Preliminary results on the effects of orthopedic implant stiffness fixed to the cut end of the femur on the stress at the stump-prosthetic interface

A lot of trans-femoral amputation patients experience skin breakdown due to the pressures and shear stresses in the stump-prosthesis interface. In this study, a finite element model was employed to investigate the stresses at the stump interface in the case of an orthopedic implant fixed to the cut end of the femur. By changing the stiffness of this implant, we aim to see how the stiffness of this implant affects the stresses in the interface between the amputated limb and the prosthesis. To find out the effects of implant stiffness, five values for the elastic modulus, ranging from 0.1 to 0.5 Mpa, with an interval of 0.1 Mpa were employed in the implant structure of the FE model. Obtained results show that the implant played important role in reducing the stresses at the stump-prosthesis interface where the contact pressure did not exceed 53 Kpa and 17.3 Kpa for shear stress in the stiffer case of an implant, while the contact pressure in the case of femur without implant exceeded 79Kpa and 42 Kpa for shear stress. We also noted that the intensity of the contact pressure and the shear stress is proportional to the stiffness of the implant, as the greater the implant stiffness, the higher the peak of these stresses

Review of the mathematical foundations of data fusion techniques in surface metrology

The recent proliferation of engineered surfaces, including freeform and structured surfaces, is challenging current metrology techniques. Measurement using multiple sensors has been proposed to achieve enhanced benefits, mainly in terms of spatial frequency bandwidth, which a single sensor cannot provide. When using data from different sensors, a process of data fusion is required and there is much active research in this area. In this paper, current data fusion methods and applications are reviewed, with a focus on the mathematical foundations of the subject. Common research questions in the fusion of surface metrology data are raised and potential fusion algorithms are discussed

Quasi-degenerate neutrinos and tri-bi-maximal mixing

Assuming high-energy tri-bi-maximal mixing we study the radiative running of leptonic mixing angles and obtain limits on the high-energy scale from requiring consistency with the observed mixing. We construct a model in which a non-Abelian discrete family symmetry leads both to a quasi-degenerate neutrino mass spectrum and to near tri-bi-maximal mixing.Comment: 7 pages, to appear in the proceedings of DISCRETE'0

Renormalization Group Running of Lepton Mixing Parameters in See-Saw Models with S4S_4 Flavor Symmetry

We study the renormalization group running of the tri-bimaximal mixing predicted by the two typical $S_4$ flavor models at leading order. Although the textures of the mass matrices are completely different, the evolution of neutrino mass and mixing parameters is found to display approximately the same pattern. For both normal hierarchy and inverted hierarchy spectrum, the quantum corrections to both atmospheric and reactor neutrino mixing angles are so small that they can be neglected. The evolution of the solar mixing angle $\theta_{12}$ depends on $\tan\beta$ and neutrino mass spectrum, the deviation from its tri-bimaximal value could be large. Taking into account the renormalization group running effect, the neutrino spectrum is constrained by experimental data on $\theta_{12}$ in addition to the self-consistency conditions of the models, and the inverted hierarchy spectrum is disfavored for large $\tan\beta$. The evolution of light-neutrino masses is approximately described by a common scaling factor.Comment: 23 pages, 6figure

Right unitarity triangles and tri-bimaximal mixing from discrete symmetries and unification

We propose new classes of models which predict both tri-bimaximal lepton mixing and a right-angled Cabibbo-Kobayashi-Maskawa (CKM) unitarity triangle, alpha approximately 90 degrees. The ingredients of the models include a supersymmetric (SUSY) unified gauge group such as SU(5), a discrete family symmetry such as A4 or S4, a shaping symmetry including products of Z2 and Z4 groups as well as spontaneous CP violation. We show how the vacuum alignment in such models allows a simple explanation of alpha approximately 90 degrees by a combination of purely real or purely imaginary vacuum expectation values (vevs) of the flavons responsible for family symmetry breaking. This leads to quark mass matrices with 1-3 texture zeros that satisfy the phase sum rule and lepton mass matrices that satisfy the lepton mixing sum rule together with a new prediction that the leptonic CP violating oscillation phase is close to either 0, 90, 180, or 270 degrees depending on the model, with neutrino masses being purely real (no complex Majorana phases). This leads to the possibility of having right-angled unitarity triangles in both the quark and lepton sectors.Comment: 29 pages, 4 figures, version to be published in NP

Parametrizing the Lepton Mixing Matrix in terms of Charged Lepton Corrections

We consider a parametrization of the lepton mixing matrix in which the deviations from maximal atmospheric mixing and vanishing reactor mixing are obtained in terms of small corrections from the charged lepton sector. Relatively large deviations for the reactor mixing angle from zero as indicated by T2K experiment can be obtained in this parametrization. We are able to further reduce the number of complex phases, thus, simplifying the analysis. In addition, we have obtained the sides of unitarity triangles and the vacuum oscillation probabilities in this parametrization. The Jarlskog rephasing invariant measure of CP violation at the leading order has a single phase difference which can be identified as Dirac-type CP violating phase in this parametrization.Comment: New references added, Phys. Lett. B (to appear

The Interplay Between GUT and Flavour Symmetries in a Pati-Salam x S4 Model

Both Grand Unified symmetries and discrete flavour symmetries are appealing ways to describe apparent structures in the gauge and flavour sectors of the Standard Model. Both symmetries put constraints on the high energy behaviour of the theory. This can give rise to unexpected interplay when building models that possess both symmetries. We investigate on the possibility to combine a Pati-Salam model with the discrete flavour symmetry $S_4$ that gives rise to quark-lepton complementarity. Under appropriate assumptions at the GUT scale, the model reproduces fermion masses and mixings both in the quark and in the lepton sectors. We show that in particular the Higgs sector and the running Yukawa couplings are strongly affected by the combined constraints of the Grand Unified and family symmetries. This in turn reduces the phenomenologically viable parameter space, with high energy mass scales confined to a small region and some parameters in the neutrino sector slightly unnatural. In the allowed regions, we can reproduce the quark masses and the CKM matrix. In the lepton sector, we reproduce the charged lepton masses, including bottom-tau unification and the Georgi-Jarlskog relation as well as the two known angles of the PMNS matrix. The neutrino mass spectrum can present a normal or an inverse hierarchy, and only allowing the neutrino parameters to spread into a range of values between $\lambda^{-2}$ and $\lambda^2$, with $\lambda\simeq0.2$. Finally, our model suggests that the reactor mixing angle is close to its current experimental bound.Comment: 62 pages, 4 figures; references added, version accepted for publication in JHE

Renormalisation group corrections to neutrino mixing sum rules

Neutrino mixing sum rules are common to a large class of models based on the (discrete) symmetry approach to lepton flavour. In this approach the neutrino mixing matrix $U$ is assumed to have an underlying approximate symmetry form \tildeU_\nu, which is dictated by, or associated with, the employed (discrete) symmetry. In such a setup the cosine of the Dirac CP-violating phase $\delta$ can be related to the three neutrino mixing angles in terms of a sum rule which depends on the symmetry form of \tildeU_\nu. We consider five extensively discussed possible symmetry forms of \tildeU_\nu: i) bimaximal (BM) and ii) tri-bimaximal (TBM) forms, the forms corresponding to iii) golden ratio type A (GRA) mixing, iv) golden ratio type B (GRB) mixing, and v) hexagonal (HG) mixing. For each of these forms we investigate the renormalisation group corrections to the sum rule predictions for $\delta$ in the cases of neutrino Majorana mass term generated by the Weinberg (dimension 5) operator added to i) the Standard Model, and ii) the minimal SUSY extension of the Standard Model