The von Mises-Fisher distribution of the first exit point from the hypersphere of the drifted Brownian motion and the density of the first exit time

A characterization is provided for the von Mises–Fisher random variable, in terms of first exit point from the unit hypersphere of the drifted Wiener process. Laplace transform formulae for the first exit time from the unit hypersphere of the drifted Wiener process are provided. Post representations in terms of Bell polynomials are provided for the densities of the first exit times from the circle and from the sphere.

An efficient simulation algorithm for the generalized von Mises distribution of order two

In this article we propose an exact efficient simulation algorithm for the generalized von Mises circular distribution of order two. It is an acceptance-rejection algorithm with a piecewise linear envelope based on the local extrema and the inflexion points of the generalized von Mises density of order two. We show that these points can be obtained from the roots of polynomials and degrees four and eight, which can be easily obtained by the methods of Ferrari and Weierstrass. A comparative study with the von Neumann acceptance-rejection, with the ratio-of-uniforms and with a Markov chain Monte Carlo algorithms shows that this new method is generally the most efficient.

Helene von Mises

B. Samuel

Arthur Edler von Mises [Illustration] : geb. 1854 - gest. 1903

Scan von Monochrom-Mikroform

Univariate and bivariate truncated von Mises distributions

In this article we study the univariate and bivariate truncated von Mises distribution, as a generalization of the von Mises distribution (\cite{jupp1989}), (\cite{mardia2000directional}). This implies the addition of two or four new truncation parameters in the univariate and, bivariate cases, respectively. The results include the definition, properties of the distribution and maximum likelihood estimators for the univariate and bivariate cases. Additionally, the analysis of the bivariate case shows how the conditional distribution is a truncated von Mises distribution, whereas the marginal distribution that generalizes the distribution introduced in \cite{repe}. From the viewpoint of applications, we test the distribution with simulated data, as well as with data regarding leaf inclination angles (\cite{safari}) and dihedral angles in protein chains (\cite{prote}). This research aims to assert this probability distribution as a potential option for modelling or simulating any kind of phenomena where circular distributions are applicable.\par

Das Büchlein vom Leben nach dem Tode, von Mises.

Mode of access: Internet.

Exponentially decaying pressure pulse moving with superseismic velocity on the surface of a half space of Von Mises elastoplastic material

Mode of access: Internet.

Influence of implant-abutment angulations and crown material on stress distribution on central incisor: a 3D FEA

Aim: To investigate the effect of implant-abutment angulation and crown material on stress distribution of central incisors. Finite element method was used to simulate the clinical situation of a maxillary right central incisor restored by two different implant-abutment angulations, 15° and 25°, using two different crown materials (IPS E-Max CAD and zirconia). Methods: Two 3D finite element models were specially prepared for this research simulating the abutment angulations. Commercial engineering CAD/CAM package was used to model crown, implant abutment complex and bone (cortical and spongy) in 3D. Linear static analysis was performed by applying a 178 N oblique load. The obtained results were compared with former experimental results. Results: Implant Von Mises stress level was negligibly changed with increasing abutment angulation. The abutment with higher angulation is mechanically weaker and expected to fail at lower loading in comparison with the steeper one. Similarly, screw used with abutment angulation of 25° will fail at lower (about one-third) load value the failure load of similar screw used with abutment angulated by 15°. Conclusions: Bone (cortical and spongy) is insensitive to crown material. Increasing abutment angulation from 15° to 25°, increases stress on cortical bone by about 20% and reduces it by about 12% on spongy bone. Crown fracture resistance is dramatically reduced by increasing abutment angulation. Zirconia crown showed better performance than E-Max one.

Finite-element Analysis Of 3 Situations Of Trauma In The Human Edentulous Mandible.

Maxillofacial trauma resulting from falls in elderly patients is a major social and health care concern. Most of these traumatic events involve mandibular fractures. The aim of this study was to analyze stress distributions from traumatic loads applied on the symphyseal, parasymphyseal, and mandibular body regions in the elderly edentulous mandible using finite-element analysis (FEA). Computerized tomographic analysis of an edentulous macerated human mandible of a patient approximately 65 years old was performed. The bone structure was converted into a 3-dimensional stereolithographic model, which was used to construct the computer-aided design (CAD) geometry for FEA. The mechanical properties of cortical and cancellous bone were characterized as isotropic and elastic structures, respectively, in the CAD model. The condyles were constrained to prevent free movement in the x-, y-, and z-axes during simulation. This enabled the simulation to include the presence of masticatory muscles during trauma. Three different simulations were performed. Loads of 700 N were applied perpendicular to the surface of the cortical bone in the symphyseal, parasymphyseal, and mandibular body regions. The simulation results were evaluated according to equivalent von Mises stress distributions. Traumatic load at the symphyseal region generated low stress levels in the mental region and high stress levels in the mandibular neck. Traumatic load at the parasymphyseal region concentrated the resulting stress close to the mental foramen. Traumatic load in the mandibular body generated extensive stress in the mandibular body, angle, and ramus. FEA enabled precise mapping of the stress distribution in a human elderly edentulous mandible (neck and mandibular angle) in response to 3 different traumatic load conditions. This knowledge can help guide emergency responders as they evaluate patients after a traumatic event.

