Questioning numerical integration methods for microsphere (and microplane) constitutive equations

In the last few years, more and more complex microsphere models have been proposed to predict the mechanical response of various polymers. Similarly than for microplane models, they consist in deriving a one-dimensional force vs. stretch equation and to integrate it over the unit sphere to obtain a three-dimensional constitutive equation. In this context, the focus of authors is laid on the physics of the one-dimensional relationship, but in most of the case the influence of the integration method on the prediction is not investigated.Here we compare three numerical integration schemes: a classical Gaussian scheme, a method based on a regular geometric meshing of the sphere, and an approach based on spherical harmonics. Depending on the method, the number of integration points may vary from 4 to 983,040! Considering simple quantities, i.e. principal (large) strain invariants, it is shown that the integration method must be carefully chosen. Depending on the quantities retained to described the one-dimensional equation and the required error, the performances of the three methods are discussed. Consequences on stress–strain prediction are illustrated with a directional version of the classical Mooney–Rivlin hyperelastic model. Finally, the paper closes with some advices for the development of new microsphere constitutive equations.     

Towards a Better Prediction of Cell Settling on Nanostructure Arrays—Simple Means to Complicated Ends

Vertical arrays of nanostructures (NSs) are emerging as promising platforms for probing and manipulating live mammalian cells. The broad range of applications requires different types of interfaces, but cell settling on NS arrays is not yet fully controlled and understood. Cells are both seen to deform completely into NS arrays and to stay suspended like tiny fakirs, which have hitherto been explained with differences in NS spacing or density. Here, a better understanding of this phenomenon is provided by using a model that takes into account the extreme membrane deformation needed for a cell to settle into a NS array. It is shown that, in addition to the NS density, cell settling depends strongly on the dimensions of the single NS, and that the settling can be predicted for a given NS array geometry. The predictive power of the model is confirmed by experiments and good agreement with cases from the literature. Furthermore, the influence of cell‐related parameters is evaluated theoretically and a generic method of tuning cell settling through surface coating is demonstrated experimentally. These findings allow a more rational design of NS arrays for the numerous exciting biological applications where the mode of cell settling is crucial.     

A unified critical state model for geomaterials with an application to tunnelling

This paper is prepared in honour of Professor E.T. Brown for his outstanding contributions to rock mechanics and geotechnical engineering and also for his personal influence on the first author's research career in geomechanics and geotechnical engineering. As a result, we have picked a topic that reflects two key research areas in which Professor E.T. Brown has made seminal contributions over a long and distinguished career. These two areas are concerned with the application of the critical state concept to modelling geomaterials and the analysis of underground excavation or tunnelling in geomaterials.Partially due to Professor Brown's influence, the first author has also been conducting research in these two areas over many years. In particular, this paper aims to describe briefly the development of a unified critical state model for geomaterials together with an application to cavity contraction problems and tunnelling in soils.     

Apparent power-law distributions in animal movements can arise from intraspecific interactions

Lévy flights have gained prominence for analysis of animal movement. In a Lévy flight, step-lengths are drawn from a heavy-tailed distribution such as a power law (PL), and a large number of empirical demonstrations have been published. Others, however, have suggested that animal movement is ill fit by PL distributions or contend a state-switching process better explains apparent Lévy flight movement patterns. We used a mix of direct behavioural observations and GPS tracking to understand step-length patterns in females of two related butterflies. We initially found movement in one species (Euphydryas editha taylori) was best fit by a bounded PL, evidence of a Lévy flight, while the other (Euphydryas phaeton) was best fit by an exponential distribution. Subsequent analyses introduced additional candidate models and used behavioural observations to sort steps based on intraspecific interactions (interactions were rare in E. phaeton but common in E. e. taylori). These analyses showed a mixed-exponential is favoured over the bounded PL for E. e. taylori and that when step-lengths were sorted into states based on the influence of harassing conspecific males, both states were best fit by simple exponential distributions. The direct behavioural observations allowed us to infer the underlying behavioural mechanism is a state-switching process driven by intraspecific interactions rather than a Lévy flight.     

Multicellular Tumor Spheroids (MCTS) as a 3D In Vitro Evaluation Tool of Nanoparticles

Multicellular tumor spheroid models (MCTS) are often coined as 3D in vitro models that can mimic the microenvironment of tissues. MCTS have gained increasing interest in the nano‐biotechnology field as they can provide easily accessible information on the performance of nanoparticles without using animal models. Considering that many countries have put restrictions on animals testing, which will only tighten in the future as seen by the recent developments in the Netherlands, 3D models will become an even more valuable tool. Here, an overview on MCTS is provided, focusing on their use in cancer research as most nanoparticles are tested in MCTS for treatment of primary tumors. Thereafter, various types of nanoparticles—from self‐assembled block copolymers to inorganic nanoparticles, are discussed. A range of physicochemical parameters including the size, shape, surface chemistry, ligands attachment, stability, and stiffness are found to influence nanoparticles in MCTS. Some of these studies are complemented by animal studies confirming that lessons from MCTS can in part predict the behaviour in vivo. In summary, MCTS are suitable models to gain additional information on nanoparticles. While not being able to replace in vivo studies, they can bridge the gap between traditional 2D in vitro studies and in vivo models.     

