Search results for: laplace approximation

Authors: Lewis J. Woollin, Robert I. Davidson, Paul Watson, Philip J. Hyde

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Introduction: In-vitro testing of arthroplasty materials is of paramount importance when ensuring that they can withstand the performance requirements encountered in-vivo. One common machine used for in-vitro testing is a pin-on-plate tribometer, an early stage screening device that generates data on the wear characteristics of arthroplasty bearing materials. These devices test vertically loaded rotating cylindrical pins acting against reciprocating plates, representing the bearing surfaces. In this study, a pin-on-plate machine has been developed that provides several improvements over current technology, thereby progressing arthroplasty bearing research. Historically, pin-on-plate tribometers have been used to investigate the performance of arthroplasty bearing materials under conditions commonly encountered during a standard gait cycle; nominal operating pressures of 2-6 MPa and an operating frequency of 1 Hz are typical. There has been increased interest in using pin-on-plate machines to test more representative in-vivo conditions, due to the drive to test 'beyond compliance', as well as their testing speed and economic advantages over hip simulators. Current pin-on-plate machines do not accommodate the increased performance requirements associated with more extreme kinematic conditions, therefore a next-generation pin-on-plate tribometer has been developed to bridge the gap between current technology and future research requirements. Methodology: The design was driven by several physiologically relevant requirements. Firstly, an increased loading capacity was essential to replicate the peak pressures that occur in the natural hip joint during running and chair-rising, as well as increasing the understanding of wear rates in obese patients. Secondly, the introduction of mid-cycle load variation was of paramount importance, as this allows for an approximation of the loads present in a gait cycle to be applied and to test the fatigue properties of materials. Finally, the rig must be validated against previous-generation pin-on-plate and arthroplasty wear data. Results: The resulting machine is a twelve station device that is split into three sets of four stations, providing an increased testing capacity compared to most current pin-on-plate tribometers. The loading of the pins is generated using a pneumatic system, which can produce contact pressures of up to 201 MPa on a 3.2 mm² round pin face. This greatly exceeds currently achievable contact pressures in literature and opens new research avenues such as testing rim wear of mal-positioned hip implants. Additionally, the contact pressure of each set can be changed independently of the others, allowing multiple loading conditions to be tested simultaneously. Using pneumatics also allows the applied pressure to be switched ON/OFF mid-cycle, another feature not currently reported elsewhere, which allows for investigation into intermittent loading and material fatigue. The device is currently undergoing a series of validation tests using Ultra-High-Molecular-Weight-Polyethylene pins and 316L Stainless Steel Plates (polished to a Ra < 0.05 µm). The operating pressures will be between 2-6 MPa, operating at 1 Hz, allowing for validation of the machine against results reported previously in the literature. The successful production of this next-generation pin-on-plate tribometer will, following its validation, unlock multiple previously unavailable research avenues.

Keywords: arthroplasty, mechanical design, pin-on-plate, total joint replacement, wear testing

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Authors: Vladimir A. Basiuk, Laura J. Flores-Sanchez, Victor Meza-Laguna, Jose O. Flores-Flores, Lauro Bucio-Galindo, Elena V. Basiuk

