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The focus of the project is to validate the fluid model with different flooring materials and the measurements of an instrument to test flooring materials and its force attenuating capabilities using mathematical models to describe the signature and coefficients of the floor.As a part of improving the knowledge about the linear dynamics of vibrations involved during the sudden impact caused on hip bones of elderly people during fall. The project initiated in January 2017 and end date was set to May 2017.The main contribution of the present work focuses on the development of a mathematical fluid model for floors. The aim of the thesis was to analyze, compare different floor materials and to study the linear dynamics of falling impacts on floors. The impact of the hammer during a fall is captured by an accelerometer and response is collected using a picoscope. The collected data was analyzed using matlab least square method which is coded as per the fluid model.The finding from this thesis showed that the fluid model works with a more elastic model but it doesn't work for rigid materials like wood. The importance of parameters like velocity, mass, energy loss and other coefficients of a floor which influences the model during the impact of falling on floors were identified and a standardized testing method was set.

Este trabalho apresenta conceitos e procedimentos que devem ser considerados na análise dinâmica de fundações de máquinas. São discutidas as abordagens e os métodos de cálculo à disposição dos engenheiros, assim como os fatores que influenciam a escolha e o desenvolvimento de modelos matemáticos adequados. Três tipos diferentes de fundação (fundações em bloco rígido, fundações de martelos e fundações aporticadas) são examinados, e são utilizados exemplos para demonstrar a eficácia de técnicas simples de modelagem. / This paper presents concepts and procedures necessary to the dynamic analysis of machine foundations. Analytical approaches available to the designer, and factors which influence the choice and development of a suitable analytical model are discussed. Three different foundations (block foundations, hammer foundations and framed foundations) are examined and examples are given to demonstrate the effectiveness of simple modeling techniques.

Learning is a mechanism intrinsic to all sentient biological systems. Despite the diverse range of paradigms that exist, it appears that an artificial system has yet to be developed that can emulate learning with a comparable degree of accuracy or efficiency to the human brain. With the development of new approaches comes the opportunity to reduce this disparity in performance. A model presented by Janson and Marsden [arXiv:1107.0674 (2011)] (Memory foam model) redefines the critical features that an intelligent system should demonstrate. Rather than focussing on the topological constraints of the rigid neuron structure, the emphasis is placed on the on-line, unsupervised, classification, retention and recognition of stimuli. In contrast to traditional AI approaches, the system s memory is not plagued by spurious attractors or the curse of dimensionality. The ability to continuously learn, whilst simultaneously recognising aspects of a stimuli ensures that this model more closely embodies the operations occurring in the brain than many other AI approaches. Here we consider the pertinent deficiencies of classical artificial learning models before introducing and developing this memory foam self-shaping system. As this model is relatively new, its limitations are not yet apparent. These must be established by testing the model in various complex environments. Here we consider its ability to learn and recognize the RGB colours composing cartoons as observed via a web-camera. The self-shaping vector field of the system is shown to adjust its composition to reflect the distribution of three-dimensional inputs. The model builds a memory of its experiences and is shown to recognize unfamiliar colours by locating the most appropriate class with which to associate a stimuli. In addition, we discuss a method to map a three-dimensional RGB input onto a line spectrum of colours. The corresponding reduction of the models dimensions is shown to dramatically improve computational speed, however, the model is then restricted to a much smaller set of representable colours. This models prototype offers a gradient description of recognition, it is evident that a more complex, non-linear alternative may be used to better characterize the classes of the system. It is postulated that non-linear attractors may be utilized to convey the concept of hierarchy that relates the different classes of the system. We relate the dynamics of the van der Pol oscillator to this plastic self-shaping system, first demonstrating the recognition of stimuli with limit cycle trajectories. The location and frequency of each cycle is dependent on the topology of the systems energy potential. For a one-dimensional stimuli the dynamics are restricted to the cycle, the extension of the model to an N dimensional stimuli is approached via the coupling of N oscillators. Here we study systems of up to three mutually coupled oscillators and relate limit cycles, fixed points and quasi-periodic orbits to the recognition of stimuli.

