Numerical model of the spatio-temporal dynamics in a water strider group

The water strider group demonstrates a very complex dynamics consisting of competition for the food items, territoriality and aggression to the conspecific individuals, escaping from the predators, etc. The situation is even more complex due to the presence of different instars, which in most water strider species live in the same habitat and occupy the same niche. The presented swarm model of water striders demonstrates the realistic population dynamics. For the swarm formation in the model, attraction and repulsion forces were used. Animal motion in the model takes into account inertia and kinetic energy dissipation effects. The model includes three different rates related to the growth of individuals: food appearance rate, food assimilation rate, and stored energy loss rate. The results of our modeling show that the size distribution of individuals seems to be an adequate measure for population status, and it has a characteristic shape for different model parameter combinations. Distribution of the distances between nearest neighbors is other important measure of the population density and its dynamics. Parameters of the model can be tuned in such a way, that the shape of both distributions in a steady phase coincides with that shape observed in a natural population, which helps to understand the factors leading to particular momentary distribution of both parameters (size and distance) in the population. From this point of view, the model can predict how both distributions can further develop from certain state depending on particular combination of factors

NUMERICAL SIMULATION OF DYNAMICS OF BLOCK MEDIA BY MOVABLE LATTICE AND MOVABLE AUTOMATA METHODS

Two versions of modified Burridge-Knopoff model including state dependent friction, elastic force and thermal conductivity are derived. The friction model describes a velocity weakening of friction and elasticity between moving blocks and an increase of both static friction and rigidity during stick periods as well their weakening during motion. It provides a simplified but qualitatively correct behavior including the transition from smooth sliding to stick-slip behavior, which is often observed in various tribological and tectonic systems. Attractor properties of the model dynamics is studied also. The alternative versions of the model are proposed which apply a simulation of the motion of interacting elastically connected mesh elements and motion of relatively large solid blocks, utilizing technique of the movable cellular automata. First version of the model was already basically studied before. Its advanced version here involves all components of the real system: state-depending friction and changeable rigidity, as well as heat production and thermal conductivity. Model based on the movable automata also involves the components included into traditional lattice model. It has its own ad-vantages and disadvantages which are also discussed in the paper

Root Hair Adhesion in Posidonia oceanica (L.) Delile Seedlings: A Numerical Modelling Approach

Animals and plants use adhesion to move, to anchor to a substrate, or to disperse seeds and fruits. Some plants developed a root pad as a common strategy to adhere to consolidated substrates. In the marine environment, the seagrass Posidonia oceanica attaches fi rmly to consolidated substrates via adhesive root hairs, forming a pad structure. We used novel morphological and ultrastructural data to develop a numerical model to study the dynamics of root hair adhesion during contact formation on rough consolidated substrates for this species. Morphological analysis, conducted using Scanning Electron Microscope, highlighted the role of root hair branching in pad formation. Transmission Electron Microscope microscopy allowed us to identify a glue-like substance at the pad/ substrate interface. The numerical model highlighted the role played by the cell wall ’ s elasticity in pad formation and its importance in guaranteeing a fi rm adhesion. Furthermore, the effectiveness of these mechanisms was assessed at different simulated roughness levels. Increasing knowledge on the adhesion mechanism of seagrass to consolidated substrates could be pivotal in developing advanced seedling-based restoration protocols. The fi ndings of this study could contribute to restoration activities planned to contrast seagrass regression. Transplanting initiatives using seedlings can now better address the search for suitable and low-impact ways to fi x germinated plants to the substrate

Influence of tangential displacement on the adhesion strength of a contact between a parabolic profile and an elastic half-space

The adhesion strength of a contact between a rotationally symmetric indenter and an elastic half-space is analysed analytically and numerically using an extension of the method of dimensionality reduction for superimposed normal/tangential adhesive contacts. In particular, the dependence of the critical adhesion force on the simultaneously applied tangential force is obtained and the relevant dimensionless parameters of the problem are identified. The fracture criterion used coincides with that suggested by Johnson. In this paper, it is used to develop a method that is applicable straightforwardly to adhesive contacts of arbitrary bodies of revolution with compact contact area

Influence of tangential displacement on the adhesion strength of a contact between a parabolic profile and an elastic half-space

The adhesion strength of a contact between a rotationally symmetric indenter and an elastic half-space is analysed analytically and numerically using an extension of the method of dimensionality reduction for superimposed normal/tangential adhesive contacts. In particular, the dependence of the critical adhesion force on the simultaneously applied tangential force is obtained and the relevant dimensionless parameters of the problem are identified. The fracture criterion used coincides with that suggested by Johnson. In this paper, it is used to develop a method that is applicable straightforwardly to adhesive contacts of arbitrary bodies of revolution with compact contact area

Manifold Topology Divergence: a Framework for Comparing Data Manifolds

We develop a framework for comparing data manifolds, aimed, in particular, towards the evaluation of deep generative models. We describe a novel tool, Cross-Barcode(P,Q), that, given a pair of distributions in a high-dimensional space, tracks multiscale topology spacial discrepancies between manifolds on which the distributions are concentrated. Based on the Cross-Barcode, we introduce the Manifold Topology Divergence score (MTop-Divergence) and apply it to assess the performance of deep generative models in various domains: images, 3D-shapes, time-series, and on different datasets: MNIST, Fashion MNIST, SVHN, CIFAR10, FFHQ, chest X-ray images, market stock data, ShapeNet. We demonstrate that the MTop-Divergence accurately detects various degrees of mode-dropping, intra-mode collapse, mode invention, and image disturbance. Our algorithm scales well (essentially linearly) with the increase of the dimension of the ambient high-dimensional space. It is one of the first TDA-based practical methodologies that can be applied universally to datasets of different sizes and dimensions, including the ones on which the most recent GANs in the visual domain are trained. The proposed method is domain agnostic and does not rely on pre-trained networks