Bending fatigue of stainless steel shear pins belonging to a hydroelectric plant

Coaracy Nunes was the first hydroelectric power plant in the Amazon region, being located in Araguari River, Amapa State, Brazil. The plant operates since 1976, presenting now a nominal capacity of 78 MW. The shear pins, which are installed in the turbine hydraulic arms to control the wicket gate and regulate the water flow into the turbine blades, suffered several breakdowns since 2004. These shear pins are made of an ASTM 410 stainless steel and were designed to break by a shear overload of 120 kN. Fractographic investigation of the pins, however, revealed two types of fracture topographies: a region of stable crack propagation area, with non-pronounced striation and secondary cracks; and a region of unstable propagation, featuring elongated dimples. These results indicated that the stable crack propagation occurred by fatigue (bidirectional bending), which was nucleated at machining marks under high nominal load. Finite element analysis was carried out using two loading conditions (pure shear and a combination of shear and bending) and the results indicated that the presence of a bending stress strongly increased the stress concentration factor (85% rise in the shear stress and 130% rise in the Von Mises stress). Misalignment during shear pins assembly associated with vibration might have promoted the premature failure of the shear by bending fatigue. (C) 2008 Elsevier Ltd. All rights reserved.

Wall material properties of yeast cells. Part II. Analysis

In the preceding paper (Part I) force-deformation data were measured with the compression experiment in conjunction with the initial radial stretch ratio and the initial wall-thickness to cell-radius ratio for baker's yeast (Saccharomyces cerevisiae). In this paper, these data have been analysed with the mechanical model of Smith et al. (Smith, Moxham & Middelberg (1998) Chemical Engineering Science, 53, 3913-3922) with the wall constitutive behaviour defined a priori as incompressible and linear-elastic. This analysis determined the mean Young's modulus ((E) over bar), mean maximum von Mises stress-at-failure (<(sigma)over bar>(VM,f)) and mean maximum von Mises strain-at failure (<(epsilon)over bar>(VM,f)) to be (E) over bar = 150 +/- 15 MPa, <(sigma)over bar>(VM,f) = 70 +/- 4 MPa and <(epsilon)over bar>(VM,f) = 0.75 +/- 0.08, respectively. The mean Young's modulus was not dependent (P greater than or equal to 0.05) on external osmotic pressure (0-0.8 MPa) nor compression rate (1.03-7.68 mu m/s) suggesting the incompressible linear-elastic relationship is representative of the actual cell-wall constitutive behaviour. Hydraulic conductivities were also determined and were comparable to other similar cell types (0-2.5 mu m/MPa s). The hydraulic conductivity distribution was not dependent on external osmotic pressure (0-0.8 MPa) nor compression rate (1.03-7.68 mu m/s) suggesting inclusion of cell-wall permeability in the mechanical model is justified. <(epsilon)over bar>(VM,f) was independent of cell diameter and to a first-approximation unaffected (P greater than or equal to 0.01) by external osmotic pressure and compression rate, thus providing a reasonable failure criterion. This criterion states that the cell-wall material will break when the strain exceeds <(epsilon)over bar>(VM,f) = 0.75 +/- 0.08. Variability in overall cell strength during compression was shown to be primarily due to biological variability in the maximum von Mises strain-at-failure. These data represent the first estimates of cell-wall material properties for yeast and the first fundamental analysis of cell-compression data. They are essential for describing cell-disruption at the fundamental level of fluid-cell interactions in general bioprocesses. They also provide valuable new measurements for yeast-cell physiologists. (C) 2000 Elsevier Science Ltd. All rights reserved.

Finite Element Analysis of 2 Immediate Loading Systems in Edentulous Mandible: Rigid and Semirigid Splinting of Implants

Purpose: The objective of this study was to evaluate the stress on the cortical bone around single body dental implants supporting mandibular complete fixed denture with rigid (Neopronto System-Neodent) or semirigid splinting system (Barra Distal System-Neodent). Methods and Materials: Stress levels on several system components were analyzed through finite element analysis. Focusing on stress concentration at cortical bone around single body dental implants supporting mandibular complete fixed dentures with rigid ( Neopronto System-Neodent) or semirigid splinting system ( Barra Distal System-Neodent), after axial and oblique occlusal loading simulation, applied in the last cantilever element. Results: The results showed that semirigid implant splinting generated lower von Mises stress in the cortical bone under axial loading. Rigid implant splinting generated higher von Mises stress in the cortical bone under oblique loading. Conclusion: It was concluded that the use of a semirigid system for rehabilitation of edentulous mandibles by means of immediate implant-supported fixed complete denture is recommended, because it reduces stress concentration in the cortical bone. As a consequence, bone level is better preserved, and implant survival is improved. Nevertheless, for both situations the cortical bone integrity was protected, because the maximum stress level findings were lower than those pointed in the literature as being harmful. The maximum stress limit for cortical bone (167 MPa) represents the threshold between plastic and elastic state for a given material. Because any force is applied to an object, and there is no deformation, we can conclude that the elastic threshold was not surpassed, keeping its structural integrity. If the force is higher than the plastic threshold, the object will suffer permanent deformation. In cortical bone, this represents the beginning of bone resorption and/or remodeling processes, which, according to our simulated loading, would not occur. ( Implant Dent 2010; 19:39-49)

