Studies on integrating kinematic design method with mechanical systems simulation techniques

Theultimate goal of any research in the mechanism/kinematic/design area may be called predictive design, ie the optimisation of mechanism proportions in the design stage without requiring extensive life and wear testing. This is an ambitious goal and can be realised through development and refinement of numerical (computational) technology in order to facilitate the design analysis and optimisation of complex mechanisms, mechanical components and systems. As a part of the systematic design methodology this thesis concentrates on kinematic synthesis (kinematic design and analysis) methods in the mechanism synthesis process. The main task of kinematic design is to find all possible solutions in the form of structural parameters to accomplish the desired requirements of motion. Main formulations of kinematic design can be broadly divided to exact synthesis and approximate synthesis formulations. The exact synthesis formulation is based in solving n linear or nonlinear equations in n variables and the solutions for the problem areget by adopting closed form classical or modern algebraic solution methods or using numerical solution methods based on the polynomial continuation or homotopy. The approximate synthesis formulations is based on minimising the approximation error by direct optimisation The main drawbacks of exact synthesis formulationare: (ia) limitations of number of design specifications and (iia) failure in handling design constraints- especially inequality constraints. The main drawbacks of approximate synthesis formulations are: (ib) it is difficult to choose a proper initial linkage and (iib) it is hard to find more than one solution. Recentformulations in solving the approximate synthesis problem adopts polynomial continuation providing several solutions, but it can not handle inequality const-raints. Based on the practical design needs the mixed exact-approximate position synthesis with two exact and an unlimited number of approximate positions has also been developed. The solutions space is presented as a ground pivot map but thepole between the exact positions cannot be selected as a ground pivot. In this thesis the exact synthesis problem of planar mechanism is solved by generating all possible solutions for the optimisation process ¿ including solutions in positive dimensional solution sets - within inequality constraints of structural parameters. Through the literature research it is first shown that the algebraic and numerical solution methods ¿ used in the research area of computational kinematics ¿ are capable of solving non-parametric algebraic systems of n equations inn variables and cannot handle the singularities associated with positive-dimensional solution sets. In this thesis the problem of positive-dimensional solutionsets is solved adopting the main principles from mathematical research area of algebraic geometry in solving parametric ( in the mathematical sense that all parameter values are considered ¿ including the degenerate cases ¿ for which the system is solvable ) algebraic systems of n equations and at least n+1 variables.Adopting the developed solution method in solving the dyadic equations in direct polynomial form in two- to three-precision-points it has been algebraically proved and numerically demonstrated that the map of the ground pivots is ambiguousand that the singularities associated with positive-dimensional solution sets can be solved. The positive-dimensional solution sets associated with the poles might contain physically meaningful solutions in the form of optimal defectfree mechanisms. Traditionally the mechanism optimisation of hydraulically driven boommechanisms is done at early state of the design process. This will result in optimal component design rather than optimal system level design. Modern mechanismoptimisation at system level demands integration of kinematic design methods with mechanical system simulation techniques. In this thesis a new kinematic design method for hydraulically driven boom mechanism is developed and integrated in mechanical system simulation techniques. The developed kinematic design method is based on the combinations of two-precision-point formulation and on optimisation ( with mathematical programming techniques or adopting optimisation methods based on probability and statistics ) of substructures using calculated criteria from the system level response of multidegree-of-freedom mechanisms. Eg. by adopting the mixed exact-approximate position synthesis in direct optimisation (using mathematical programming techniques) with two exact positions and an unlimitednumber of approximate positions the drawbacks of (ia)-(iib) has been cancelled.The design principles of the developed method are based on the design-tree -approach of the mechanical systems and the design method ¿ in principle ¿ is capable of capturing the interrelationship between kinematic and dynamic synthesis simultaneously when the developed kinematic design method is integrated with the mechanical system simulation techniques.

Weierstrass integrability of differential equations

The integrability problem consists in finding the class of functions a first integral of a given planar polynomial differential system must belong to. We recall the characterization of systems which admit an elementary or Liouvillian first integral. We define {\it Weierstrass integrability} and we determine which Weierstrass integrable systems are Liouvillian integrable. Inside this new class of integrable systems there are non--Liouvillian integrable systems.

Cyclicity versus center problem

We prove that there are one-parameter families of planar differential equations for which the center problem has a trivial solution and on the other hand the cyclicity of the weak focus is arbitrarily high. We illustrate this phenomenon in several examples for which this cyclicity is computed.

