Numerical techniques for the variable order time fractional diffusion equation

In this paper we consider the variable order time fractional diffusion equation. We adopt the Coimbra variable order (VO) time fractional operator, which defines a consistent method for VO differentiation of physical variables. The Coimbra variable order fractional operator also can be viewed as a Caputo-type definition. Although this definition is the most appropriate definition having fundamental characteristics that are desirable for physical modeling, numerical methods for fractional partial differential equations using this definition have not yet appeared in the literature. Here an approximate scheme is first proposed. The stability, convergence and solvability of this numerical scheme are discussed via the technique of Fourier analysis. Numerical examples are provided to show that the numerical method is computationally efficient. Crown Copyright © 2012 Published by Elsevier Inc. All rights reserved.

Analytical solutions for the multi-term time-fractional diffusion-wave/diffusion equations in a finite domain

Multi-term time-fractional differential equations have been used for describing important physical phenomena. However, studies of the multi-term time-fractional partial differential equations with three kinds of nonhomogeneous boundary conditions are still limited. In this paper, a method of separating variables is used to solve the multi-term time-fractional diffusion-wave equation and the multi-term time-fractional diffusion equation in a finite domain. In the two equations, the time-fractional derivative is defined in the Caputo sense. We discuss and derive the analytical solutions of the two equations with three kinds of nonhomogeneous boundary conditions, namely, Dirichlet, Neumann and Robin conditions, respectively.

Solution methods for advection-diffusion-reaction equations on growing domains and subdomains, with application to modelling skin substitutes

Problems involving the solution of advection-diffusion-reaction equations on domains and subdomains whose growth affects and is affected by these equations, commonly arise in developmental biology. Here, a mathematical framework for these situations, together with methods for obtaining spatio-temporal solutions and steady states of models built from this framework, is presented. The framework and methods are applied to a recently published model of epidermal skin substitutes. Despite the use of Eulerian schemes, excellent agreement is obtained between the numerical spatio-temporal, numerical steady state, and analytical solutions of the model.

Langevin dynamics modeling of the water diffusion tensor in partially aligned collagen networks

In this work, a Langevin dynamics model of the diffusion of water in articular cartilage was developed. Numerical simulations of the translational dynamics of water molecules and their interaction with collagen fibers were used to study the quantitative relationship between the organization of the collagen fiber network and the diffusion tensor of water in model cartilage. Langevin dynamics was used to simulate water diffusion in both ordered and partially disordered cartilage models. In addition, an analytical approach was developed to estimate the diffusion tensor for a network comprising a given distribution of fiber orientations. The key findings are that (1) an approximately linear relationship was observed between collagen volume fraction and the fractional anisotropy of the diffusion tensor in fiber networks of a given degree of alignment, (2) for any given fiber volume fraction, fractional anisotropy follows a fiber alignment dependency similar to the square of the second Legendre polynomial of cos(θ), with the minimum anisotropy occurring at approximately the magic angle (θMA), and (3) a decrease in the principal eigenvalue and an increase in the transverse eigenvalues is observed as the fiber orientation angle θ progresses from 0◦ to 90◦. The corresponding diffusion ellipsoids are prolate for θ < θMA, spherical for θ ≈ θMA, and oblate for θ > θMA. Expansion of the model to include discrimination between the combined effects of alignment disorder and collagen fiber volume fraction on the diffusion tensor is discussed.

Lateral movements in composite high-rise buildings under seismic action

Daring human nature has already led to the construction of high-rise buildings in naturally challenging geological regions and in worse environments of the world. However; literature review divulges that there is a lag in research of certain generic principles and rules for the prediction of lateral movement in multistorey construction. The present competitive trend orders the best possible used of available construction material and resources. Hence; the mixed used of reinforced concrete with structural steel is gaining prevalence day by day. This paper investigates the effects of Seismic load on composite multistorey building provided with core wall and trusses through FEM modelling. The results showed that increased rigidity corresponds to lower period of vibration and hence higher seismic forces. Since Seismic action is a function of mass and response acceleration, therefore; mass increment generate higher earthquake load and thus cause higher impact base shear and overturning movement. Whereas; wind force depends on building exposed, larger the plan dimension greater is the wind impact. Nonetheless; outriggers trusses noticeably contribute, in improving the serviceability of structure subjected to wind and earthquake forces.