Optimising the design and manufacture of a customised, prescription fit, Maxillo-facial prosthesis

This thesis is a continuation of the Enterprise-Ireland Research Innovation Fund (RIF) Project entitled’ "Design and Manufacturing of Customised Maxillo-Facial Prostheses" The primary objective of this Internal Research Development Program (IRDP) project was to investigate two fundamental design changes 1 To incorporate the over-denture abutments directly into the implant. 2 To remove the restraining wings by the addition of screws, which affix the. implant to the dense material of the jawbone. The prosthetic was redesigned using the ANSYS Finite Element Analysis software program and analysed to* • Reduce the internal von Mises stress distribution The new prosthetic had a -63.63 % lower von Mises stress distribution when compared with the original prosthetic. • Examine the screw preload effects. A maximum relative displacement of 22 6 * lO^mm between the bone and screw was determined, which is well below the critical threshold of micromotion which prevents osseointegration • Investigate the prosthetic-bone contact interface. Three models of the screw, prosthesis, and bone, were studied. (Axisymmetnc, quarter volume, and full volume), a recommended preload torque of 0 32 Nm was applied to the prosthetic and a maximum von Mises stress of 1.988 MPa was predicted • Study the overdenture removal forces. This analysis could not be completed because the correct plastic multilinear properties of the denture material could not be established The redesigned prosthetic was successfully manufactured on a 3-axis milling machine with an indexing system The prosthetic was examined for dimensional quality and strength The research established the feasibility of the new design and associated manufacturing method.

Computational modeling of stented coronary arteries

The application of computational fluid dynamics (CFD) and finite element analysis (FEA) has been growing rapidly in the various fields of science and technology. One of the areas of interest is in biomedical engineering. The altered hemodynamics inside the blood vessels plays a key role in the development of the arterial disease called atherosclerosis, which is the major cause of human death worldwide. Atherosclerosis is often treated with the stenting procedure to restore the normal blood flow. A stent is a tubular, flexible structure, usually made of metals, which is driven and expanded in the blocked arteries. Despite the success rate of the stenting procedure, it is often associated with the restenosis (re-narrowing of the artery) process. The presence of non-biological device in the artery causes inflammation or re-growth of atherosclerotic lesions in the treated vessels. Several factors including the design of stents, type of stent expansion, expansion pressure, morphology and composition of vessel wall influence the restenosis process. Therefore, the role of computational studies is crucial in the investigation and optimisation of the factors that influence post-stenting complications. This thesis focuses on the stent-vessel wall interactions followed by the blood flow in the post-stenting stage of stenosed human coronary artery. Hemodynamic and mechanical stresses were analysed in three separate stent-plaque-artery models. Plaque was modeled as a multi-layer (fibrous cap (FC), necrotic core (NC), and fibrosis (F)) and the arterial wall as a single layer domain. CFD/FEA simulations were performed using commercial software packages in several models mimicking the various stages and morphologies of atherosclerosis. The tissue prolapse (TP) of stented vessel wall, the distribution of von Mises stress (VMS) inside various layers of vessel wall, and the wall shear stress (WSS) along the luminal surface of the deformed vessel wall were measured and evaluated. The results revealed the role of the stenosis size, thickness of each layer of atherosclerotic wall, thickness of stent strut, pressure applied for stenosis expansion, and the flow condition in the distribution of stresses. The thicknesses of FC, and NC and the total thickness of plaque are critical in controlling the stresses inside the tissue. A small change in morphology of artery wall can significantly affect the distribution of stresses. In particular, FC is the most sensitive layer to TP and stresses, which could determine plaque’s vulnerability to rupture. The WSS is highly influenced by the deflection of artery, which in turn is dependent on the structural composition of arterial wall layers. Together with the stenosis size, their roles could play a decisive role in controlling the low values of WSS (<0.5 Pa) prone to restenosis. Moreover, the time dependent flow altered the percentage of luminal area with WSS values less than 0.5 Pa at different time instants. The non- Newtonian viscosity model of the blood properties significantly affects the prediction of WSS magnitude. The outcomes of this investigation will help to better understand the roles of the individual layers of atherosclerotic vessels and their risk to provoke restenosis at the post-stenting stage. As a consequence, the implementation of such an approach to assess the post-stented stresses will assist the engineers and clinicians in optimizing the stenting techniques to minimize the occurrence of restenosis.