A survey on the inverse integrating factor

The relation between limit cycles of planar differential systems and the inverse integrating factor was first shown in an article of Giacomini, Llibre and Viano appeared in 1996. From that moment on, many research articles are devoted to the study of the properties of the inverse integrating factor and its relationwith limit cycles and their bifurcations. This paper is a summary of all the results about this topic. We include a list of references together with the corresponding related results aiming at being as much exhaustive as possible. The paper is, nonetheless, self-contained in such a way that all the main results on the inverse integrating factor are stated and a complete overview of the subject is given. Each section contains a different issue to which the inverse integrating factor plays a role: the integrability problem, relation with Lie symmetries, the center problem, vanishing set of an inverse integrating factor, bifurcation of limit cycles from either a period annulus or from a monodromic ω-limit set and some generalizations.

Development of advanced silicon radiation detectors for harsh radiation environment

This thesis describes the development of advanced silicon radiation detectors and their characterization by simulations, used in the work for searching elementary particles in the European Organization for Nuclear Research, CERN. Silicon particle detectors will face extremely harsh radiation in the proposed upgrade of the Large Hadron Collider, the future high-energy physics experiment Super-LHC. The increase in the maximal fluence and the beam luminosity up to 1016 neq / cm2 and 1035 cm-2s-1 will require detectors with a dramatic improvement in radiation hardness, when such a fluence will be far beyond the operational limits of the present silicon detectors. The main goals of detector development concentrate on minimizing the radiation degradation. This study contributes mainly to the device engineering technology for developing more radiation hard particle detectors with better characteristics. Also the defect engineering technology is discussed. In the nearest region of the beam in Super-LHC, the only detector choice is 3D detectors, or alternatively replacing other types of detectors every two years. The interest in the 3D silicon detectors is continuously growing because of their many advantages as compared to conventional planar detectors: the devices can be fully depleted at low bias voltages, the speed of the charge collection is high, and the collection distances are about one order of magnitude less than those of planar technology strip and pixel detectors with electrodes limited to the detector surface. Also the 3D detectors exhibit high radiation tolerance, and thus the ability of the silicon detectors to operate after irradiation is increased. Two parameters, full depletion voltage and electric field distribution, is discussed in more detail in this study. The full depletion of the detector is important because the only depleted area in the detector is active for the particle tracking. Similarly, the high electric field in the detector makes the detector volume sensitive, while low-field areas are non-sensitive to particles. This study shows the simulation results of full depletion voltage and the electric field distribution for the various types of 3D detectors. First, the 3D detector with the n-type substrate and partial-penetrating p-type electrodes are researched. A detector of this type has a low electric field on the pixel side and it suffers from type inversion. Next, the substrate is changed to p-type and the detectors having electrodes with one doping type and the dual doping type are examined. The electric field profile in a dual-column 3D Si detector is more uniform than that in the single-type column 3D detector. The dual-column detectors are the best in radiation hardness because of their low depletion voltages and short drift distances.

From Full stopping to transparency in a holographic model of heavy ion collisions

We numerically simulate planar shock wave collisions in anti-de Sitter space as a model for heavy ion collisions of large nuclei. We uncover a crossover between two different dynamical regimes as a function of the collision energy. At low energies the shocks first stop and then explode in a manner approximately described by hydrodynamics, in close similarity with the Landau model. At high energies the receding fragments move outwards at the speed of light, with a region of negative energy density and negative longitudinal pressure trailing behind them. The rapidity distribution of the energy density at late times around midrapidity is not approximately boost invariant but Gaussian, albeit with a width that increases with the collision energy.

Sherali-Adams Relaxations and Indistinguishability in Counting Logics

Two graphs with adjacency matrices $\mathbf{A}$ and $\mathbf{B}$ are isomorphic if there exists a permutation matrix $\mathbf{P}$ for which the identity $\mathbf{P}^{\mathrm{T}} \mathbf{A} \mathbf{P} = \mathbf{B}$ holds. Multiplying through by $\mathbf{P}$ and relaxing the permutation matrix to a doubly stochastic matrix leads to the linear programming relaxation known as fractional isomorphism. We show that the levels of the Sherali--Adams (SA) hierarchy of linear programming relaxations applied to fractional isomorphism interleave in power with the levels of a well-known color-refinement heuristic for graph isomorphism called the Weisfeiler--Lehman algorithm, or, equivalently, with the levels of indistinguishability in a logic with counting quantifiers and a bounded number of variables. This tight connection has quite striking consequences. For example, it follows immediately from a deep result of Grohe in the context of logics with counting quantifiers that a fixed number of levels of SA suffice to determine isomorphism of planar and minor-free graphs. We also offer applications in both finite model theory and polyhedral combinatorics. First, we show that certain properties of graphs, such as that of having a flow circulation of a prescribed value, are definable in the infinitary logic with counting with a bounded number of variables. Second, we exploit a lower bound construction due to Cai, Fürer, and Immerman in the context of counting logics to give simple explicit instances that show that the SA relaxations of the vertex-cover and cut polytopes do not reach their integer hulls for up to $\Omega(n)$ levels, where $n$ is the number of vertices in the graph.

