scholarly journals Gaussian Random Particles with Flexible Hausdorff Dimension

2015 ◽  
Vol 47 (2) ◽  
pp. 307-327 ◽  
Author(s):  
Linda V. Hansen ◽  
Thordis L. Thorarinsdottir ◽  
Evgeni Ovcharov ◽  
Tilmann Gneiting ◽  
Donald Richards
Keyword(s):  
Correlation Function ◽  
Hausdorff Dimension ◽  
Random Field ◽  
Kernel Smoothing ◽  
Three Dimensional ◽  
Random Sets ◽  
Closed Form Expression ◽  
Spherical Cap ◽  
Fractal Index ◽  
Von Mises

Gaussian particles provide a flexible framework for modelling and simulating three-dimensional star-shaped random sets. In our framework, the radial function of the particle arises from a kernel smoothing, and is associated with an isotropic random field on the sphere. If the kernel is a von Mises-Fisher density, or uniform on a spherical cap, the correlation function of the associated random field admits a closed form expression. The Hausdorff dimension of the surface of the Gaussian particle reflects the decay of the correlation function at the origin, as quantified by the fractal index. Under power kernels we obtain particles with boundaries of any Hausdorff dimension between 2 and 3.

scholarly journals Gaussian Random Particles with Flexible Hausdorff Dimension

2015 ◽  
Vol 47 (02) ◽  
pp. 307-327
Author(s):  
Linda V. Hansen ◽  
Thordis L. Thorarinsdottir ◽  
Evgeni Ovcharov ◽  
Tilmann Gneiting ◽  
Donald Richards
Keyword(s):  
Correlation Function ◽  
Hausdorff Dimension ◽  
Random Field ◽  
Kernel Smoothing ◽  
Three Dimensional ◽  
Random Sets ◽  
Closed Form Expression ◽  
Spherical Cap ◽  
Fractal Index ◽  
Von Mises

Gaussian particles provide a flexible framework for modelling and simulating three-dimensional star-shaped random sets. In our framework, the radial function of the particle arises from a kernel smoothing, and is associated with an isotropic random field on the sphere. If the kernel is a von Mises-Fisher density, or uniform on a spherical cap, the correlation function of the associated random field admits a closed form expression. The Hausdorff dimension of the surface of the Gaussian particle reflects the decay of the correlation function at the origin, as quantified by the fractal index. Under power kernels we obtain particles with boundaries of any Hausdorff dimension between 2 and 3.

Simulation of a random field with given distribution of one-dimensional integral

2019 ◽  
Vol 34 (6) ◽  
pp. 327-338 ◽  
Author(s):  
Evgeniya G. Kablukova ◽  
Guennady A. Mikhailov ◽  
Vasily A. Ogorodnikov ◽  
Sergei M. Prigarin
Keyword(s):  
Correlation Function ◽  
Random Field ◽  
Gamma Distribution ◽  
Three Dimensional ◽  
One Dimensional ◽  
Basic Model ◽  
Dimensional Distribution ◽  
The One ◽  
The Given ◽  
Horizontal Layers

Abstract The problem of constructing a numerically realizable model of a three-dimensional homogeneous random field in a layer 0 < z < H with given one-dimensional distribution and correlation function of the integral over coordinate z is solved. The gamma distribution with shape parameter ν and scale parameter θ is used in the work. An aggregate of n independent elementary horizontal layers of thickness h = H/n vertically shifted by a random value uniformly distributed in the interval (0, h) is considered as a basic model. For each elementary random field, the normalized correlation function of the corresponding integral over z coincides with the given one, the gamma distribution with parameters depending on the number of horizontal layers is used as a one-dimensional distribution. It is proved that for the constructed model the normalized correlation function of the integral over z coincides with the given normalized ‘horizontal’ correlation function, and the parameters of the one-dimensional distribution asymptotically converge to given values for n → + ∞, but the corresponding mathematical expectation and variance coincide exactly with given values. To extend the class of possible models, an additional randomization of the basic model is considered. In the conclusion the results of computations for a realistic version of the problem are presented.