In this thesis we investigate the mechanisms underlying the generation of abnormal EEG rhythms in epilepsy, which is a crucial step towards better treatment of this disorder in the future. To this end, macroscopic scale mathematical models of the interactions between neuronal populations are examined. In particular, the role of interactions between neural masses that are spatially distributed in cortical networks are explored. In addition, two other important aspects of the modelling process are addressed, namely the conversion of macroscopic model variables into EEG output and the comparison of multivariate, spatio-temporal data. For the latter, we adopt a vectorisation of the correlation matrix of windowed data and subsequent comparison of data by vector distance measures. Our modelling studies indicate that excitatory connectivity between neural masses facilitates self-organised dynamics. In particular, we report for the first time the production of complex rhythmic transients and the generation of intermittent periods of 'abnormal' rhythmic activity in two different models of epileptogenic tissue. These models therefore provide novel accounts of the spontaneous, intermittent transition between normal and pathological rhythms in primarily generalised epilepsies and the evocation of complex, self-terminating, spatio-temporal dynamics by brief stimulation in focal epilepsies. Two key properties of these models are excitability at the macroscopic level and the presence of spatial heterogeneities. The identification of neural mass excitability as an important processes in spatially extended brain networks is a step towards uncovering the multi-scale nature of the pathological mechanisms of epilepsy. A direct consequence of this work is therefore that novel experimental investigations are proposed, which in itself is a validation of our modelling approach. In addition, new considerations regarding the nature of dynamical systems as applied to problems of transitions between rhythmic states are proposed and will prompt future investigations of complex transients in spatio-temporal excitable systems.

The Ph.D. Thesis “Strong mixing measures and invariant sets in linear dynamics” has three differenced parts. Chapter 0 introduces the notation, definitions and the basic results that will be needed troughout the thesis. There is a first part consisting of Chapters 1 and 2, where we study the relation between the Frequent Hypercyclicity Criterion and the existence of strongly-mixing Borel probability measures. A third chapter, where we focus our attention on frequent hypercyclicity for translation C0-semigroups, and the last part corresponding to Chapters 4 and 5, where we study dynamical properties satisfied by autonomous and non-autonomous linear dynamical systems on certain invariant sets. In what follows, we give a brief description of each chapter: In Chapter 1, we construct strongly mixing Borel probability T-invariant measures with full support for operators on F-spaces which satisfy the Frequent Hypercyclicity Criterion. Moreover, we provide examples of operators that verify this criterion and we also show that this result can be improved in the case of chaotic unilateral backward shifts. The contents of this chapter have been published in [88] and [12]. In Chapter 2, we show that the Frequent Hypercyclicity Criterion for C0- semigroups, which was given by Mangino and Peris in [82], ensures the existence of invariant strongly mixing measures with full support. We will provide several examples, that range from birth-and-death models to the Black-Scholes equation, which illustrate these results. All the results of this chapter have been published in [86]. In Chapter 3, we focus our attention on one of the most important tests C0-semigroups, the translation semigroup. Inspired in the work of Bayart and Ruzsa in [22], where they characterize frequent hypercyclicity of weighted backward shifts we characterize frequently hypercyclic translation C0-semigroups on C ρ 0 (R) and L ρ p(R). Moreover, we first review some known results on the dynamics of the translation C0-semigroups. Later we state and prove a characterization of frequent hypercyclicity for weighted pseudo shifts in terms of the weights that will be used later to obtain a characterization of frequent hypercyclicity for translation C0-semigroups on C ρ 0 (R). Finally we study the case of L ρ p(R). We will also establish an analogy between the study of frequent hypercyclicity for the translation C0-semigroup in L ρ p(R) and the corresponding one for backward shifts on weighted sequence spaces. The contents of this chapter have been included in [81]. Chapter 4 is devoted to study hypercyclicity, Devaney chaos, topological mixing properties and strong mixing in the measure-theoretic sense for operators on topological vector spaces with invariant sets. More precisely, we establish links between the fact of satisfying any of our dynamical properties on certain invariant sets, and the corresponding property on the closed linear span of the invariant set, or on the union of the invariant sets. Viceversa, we give conditions on the operator (or C0-semigroup) to ensure that, when restricted to the invariant set, it satisfies certain dynamical property. Particular attention is given to the case of positive operators and semigroups on lattices, and the (invariant) positive cone. The contents of this chapter have been published in [85]. In the last chapter, motivated by the work of Balibrea and Oprocha [4], where they obtained several results about weak mixing and chaos for nonautonomous discrete systems on compact sets, we study mixing properties for nonautonomous linear dynamical systems that are induced by the corresponding dynamics on certain invariant sets. All the results of this chapter have been published in [87]. / Murillo Arcila, M. (2015). Strong mixing measures and invariant sets in linear dynamics [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/48519 / TESIS

