We compare the performance of line Gauss-Seidel (LGS), point Gauss-Seidel (PGS), and alternating ... more We compare the performance of line Gauss-Seidel (LGS), point Gauss-Seidel (PGS), and alternating direction implicit (ADI) linear solvers used in the artificial compressibility method for the numerical solution of the three-dimensional incompressible Navier-Stokes equations. Spatial discretization is carried out using a fifth-order WENO scheme for the convective terms and a second-order central difference scheme for the viscous terms. A comparison is made by simulating the spherical Couette flow problem, with only the inner sphere rotating and the outer one fixed. OpenMP is used for numerical computation in parallel for the three schemes. First, we compare the numerical efficiency of the solvers by computing 0-vortex flow for a medium-gap σ = (R 2 − R 1)/R 1 = 0.25. Second, we make a residual comparison for a steadystate flow calculation based on the CFL number and artificial compressibility factor. Finally, we compare the three solvers for unsteady flow computations based on the artificial compressibility factor. The results show that the LGS solver is more reliable than the PGS and the ADI solvers. To show the accuracy of the LGS scheme, we compute different flow modes for an intermediate-gap clearance ratio σ = (R 2 − R 1)/R 1 = 0.14. The computed results have good agreement with the existing numerical results.
Comparative Analysis of Low Versus High Implant Density in Decreasing Cobb Angle in Lenke Type 1 Adolescents Idiopathic Scoliosis
Objective: To compare low versus high implant density in decreasing Cobb angle in Lenke Type 1 Ad... more Objective: To compare low versus high implant density in decreasing Cobb angle in Lenke Type 1 Adolescent Idiopathic Scoliosis(AIS) treated with segmental spinal instrumentation and pedicle screws. Methods: This retrospective Cohort study was conducted at Department of Orthopedic and Spine Surgery, Ghurki Trust Teaching Hospital/ Lahore Medical and Dental College, Lahore. The medical records of patients between 15th June 2015 to 15th June 2019 who underwent segmental spinal instrumentation for Lenke type 1 adolescent idiopathic scoliosis were reviewed. Low implant density was defined as patients with pedicle screw density per fused segment of 60 %( ?1.2) or less while high density patients had more than 60 % (> 1.2) screw density. Radiographs were evaluated preoperatively for Cobb angle of main thoracic curve, sagittal and lumbar modifier. Postoperative evaluation included postoperative Cobb angle, percent Cobb angle decease, implant density and implant cost. Independent sample t...
International Journal of Advanced and Applied Sciences, 2018
Article history: Received 9 August 2017 Received in revised form 20 November 2017 Accepted 30 Nov... more Article history: Received 9 August 2017 Received in revised form 20 November 2017 Accepted 30 November 2017 In this paper, accurate and efficient calculations of the flow inside different types of cavities are presented. The incompressible Navier-Stokes equations are expressed in generalized curvilinear coordinates using artificial compressibility method. The governing equation in conservative form is solved numerically using an upwind compact finite difference scheme. The solution algorithm for solving the resulting linear system of equation is approximate factorization based ADI scheme. The computed results are compared with the results in the literature and the agreement is good. Also the presence of multiple solution and critical value of aspect ratio and Reynolds number for two sided cavity calculated and compared.