Quantitative studies of lower motor neuron degeneration in amyotrophic lateral sclerosis : Evidence for exponential decay of motor unit numbers and greatest rate of loss at the site of onset

Objective: To use our Bayesian method of motor unit number estimation (MUNE) to evaluate lower motor neuron degeneration in ALS. Methods: In subjects with ALS we performed serial MUNE studies. We examined the repeatability of the test and then determined whether the loss of MUs was fitted by an exponential or Weibull distribution. Results: The decline in motor unit (MU) numbers was well-fitted by an exponential decay curve. We calculated the half life of MUs in the abductor digiti minimi (ADM), abductor pollicis brevis (APB) and/or extensor digitorum brevis (EDB) muscles. The mean half life of the MUs of ADM muscle was greater than those of the APB or EDB muscles. The half-life of MUs was less in the ADM muscle of subjects with upper limb than in those with lower limb onset. Conclusions: The rate of loss of lower motor neurons in ALS is exponential, the motor units of the APB decay more quickly than those of the ADM muscle and the rate of loss of motor units is greater at the site of onset of disease. Significance: This shows that the Bayesian MUNE method is useful in following the course and exploring the clinical features of ALS. 2012 International Federation of Clinical Neurophysiology.

Effect of body position on measurements of diffusion capacity after exercise

Background--Pulmonary diffusing capacity for carbon monoxide (Dlco), alveolar capillary membrane diffusing capacity (Dm), and pulmonary capillary blood volume (Vc) are all significantly reduced after exercise. Objective--To investigate whether measurement position affects this impaired gas transfer. Methods--Before and one, two, and four hours after incremental cycle ergometer exercise to fatigue, single breath Dlco, Dm, and Vc measurements were obtained in 10 healthy men in a randomly assigned supine and upright seated position. Results--After exercise, Dlco, Dm, and Vc were significantly depressed compared with baseline in both positions. The supine position produced significantly higher values over time for Dlco (5.22 (0.13) v 4.66 (0.15) ml/min/mm Hg/l, p = 0.022) and Dm (6.78 (0.19) v 6.03 (0.19) ml/min/mm Hg/l, p = 0.016), but there was no significant position effect for Vc. There was a similar pattern of change over time for Dlco, Dm, and Vc in the two positions. Conclusions--The change in Dlco after exercise appears to be primarily due to a decrease in Vc. Although the mechanism for the reduction in Vc cannot be determined from these data, passive relocation of blood to the periphery as the result of gravity can be discounted, suggesting that active vasoconstriction of the pulmonary vasculature and/or peripheral vasodilatation is occurring after exercise.

Measurement constructs to explore innovation diffusion in construction

Although the drivers of innovation have been studied extensively in construction, greater attention is required on how innovation diffusion can be effectively assessed within this complex and interdependent project-based industry. The authors draw on a highly cited innovation diffusion model by Rogers (2006) and develop a tailored conceptual framework to guide future empirical work aimed at assessing innovation diffusion in construction. The conceptual framework developed and discussed in this paper supports a five-stage process model of innovation diffusion namely: 1) knowledge and idea generation, 2) persuasion and evaluation; 3) decision to adopt, 4) integration and implementation, and 5) confirmation. As its theoretical contribution, this paper proposes three critical measurements constructs which can be used to assess the effectiveness of the diffusion process. These measurement constructs comprise: 1) nature and introduction of an innovative idea, 2) organizational capacity to acquire, assimilate, transform and exploit an innovation, and 3) rates of innovation facilitation and adoption. The constructs are interpreted in the project-based context of the construction industry, extending the contribution of general management theorists. Research planned by the authors will test the validity and reliability of the constructs developed in this paper.

Comparative study of depth-dependent characteristics of equine and human osteochondral tissue from the medial and lateral femoral condyles

Articular cartilage defects are common after joint injuries. When left untreated, the biomechanical protective function of cartilage is gradually lost, making the joint more susceptible to further damage, causing progressive loss of joint function and eventually osteoarthritis (OA). In the process of translating promising tissue-engineering cartilage repair approaches from bench to bedside, pre-clinical animal models including mice, rabbits, goats, and horses, are widely used. The equine species is becoming an increasingly popular model for the in vivo evaluation of regenerative orthopaedic approaches. As there is also an increasing body of evidence suggesting that successful lasting tissue reconstruction requires an implant that mimics natural tissue organization, it is imperative that depth-dependent characteristics of equine osteochondral tissue are known, to assess to what extent they resemble those in humans. Therefore, osteochondral cores (4-8 mm) were obtained from the medial and lateral femoral condyles of equine and human donors. Cores were processed for histology and for biochemical quantification of DNA, glycosaminoglycan (GAG) and collagen content. Equine and human osteochondral tissues possess similar geometrical (thickness) and organizational (GAG, collagen and DNA distribution with depth) features. These comparable trends further underscore the validity of the equine model for the evaluation of regenerative approaches for articular cartilage.

