The asymptotic homogenization elasticity tensor properties for composites with material discontinuities

The classical asymptotic homogenization approach for linear elastic composites with discontinuous material properties is considered as a starting point. The sharp length scale separation between the fine periodic structure and the whole material formally leads to anisotropic elastic-type balance equations on the coarse scale, where the arising fourth rank operator is to be computed solving single periodic cell problems on the fine scale. After revisiting the derivation of the problem, which here explicitly points out how the discontinuity in the individual constituents’ elastic coefficients translates into stress jump interface conditions for the cell problems, we prove that the gradient of the cell problem solution is minor symmetric and that its cell average is zero. This property holds for perfect interfaces only (i.e., when the elastic displacement is continuous across the composite’s interface) and can be used to assess the accuracy of the computed numerical solutions. These facts are further exploited, together with the individual constituents’ elastic coefficients and the specific form of the cell problems, to prove a theorem that characterizes the fourth rank operator appearing in the coarse-scale elastic-type balance equations as a composite material effective elasticity tensor. We both recover known facts, such as minor and major symmetries and positive definiteness, and establish new facts concerning the Voigt and Reuss bounds. The latter are shown for the first time without assuming any equivalence between coarse and fine-scale energies (Hill’s condition), which, in contrast to the case of representative volume elements, does not identically hold in the context of asymptotic homogenization. We conclude with instructive three-dimensional numerical simulations of a soft elastic matrix with an embedded cubic stiffer inclusion to show the profile of the physically relevant elastic moduli (Young’s and shear moduli) and Poisson’s ratio at increasing (up to 100 %) inclusion’s volume fraction, thus providing a proxy for the design of artificial elastic composites

Can a continuous mineral foam explain the stiffening of aged bone tissue? A micromechanical approach to mineral fusion in musculoskeletal tissues

Recent experimental data revealed a stiffening of aged cortical bone tissue, which could not be explained by common multiscale elastic material models. We explain this data by incorporating the role of mineral fusion via a new hierarchical modeling approach exploiting the asymptotic (periodic) homogenization (AH) technique for three-dimensional linear elastic composites. We quantify for the first time the stiffening that is obtained by considering a fused mineral structure in a softer matrix in comparison with a composite having non-fused cubic mineral inclusions. We integrate the AH approach in the Eshelby-based hierarchical mineralized turkey leg tendon model (Tiburtius et al 2014 Biomech. Model. Mechanobiol. 13 1003–23), which can be considered as a base for musculoskeletal mineralized tissue modeling. We model the finest scale compartments, i.e. the extrafibrillar space and the mineralized collagen fibril, by replacing the self-consistent scheme with our AH approach. This way, we perform a parametric analysis at increasing mineral volume fraction, by varying the amount of mineral that is fusing in the axial and transverse tissue directions in both compartments. Our effective stiffness results are in good agreement with those reported for aged human radius and support the argument that the axial stiffening in aged bone tissue is caused by the formation of a continuous mineral foam. Moreover, the proposed theoretical and computational approach supports the design of biomimetic materials which require an overall composite stiffening without increasing the amount of the reinforcing material

Zur Regenerationsfähigkeit von Laufkäferzönosen (Col., Carabidae) nach einem extremen Sommerhochwasser an der Mittleren Elbe

Laufkäfer gehören zu den häufigsten Makroinvertebraten in terrestrischen und semiterrestrischen Lebensräumen und erfüllen aufgrund ihrer vielfach räuberischen Lebensweise wichtige regulatorische Funktionen in Ökosystemen. Dank zahlreicher Freiland-Untersuchungen in den letzten Jahrzehnten sind die ökologischen Ansprüche vieler Laufkäfer relativ gut bekannt. Durch ihre hohe Mobilität - viele Arten sind flugfähig - können Laufkäfer sehr schnell auf Veränderungen ihrer Umwelt reagieren. Gleichzeitig besitzen Laufkäfer die Fähigkeit, Umwelteinflüsse über eine längere Zeit zu integrieren. So können sich z. B. die Auswirkungen von Störungen stark in den Dominanzen einzelner Arten oder im Fehlen von Arten mit bestimmten ökologischen Ansprüchen widerspiegeln und somit noch mehrere Jahre nach dem Ereignis in den Artengemeinschaften sichtbar sein. Diese Eigenschaften machen Laufkäfer als Zeigerarten für biotische und abiotische Veränderungen der Umwelt interessant, weshalb sie auch als Modelltiergruppe gelten. Die vorliegende Arbeit beschreibt die kurz- und mittelfristigen Auswirkungen des extremen Sommerhochwassers auf die Laufkäferfauna von Auengrünlandstandorten an der Mittleren Elbe

