Visualization of Input Parameters for Stream and Pathline Seeding

Takagi-Sugeno (TS) fuzzy models have been the popular choice for multi-model based nonlinear system identification for controller design. However, the interpretation of the model from a dynamical systems point of view is still unclear. In this paper, we investigate the interpretation of the TS fuzzy models in terms of local dynamics of nonlinear systems in state space. The investigation is based on the comparison between the constant-affine recursive i/o equation and constant-affine state space representations. We show that the true local dynamics is not identifiable by TS fuzzy models by analysis and example. For the identification of constant-affine state space models, a subspace identification algorithm is proposed to identify the true local dynamics with zero initial conditions.

Commentary to “pharmacokinetics from a dynamical systems point of view”

The 120-year old so-called Painleve paradox involves the loss of determinism in models of planar rigid bodies in point contact with a rigid surface, subject to Coulomb-like dry friction. The phenomenon occurs due to coupling between normal and rotational degrees-of-freedom such that the effective normal force becomes attractive rather than repulsive. Despite a rich literature, the forward evolution problem remains unsolved other than in certain restricted cases in 2D with single contact points. Various practical consequences of the theory are revisited, including models for robotic manipulators, and the strange behaviour of chalk when pushed rather than dragged across a blackboard. Reviewing recent theory, a general formulation is proposed, including a Poisson or energetic impact law. The general problem in 2D with a single point of contact is discussed and cases or inconsistency or indeterminacy enumerated. Strategies to resolve the paradox via contact regularisation are discussed from a dynamical systems point of view. By passing to the infinite stiffness limit and allowing impact without collision, inconsistent and indeterminate cases are shown to be resolvable for all open sets of conditions. However, two unavoidable ambiguities that can be reached in finite time are discussed in detail, so called dynamic jam and reverse chatter. A partial review is given of 2D cases with two points of contact showing how a greater complexity of inconsistency and indeterminacy can arise. Extension to fully three-dimensional analysis is briefly considered and shown to lead to further possible singularities. In conclusion, the ubiquity of the Painleve paradox is highlighted and open problems are discussed.

In their pioneering work BUSSE & HEIKES [2] looked at the classical Benard problem in a rotating frame. They observed rolls with a certain axial direction which seem to be stable, ie they remain unchanged for long periods of time, but suddenly the behavior changes: new rolls appear which are rotated with respect to the original rolls by approximately 60 degrees. GUCKENHEIMER & HOLMES [15] looked at the Busse-Heikes problem from a theoretical point of view. They derived a three dimensional ODE exhibiting heteroclinic cycles. Thereafter many papers have dealt with various aspects of cycles: existence, stability, bifurcations and structural stability under certain settings: [1, 3, 4, 5, 7, 8, 16, 17, 18, 20, 21, 22, 25, 23, 24, 26, 27, 28, 29]. Due to the fact that solutions which pass near steady states remain there for a long time heteroclinic cycles serve as a model for metastable behavior. We see such a metastable behavior if we look at the polarity reversals of the magnetic field of the Earth, see for example GHIL & CHILDRESS [13]. Since the origin of the magnetic field and the mechanism of its reversals are unknown we try to look at it from a dynamical systems point of view and ask ourselves whether there are heteroclinic cycles in this problem. Here, we only look at the fluid mechanical part and not at full MHD-equations. In this paper we emphasize the role of rotation and the question what happens to heteroclinic cycles in the presence of rotations. Of course this approach dictates to look at the non rotating case first and treat the rotating case as a perturbation of the non rotating one. It is not clear whether such a approach is reasonable for studying the Earth’ field but on the other hand numerical computations indicate that the region of validity of the results which are presented here exceeds the marginal speeds of rotation allowed by the usual perturbation methods.

Flow invariant subspaces for lattice dynamical systems by F. Antoneli, A. P. S. Dias, M. Golubitsky, and Y. Wang Waves in extended systems: From low- to high-dimensional behavior by O. Batiste and E. Knobloch Mixed mode oscillations due to the generalized Canard phenomenon by M. Brons, M. Krupa, and M. Wechselberger Bioremediation of waste in a porous medium by C. Chen and J. Chadam Bifurcations of gyroscopic systems near a 0: 1 resonance by R. J. McDonald, N. S. Namachchivaya, and W. Nagata High dimensional data clustering from a dynamical systems point of view by J. Wu Computation of limit cycles-The second part of Hilbert's 16th problem by P. Yu.

