Fluid Flow Analysis of Integrated Porous Bone Scaffold and Cancellous Bone at Different Skeletal Sites: In Silico Study

The dynamic characteristic of bone is its ability to remodel itself through mechanobiological responses. Bone regeneration is triggered by mechanical cues from physiological activities that generate structural strain and cause bone marrow movement. This phenomenon is crucial for bone scaffold when implanted in the cancellous bone as host tissue. Often, the fluid movement of bone scaffold and cancellous bone is studied separately, which does not represent the actual environment once implanted. In the present study, the fluid flow analysis properties of bone scaffold integrated into the cancellous bone at different skeletal sites are investigated. Three types of porous bone scaffolds categorized based on pore size configurations: 1 mm, 0.8 mm and hybrid (0.8 mm interlaced with 0.5 mm) were used. Three different skeletal sites of femoral bone were selected: neck, lateral condyle and medial condyle. Computational fluid dynamics was utilized to analyze the fluid flow properties of bone scaffold integrated cancellous bone. The results of this study reveal that the localization and maximum value of shear stress in an independent bone scaffold are significantly different compared to the bone scaffold integrated with cancellous bone by about 160% to 448% percentage difference. Low shear stress and high permeability were found across models that have higher Tb.Sp (trabecular separation). Specimen C and femoral lateral condyle showed the highest permeability in their respective category.

     

Multiscale data sampling and function extension

We introduce a multiscale scheme for sampling scattered data and extending functions defined on the sampled data points, which overcomes some limitations of the Nyström interpolation method. The multiscale extension (MSE) method is based on mutual distances between data points. It uses a coarse-to-fine hierarchy of the multiscale decomposition of a Gaussian kernel. It generates a sequence of subsamples, which we refer to as adaptive grids, and a sequence of approximations to a given empirical function on the data, as well as their extensions to any newly-arrived data point. The subsampling is done by a special decomposition of the associated Gaussian kernel matrix in each scale in the hierarchical procedure.     

Molecular dynamics simulation of gas adsorption on defected graphene

Gas sensing is one of the most promising applications for graphene. Using molecular dynamics simulation method, adsorption isotherm of xenon (Xe) gas on defected and perfect graphene is studied in order to investigate sensing properties of graphene for Xe gas. In this method, first generation of Brenner many-body potential is used to simulate the interaction of carbon–carbon (C) atoms in graphene, and Lennard–Jones two-body potential is used to simulate interaction of Xe–Xe and Xe–C atoms. In the simulated systems, adsorption coverage, radial distribution function, heat of adsorption, binding energy and specific heat capacity at constant volume are calculated for several temperatures between 90 K and 130 K, and various pressures. It was found that both of the defected and perfect graphene could be introduced as very good candidates for adsorption of Xe gas.     

A note on simultaneous preconditioning and symmetrization of non‐symmetric linear systems

Motivated by the theory of self‐duality that provides a variational formulation and resolution for non‐self‐adjoint partial differential equations (Ann. Inst. Henri Poincaré (C) Anal Non Linéaire 2007; 24 :171–205; Selfdual Partial Differential Systems and Their Variational Principles. Springer: New York, 2008), we propose new templates for solving large non‐symmetric linear systems. The method consists of combining a new scheme that simultaneously preconditions and symmetrizes the problem, with various well‐known iterative methods for solving linear and symmetric problems. The approach seems to be efficient when dealing with certain ill‐conditioned, and highly non‐symmetric systems. The numerical and theoretical results are provided to show the efficiency of our approach. Copyright © 2010 John Wiley & Sons, Ltd.     

Improved photonic crystal directional coupler with short length

We investigate a photonic crystal (PC) waveguide coupler which is formed by two closely spaced linear waveguides in a two-dimensional triangular lattice of air holes. Our study shows that shifting one row of the air holes between the waveguides affects the dispersion curves of the guided modes and if the triangular lattice of air holes between the waveguides is replaced by a rectangular lattice, this modification results in an ultra-short coupling structure with coupling length less than 3a, where a is the lattice constant. Also, we investigate the effect of changing the radii of air holes that are adjacent to or between the waveguides on the coupling length and show that increasing the radius of air holes between the waveguides decreases the coupling length. We analyze the output spectrum of an ultra-short channel drop filter designed based on this structure.     

A recyclable chiral Ru catalyst for enantioselective olefin metathesis. Efficient catalytic asymmetric ring-opening/cross metathesis in air

The synthesis and structure of a new chiral bidentate imidazolinylidene ligand and a derived chiral Ru-based carbene are disclosed. The Ru complex is stereogenic at the metal center; it can be prepared in >98% diastereoselectivity and purified by silica gel chromatography with undistilled solvents. The air-stable Ru complex efficiently catalyzes ring-closing and ring-opening metathesis and is recyclable. The chiral complex is highly effective (0.5-10 mol % loading) in promoting enantioselective ring-opening/cross metathesis reactions (up to >98% ee). These enantioselective transformations can be effected in air, with unpurified solvent and with substrates that would only polymerize with Mo-based catalysts.     

On parallel asynchronous high-order solutions of parabolic PDEs

In achieving significant speed-up on parallel machines, a major obstacle is the overhead associated with synchronizing the concurrent processes. This paper presents high-orderparallel asynchronous schemes, which are schemes that are specifically designed to minimize the associated synchronization overhead of a parallel machine in solving parabolic PDEs. They are asynchronous in the sense that each processor is allowed to advance at its own speed. Thus, these schemes are suitable for single (or multi) user shared memory or (message passing) MIMD multiprocessors. Our approach is demonstrated for the solution of the multidimensional heat equation, of which we present a spatial second-order Parametric Asynchronous Finite-Difference (PAFD) scheme. The well-known synchronous schemes are obtained as its special cases. This is a generalization and expansion of the results in [5] and [7]. The consistency, stability and convergence of this scheme are investigated in detail. Numerical tests show that although PAFD provides the desired order of accuracy, its efficiency is inadequate when performed on each grid point.In an alternative approach that uses domain decomposition, the problem domain is divided among the processors. Each processor computes its subdomain mostly independently, while the PAFD scheme provides the solutions at the subdomains' boundaries. We use high-order finite-difference implicit scheme within each subdomain and determine the values at subdomains' boundaries by the PAFD scheme. Moreover, in order to allow larger time-step, we use remote neighbors' values rather than those of the immediate neighbors. Numerical tests show that this approach provides high efficiency and in the case which uses remote neighbors' values an almost linear speedup is achieved. Schemes similar to the PAFD can be developed for other types of equations [3].This research was supported by the fund for promotion of research at the Technion.