A mathematical framework for contact detection between quadric and superquadric surfaces

The calculation of the minimum distance between surfaces plays an important role in computational mechanics, namely, in the study of constrained multibody systems where contact forces take part. In this paper, a general rigid contact detection methodology for non-conformal bodies, described by ellipsoidal and superellipsoidal surfaces, is presented. The mathematical framework relies on simple algebraic and differential geometry, vector calculus, and on the C2 continuous implicit representations of the surfaces. The proposed methodology establishes a set of collinear and orthogonal constraints between vectors defining the contacting surfaces that, allied with loci constraints, which are specific to the type of surface being used, formulate the contact problem. This set of non-linear equations is solved numerically with the Newton-Raphson method with Jacobian matrices calculated analytically. The method outputs the coordinates of the pair of points with common normal vector directions and, consequently, the minimum distance between both surfaces. Contrary to other contact detection methodologies, the proposed mathematical framework does not rely on polygonal-based geometries neither on complex non-linear optimization formulations. Furthermore, the methodology is extendable to other surfaces that are (strictly) convex, interact in a non-conformal fashion, present an implicit representation, and that are at least C2 continuous. Two distinct methods for calculating the tangent and binormal vectors to the implicit surfaces are introduced: (i) a method based on the Householder reflection matrix; and (ii) a method based on a square plate rotation mechanism. The first provides a base of three orthogonal vectors, in which one of them is collinear to the surface normal. For the latter, it is shown that, by means of an analogy to the referred mechanism, at least two non-collinear vectors to the normal vector can be determined. Complementarily, several mathematical and computational aspects, regarding the rigid contact detection methodology, are described. The proposed methodology is applied to several case tests involving the contact between different (super)ellipsoidal contact pairs. Numerical results show that the implemented methodology is highly efficient and accurate for ellipsoids and superellipsoids.Fundação para a Ciência e a Tecnologia (FCT

Modeling of the condyle elements within a biomechanical knee model

The development of a computational multibody knee model able to capture some of the fundamental properties of the human knee articulation is presented. This desideratum is reached by including the kinetics of the real knee articulation. The research question is whether an accurate modeling of the condyle contact in the knee will lead to reproduction of the complex combination of flexion/extension, abduction/adduction and tibial rotation ob-served in the real knee? The model is composed by two anatomic segments, the tibia and the femur, whose characteristics are functions of the geometric and anatomic properties of the real bones. The biomechanical model characterization is developed under the framework of multibody systems methodologies using Cartesian coordinates. The type of approach used in the proposed knee model is the joint surface contact conditions between ellipsoids, represent-ing the two femoral condyles, and points, representing the tibial plateau and the menisci. These elements are closely fitted to the actual knee geometry. This task is undertaken by con-sidering a parameter optimization process to replicate experimental data published in the lit-erature, namely that by Lafortune and his co-workers in 1992. Then, kinematic data in the form of flexion/extension patterns are imposed on the model corresponding to the stance phase of the human gait. From the results obtained, by performing several computational simulations, it can be observed that the knee model approximates the average secondary mo-tion patterns observed in the literature. Because the literature reports considerable inter-individual differences in the secondary motion patterns, the knee model presented here is also used to check whether it is possible to reproduce the observed differences with reasonable variations of bone shape parameters. This task is accomplished by a parameter study, in which the main variables that define the geometry of condyles are taken into account. It was observed that the data reveal a difference in secondary kinematics of the knee in flexion ver-sus extension. The likely explanation for this fact is the elastic component of the secondary motions created by the combination of joint forces and soft tissue deformations. The proposed knee model is, therefore, used to investigate whether this observed behavior can be explained by reasonable elastic deformations of the points representing the menisci in the model.Fundação para a Ciência e a Tecnologia (FCT) - PROPAFE – Design and Development of a Patello-Femoral Prosthesis (PTDC/EME-PME/67687/2006), DACHOR - Multibody Dynamics and Control of Hybrid Active Orthoses MIT-Pt/BSHHMS/0042/2008, BIOJOINTS - Development of advanced biological joint models for human locomotion biomechanics (PTDC/EME-PME/099764/2008)

Comparison and Implementation of a Rigid and a Flexible Multibody Planetary Gearbox Model

We propose algorithms for developing (1) a rigid (constrained) and (2) a flexible planetary gearbox model. The two methods are compared against each other and advantages/disadvantages of each method are discussed. The rigid model (1) has gear tooth reaction forces expressed by Lagrange multipliers. The flexible approach (2) is being compared with the gear tooth forces from the rigid approach, first without damping and second the influence of damping is examined. Variable stiffness as a function of base circle arc length is implemented in the flexible approach such that it handles the realistic switch between one and two gear teeth in mesh. The final results are from modelling the planetary gearbox in a 500 kW wind turbine which we also described in Jørgensen et.al (2013)

Drought Impact Is Alleviated in Sugar Beets (Beta vulgaris L.) by Foliar Application of Fullerenol Nanoparticles