cAMP activates adenylate and guanylate cyclase of Dictyostelium discoideum cells by binding to different classes of cell-surface receptors. A study with extracellular Ca2+

cAMP induces a transient increase of cAMP and cGMP levels in Dictyostelium discoideum cells. Fast binding experiments reveal three types of cAMP-binding site (S, H and L), which have different off-rates (t0.5, 0.7-15 s) and different affinities (Kd, 15-450 nM). A time- and cAMP-concentration-dependent transition of H- to L-sites occurs during the binding reaction. Extracellular Ca2+ had multiple effects on cAMP-binding sites. (i) The number of H + L-sites increased 2.5-fold, while the number of S-sites was not strongly affected. (ii) The Kd of the S-sites was reduced from 16 nM to 5 nM (iii) The conversion of H-sites to L-sites was inhibited up to 80%. The kinetics of the cAMP-induced cAMP accumulation was not strongly altered by Ca2+, but the amount of cAMP produced was inhibited up to 80%. The kinetics of the cAMP-induced cGMP accumulation was strongly altered; maximal levels were obtained sooner, and the Ka was reduced from 15 to 3.5 nM cAMP. Ca2+, Mg2+ and Mn2+ increased the number of binding sites, all with EC50 = 0.5 mM. The S-sites and the cGMP response were modified by equal Ca2+ concentrations and by higher concentrations of Mg2+ and Mn2+ (EC50 are respectively 0.4 mM, 2.5 mM and about 25 mM). The conversion of H- to L-sites and the cAMP response were specifically inhibited by Ca2+ with EC50 = 20 µM. It is concluded that cAMP activates guanylate cyclase through the S-sites; adenylate cyclase is activated by the H + L-sites, in which the appearance of the L-sites during the binding reaction represents the coupling of occupied surface cAMP receptors to adenylate cyclase.

Differenzierung von Laufkäfergemeinschaften (Col., Carabidae) an der Mittleren Elbe am Beispiel des Roßlauer Oberluchs

Im Rahmen der wissenschaftlichen Begleitforschung zum Deichrückverlegungsvorhaben im Roßlauer Oberluch wurden auch die Laufkäfer untersucht. Aufgrund ihrer hohen Mobilität reagieren Laufkäfer relativ schnell auf sich ändernde Umweltbedingungen, vor allem in dynamischen Lebensräumen wie Auen. Darüber hinaus weisen viele Arten eine spezielle Habitatbindung auf und eignen sich daher sehr gut als Bioindikatoren für hydrologische Veränderungen in Auen. Da auch die Biologie und die Ökologie dieser Artengruppe relativ gut bekannt sind, wurden die Laufkäfer als Modelltiergruppe ausgewählt, um die Auswirkungen von Rückdeichungen zu quantifizieren. Bisher weiß man relativ wenig darüber, wie Laufkäfer auf solche Maßnahmen reagieren. Der vorliegende Artikel soll weniger auf die Auswirkungen von Rückdeichungen eingehen, sondern vielmehr einen Überblick über den Status-Quo-Zustand der Laufkäferfauna vor der Deichöffnung geben

Cross-diffusion in reaction-diffusion models: analysis, numerics and applications

Cross-diffusion terms are nowadays widely used in reaction-diffusion equations encountered in models from mathematical biology and in various engineering applications. In this contribution we review the basic model equations of such systems, give an overview of their mathematical analysis, with an emphasis on pattern formation and positivity preservation, and finally we present numerical simulations that highlight special features of reaction-cross-diffusion models

Heuschreckengemeinschaften im Roßlauer Oberluch an der Mittleren Elbe

Deichrückverlegungsprojekte, wie das im Roßlauer Oberluch an der Mittleren Elbe, stellen für den Naturschutz sowohl Chance als auch Herausforderung dar. Es wird argumentiert, dass solche Maßnahmen einerseits dem Hochwasserschutz, auf der anderen Seite auch dem Arten- und Biotopschutz dienen sollen. Die Auswirkungen von Deichrückbauvorhaben auf Natur und Landschaft sind bisher jedoch nur unzureichend bekannt. Dies ist primär der Tatsache geschuldet, dass für viele Arten die Kenntnisse über die Wechselwirkungen mit ihrer Umwelt noch immer defizitär sind und somit die Auswirkungen von Umweltveränderungen auf Flora und Fauna nicht effektiv quantifiziert werden können. Das gilt auch und gerade für Heuschrecken in Feuchtlebensräumen, wie z. B. in Flussauen. In der vorliegenden Arbeit wurden die Zusammenhänge zwischen wichtigen Umweltvariablen und den Vorkommen von Heuschrecken genauer betrachtet