Model Selection for Unsupervised Learning of Visual Context

This study addresses the problem of choosing the most suitable probabilistic model selection criterion for unsupervised learning of visual context of a dynamic scene using mixture models. A rectified Bayesian Information Criterion (BICr) and a Completed Likelihood Akaike’s Information Criterion (CL-AIC) are formulated to estimate the optimal model order (complexity) for a given visual scene. Both criteria are designed to overcome poor model selection by existing popular criteria when the data sample size varies from small to large and the true mixture distribution kernel functions differ from the assumed ones. Extensive experiments on learning visual context for dynamic scene modelling are carried out to demonstrate the effectiveness of BICr and CL-AIC, compared to that of existing popular model selection criteria including BIC, AIC and Integrated Completed Likelihood (ICL). Our study suggests that for learning visual context using a mixture model, BICr is the most appropriate criterion given sparse data, while CL-AIC should be chosen given moderate or large data sample sizes.     

Quantitative pharmacophore models with inductive logic programming

Three-dimensional models, or pharmacophores, describing Euclidean constraints on the location on small molecules of functional groups (like hydrophobic groups, hydrogen acceptors and donors, etc.), are often used in drug design to describe the medicinal activity of potential drugs (or ‘ligands’). This medicinal activity is produced by interaction of the functional groups on the ligand with a binding site on a target protein. In identifying structure-activity relations of this kind there are three principal issues: (1) It is often difficult to “align” the ligands in order to identify common structural properties that may be responsible for activity; (2) Ligands in solution can adopt different shapes (or `conformations’) arising from torsional rotations about bonds. The 3-D molecular substructure is typically sought on one or more low-energy conformers; and (3) Pharmacophore models must, ideally, predict medicinal activity on some quantitative scale. It has been shown that the logical representation adopted by Inductive Logic Programming (ILP) naturally resolves many of the difficulties associated with the alignment and multi-conformation issues. However, the predictions of models constructed by ILP have hitherto only been nominal, predicting medicinal activity to be present or absent. In this paper, we investigate the construction of two kinds of quantitative pharmacophoric models with ILP: (a) Models that predict the probability that a ligand is “active”; and (b) Models that predict the actual medicinal activity of a ligand. Quantitative predictions are obtained by the utilising the following statistical procedures as background knowledge: logistic regression and naive Bayes, for probability prediction; linear and kernel regression, for activity prediction. The multi-conformation issue and, more generally, the relational representation used by ILP results in some special difficulties in the use of any statistical procedure. We present the principal issues and some solutions. Specifically, using data on the inhibition of the protease Thermolysin, we demonstrate that it is possible for an ILP program to construct good quantitative structure-activity models. We also comment on the relationship of this work to other recent developments in statistical relational learning. Editors: Tamás Horváth and Akihiro Yamamoto     

The Influence and Interpretation of Surface Parameters for Wetting Transitions in Ternary Mixtures

Starting from a microscopic Hamiltonian defined on a semi-infinite cubic lattice, and employing a mean-field approximation, the surface parameters relevant for wetting in confined ternary mixtures are derived. These are found in terms of the microscopic coupling constants, and yield a physical interpretation of their origins. In comparison with the standard expression for the surface free-energy density, several new terms arising from the derivation are identified. The influence of the surface parameters on a predicted unbinding transition in a mixture of oil, water, and amphiphile demonstrate that existing results are robust to the addition of the extra surface terms.     

River Bifurcation Analysis by Physical and Numerical Modeling

In the framework of a river regulation design of the Po River Delta (Northern Italy), a study on a large physical model of the bifurcation Po di Goro-Po di Venezia was conducted with the main objective of determining the discharge subdivision rate at the river node, in order to assess the inflow conditions in the Po di Goro River for flood risk analysis. In this context, a two-dimensional depth averaged numerical model was tested against measured values, with reference to the prototype. In this paper a comprehensive analysis and discussion of the results is reported in order to highlight the applicability of numerical models in comparison with physical ones in river engineering applications.     

Chemische Zusammensetzung und Mikrostruktur polymerabgeleiteter Gläser und Keramiken im System Si–C–O. Teil 2: Charakterisierung der Gefügeausbildung mittels hochauflösender Durchstrahlungselektronenmikroskopie und Feinbereichsbeugung

Chemical Composition and Microstructure of Polymer‐Derived Glasses and Ceramics in the Si–C–O System. Part 2: Characterization of microstructure formation by means of high‐resolution transmission electron microscopy and selected area diffraction Liquid or solid silicone resins represent the economically most interesting class of organic precursors for the pyrolytic production of glass and ceramics materials on silicon basis. As dense, dimensionally stable components can be cost‐effectively achieved by admixing reactive filler powders, chemical composition and microstructure development of the polymer‐derived residues must be exactly known during thermal decomposition. Thus, in the present work, glasses and ceramics produced by pyrolysis of the model precursor polymethylsiloxane at temperatures from 525 to 1550 °C are investigated. In part 1, by means of analytical electron microscopy, the bonding state of silicon was determined on a nanometre scale and the phase separation of the metastable Si–C–O matrix into SiO₂, C and SiC was proved. The in‐situ crystallization could be considerably accelerated by adding fine‐grained powder of inert fillers, such as Al₂O₃ or SiC, which permits effective process control. In part 2, the microstructure is characterized by high‐resolution transmission electron microscopy and selected area diffraction. Turbostratic carbon and cubic β‐SiC precipitate as crystallization products. Theses phases are embedded in an amorphous matrix. Inert fillers reduce the crystallization temperature by several hundred °C. In this case, the polymer‐derived Si–C–O material acts as a binding agent between the powder particles. Reaction layer formation does not occur. On the investigated pyrolysis conditions, no crystallization of SiO₂ was observed.