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Noncovalent nanohybrid materials combining carbon nanotubes (CNTs) with phthalocyanines (Pcs) is a subject of increasing research effort, with a particular emphasis on the design of new heterogeneous catalysts, efficient organic photovoltaic cells, lithium batteries, gas sensors, field effect transistors, among other possible applications. The possibility of using unsubstituted Pcs for CNT functionalization is very attractive due to their very moderate cost and easy commercial availability. However, unfortunately, the deposition of unsubstituted Pcs onto nanotube sidewalls through the traditional liquid-phase protocols turns to be very problematic due to extremely poor solubility of Pcs. On the other hand, unsubstituted free-base H₂Pc phthalocyanine ligand, as well as many of its transition metal complexes, exhibit very high thermal stability and considerable volatility under reduced pressure, which opens the possibility for their physical vapor deposition onto solid surfaces, including nanotube sidewalls. In the present work, we show the possibility of simple, fast and efficient noncovalent functionalization of single-walled carbon nanotubes (SWNTs) with a series of 3d metal(II) phthalocyanines Me(II)Pc, where Me= Co, Ni, Cu, and Zn. The functionalization can be performed in a temperature range of 400-500 °C under moderate vacuum and requires about 2-3 h only. The functionalized materials obtained were characterized by means of Fourier-transform infrared (FTIR), Raman, UV-visible and energy-dispersive X-ray spectroscopy (EDS), scanning and transmission electron microscopy (SEM and TEM, respectively) and thermogravimetric analysis (TGA). TGA suggested that Me(II)Pc weight content is 30%, 17% and 35% for NiPc, CuPc, and ZnPc, respectively (CoPc exhibited anomalous thermal decomposition behavior). The above values are consistent with those estimated from EDS spectra, namely, of 24-39%, 27-36% and 27-44% for CoPc, CuPc, and ZnPc, respectively. A strong increase in intensity of D band in the Raman spectra of SWNT‒Me(II)Pc hybrids, as compared to that of pristine nanotubes, implies very strong interactions between Pc molecules and SWNT sidewalls. Very high absolute values of binding energies of 32.46-37.12 kcal/mol and the highest occupied and lowest unoccupied molecular orbital (HOMO and LUMO, respectively) distribution patterns, calculated with density functional theory by using Perdew-Burke-Ernzerhof general gradient approximation correlation functional in combination with the Grimme’s empirical dispersion correction (PBE-D) and the double numerical basis set (DNP), also suggested that the interactions between Me(II) phthalocyanines and nanotube sidewalls are very strong. The authors thank the National Autonomous University of Mexico (grant DGAPA-IN200516) and the National Council of Science and Technology of Mexico (CONACYT, grant 250655) for financial support. The authors are also grateful to Dr. Natalia Alzate-Carvajal (CCADET of UNAM), Eréndira Martínez (IF of UNAM) and Iván Puente-Lee (Faculty of Chemistry of UNAM) for technical assistance with FTIR, TGA measurements, and TEM imaging, respectively.

Keywords: carbon nanotubes, functionalization, gas-phase, metal(II) phthalocyanines

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Authors: G. Hubert, S. Aubry

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The earth is constantly bombarded by cosmic rays that can be of either galactic or solar origin. Thus, humans are exposed to high levels of galactic radiation due to altitude aircraft. The typical total ambient dose equivalent for a transatlantic flight is about 50 μSv during quiet solar activity. On the contrary, estimations differ by one order of magnitude for the contribution induced by certain solar particle events. Indeed, during Ground Level Enhancements (GLE) event, the Sun can emit particles of sufficient energy and intensity to raise radiation levels on Earth's surface. Analyses of GLE characteristics occurring since 1942 showed that for the worst of them, the dose level is of the order of 1 mSv and more. The largest of these events was observed on February 1956 for which the ambient dose equivalent rate is in the orders of 10 mSv/hr. The extra dose at aircraft altitudes for a flight during this event might have been about 20 mSv, i.e. comparable with the annual limit for aircrew. The most recent GLE, occurred on September 2017 resulting from an X-class solar flare, and it was measured on the surface of both the Earth and Mars using the Radiation Assessment Detector on the Mars Science Laboratory's Curiosity Rover. Recently, Hubert et al. proposed a GLE model included in a particle transport platform (named ATMORAD) describing the extensive air shower characteristics and allowing to assess the ambient dose equivalent. In this approach, the GCR is based on the Force-Field approximation model. The physical description of the Solar Cosmic Ray (i.e. SCR) considers the primary differential rigidity spectrum and the distribution of primary particles at the top of the atmosphere. ATMORAD allows to determine the spectral fluence rate of secondary particles induced by extensive showers, considering altitude range from ground to 45 km. Ambient dose equivalent can be determined using fluence-to-ambient dose equivalent conversion coefficients. The objective of this paper is to analyze the GCR and SCR impacts on ambient dose equivalent considering a high number statistic of world-flight paths. Flight trajectories are based on the Eurocontrol Demand Data Repository (DDR) and consider realistic flight plan with and without regulations or updated with Radar Data from CFMU (Central Flow Management Unit). The final paper will present exhaustive analyses implying solar impacts on ambient dose equivalent level and will propose detailed analyses considering route and airplane characteristics (departure, arrival, continent, airplane type etc.), and the phasing of the solar event. Preliminary results show an important impact of the flight path, particularly the latitude which drives the cutoff rigidity variations. Moreover, dose values vary drastically during GLE events, on the one hand with the route path (latitude, longitude altitude), on the other hand with the phasing of the solar event. Considering the GLE occurred on 23 February 1956, the average ambient dose equivalent evaluated for a flight Paris - New York is around 1.6 mSv, which is relevant to previous works This point highlights the importance of monitoring these solar events and of developing semi-empirical and particle transport method to obtain a reliable calculation of dose levels.