Stromal upregulation of lateral epithelial adhesions : gene expression analysis of signalling pathways in prostate epithelium

BACKGROUND: Stromal signalling increases the lateral cell adhesions of prostate epithelial cells grown in 3D culture. The aim of this study was to use microarray analysis to identify significant epithelial signalling pathways and genes in this process. METHODS: Microarray analysis was used to identify genes that were differentially expressed when epithelial cells were grown in 3D Matrigel culture with stromal co-culture compared to without stroma. Two culture models were employed: primary epithelial cells (ten samples) and an epithelial cell line (three experiments). A separate microarray analysis was performed on each model system and then compared to identify tissue-relevant genes in a cell line model. RESULTS: TGF beta signalling was significantly ranked for both model systems and in both models the TGF beta signalling gene SOX4 was significantly down regulated. Analysis of all differentially expressed genes to identify genes that were common to both models found several morphology related gene clusters; actin binding (DIAPH2, FHOD3, ABLIM1, TMOD4, MYH10), GTPase activator activity (BCR, MYH10), cytoskeleton (MAP2, MYH10, TMOD4, FHOD3), protein binding (ITGA6, CD44), proteinaceous extracellular matrix (NID2, CILP2), ion channel/ ion transporter activity (CACNA1C, CACNB2, KCNH2, SLC8A1, SLC39A9) and genes associated with developmental pathways (POFUT1, FZD2, HOXA5, IRX2, FGF11, SOX4, SMARCC1). CONCLUSIONS: In 3D prostate cultures, stromal cells increase lateral epithelial cell adhesions. We show that this morphological effect is associated with gene expression changes to TGF beta signalling, cytoskeleton and anion activity.

Stroma regulates increased epithelial lateral cell adhesion in 3D culture : a role for actin/cadherin dynamics

BACKGROUND: Cell shape and tissue architecture are controlled by changes to junctional proteins and the cytoskeleton. How tissues control the dynamics of adhesion and cytoskeletal tension is unclear. We have studied epithelial tissue architecture using 3D culture models and found that adult primary prostate epithelial cells grow into hollow acinus-like spheroids. Importantly, when co-cultured with stroma the epithelia show increased lateral cell adhesions. To investigate this mechanism further we aimed to: identify a cell line model to allow repeatable and robust experiments; determine whether or not epithelial adhesion molecules were affected by stromal culture; and determine which stromal signalling molecules may influence cell adhesion in 3D epithelial cell cultures. METHODOLOGY/PRINCIPAL FINDINGS: The prostate cell line, BPH-1, showed increased lateral cell adhesion in response to stroma, when grown as 3D spheroids. Electron microscopy showed that 9.4% of lateral membranes were within 20 nm of each other and that this increased to 54% in the presence of stroma, after 7 days in culture. Stromal signalling did not influence E-cadherin or desmosome RNA or protein expression, but increased E-cadherin/actin co-localisation on the basolateral membranes, and decreased paracellular permeability. Microarray analysis identified several growth factors and pathways that were differentially expressed in stroma in response to 3D epithelial culture. The upregulated growth factors TGFβ2, CXCL12 and FGF10 were selected for further analysis because of previous associations with morphology. Small molecule inhibition of TGFβ2 signalling but not of CXCL12 and FGF10 signalling led to a decrease in actin and E-cadherin co-localisation and increased paracellular permeability. CONCLUSIONS/SIGNIFICANCE: In 3D culture models, paracrine stromal signals increase epithelial cell adhesion via adhesion/cytoskeleton interactions and TGFβ2-dependent mechanisms may play a key role. These findings indicate a role for stroma in maintaining adult epithelial tissue morphology and integrity.

A note on a reaction-diffusion model describing the bone morphogen protein gradient in Drosophila embryonic patterning

In this article, we consider the Eldar model [3] from embryology in which a bone morphogenic protein, a short gastrulation protein, and their compound react and diffuse. We carry out a perturbation analysis in the limit of small diffusivity of the bone morphogenic protein. This analysis establishes conditions under which some elementary results of [3] are valid.

Near-Wall Turbulent Pressure Diffusion Modeling and Influence in Three-Dimensional Secondary Flows

The purpose of this paper is to develop a second-moment closure with a near-wall turbulent pressure diffusion model for three-dimensional complex flows, and to evaluate the influence of the turbulent diffusion term on the prediction of detached and secondary flows. A complete turbulent diffusion model including a near-wall turbulent pressure diffusion closure for the slow part was developed based on the tensorial form of Lumley and included in a re-calibrated wall-normal-free Reynolds-stress model developed by Gerolymos and Vallet. The proposed model was validated against several one-, two, and three-dimensional complex flows.