Plant growth regulators and EDTA improve phytoremediation potential and antioxidant response of Dysphania ambrosioides (L.) Mosyakin & Clemants in a Cd-spiked soil
Environmental Science and Pollution Research, 2021
Soil pollution due to potentially toxic elements is a worldwide challenge for health and food sec... more Soil pollution due to potentially toxic elements is a worldwide challenge for health and food security. Chelate-assisted phytoextraction along with the application of plant growth regulators (PGRs) could increase the phytoremediation efficiency of metal-contaminated soils. The present study was conducted to investigate the effect of different PGRs [Gibberellic acid (GA3) and indole acetic acid (IAA)] and synthetic chelator (EDTA) on growth parameters and Cd phytoextraction potential of Dysphania ambrosioides (L.) Mosyakin & Clemants grown under Cd-spiked soil. GA3 (10−7 M) and IAA (10−5 M) were applied four times with an interval of 10 days through a foliar spray, while EDTA (40 mg kg−1 soil) was once added to the soil. The results showed that Cd stress significantly decreased fresh biomass, dry biomass, total water contents, and photosynthetic pigments as compared to control. Application of PGRs significantly enhanced plant growth and Cd phytoextraction. The combined application of GA3 and IAA with EDTA significantly increased Cd accumulation (6.72 mg pot−1 dry biomass) and bioconcentration factor (15.21) as compared to C1 (Cd only). The same treatment significantly increased chlorophyll, proline, phenolic contents, and antioxidant activities (CAT, SOD, and POD) while MDA contents were reduced. In roots, Cd accumulation showed a statistically significant and positive correlation with proline, phenolics, fresh biomass, and dry biomass. Similarly, Cd accumulation showed a positive correlation with antioxidant enzyme activities in leaves. D. ambrosioides showed hyperaccumulation potential for Cd, based on bioconcentration factor (BCF) > 1. In conclusion, exogenous application of GA3 and IAA reduces Cd stress while EDTA application enhances Cd phytoextraction and ultimately the phytoremediation potential of D. ambrosioides.
A modified Hager-Zhang conjugate gradient method with optimal choices for solving monotone nonlinear equations
International Journal of Computer Mathematics, 2021
The conjugate gradient method is one of the most robust algorithms to solve large-scale monotone ... more The conjugate gradient method is one of the most robust algorithms to solve large-scale monotone problems due to its limited memory requirements. However, in this article, we used the modified secant equation and proposed two optimal choices for the non-negative constant of the Hager-Zhang (HZ) conjugate gradient method by minimizing the upper bound of the condition number for the HZ search direction matrix. Two algorithms for solving large-scale non-linear monotone equations that incorporate the concept of projection method are provided. Based on monotone and Lipschitz continuous assumptions, we developed the global convergence of the methods. Computational results indicate that the proposed algorithms are effective and efficient.
Solving nonlinear monotone operator equations via modified SR1 update
Journal of Applied Mathematics and Computing, 2021
In this paper, we propose two algorithms for solving nonlinear monotone operator equations. The t... more In this paper, we propose two algorithms for solving nonlinear monotone operator equations. The two algorithms are based on the conjugate gradient method. The corresponding search directions were obtained via a modified memoryless symmetric rank-one (SR1) update. Independent of the line search, the two directions were shown to be sufficiently descent and bounded. Moreover, the convergence of the algorithms were established under suitable assumptions on the operator under consideration. In addition, numerical experiments were conducted on some benchmark test problems to depict the efficiency and competitiveness of the algorithms compared with existing algorithms. From the results of the experiments, we can conclude that the proposed algorithms are more efficient and robust.
In this article, we proposed two Conjugate Gradient (CG) parameters using the modified Dai–Liao c... more In this article, we proposed two Conjugate Gradient (CG) parameters using the modified Dai–Liao condition and the descent three-term CG search direction. Both parameters are incorporated with the projection technique for solving large-scale monotone nonlinear equations. Using the Lipschitz and monotone assumptions, the global convergence of methods has been proved. Finally, numerical results are provided to illustrate the robustness of the proposed methods.
A derivative‐free scaling memoryless Broyden–Fletcher–Goldfarb–Shanno method for solving a system of monotone nonlinear equations
Numerical Linear Algebra with Applications, 2021
This paper presents the two‐parameter scaling memoryless Broyden–Fletcher–Goldfarb–Shanno (BFGS) ... more This paper presents the two‐parameter scaling memoryless Broyden–Fletcher–Goldfarb–Shanno (BFGS) method for solving a system of monotone nonlinear equations. The optimal values of the scaling parameters are obtained by minimizing the measure function involving all the eigenvalues of the memoryless BFGS matrix. The optimal values can be used in the analysis of the quasi‐Newton method for ill‐conditioned matrices. This algorithm can also be described as a combination of the projection technique and memoryless BGFS method. Global convergence of the method is provided. For validation and efficiency of the scheme, some test problems are computed and compared with existing results.