Hysteresis bifurcation and application to delayed FitzHugh-Nagumo neural systems

In the present paper, we study a new kind of p-adic measures for q + 1-state Potts model, called p-adic quasi Gibbs measure. For such a model, we derive a recursive relations with respect to boundary conditions. Note that we consider two mode of interactions: ferromagnetic and antiferromagnetic. In both cases, we investigate a phase transition phenomena from the associated dynamical system point of view. Namely, using the derived recursive relations we define a fractional p-adic dynamical system. In ferromagnetic case, we establish that if q is divisible by p, then such a dynamical system has two repelling and one attractive fixed points. We find basin of attraction of the fixed point. This allows us to describe all solutions of the nonlinear recursive equations. Moreover, in that case there exists the strong phase transition. If q is not divisible by p, then the fixed points are neutral, and this yields that the existence of the quasi phase transition. In antiferromagnetic case, there are two attractive fixed points, and we find basins of attraction of both fixed points, and describe solutions of the nonlinear recursive equation. In this case, we prove the existence of a quasi phase transition.

We investigate the effect and the impact of predator-prey interactions, diffusivity and chemotaxis on the ability of survival of multiple consumer levels in a predator-prey microbial food chain. We aim at answering the question of how many consumer levels can survive from a dynamical system point of view. To solve this standing issue on food-chain length, first we construct a chemotactic food chain model. A priori bounds of the steady state populations are obtained. Then under certain sufficient conditions combining the effect of conversion efficiency, diffusivity and chemotaxis parameters, we derive the co-survival of all consumer levels, thus obtaining the food chain length of our model. Numerical simulations not only confirm our theoretical results, but also demonstrate the impact of conversion efficiency, diffusivity and chemotaxis behavior on the survival and stability of various consumer levels.

We construct stable manifolds for a class of singular evolution equations including the steady Boltzmann equation, establishing in the process exponential decay of associated kinetic shock and boundary layers to their limiting equilibrium states. Our analysis is from a classical dynamical systems point of view, but with a number of interesting modifications to accomodate ill-posedness with respect to the Cauchy problem of the underlying evolution equation.

Predicting foreign exchange rates and stock market indices have been a well researched topic in the field of financial engineering. However, most methods suffer from serious drawback due to the inherent uncertainty in the data acquisition process. Here, we have analyzed the very nature of the time series data from a pure dynamic system point of view and explored the deterministic chaotic characteristic in it. In this research, the concept of chaos has been analyzed thoroughly and the relationships among chaos, stability and order have been explained with respect to the concept of time. A method of predicting time series data based on deterministic dynamically system has been presented in this monograph. The present research revolves around the concepts of embedding and fuzzy reconstruction. In this regard, the necessary and sufficient condition for this reconstruction of the state space of the dynamic system in a multi-dimensional Euclidean space has been substantiated in accordance to Theory of embedding. Finally, a fuzzy reconstruction method based on fuzzy multiple regression analysis method has been used to predict the foreign exchange rates with accuracy.

Most of us are not familiar with the concept that an internal combustion (IC) engine is working on a four-stroke six-event principle. The six events are suction, compression, combustion, expansion, blow-down and exhaust. However, the expansion and blow-down happen in the power stroke and they can be clubbed together. Therefore, we can say that an engine, whether diesel or gasoline, is working on four-stroke five-event principle. The purpose of this chapter is to make the reader to familiarize with the complexities involved in the working of a four-stroke engine. The five events which are completed in four strokes are: suction, compression, combustion, expansion and exhaust. Application of computational fluid dynamics (CFD) principles for each process mentioned above is a challenging job. The difficulty in understanding the working of an IC engine is due to the fact that we cannot see what is happening inside the cylinder piston arrangement. All that is described in textbooks is based on our knowledge gained over a period of time by conducting experiments. There is no doubt in saying that “seeing is believing”. As it is next to impossible to have a complete experimental flow visualization, nowadays CFD comes in handy to have theoretical flow visualization. Well-developed software is available for the simulation in 3D geometries. In this chapter, we explain step-by-step the details required for the CFD simulation of various processes in an IC engine. Extensive results obtained over a period of 20 years of research by the application of CFD in analysing the flow in engines are comprehensively presented and discussed. CFD can be very well applied for analysing any particular process. It can also be used for the modification of the existing engine design or can also be employed for a new design of an engine. It is hoped that readers may be benefitted in understanding the application of CFD for fluid flow analysis and engine design by reading this chapter. Therefore, the main aim of this chapter is to make the reader appreciate how exactly CFD can be applied for design of an engine. As it is application oriented, we are not going deep into the equations, modelling, etc. A number of case studies are presented and discussed.