Keywords: cosmic ray, human dose, solar flare, aviation

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Authors: Adrian W. Egger, Savvas P. Triantafyllou, Eleni N. Chatzi

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The scaled boundary finite element method (SBFEM) is a semi-analytical numerical method, which introduces a scaling center in each element’s domain, thus transitioning from a Cartesian reference frame to one resembling polar coordinates. Consequently, an analytical solution is achieved in radial direction, implying that only the boundary need be discretized. The only limitation imposed on the resulting polygonal elements is that they remain star-convex. Further arbitrary p- or h-refinement may be applied locally in a mesh. The polygonal nature of SBFEM elements has been exploited in quadtree meshes to alleviate all issues conventionally associated with hanging nodes. Furthermore, since in 2D this results in only 16 possible cell configurations, these are precomputed in order to accelerate the forward analysis significantly. Any cells, which are clipped to accommodate the domain geometry, must be computed conventionally. However, since SBFEM permits polygonal elements, significantly coarser meshes at comparable accuracy levels are obtained when compared with conventional quadtree analysis, further increasing the computational efficiency of this scheme. The generalized stress intensity factors (gSIFs) are computed by exploiting the semi-analytical solution in radial direction. This is initiated by placing the scaling center of the element containing the crack at the crack tip. Taking an analytical limit of this element’s stress field as it approaches the crack tip, delivers an expression for the singular stress field. By applying the problem specific boundary conditions, the geometry correction factor is obtained, and the gSIFs are then evaluated based on their formal definition. Since the SBFEM solution is constructed as a power series, not unlike mode superposition in FEM, the two modes contributing to the singular response of the element can be easily identified in post-processing. Compared to the extended finite element method (XFEM) this approach is highly convenient, since neither enrichment terms nor a priori knowledge of the singularity is required. Computation of the gSIFs by SBFEM permits exceptional accuracy, however, when combined with hybrid quadtrees employing linear elements, this does not always hold. Nevertheless, it has been shown that crack propagation schemes are highly effective even given very coarse discretization since they only rely on the ratio of mode one to mode two gSIFs. The absolute values of the gSIFs may still be subject to large errors. Hence, we propose a post-processing scheme, which minimizes the error resulting from the approximation space of the cracked element, thus limiting the error in the gSIFs to the discretization error of the quadtree mesh. This is achieved by h- and/or p-refinement of the cracked element, which elevates the amount of modes present in the solution. The resulting numerical description of the element is highly accurate, with the main error source now stemming from its boundary displacement solution. Numerical examples show that this post-processing procedure can significantly improve the accuracy of the computed gSIFs with negligible computational cost even on coarse meshes resulting from hybrid quadtrees.

Keywords: linear elastic fracture mechanics, generalized stress intensity factors, scaled finite element method, hybrid quadtrees

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Authors: Ece A. Irmak, Amdulla O. Mekhrabov, M. Vedat Akdeniz