This is a PDF file of an article that has undergone enhancements after acceptance, such as the ad... more This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
In this paper, an approximate analytical solution of the bistable Allen-Cahn equation is given. T... more In this paper, an approximate analytical solution of the bistable Allen-Cahn equation is given. The Allen-Cahn equation is a mathematical model to study the phase separation process in binary alloys and emerged as a convection-diffusion equation in fluid dynamics or reaction-diffusion equation in material sciences. A phase transition occurs at the interface when one material changes its composition or structure. The homotopy perturbation method and homotopy analysis method are used for finding the approximate solution. These methods don't need the use of any transformation, discretization, unrealistic restriction and assumption. The error estimates are computed by comparing with a numerical method, and a good agreement is observed.
The purpose of this paper is to simulate a two-dimensional Rayleigh-Taylor instability problem us... more The purpose of this paper is to simulate a two-dimensional Rayleigh-Taylor instability problem using the diffuse-interface formulation of the incompressible Navier-Stokes equations. The governing equations consist of a system of coupled nonlinear partial differential equations for conservation of mass, momentum and phase transport. The Boussinesq approximation is introduced in the momentum equation to relax the complexity of variable density formulation. Due to the simplicity, this approximation can be used for small density variations in simulating two-phase flows. The numerical scheme is based on an artificial compressibility formulation with a finite difference scheme for the space discretization. To validate the method, the penetration of a heavier fluid into the lighter one is computed and illustrated graphically.
An efficient time-stepping scheme for numerical simulation of dendritic crystal growth
European Journal of Computational Mechanics, 2016
In this article, we present an adaptive time-stepping technique for numerical simulation of dendr... more In this article, we present an adaptive time-stepping technique for numerical simulation of dendritic crystal growth model. The diagonally implicit fractional step -scheme for time discretisation and conforming finite-element method for space discretisation are used. The performance of the scheme is illustrated by simulating two-dimensional dendritic crystal growth problem, allowing the comparison with other numerical methods. In addition, traditional diagonally implicit Runge–Kutta method is used and comparison is given with the proposed scheme. Robustness is observed for the present scheme. Parametric effects on the growth and shape of dendrites are also given.
Journal of the Brazilian Society of Mechanical Sciences and Engineering, 2018
We study the existence regime of symmetric and asymmetric Taylor vortices in wide-gap spherical C... more We study the existence regime of symmetric and asymmetric Taylor vortices in wide-gap spherical Couette flow by time marching the three-dimensional incompressible Navier-Stokes equations numerically. Three wide-gap clearance ratios, b ¼ R 2 À R 1 ð Þ =R 1 ¼ 0:33, 0.38 and 0.42 are investigated for a range of Reynolds numbers respectively. Using the 1-vortex flow for clearance ratio b ¼ 0:18 at Reynolds number Re ¼ 700 as the initial conditions and suddenly increasing b to the target value, we can compute Taylor vortices for the three wide gaps. For b ¼ 0:33, Taylor vortices exist in the range 450 Re 2050. With increasing Re the steady symmetric 1-vortex flow becomes steady asymmetric at Re ¼ 1850, and then become periodic at Re ¼ 2000. When Re [ 2050 the flow returns back to the steady basic flow state with no Taylor vortices. For b ¼ 0:38, Taylor vortices can exist in the range 500 Re 1400. With increasing Re, the steady symmetric 1-vortex flow become steady asymmetric at Re ¼ 1200, and then the flow evolves into the steady basic flow for Re [ 1400. For b ¼ 0:42, Taylor vortices can exist in the range 650 Re 1300. With increasing Re, steady asymmetric Taylor vortices occur at Re ¼ 1150, and then the flow evolves into the steady basic flow for Re [ 1300. The present numerical results are in good agreement with available numerical and experimental results. Furthermore, the existence regime of Taylor vortices in the ðb; ReÞ plane for b ! 0:33 and the three-dimensional transition process from periodic asymmetric vortex flow to steady basic flow with increasing Re are presented for the first time. Keywords Spherical Couette flow Á Wide gap Á Symmetric Taylor vortices Á Asymmetric Taylor vortices