Hormonal Signal Amplification Mediates Environmental Conditions during Development and Controls an Irreversible Commitment to Adulthood

Many animals can choose between different developmental fates to maximize fitness. Despite the complexity of environmental cues and life history, different developmental fates are executed in a robust fashion. The nematode Caenorhabditis elegans serves as a powerful model to examine this phenomenon because it can adopt one of two developmental fates (adulthood or diapause) depending on environmental conditions. The steroid hormone dafachronic acid (DA) directs development to adulthood by regulating the transcriptional activity of the nuclear hormone receptor DAF-12. The known role of DA suggests that it may be the molecular mediator of environmental condition effects on the developmental fate decision, although the mechanism is yet unknown. We used a combination of physiological and molecular biology techniques to demonstrate that commitment to reproductive adult development occurs when DA levels, produced in the neuroendocrine XXX cells, exceed a threshold. Furthermore, imaging and cell ablation experiments demonstrate that the XXX cells act as a source of DA, which, upon commitment to adult development, is amplified and propagated in the epidermis in a DAF-12 dependent manner. This positive feedback loop increases DA levels and drives adult programs in the gonad and epidermis, thus conferring the irreversibility of the decision. We show that the positive feedback loop canalizes development by ensuring that sufficient amounts of DA are dispersed throughout the body and serves as a robust fate-locking mechanism to enforce an organism-wide binary decision, despite noisy and complex environmental cues. These mechanisms are not only relevant to C. elegans but may be extended to other hormonal-based decision-making mechanisms in insects and mammals

Habitat disturbance and hydrological parameters determine the body size and reproductive strategy of alluvial ground beetles

Environmental variability is the main driver for the variation of biological characteristics (life-history traits) of species. Therefore, life-history traits are particularly suited to identify mechanistic linkages between environmental variability and species occurrence and can help in explaining ecological patterns. For ground beetles, few studies directly related species traits to environmental variables. This study aims to analyse how life-history traits of alluvial ground beetles are controlled by environmental factors. I expected that the occurrence of species and the occurrence of specific traits are closely related to hydrological and disturbance parameters. Furthermore I expected most of the trait-variation to be explained by a combination of environmental variables, rather than by their isolated effects. Ground beetles were sampled in the year 2005 in floodplain grassland along the Elbe River in Germany. I used redundancy analysis to quantify the effects of hydrological, sediment, and disturbance related parameters on both species occurrence and species traits. I applied variation partitioning to analyse which environmental compartments explain most of the trait variation. Species occurrence and trait variation were both mainly controlled by hydrological and flood disturbance parameters. I could clearly identify reproductive traits and body size as key traits for floodplain ground beetles to cope with the environmental variability. Furthermore, combinations of hydrological, habitat disturbance, habitat type, and species diversity parameters, rather than their isolated effects, explained large parts of ground beetle trait variation. Thus, a main conclusion of this study is that ground beetle occurrence is mainly determined by complex, multi-scale interactions between environmental variability and their life-history traits

Chemotaxis: a feedback-based computational model robustly predicts multiple aspects of real cell behaviour

The mechanism of eukaryotic chemotaxis remains unclear despite intensive study. The most frequently described mechanism acts through attractants causing actin polymerization, in turn leading to pseudopod formation and cell movement. We recently proposed an alternative mechanism, supported by several lines of data, in which pseudopods are made by a self-generated cycle. If chemoattractants are present, they modulate the cycle rather than directly causing actin polymerization. The aim of this work is to test the explanatory and predictive powers of such pseudopod-based models to predict the complex behaviour of cells in chemotaxis. We have now tested the effectiveness of this mechanism using a computational model of cell movement and chemotaxis based on pseudopod autocatalysis. The model reproduces a surprisingly wide range of existing data about cell movement and chemotaxis. It simulates cell polarization and persistence without stimuli and selection of accurate pseudopods when chemoattractant gradients are present. It predicts both bias of pseudopod position in low chemoattractant gradients and-unexpectedly-lateral pseudopod initiation in high gradients. To test the predictive ability of the model, we looked for untested and novel predictions. One prediction from the model is that the angle between successive pseudopods at the front of the cell will increase in proportion to the difference between the cell's direction and the direction of the gradient. We measured the angles between pseudopods in chemotaxing Dictyostelium cells under different conditions and found the results agreed with the model extremely well. Our model and data together suggest that in rapidly moving cells like Dictyostelium and neutrophils an intrinsic pseudopod cycle lies at the heart of cell motility. This implies that the mechanism behind chemotaxis relies on modification of intrinsic pseudopod behaviour, more than generation of new pseudopods or actin polymerization by chemoattractant