11 resultados para Euler polynomials and numbers
em Universidade do Minho
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This chapter deals with the different approaches for describing the rotational coordinates in spatial multibody systems. In this process, Euler angles and Bryant angles are briefly characterized. Particular emphasis is given to Euler parameters, which are utilized to describe the rotational coordinates in the present work. In addition, for all the types of coordinates considered in this chapter, a characterization of the transformation matrix is fully described.
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Dissertação de mestrado em Engenharia Industrial
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Tese de Doutoramento em Psicologia - Especialidade em Psicologia Experimental e Ciências Cognitivas
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This work presents a numerical study of the 4:1 planar contraction flow of a viscoelastic fluid described by the simplified Phan-Thien–Tanner model under the influence of slip boundary conditions at the channel walls. The linear Navier slip law was considered with the dimensionless slip coefficient varying in the range ½0; 4500. The simulations were carried out for a small constant Reynolds number of 0.04 and Deborah numbers (De) varying between 0 and 5. Convergence could not be achieved for higher values of the Deborah number, especially for large values of the slip coefficient, due to the large stress gradients near the singularity of the reentrant corner. Increasing the slip coefficient leads to the formation of two vortices, a corner and a lip vortex. The lip vortex grows with increasing slip until it absorbs the corner vortex, creating a single large vortex that continues to increase in size and intensity. In the range De = 3–5 no lip vortex was formed. The flow is characterized in detail for De ¼ 1 as function of the slip coefficient, while for the remaining De only the main features are shown for specific values of the slip coefficient.
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Studies of the spin and parity quantum numbers of the Higgs boson in the WW∗→eνμν final state are presented, based on proton--proton collision data collected by the ATLAS detector at the Large Hadron Collider, corresponding to an integrated luminosity of 20.3 fb−1 at a centre-of-mass energy of s√=8 TeV. The Standard Model spin-parity JCP=0++ hypothesis is compared with alternative hypotheses for both spin and CP. The case where the observed resonance is a mixture of the Standard-Model-like Higgs boson and CP-even (JCP=0++) or CP-odd (JCP=0+−) Higgs boson in scenarios beyond the Standard Model is also studied. The data are found to be consistent with the Standard Model prediction and limits are placed on alternative spin and CP hypotheses, including CP mixing in different scenarios.
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The theory of orthogonal polynomials of one real or complex variable is well established as well as its generalization for the multidimensional case. Hypercomplex function theory (or Clifford analysis) provides an alternative approach to deal with higher dimensions. In this context, we study systems of orthogonal polynomials of a hypercomplex variable with values in a Clifford algebra and prove some of their properties.
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Studies of the spin, parity and tensor couplings of the Higgs boson in the H→ZZ∗→4ℓ , H→WW∗→eνμν and H→γγ decay processes at the LHC are presented. The investigations are based on 25 fb−1 of pp collision data collected by the ATLAS experiment at s√=7 TeV and s√=8 TeV. The Standard Model (SM) Higgs boson hypothesis, corresponding to the quantum numbers JP=0+, is tested against several alternative spin scenarios, including non-SM spin-0 and spin-2 models with universal and non-universal couplings to fermions and vector bosons. All tested alternative models are excluded in favour of the SM Higgs boson hypothesis at more than 99.9% confidence level. Using the H→ZZ∗→4ℓ and H→WW∗→eνμν decays, the tensor structure of the HVV interaction in the spin-0 hypothesis is also investigated. The observed distributions of variables sensitive to the non-SM tensor couplings are compatible with the SM predictions and constraints on the non-SM couplings are derived.
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Among the various possible embodiements of Advanced Therapies and in particular of Tissue Engineering the use of temporary scaffolds to regenerate tissue defects is one of the key issues. The scaffolds should be specifically designed to create environments that promote tissue development and not merely to support the maintenance of communities of cells. To achieve that goal, highly functional scaffolds may combine specific morphologies and surface chemistry with the local release of bioactive agents. Many biomaterials have been proposed to produce scaffolds aiming the regeneration of a wealth of human tissues. We have a particular interest in developing systems based in nanofibrous biodegradable polymers1,2. Those demanding applications require a combination of mechanical properties, processability, cell-friendly surfaces and tunable biodegradability that need to be tailored for the specific application envisioned. Those biomaterials are usually processed by different routes into devices with wide range of morphologies such as biodegradable fibers and meshes, films or particles and adaptable to different biomedical applications. In our approach, we combine the temporary scaffolds populated with therapeutically relevant communities of cells to generate a hybrid implant. For that we have explored different sources of adult and also embryonic stem cells. We are exploring the use of adult MSCs3, namely obtained from the bone marrow for the development autologous-based therapies. We also develop strategies based in extra-embryonic tissues, such as amniotic fluid (AF) and the perivascular region of the umbilical cord4 (Whartonâ s Jelly, WJ). Those tissues offer many advantages over both embryonic and other adult stem cell sourcess. These tissues are frequently discarded at parturition and its extracorporeal nature facilitates tissue donation by the patients. The comparatively large volume of tissue and ease of physical manipulation facilitates the isolation of larger numbers of stem cells. The fetal stem cells appear to have more pronounced immunomodulatory properties than adult MSCs. This allogeneic escape mechanism may be of therapeutic value, because the transplantation of readily available allogeneic human MSCs would be preferable as opposed to the required expansion stage (involving both time and logistic effort) of autologous cells. Topics to be covered: This talk will review our latest developments of nanostructured-based biomaterials and scaffolds in combination with stem cells for bone and cartilage tissue engineering.
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We consider implicit signatures over finite semigroups determined by sets of pseudonatural numbers. We prove that, under relatively simple hypotheses on a pseudovariety V of semigroups, the finitely generated free algebra for the largest such signature is closed under taking factors within the free pro-V semigroup on the same set of generators. Furthermore, we show that the natural analogue of the Pin-Reutenauer descriptive procedure for the closure of a rational language in the free group with respect to the profinite topology holds for the pseudovariety of all finite semigroups. As an application, we establish that a pseudovariety enjoys this property if and only if it is full.
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In this chapter, a complete characterization of the angular velocity and angular acceleration for rigid bodies in spatial multibody systems are presented. For both cases, local and global formulations are described taking into account the advantages of using Euler parameters. In this process, the transformation between global and local components of the angular velocity and time derivative of the Euler parameters are analyzed and discussed in this chapter.
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This chapter describes the how the vector of coordinates are defined in the formulation of spatial multibody systems. For this purpose, the translational motion is described in terms of Cartesian coordinates, while rotational motion is specified using the technique of Euler parameters. This approach avoids the computational difficulties associated with the singularities in the case of using Euler angles or Bryant angles. Moreover, the formulation of the velocities vector and accelerations vector is presented and analyzed here. These two sets of vectors are defined in terms of translational and rotational coordinates.