled magnetic-data storage or highly sensitive magnetic-field sensors. In general, ME materials exhibit both a spontaneous magnetization and a spontaneous polarization. In this respect, they feature two ferroic states at the same time and are thus termed magneto-electric multiferroics. However, all natural and most of the synthesized ME multiferroics do not show an interaction between magnetization and electric polarization in the technically relevant temperature range. Thus, there is need for alternative realizations for ME coupling materials. A promising idea lies in the design and manufacturing of ME composites. These materials consist of a magnetostrictive and a piezoelectric phase and generate the ME coupling as a strain-induced product property. Since there exists a wealth of stable magnetostrictive and piezoelectric materials at ambient temperature, such composites yield the desired ME coupling also in a technically useful temperature range. In any case, the effective ME coupling is driven by microscopic interactions between the individual phases and thus highly depends on the microstructure of the composite. This calls for powerful homogenization methods that are able to predict the effective coupling for arbitrary microstructural morphologies. Motivated by that, we apply a two-scale computational homogenization framework for magneto-electro-mechanically coupled boundary value problems, which allows us to analyze the ME composite structures and calculate the effective ME-coefficient. Furthermore, by using a non-linear ferroelectric material model on the micro-level, we are able to simulate the polarization process of the ferroelectric phase. We show that this has a significant impact on the obtainable ME-coefficient

Electrochemical strain microscopy time spectroscopy: Model and experiment on LiMn2O4

Electrochemical Strain Microscopy (ESM) can provide useful information on ionic diffusion in solids at the local scale. In this work, a finite element model of ESM measurements was developed and applied to commercial lithium manganese (III,IV) oxide (LiMn2O4) particles. ESM time spectroscopy was used, where a direct current (DC) voltage pulse locally disturbs the spatial distribution of mobile ions. After the pulse is off, the ions return to equilibrium at a rate which depends on the Li diffusivity in the material. At each stage, Li diffusivity is monitored by measuring the ESM response to a small alternative current (AC) voltage simultaneously applied to the tip. The model separates two different mechanisms, one linked to the response to DC bias and another one related to the AC excitation. It is argued that the second one is not diffusion-driven hut is rather a contribution of the sum of several mechanisms with at least one depending on the lithium ion concentration explaining the relaxation process. With proper fitting of this decay, diffusion coefficients of lithium hosts could be extracted. Additionally, the effect of phase transition in LiMn2O4 is taken into account, explaining some experimental observations. (C) 2015 AIP Publishing LLC