Effects of occlusal scheme on All-on-Four abutments, screws and prostheses: A three-dimensional finite element study

2020 ◽  
Author(s):  
Nurullah Türker ◽  
Hümeyra Tercanlı Alkış ◽  
Steven J Sadowsky ◽  
Ulviye Şebnem Büyükkaplan
Keyword(s):  
Finite Element ◽  
Three Dimensional ◽  
Good Prognosis ◽  
Von Mises Stress ◽  
Element Analysis ◽  
Group Function ◽  
Occlusal Contact ◽  
Maximum Deformation ◽  
Contact Points ◽  
Von Mises

An ideal occlusal scheme plays an important role in a good prognosis of All-on-Four applications, as it does for other implant therapies, due to the potential impact of occlusal loads on implant prosthetic components. The aim of the present three-dimensional (3D) finite element analysis (FEA) study was to investigate the stresses on abutments, screws and prostheses that are generated by occlusal loads via different occlusal schemes in the All-on-Four concept. Three-dimensional models of the maxilla, mandible, implants, implant substructures and prostheses were designed according to the All-on-Four concept. Forces were applied from the occlusal contact points formed in maximum intercuspation and eccentric movements in canine guidance occlusion (CGO), group function occlusion (GFO) and lingualized occlusion (LO). The von Mises stress values for abutment and screws and deformation values for prostheses were obtained and results were evaluated comparatively. It was observed that the stresses on screws and abutments were more evenly distributed in GFO. Maximum deformation values for prosthesis were observed in the CFO model for lateral movement both in the maxilla and mandible. Within the limits of the present study, GFO may be suggested to reduce stresses on screws, abutments and prostheses in the All-on-Four concept.

scholarly journals Effects of intracorneal ring segments implementation technique and design on corneal biomechanics and keratometry in a personalized computational analysis

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Niksa Mohammadi Bagheri ◽  
Mahmoud Kadkhodaei ◽  
Shiva Pirhadi ◽  
Peiman Mosaddegh
Keyword(s):  
Clinical Data ◽  
Three Dimensional ◽  
Element Model ◽  
Von Mises Stress ◽  
Patient Specific ◽  
Average Error ◽  
Constant Thickness ◽  
Arc Length ◽  
Implementation Techniques ◽  
Von Mises

AbstractThe implementation of intracorneal ring segments (ICRS) is one of the successfully applied refractive operations for the treatment of keratoconus (kc) progression. The different selection of ICRS types along with the surgical implementation techniques can significantly affect surgical outcomes. Thus, this study aimed to investigate the influence of ICRS implementation techniques and design on the postoperative biomechanical state and keratometry results. The clinical data of three patients with different stages and patterns of keratoconus were assessed to develop a three-dimensional (3D) patient-specific finite-element model (FEM) of the keratoconic cornea. For each patient, the exact surgery procedure definitions were interpreted in the step-by-step FEM. Then, seven surgical scenarios, including different ICRS designs (complete and incomplete segment), with two surgical implementation methods (tunnel incision and lamellar pocket cut), were simulated. The pre- and postoperative predicted results of FEM were validated with the corresponding clinical data. For the pre- and postoperative results, the average error of 0.4% and 3.7% for the mean keratometry value ($$\text {K}_{\text{mean}}$$ K mean ) were predicted. Furthermore, the difference in induced flattening effects was negligible for three ICRS types (KeraRing segment with arc-length of 355, 320, and two separate 160) of equal thickness. In contrast, the single and double progressive thickness of KeraRing 160 caused a significantly lower flattening effect compared to the same type with constant thickness. The observations indicated that the greater the segment thickness and arc-length, the lower the induced mean keratometry values. While the application of the tunnel incision method resulted in a lower $$\text {K}_{\text{mean}}$$ K mean value for moderate and advanced KC, the induced maximum Von Mises stress on the postoperative cornea exceeded the induced maximum stress on the cornea more than two to five times compared to the pocket incision and the preoperative state of the cornea. In particular, an asymmetric regional Von Mises stress on the corneal surface was generated with a progressive ICRS thickness. These findings could be an early biomechanical sign for a later corneal instability and ICRS migration. The developed methodology provided a platform to personalize ICRS refractive surgery with regard to the patient’s keratoconus stage in order to facilitate the efficiency and biomechanical stability of the surgery.