Kalibrointimenetelmä planaaristen siirtojohtojen mittaamiseen

Tässä diplomityössä tutkittiin TRL-kalibroinnin käyttämistä tasomaisten siirtojohtojen sähköisten parametrien määrittämisessä taajuusalueella 0,3 – 12 GHz. Työssä perehdyttiin TRL-kalibroinnin käyttämiseen piirianalysaattorilla toteutettujen mittauksien mittauskalibrointiin sekä kalibrointiin tarvittavien kalibrointistandardien mitoittamiseen. Kalibrointistandardit suunniteltiin ja toteutettiin sekä mikroliuska- että liuskajohdoille, joiden toiminnallisuutta tarkasteltiin sekä taajuustason että aikatason mittausten avulla. Työssä perehdyttiin myös kalibrointistandardien liityntärajapinnan suunniteluun ja toteuttamiseen. Saatujen tulosten perusteella voitiin osoittaa mikroliuskajohtokitin soveltuvan hyvin mittauskalibroinnin toteuttamiseen tarkoissa mittaussovelluksissa.

MorphoGraphX: A platform for quantifying morphogenesis in 4D.

Morphogenesis emerges from complex multiscale interactions between genetic and mechanical processes. To understand these processes, the evolution of cell shape, proliferation and gene expression must be quantified. This quantification is usually performed either in full 3D, which is computationally expensive and technically challenging, or on 2D planar projections, which introduces geometrical artifacts on highly curved organs. Here we present MorphoGraphX ( www.MorphoGraphX.org), a software that bridges this gap by working directly with curved surface images extracted from 3D data. In addition to traditional 3D image analysis, we have developed algorithms to operate on curved surfaces, such as cell segmentation, lineage tracking and fluorescence signal quantification. The software's modular design makes it easy to include existing libraries, or to implement new algorithms. Cell geometries extracted with MorphoGraphX can be exported and used as templates for simulation models, providing a powerful platform to investigate the interactions between shape, genes and growth.

Tailoring the surface density of silicon nanocrystals embedded in SiOx single layers

In this article, we explore the possibility of modifying the silicon nanocrystal areal density in SiOx single layers, while keeping constant their size. For this purpose, a set of SiOx monolayers with controlled thickness between two thick SiO2 layers has been fabricated, for four different compositions (x=1, 1.25, 1.5, or 1.75). The structural properties of the SiO x single layers have been analyzed by transmission electron microscopy (TEM) in planar view geometry. Energy-filtered TEM images revealed an almost constant Si-cluster size and a slight increase in the cluster areal density as the silicon content increases in the layers, while high resolution TEM images show that the size of the Si crystalline precipitates largely decreases as the SiO x stoichiometry approaches that of SiO2. The crystalline fraction was evaluated by combining the results from both techniques, finding a crystallinity reduction from 75% to 40%, for x = 1 and 1.75, respectively. Complementary photoluminescence measurements corroborate the precipitation of Si-nanocrystals with excellent emission properties for layers with the largest amount of excess silicon. The integrated emission from the nanoaggregates perfectly scales with their crystalline state, with no detectable emission for crystalline fractions below 40%. The combination of the structural and luminescence observations suggests that small Si precipitates are submitted to a higher compressive local stress applied by the SiO2 matrix that could inhibit the phase separation and, in turn, promotes the creation of nonradiative paths.

Sähköisen ja optisen signaalin käyttö samalla piirilevyllä

Työssä tutkittiin sähköisen ja optisen signaalin siirtoa samalla piirilevyllä. Optisen siirtotien komponentit ja niiden toiminta esiteltiin teoriakappaleessa. Valosignaalin vaimentumisilmiö selitettiin pääasiassa johtuvan absorption ja sironnan vaikutuksesta. Sironnan ja absorption vaikutusta valokuidussa käytettävään aallonpituusalueeseen tutkittiin ja esiteltiin valon yleisin modulaatiomenetelmä WDM. Työssä esiteltiin myös dispersion aiheuttama aikahajonta. Optisen signaalin siirrossa piirilevyllä keskityttiin valokanava- ja free-space-siirtoon. Valokanavamateriaalin vaikutusta heijastuksiin optisessa tiedonsiirrossa piirilevyllä tutkittiin. Nykyisten piirilevyjen tuotantomenetelmien käytön mahdollisuutta valokanavapiirilevyn valmistuksessa tutkittiin eri materiaaleille. Moduulien sisäisten tiedonsiirtoteiden integroinnin yleistymistä tulevaisuudessa perusteltiin. Lopuksi työssä esiteltiin kolme uutta keksintöä liittyen optiseen tiedonsiirtoon. Tarkoituksena oli esittää alan moninaisuutta ja uusien sovellusten mahdollisuuksia.