The final thesis „Explicit and Implicit methods in nonlinear dynamics“ deals with the issue of geometrical and physical nonlinear analysis of structures exposed to seismic loading by the methods of direct integration of equations of motion. Solution by the explicit and the implicit method is compared for three material models. While the differences between the results of the explicit method and the implicit Newmark method are small as expected, the differences are substantial between the results of different material models. However, these differences are explained and they are in full concordance with the theoretical assumptions for the pertinent material models. The conclusion of the final thesis is check of correctness of the results of the new module of the program system RFEM for both tested numerical methods and all three analyzed material models. (linear elastic, plastic Drucker-Prager and the Mazars damage model). With sufficient precision of results, both explicit and implicit numerical methods showed to be suitable for seismic analysis. The implicit method can provide several times faster calculation than the explicit one, but the determination of the optimal time step is problematic and time consuming, so the suitability of use of both methods for seismic analysis is comparable.

Dispersed particle flows occur in many industrial, biological and geophysical applications. The knowledge of how these flow behave can for example lead to improved material processes, better predictions of vascular diseases or more accurate climate models. These particle flows have certain properties that depend on single particle motion in fluid flows and especially how they are distributed both in terms of spatial position and, if they are non-spherical, in terms of orientation. Much is already known about the motion of perfectly spherical particles. For non-spherical particles, apart from their translation, it is important to know the the rotational motion due to local velocity gradients. Such studies have usually been restricted by the assumption that particles are extremely small compared to fluid length scales. In this limit, both inertia of the particle and inertia of the fluid can be neglected for the particle motion. This thesis gives a complete picture of how a spheroidal particle (a particle described by a rotation of an ellipse around one of its principal axes) behave in a linear shear flow when including both fluid and particle inertia, using numerical simulations. It is observed that this very simple problem possess very interesting dynamical behavior with different stable rotational states appearing as a competition between the two types of inertia. The effect of particle inertia leads to a rotation where the mass of the particle is concentrated as far away from the rotational axis as possible, i.e.\ a rotation around the minor axis. Typically, the effect of fluid inertia is instead that it tries to force the particle in a rotation where the streamlines of the flow remain as straight as possible. The first effect of fluid inertia is thus the opposite of particle inertia and instead leads to a particle rotation around the major axis. Depending on rotational state, the particles also affect the apparent viscosity of the particle dispersion. The different transitions and bifurcations between rotational states are characterized in terms of non-linear dynamics, which reveal that the particle motion probably can be described by some reduced model. The results in this theses provides fundamental knowledge and is necessary to understand flows containing non-spherical particles. / Flöden med dispergerade partiklar påträffas i många industriella, biologiska och geofysiska tillämpningar. Kunskap om hur dessa flöden beter sig kan bl.a. leda till förbättrade materialprocesser, bättre förutsägelser om hjärt- och kärlsjukdomar eller mer noggranna väderprognoser. Dessa flödens egenskaper beror på hur enskilda partiklar rör sig i en fluid och speciellt hur de är fördelade både i termer av position och, om de är icke-sfäriska, i termer av orientering. Mycket är redan känt om rörelsen av perfekt sfäriska partiklar. För icke-sfäriska partiklar är det inte bara translationen som är av intresse utan det är även viktigt att veta hur partiklarna roterar till följd av lokala hastighetsgradienter. Sådana studier har tidigare varit begränsade av antagandet att partiklarna är extremt små jämfört med fluidens typiska längdskalor. I denna gräns kan både partikelns och fluidens tröghet antas försumbar. Den här avhandlingen ger en komplett bild av hur en sfäroidisk partikel (en partikel som beskrivs av en rotation av en ellips runt en av dess huvudaxlar) beter sig i ett linjärt skjuvflöde när tröghetseffekter inkluderas. Resultaten har erhållits genom numeriska simuleringar. Det visar sig att detta enkla problem är väldigt rikt på olika dynamiska beteenden med flera stabila rotationstillstånd som uppstår tilll följd av både partikel- och fluidtröghet. Inverkan av partikeltröghet leder till en rotation där massan av partikeln är koncentrerad så långt ifrån rotationsaxeln som möjligt, d.v.s. en rotation runt lillaxeln. Den typiska inverkan av fluidtröghet är istället att fluiden försöker påtvinga partikeln en rotation där strömlinjer förblir så raka som möjligt. Primärt leder detta till att partikeln istället roterar runt storaxeln. Beroende på rotationstillstånd, så har partikeln även olika inverkan på den märkbara viskositeten av partikeldispersionen. De olika övergångarna och bifurkationerna mellan rotationstillstånd är karaktäriserade i termer av icke-linjär dynamik, vilket visar på att partikelrörelserna förmodligen kan beskrivas med en reducerad modell. Resultaten i denna avhandling är därför fundamental kunskap och ett nödvändigt steg mot att förstå beteendet av flöden med dispergerade, icke-sfäriska partiklar. / <p>QC 20140328</p>