As a leading journal for members of the indoor environment community, Indoor Air strives for excellence in all published papers. For experimental findings or investigations with human subjects, measurement uncertainties and statistical significance of results are routinely reported. The editors of Indoor Air also wish to promote papers using Computational Fluid Dynamics (CFD) as a research tool. For such investigations, there are a number of corresponding measures that qualify the results and ensure quality. For that reason, we have been asked to suggest the minimum amount of information that should be included in CFD related papers submitted to the journal. Naturally, such suggestions will be biased by our personal experience, but we believe that we have covered the major topics of concern. Full assessment of the quality of a given CFD article requires 1) Adequate information pertinent to the governing equations and numerical methods, 2) justified estimates of the expected accuracy of the numerical results. If either of these is omitted, excellent studies may be considered poor and vice versa. Specifically, to ensure that all papers in Indoor Air are of high quality, our suggestion to the editors (and reviewers) is that CFD related articles contain the following information: The description of the CFD code, boundary/initial conditions, and turbulence model should be detailed enough so that the calculations can be reproduced by another investigator. Existing CFD codes should be fully cited. Topology and size of the computational grid should be described. The choice of differencing scheme should be described. Use of differencing schemes that are first order accurate (in space or time) is discouraged and solid justification should be provided if a first order scheme is used. Influence from grid-dependency should be addressed and, at a minimum, a qualitative estimate of the expected deviations from the exact solution to the governing equations must be given. The range of y+ should be stated and justified in accordance with the employed turbulence model. If possible, calculations should be validated against measurement or standard test cases of a similar problem. For researches, who routinely impose quality control in their work, it will be straightforward to comply with the above points. We do realize that, for the majority of CFD studies, significant human and computational efforts are necessary to meet the requirements. Nevertheless, we believe that the additional effort is more than compensated by the fact that the article (if accepted) is published in an archival journal that sets standards for CFD studies, therefore increasing the importance of the article. For more details on quality control for CFD calculations, see the paper by Sørensen and Nielsen (2003) in this issue of Indoor Air, as well as references herein. We strongly recommend the cited publication by the European Research Community on Flow, Turbulence and Combustion (ERCOFTAC), giving a valuable set of guidelines for CFD practitioners (Casey and Wintergerste, 2000).

The study of fluid behaviors has been a challenging topic. Flow visualization enables us to visually acquire qualitative and quantitative flow information. There exist various software tools performing different flow visualization tasks. However, we lack tools that help students learn important flow field concepts. In this paper, we present a visualization app, named FlowVisual which runs on iOS devices, to illustrate basic flow field concepts in 3D. In order to meet a comprehensive learning goal for students, we integrate a number of techniques into FlowVisual design, including field-line tracing, field-line comparison, critical point detection and classification, template-based seeding, and surface visualization. We evaluate and demonstrate the effectiveness of FlowVisual by conducting a formal user study including an introduction and training session, an auto-grading test, and a post-questionnaire survey.

Recently, a method for numerical reproduction of measured irregular wave events has been developed. The measured motion of the wave maker flaps defines the wave kinematics at the boundary of the numerical simulation in order to generate the waves. When such data are not available, the control signal of the wave maker can, instead, be generated from a given free surface elevation following the same procedure as in model tests. This procedure is applied to a model test case with extreme irregular wave events and resulting nonlinear global wave loads on a vertical cylinder, focusing on higher-order ringing excitation. The purpose of the investigation is twofold: (1) to validate the wave reconstruction procedure and (2) to validate the resulting computational fluid dynamics (CFD) ringing loads with the given waves. In order to better understand the frequency content in the CFD-generated loads, wavelet analysis as well as the response of a single degree-of-freedom (SDOF) oscillator is examined and compared with the corresponding results for the third-order wave forcing based on the MacCamy–Fuchs (MF) and Faltinsen, Newman, Vinje (FNV) formulations. The results show generally good agreement between CFD and experiment both in the waves and in the loads; discrepancies found in the loads mainly originate from corresponding uncertainties in the wave reconstruction. Wave breaking may be one source of uncertainty. The MF + FNV formulation showed reasonable prediction of the maximum responses of an SDOF oscillator, but could not capture the loads well at all of the important frequencies.

Computational Fluid Dynamics (CFD) is an important research field with a broad spectrum, requiring a close interplay between mathematical modeling, numerical methods, software development, and high performance computing. Programming CFD applications is an inherently difficult task due to many factors related to numerics and software. For modern CFD applications, use of parallel computers is a must, which makes the CFD code development even more challenging. Rapid and flexible programming of a parallel CFD application calls for re-usable serial and parallel software components plus a modular overall parallel framework that allows an easy coupling between different components. Moreover, more attention needs to be put on securing the performance of the software components. This minisymposium thus attempts to shed some light into the recent developments in respect of CFD-related numerical methods, programming techniques and software libraries.