Journal of the Brazilian Society of Mechanical Sciences and Engineering, 2019
We study the multiple steady and unsteady flow modes in a medium-gap spherical Couette flow (SCF)... more We study the multiple steady and unsteady flow modes in a medium-gap spherical Couette flow (SCF) by solving the three-dimensional incompressible Navier-Stokes equations. We have used an artificial compressibility method with an implicit line Gauss-Seidel scheme. The simulations are performed in SCF with only the inner sphere rotating. A mediumgap clearance ratio, = R 2 − R 1 ∕R 1 = 0.25, has been used to investigate various flow states in a range of Reynolds numbers, Re ∈ [400, 6500]. First, we compute the 0-vortex basic flow directly from the Stokes flow as an initial condition. This flow exists up to Re = 4900 after which it evolves into spiral 0-vortex flows with wavenumber s p = 3, 4 in the range Re ∈ [4900, 6000] , and then the flows become turbulent when Re > 6000. Second, we obtain the steady 1-vortex flow by using the 1-vortex flow at Re = 700 for = 0.18 as the initial conditions and found that it exists for Re ∈ [480, 4300]. The 1-vortex flow becomes wavy 1-vortex in the range Re ∈ [4400, 5000]. Further increasing the Reynolds number, we obtain new spiral waves of wavenumber s p = 3 for Re ∈ [5000, 6000]. The flow becomes turbulent when Re > 6000. Third, we obtain the steady 2-vortex flow by using the 2-vortex flow at Re = 900 for = 0.18 as the initial conditions and found that it exists for Re ∈ [700, 1900]. With increasing Reynolds number the 2-vortex flow becomes partially wavy 2-vortex in the small range Re ∈ [1900, 2100]. We obtain distorted spiral wavy 2-vortex in the range Re ∈ [4000, 5000]. when Re > 6000 the flow evolves into spiral 0-vortex flow and becomes turbulent. The present flow scenarios with increasing Re agree well with the experimental results and further we obtain new flow states for the 1-vortex and 2-vortex flows.
Numerical Methods for Partial Differential Equations, 2018
This article presents an efficient and robust algorithm for the numerical solution of the Allen-C... more This article presents an efficient and robust algorithm for the numerical solution of the Allen-Cahn equation, which represents the motion of antiphase boundaries. The proposed algorithm is based on the diagonally implicit fractional-step θ− scheme for time discretization and the conforming finite element method for space discretization. For the steady-state solution, both uniform and adaptive grids are used to illustrate the effectiveness of adaptive grids over uniform grids. For the unsteady solution, the diagonally implicit fractionalstep θ− scheme is compared with other time discretization schemes in terms of computational cost and temporal error estimation accuracy. Numerical examples are presented to illustrate the capabilities of the proposed algorithm in solving nonlinear partial differential equations.
microRNAs (miRNAs) are critical regulators of gene expression. For elucidating functional roles o... more microRNAs (miRNAs) are critical regulators of gene expression. For elucidating functional roles of miRNAs, it is critical to identify their direct targets. There are debates about whether pulldown of biotinylated miRNA mimics can be used to identify miRNA targets or not. Here we show that biotin-labelled miR-34a can be loaded to AGO2, and AGO2 immunoprecipitation can pulldown biotinylated miR-34a (Bio-miR pulldown). RNA-sequencing (RNA-seq) of the Bio-miR pulldown RNAs efficiently identified miR-34a mRNA targets, which could be verified with luciferase assays. In contrast to the approach of Bio-miR pulldown, RNA-seq of miR-34a overexpression samples had limited value in identifying direct targets of miR-34a. It seems that pulldown of 3'-Biotin-tagged miRNA can identify bona fide microRNA targets at least for miR-34a.