Mechanics of Composite Layered Rough Medium in Contact

2013 ◽  
Vol 703 ◽  
pp. 200-203
Author(s):  
Shao Biao Cai ◽  
Yong Li Zhao
Keyword(s):  
Material Properties ◽  
Three Dimensional ◽  
Shear Stresses ◽  
Normal Loading ◽  
Layered Coatings ◽  
Pressure Profiles ◽  
Tangential Traction ◽  
Von Mises ◽  
Von Mises Stresses ◽  
Tangential Friction

This study presents a first attempt to develop a numerical three-dimensional multilayered (more than 2 composite layered coatings) elasticperfectly plastic rough solids model to investigate the contact behavior under combined normal loading and tangential traction. Contact analyses are performed to study the effects composite thin film layers. Local contact pressure profiles, von Mises stresses, and shear stresses as a function of material properties and applied normal and tangential friction loads are calculated.

scholarly journals Biomechanical assessment of different fixation methods in mandibular high sagittal oblique osteotomy using a three-dimensional finite element analysis model

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Charles Savoldelli ◽  
Elodie Ehrmann ◽  
Yannick Tillier
Keyword(s):  
Finite Element ◽  
Stress Distribution ◽  
Three Dimensional ◽  
Von Mises Stress ◽  
Analysis Model ◽  
Element Analysis ◽  
Fixation Methods ◽  
Oblique Osteotomy ◽  
Von Mises

AbstractWith modern-day technical advances, high sagittal oblique osteotomy (HSOO) of the mandible was recently described as an alternative to bilateral sagittal split osteotomy for the correction of mandibular skeletal deformities. However, neither in vitro nor numerical biomechanical assessments have evaluated the performance of fixation methods in HSOO. The aim of this study was to compare the biomechanical characteristics and stress distribution in bone and osteosynthesis fixations when using different designs and placing configurations, in order to determine a favourable plating method. We established two finite element models of HSOO with advancement (T1) and set-back (T2) movements of the mandible. Six different configurations of fixation of the ramus, progressively loaded by a constant force, were assessed for each model. The von Mises stress distribution in fixations and in bone, and bony segment displacement, were analysed. The lowest mechanical stresses and minimal gradient of displacement between the proximal and distal bony segments were detected in the combined one-third anterior- and posterior-positioned double mini-plate T1 and T2 models. This suggests that the appropriate method to correct mandibular deformities in HSOO surgery is with use of double mini-plates positioned in the anterior one-third and posterior one-third between the bony segments of the ramus.

scholarly journals Elasto-plastic analysis of the contact region between a rigid ellipsoid and a semi-flat surface

2018 ◽  
Vol 10 (9) ◽  
pp. 168781401879739 ◽  
Author(s):  
Pengyang Li ◽  
Lingxia Zhou ◽  
Fangyuan Cui ◽  
Quandai Wang ◽  
Meiling Guo ◽  
...  
Keyword(s):  
Residual Stress ◽  
Plastic Deformation ◽  
Plastic Strain ◽  
Contact Pressure ◽  
Contact Region ◽  
Three Dimensional ◽  
Von Mises Stress ◽  
Effective Plastic Strain ◽  
Normal Forces ◽  
Von Mises

When the load acting on a mechanical structure is greater than the yield strength of the material, the contact surface will undergo plastic deformation. Cumulative plastic deformation has an important influence on the lifespan of mechanical parts. This article presents a three-dimensional semi-analytical model based on the conjugate gradient method and fast Fourier transform algorithm, with the aim of studying the characteristic parameters of the contact region between a rigid ellipsoid and elasto-plastic half-space. Moreover, normal forces and tangential traction were considered, as well as the contact pressure resulting from various sliding speeds and friction coefficients. The contact pressure, effective plastic strain, von Mises stress, and residual stress were measured and shown to increase with increasing sliding velocity. Finally, when the friction coefficient, contact pressure, and effective plastic strain are increased, the von Mises stress is also shown to increase, whereas the residual stress decreases.

scholarly journals The Hausdorff dimension and exact Hausdorff measure of random recursive sets with overlapping

2002 ◽  
Vol 31 (1) ◽  
pp. 11-21 ◽  
Author(s):  
Hongwen Guo ◽  
Dihe Hu
Keyword(s):  
Hausdorff Dimension ◽  
Hausdorff Measure ◽  
Intersection Property ◽  
Random Sets ◽  
Hausdorff Measures ◽  
Open Set Condition ◽  
Finite Intersection ◽  
Open Set ◽  
Finite Intersection Property

We weaken the open set condition and define a finite intersection property in the construction of the random recursive sets. We prove that this larger class of random sets are fractals in the sense of Taylor, and give conditions when these sets have positive and finite Hausdorff measures, which in certain extent generalize some of the known results, about random recursive fractals.

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