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There is a growing interest in the modeling and simulation of magnetic nanoalloys by various computational methods. Magnetic crystalline/amorphous nanoparticles (NP) are interesting materials from both the applied and fundamental points of view, as their properties differ from those of bulk materials and are essential for advanced applications such as high-performance permanent magnets, high-density magnetic recording media, drug carriers, sensors in biomedical technology, etc. As an important magnetic material, Fe-Ni based nanoalloys have promising applications in the chemical industry (catalysis, battery), aerospace and stealth industry (radar absorbing material, jet engine alloys), magnetic biomedical applications (drug delivery, magnetic resonance imaging, biosensor) and computer hardware industry (data storage). The physical and chemical properties of the nanoalloys depend not only on the particle or crystallite size but also on composition and atomic ordering. Therefore, computer modeling is an essential tool to predict structural, electronic, magnetic and optical behavior at atomistic levels and consequently reduce the time for designing and development of new materials with novel/enhanced properties. Although first-principles quantum mechanical methods provide the most accurate results, they require huge computational effort to solve the Schrodinger equation for only a few tens of atoms. On the other hand, molecular dynamics method with appropriate empirical or semi-empirical inter-atomic potentials can give accurate results for the static and dynamic properties of larger systems in a short span of time. In this study, structural evolutions, magnetic and electronic properties of Fe-Ni based nanoalloys have been studied by using molecular dynamics (MD) method in Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) and Density Functional Theory (DFT) in the Vienna Ab initio Simulation Package (VASP). The effects of particle size (in 2-10 nm particle size range) and temperature (300-1500 K) on stability and structural evolutions of amorphous and crystalline Fe-Ni bulk/nanoalloys have been investigated by combining molecular dynamic (MD) simulation method with Embedded Atom Model (EAM). EAM is applicable for the Fe-Ni based bimetallic systems because it considers both the pairwise interatomic interaction potentials and electron densities. Structural evolution of Fe-Ni bulk and nanoparticles (NPs) have been studied by calculation of radial distribution functions (RDF), interatomic distances, coordination number, core-to-surface concentration profiles as well as Voronoi analysis and surface energy dependences on temperature and particle size. Moreover, spin-polarized DFT calculations were performed by using a plane-wave basis set with generalized gradient approximation (GGA) exchange and correlation effects in the VASP-MedeA package to predict magnetic and electronic properties of the Fe-Ni based alloys in bulk and nanostructured phases. The result of theoretical modeling and simulations for the structural evolutions, magnetic and electronic properties of Fe-Ni based nanostructured alloys were compared with experimental and other theoretical results published in the literature.

Keywords: density functional theory, embedded atom model, Fe-Ni systems, molecular dynamics, nanoalloys

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Authors: Artur Tyliszczak, Ewa Szymanek, Maciej Marek

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Flow through granular materials is important to a vast array of industries, for instance in construction industry where granular layers are used for bulkheads and isolators, in chemical engineering and catalytic reactors where large surfaces of packed granular beds intensify chemical reactions, or in energy production systems, where granulates are promising materials for heat storage and heat transfer media. Despite the common usage of granulates and extensive research performed in this field, phenomena occurring between granular solid elements or between solids and fluid are still not fully understood. In the present work we analyze the heat exchange process between the flowing medium (gas, liquid) and solid material inside the granular layers. We consider them as a composite of isolated solid elements and inter-granular spaces in which a gas or liquid can flow. The structure of the layer is controlled by shapes of particular granular elements (e.g., spheres, cylinders, cubes, Raschig rings), its spatial distribution or effective characteristic dimension (total volume or surface area). We will analyze to what extent alteration of these parameters influences on flow characteristics (turbulent intensity, mixing efficiency, heat transfer) inside the layer and behind it. Analysis of flow inside granular layers is very complicated because the use of classical experimental techniques (LDA, PIV, fibber probes) inside the layers is practically impossible, whereas the use of probes (e.g. thermocouples, Pitot tubes) requires drilling of holes inside the solid material. Hence, measurements of the flow inside granular layers are usually performed using for instance advanced X-ray tomography. In this respect, theoretical or numerical analyses of flow inside granulates seem crucial. Application of discrete element methods in combination with the classical finite volume/finite difference approaches is problematic as a mesh generation process for complex granular material can be very arduous. A good alternative for simulation of flow in complex domains is an immersed boundary-volume penalization (IB-VP) in which the computational meshes have simple Cartesian structure and impact of solid objects on the fluid is mimicked by source terms added to the Navier-Stokes and energy equations. The present paper focuses on application of the IB-VP method combined with large eddy simulation (LES). The flow solver used in this work is a high-order code (SAILOR), which was used previously in various studies, including laminar/turbulent transition in free flows and also for flows in wavy channels, wavy pipes and over various shape obstacles. In these cases a formal order of approximation turned out to be in between 1 and 2, depending on the test case. The current research concentrates on analyses of the flows in dense granular layers with elements distributed in a deterministic regular manner and validation of the results obtained using LES-IB method and body-fitted approach. The comparisons are very promising and show very good agreement. It is found that the size, number of elements and their distribution have huge impact on the obtained results. Ordering of the granular elements (or lack of it) affects both the pressure drop and efficiency of the heat transfer as it significantly changes mixing process.

Keywords: granular layers, heat transfer, immersed boundary method, numerical simulations

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