Computers & Mathematics with Applications, 2017
Solid tumor includes the areas where oxygen concentration is very low called hypoxia, often in th... more Solid tumor includes the areas where oxygen concentration is very low called hypoxia, often in the surrounding areas of necrosis. Hypoxic cells in these areas are resistant to chemotherapy and radiation therapy. The presence of hypoxia and necrosis enables tumorselective treatment, including hypoxia-activated prodrugs, tumor hypoxia-specific gene therapy and tumor-targeting bacterial therapy. This article deals with the mathematical formulation of tumor hypoxia-targeting by introducing a decay parameter of oxygen in the model given by Kolobov et al. (2009) and Avila et al. (2013). The well-posedness of the governing partial differential equations and numerical simulation are provided. For the purpose of numerical simulations, the conforming Q 1 finite element method for space discretization and second-order diagonally implicit fractional step θ-scheme for temporal discretization are used. The effect of oxygen on hypoxia, necrotic region decay and the maximum age of growing tumor cells are computed and illustrated graphically. It is observed that the distribution of nutrients in tissues have substantial effect on tumor growth rate and structure.
International journal of molecular sciences, Jan 29, 2017
MicroRNAs (miRNAs) play important roles under multiple cellular conditions including endoplasmic ... more MicroRNAs (miRNAs) play important roles under multiple cellular conditions including endoplasmic reticulum (ER) stress. We found that miR-3648, a human specific microRNA, was induced under ER stress. Moreover, Adenomatous polyposis coli 2 (APC2), a tumor suppressor and a negative regulator of Wnt signaling, was found to be the direct target of miR-3648. Levels of APC2 were downregulated when cells were under ER stress or after overexpressing miR-3648. Inhibition of miR-3648 by antagomir increased APC2 levels and decreased cell proliferation. Conversely, when miR-3648 was overexpressed, APC2 levels were decreased and the cell growth increased. Our data demonstrated that ER stress mediated induction of miR-3648 in human cells, which then downregulated APC2 to increase cell proliferation.
Background: AS is a chronic inflammatory disease characterized by axial skeletal pain and stiffne... more Background: AS is a chronic inflammatory disease characterized by axial skeletal pain and stiffness. Fatigue is an increasingly recognized problem among AS patients. It is common, disabling and strongly associated with impaired quality of life. This study aimed to identify determinants of AS fatigue with view to informing future therapies and, among those with high fatigue, to delineate predictors of persistent fatigue so as to aid the recognition of patients in greatest need of intervention. Methods: Using the Scotland and Ireland Registry for AS (SIRAS), a registry of 1909 patients with clinically diagnosed AS at the time of study, candidate clinical data were collected at recruitment and psycho-social variables, including fatigue status, were evaluated at recruitment and 1 year later via postal questionnaire. In addition, socioeconomic status was determined by post code according to the Scottish Index of Multiple Deprivation. For the purposes of analysis, fatigue was categorized according to established Chalder Fatigue Scale cutoffs (low < 4, high ! 4). Forward stepwise Poisson regression was used to identify factors associated with high fatigue and, among subjects with high levels of fatigue, to evaluate associations of persisting high fatigue 1 year later. Results are expressed as relative risks (RR) and 95% CIs. Results: At recruitment, 46.7% of responding subjects (n ¼ 392) reported high fatigue. Pain-induced sleep disturbance, anxiety/ depression and immobility were independent risk factors (RR 1.97,
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