This licentiate thesis considers the modelling, simulation and experimental investigation of a rammer compactor machine. The purpose is to develop an efficient and verified method for simulation of rammer compactor machines to be used in the product development process. The experience gained through this work is also intended to be useful for studying other types of dynamic compactor machines. Rammer compactor machines perform impact soil compaction. This is more efficient than static compaction. The machines are often used in places where a high degree of compaction is needed, and where the space for operation is limited. The complexity of this type of machine makes design optimisation through traditional prototype testing impractical. This has pointed to the need for a theoretical model and simulation procedure for predicting the dynamic behaviour of the machine. To be useful for optimisation the theoretical model and simulation procedure must be verified. By concurrently working with theoretical modelling, simulations, experimental verifications, and optimisation an efficient analysis support for product development is achieved. This co-ordination works both ways in an iterative manner: experimental investigations are used to verify theoretical models and simulations; and theoretical models and simulations are used to design good experiments. This Complete Approach concept enables better decisions to be made earlier on in the development process, resulting in a decrease in time-to-market and improved quality. In this thesis, the Complete Approach concept is applied to a rammer soil compactor machine. An introductory iteration is described. The good agreement between theoretical and experimental results indicates that the theoretical model and simulation procedure should prove useful in introductory optimisation studies. The thesis discusses reasons for the remaining discrepancy and suggests improvements in both the theoretical model and the experimental set-up for future iterations. / I arbetet studeras det dynamiska beteendet av en jordpackningsmaskin. Syftet är att bygga upp en verifierad modell som kan ligga till grund för vidare produktutveckling. Ett samordnat arbetsätt, Complete Aproach / <p>http://epubl.luth.se/1402-/02/index.html</p>

The two body problem and the rocket equation r̈ + ∊ α ṙ + k/r3r = 0 have been expressed in numerous ways. However, the combination of the rocket equation with the two-body problem has not been studied to any degree of depth due to the intractability of the resulting non-linear, non-homogeneous equations. The goal is to use perturbation techniques to approximate solutions to the combined two-body and rocket equations.