Correcting surface coil excitation inhomogeneities in single-shot SPEN MRI.

Given their high sensitivity and ability to limit the field of view (FOV), surface coils are often used in magnetic resonance spectroscopy (MRS) and imaging (MRI). A major downside of surface coils is their inherent radiofrequency (RF) B1 heterogeneity across the FOV, decreasing with increasing distance from the coil and giving rise to image distortions due to non-uniform spatial responses. A robust way to compensate for B1 inhomogeneities is to employ adiabatic inversion pulses, yet these are not well adapted to all imaging sequences - including to single-shot approaches like echo planar imaging (EPI). Hybrid spatiotemporal encoding (SPEN) sequences relying on frequency-swept pulses provide another ultrafast MRI alternative, that could help solve this problem thanks to their built-in heterogeneous spatial manipulations. This study explores how this intrinsic SPEN-based spatial discrimination, could be used to compensate for the B1 inhomogeneities inherent to surface coils. Experiments carried out in both phantoms and in vivo rat brains demonstrate that, by suitably modulating the amplitude of a SPEN chirp pulse that progressively excites the spins in a direction normal to the coil, it is possible to compensate for the RF transmit inhomogeneities and thus improve sensitivity and image fidelity.

Fusion weld metal solidification:Continuum from weld interface to centerline

We present a brief résumé of the history of solidification research and key factors affecting the solidification of fusion welds. There is a general agreement of the basic solidification theory, albeit differing - even confusing - nomenclatures do exist, and Cases 2 and 3 (the Chalmers' basic boundary conditions for solidification, categorized by Savage as Cases) are variably emphasized. Model Frame, a tool helping to model the continuum of fusion weld solidification from start to end, is proposed. It incorporates the general solidification models, of which the pertinent ones are selected for the actual modeling. The basic models are the main solidification Cases 1…4. These discrete Cases are joined with Sub-Cases: models of Pfann, Flemings and others, bringing needed Sub-Case variables into the model. Model Frame depicts a grain growing from the weld interface to its centerline. Besides modeling, the Model Frame supports education and academic debate. The new mathematical modeling techniques will extend its use into multi-dimensional modeling, introducing new variables and increasing the modeling accuracy. We propose a model: melting/solidification-model (M/S-model) - predicting the solute profile at the start of the solidification of a fusion weld. This Case 3-based Sub-Case takes into account the melting stage, the solute back-diffusion in the solid, and the growth rate acceleration typical to fusion welds. We propose - based on works of Rutter & Chalmers, David & Vitek and our experimental results on copper - that NEGS-EGS-transition is not associated only with cellular-dendritic-transition. Solidification is studied experimentally on pure and doped copper with welding speed range from 0 to 200 cm/min, with one test at 3000 cm/min. Found were only planar and cellular structures, no dendrites - columnar or equiaxed. Cell sub structures: rows of cubic elements we call "cubelettes", "cell-bands" and "micro-cells", as well as an anomalous crack morphology "crack-eye", were detected, as well as microscopic hot crack nucleus we call "grain-lag cracks", caused by a grain slightly lagging behind its neighbors in arrival to the weld centerline. Varestraint test and R-test revealed a change of crack morphologies from centerline cracks to grainand cell boundary cracks with an increasing welding speed. High speed made the cracks invisible to bare eye and hardly detectable with light microscope, while electron microscope often revealed networks of fine micro-cracks.

Effect of the surface charge discretization on electric double layers. A Monte Carlo simulation study

The structure of the electric double layer in contact with discrete and continuously charged planar surfaces is studied within the framework of the primitive model through Monte Carlo simulations. Three different discretization models are considered together with the case of uniform distribution. The effect of discreteness is analyzed in terms of charge density profiles. For point surface groups,a complete equivalence with the situation of uniformly distributed charge is found if profiles are exclusively analyzed as a function of the distance to the charged surface. However, some differences are observed moving parallel to the surface. Significant discrepancies with approaches that do not account for discreteness are reported if charge sites of finite size placed on the surface are considered.

Simulation-based evaluation of susceptibility distortion correction methods in diffusion MRI for connectivity analysis

Connectivity analysis on diffusion MRI data of the whole- brain suffers from distortions caused by the standard echo- planar imaging acquisition strategies. These images show characteristic geometrical deformations and signal destruction that are an important drawback limiting the success of tractography algorithms. Several retrospective correction techniques are readily available. In this work, we use a digital phantom designed for the evaluation of connectivity pipelines. We subject the phantom to a âeurooetheoretically correctâeuro and plausible deformation that resembles the artifact under investigation. We correct data back, with three standard methodologies (namely fieldmap-based, reversed encoding-based, and registration- based). Finally, we rank the methods based on their geometrical accuracy, the dropout compensation, and their impact on the resulting connectivity matrices.