Force localization in contracting cell layers

Epithelial cell layers on soft elastic substrates or pillar arrays are commonly used as model systems for investigating the role of force in tissue growth, maintenance, and repair. Here we show analytically that the experimentally observed localization of traction forces to the periphery of the cell layers does not necessarily imply increased local cell activity, but follows naturally from the elastic problem of a finite-sized contractile layer coupled to an elastic foundation. For homogeneous contractility, the force localization is determined by one dimensionless parameter interpolating between linear and exponential force profiles for the extreme cases of very soft and very stiff substrates, respectively. If contractility is sufficiently increased at the periphery, outward directed displacements can occur at intermediate positions. We also show that anisotropic extracellular stiffness can lead to force localization in the stiffer direction, as observed experimentally.     

Reduktionsverfahren für Differenzengleichungen bei Randwertaufgaben II

Summary In a recent paper [11], two of the authors investigated a fast reduction method for solving difference equations which approximate certain boundary value problems for Poisson's equation. In this second paper, we prove the numerical stability of the reduction method, and also report on further developments of the method. For the general case, the provided bounds for the numerical errors behave roughly like the condition numberO(n ²) of the linear system; for more realistic model problems estimates of order less thanO(n) are obtained (n ^–1=h=mesh width). The number of operations required for the reduction method isO(n ² ), for the usual five-point difference formula, as well as for the common nine-point formula with discretization error of orderh ⁴.     

Über Untergruppen Endlicher Algebraischer Gruppen

Let k be a commutative ring, GG finite affine algebraic k-groups, and HH the dual Hopfalgebras of the affine algebras of G resp. G. The main results of this paper are: (I) If k is semilocal (e.g. k a field) there is an H-linear, HH-colinear, unitary, augmented isomorphism HHH H, where HH is the coalgebra belonging to G/G. (II) If the k-submodule of the fixelements of (HH)^* is isomorphic to k (e.g. k principal or semilocal), then HH is a Frobeniusextension of the second kind.     

Über die Multiplikatorensysteme zur Gruppe der ganzen Modulsubstitutionenn-ten Grades

Ohne Zusammenfassung     

A note on mixed A-reflexive groups

This paper presents a Warfield-type characterization of A-reflexive groups in the case that A is a mixed abelian group of torsion-free rank 1.     

Nanoscopic Porous Iridium/Iridium Dioxide Superstructures (15 nm): Synthesis and Thermal Conversion by In Situ Transmission Electron Microscopy

Porous particle superstructures of about 15 nm diameter, consisting of ultrasmall nanoparticles of iridium and iridium dioxide, are prepared through the reduction of sodium hexachloridoiridate(+IV) with sodium citrate/sodium borohydride in water. The water-dispersible porous particles contain about 20 wt % poly(N-vinylpyrrolidone) (PVP), which was added for colloidal stabilization. High-resolution transmission electron microscopy confirms the presence of both iridium and iridium dioxide primary particles (1–2 nm) in each porous superstructure. The internal porosity (≈58 vol%) is demonstrated by electron tomography. In situ transmission electron microscopy up to 1000 °C under oxygen, nitrogen, argon/hydrogen (all at 1 bar), and vacuum shows that the porous particles undergo sintering and subsequent compaction upon heating, a process that starts at around 250 °C and is completed at around 800 °C. Finally, well-crystalline iridium dioxide is obtained under all four environments. The catalytic activity of the as-prepared porous superstructures in electrochemical water splitting (oxygen evolution reaction; OER) is reduced considerably upon heating owing to sintering of the pores and loss of internal surface area.     

Fifteenth International Symposium on Biological and Environmental Reference Materials (BERM-15)

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