Over the past few years, significant efforts have been made to decrease the effects of drought stress on plant productivity and quality. We propose that fullerenol nanoparticles (FNPs, molecular formula C-60(OH)(24)) may help alleviate drought stress by serving as an additional intercellular water supply. Specifically, FNPs are able to penetrate plant leaf and root tissues, where they bind water in various cell compartments. This hydroscopic activity suggests that FNPs could be beneficial in plants. The aim of the present study was to analyse the influence of FNPs on sugar beet plants exposed to drought stress. Our results indicate that intracellular water metabolism can be modified by foliar application of FNPs in drought exposed plants. Drought stress induced a significant increase in the compatible osmolyte proline in both the leaves and roots of control plants, but not in FNP treated plants. These results indicate that FNPs could act as intracellular binders of water, creating an additional water reserve, and enabling adaptation to drought stress. Moreover, analysis of plant antioxidant enzyme activities (CAT, APx and GPx), MDA and GSH content indicate that fullerenol foliar application could have some beneficial effect on alleviating oxidative effects of drought stress, depending on the concentration of nanoparticles applied. Although further studies are necessary to elucidate the biochemical impact of FNPs on plants; the present results could directly impact agricultural practice, where available water supplies are often a limiting factor in plant bioproductivity

Systems Biology by the Rules: Hybrid Intelligent Systems for Pathway Modeling and Discovery

Background: Expert knowledge in journal articles is an important source of data for reconstructing biological pathways and creating new hypotheses. An important need for medical research is to integrate this data with high throughput sources to build useful models that span several scales. Researchers traditionally use mental models of pathways to integrate information and development new hypotheses. Unfortunately, the amount of information is often overwhelming and these are inadequate for predicting the dynamic response of complex pathways. Hierarchical computational models that allow exploration of semi-quantitative dynamics are useful systems biology tools for theoreticians, experimentalists and clinicians and may provide a means for cross-communication. Results: A novel approach for biological pathway modeling based on hybrid intelligent systems or soft computing technologies is presented here. Intelligent hybrid systems, which refers to several related computing methods such as fuzzy logic, neural nets, genetic algorithms, and statistical analysis, has become ubiquitous in engineering applications for complex control system modeling and design. Biological pathways may be considered to be complex control systems, which medicine tries to manipulate to achieve desired results. Thus, hybrid intelligent systems may provide a useful tool for modeling biological system dynamics and computational exploration of new drug targets. A new modeling approach based on these methods is presented in the context of hedgehog regulation of the cell cycle in granule cells. Code and input files can be found at the Bionet website: www.chip.ord/~wbosl/Software/Bionet. Conclusion: This paper presents the algorithmic methods needed for modeling complicated biochemical dynamics using rule-based models to represent expert knowledge in the context of cell cycle regulation and tumor growth. A notable feature of this modeling approach is that it allows biologists to build complex models from their knowledge base without the need to translate that knowledge into mathematical form. Dynamics on several levels, from molecular pathways to tissue growth, are seamlessly integrated. A number of common network motifs are examined and used to build a model of hedgehog regulation of the cell cycle in cerebellar neurons, which is believed to play a key role in the etiology of medulloblastoma, a devastating childhood brain cancer

On the contact detection for contact-impact analysis in multibody systems

One of the most important and complex parts of the simulation of multibody systems with contact-impact involves the detection of the precise instant of impact. In general, the periods of contact are very small and, therefore, the selection of the time step for the integration of the time derivatives of the state variables plays a crucial role in the dynamics of multibody systems. The conservative approach is to use very small time steps throughout the analysis. However, this solution is not efficient from the computational view point. When variable time step integration algorithms are used and the pre-impact dynamics does not involve high-frequencies the integration algorithms may use larger time steps and the contact between two surfaces may start with initial penetrations that are artificially high. This fact leads either to a stall of the integration algorithm or to contact forces that are physically impossible which, in turn, lead to post-impact dynamics that is unrelated to the physical problem. The main purpose of this work is to present a general and comprehensive approach to automatically adjust the time step, in variable time step integration algorithms, in the vicinity of contact of multibody systems. The proposed methodology ensures that for any impact in a multibody system the time step of the integration is such that any initial penetration is below any prescribed threshold. In the case of the start of contact, and after a time step is complete, the numerical error control of the selected integration algorithm is forced to handle the physical criteria to accept/reject time steps in equal terms with the numerical error control that it normally uses. The main features of this approach are the simplicity of its computational implementation, its good computational efficiency and its ability to deal with the transitions between non contact and contact situations in multibody dynamics. A demonstration case provides the results that support the discussion and show the validity of the proposed methodology.Fundação para a Ciência e a Tecnologia (FCT

A discrete-Time feedback controller for containerized cloud applications

Modern Web applications exploit Cloud infrastructures to scale their resources and cope with sudden changes in the workload. While the state of practice is to focus on dynamically adding and removing virtual machines, we advocate that there are strong benefits in containerizing the applications and in scaling the containers. In this paper we present an autoscaling technique that allows containerized applications to scale their resources both at the virtual machine (VM) level and at the container level. Furthermore, applications can combine this infrastructural adaptation with platform-level adaptation. The autoscaling is made possible by our planner, which consists of a grey-box discrete-Time feedback controller. The work has been validated using two application benchmarks deployed to Amazon EC2. Our experiments show that our planner outperforms Amazon's AutoScaling by 78% on average without containers; and that the introduction of containers allows us to improve by yet another 46% on average