This paper presents a new version of the upwind compact finite difference scheme for solving the ... more This paper presents a new version of the upwind compact finite difference scheme for solving the incompressible Navier-Stokes equations in generalized curvilinear coordinates. The artificial compressibility approach is used, which transforms the elliptic-parabolic equations into the hyperbolic-parabolic ones so that flux difference splitting can be applied. The convective terms are approximated by a third-order upwind compact scheme implemented with flux difference splitting, and the viscous terms are approximated by a fourth-order central compact scheme. The solution algorithm used is the Beam-Warming approximate factorization scheme. Numerical solutions to benchmark problems of the steady plane Couette-Poiseuille flow, the liddriven cavity flow, and the constricting channel flow with varying geometry are presented. The computed results are found in good agreement with established analytical and numerical results. The third-order accuracy of the scheme is verified on uniform rectan...
Postoperative Changes and Outcomes in Intaoperative Neurophysiological Monitoring in Scoliosis Surgery
Objective: To evaluate the advantages of combined motor and sensory evoked potential monitoring d... more Objective: To evaluate the advantages of combined motor and sensory evoked potential monitoring during scoliosis surgery. Methods: We performed and analyzed the records of 107 (83 Female (77.5%) and 24 male (22.4%) Scoliosis surgery patients with Transcranial electric motor evoked potential and somatosensory evoked potential performed at spine surgery center, Ghurki Trust Teaching Hospital Lahore. Mean age was 14.7 years. Patients who showed significant up to (45%) in baseline signals loss unilateral or bilateral limbs during surgical intervention in scoliosis surgery under total intravenous anesthesia is included. Results: Motor Evoked Potentials and Somato-Sensory Evoked Potenials of 107 patients in intraoperative neurophysiological monitoring were performed jointly. 21 (19.6%) patients have mark or significant changes in baseline signals on transcranial motor evoked potentials. Seventeen 17 (15.8%) Patients have complete return of baseline signals after surgical intervention by s...
In this paper, we have analyzed the first- and second-order operator splitting schemes for the nu... more In this paper, we have analyzed the first- and second-order operator splitting schemes for the numerical solution of the Allen-Cahn equation. Different possibilities are considered for the derivation of the schemes. The numerical errors are computed in order to verify the effectiveness of each scheme. Validation of the schemes is provided by numerically solving some well-known examples.
This article presents an iterative scheme for solution of the viscous Cahn-Hilliard equation. The... more This article presents an iterative scheme for solution of the viscous Cahn-Hilliard equation. The procedure is based on the Variational Iteration Method (VIM) in which the solutions are calculated in the form of a convergent series with easily computable components. A good agreement is observed between the present solutions and that obtained by other iterative methods like Adomian Decomposition Method (ADM). However the VIM procedure is simple in implementation and provides very good and reliable results.
A study was conducted in four districts of Bangladesh, namely Faridpur sadar, Kolaroa (Satkhira),... more A study was conducted in four districts of Bangladesh, namely Faridpur sadar, Kolaroa (Satkhira), Shibaloya (Manikganj) and Natore sadar to assess arsenic (As) status in groundwater, agricultural soils, rice straw and rice grain. One hundred samples each of soil, irrigation water and plant parts (root, straw, husk and grain) were collected from the four areas for As determination. Results showed that the minimum mean of As in the soils (4 ± 0.17 ppm) and water (2 ± 1 ppb) was found in Natore Sadar, while the maximum in the soil (35 ± 16.03 ppm) and water (462 ± 28 ppb) was in Kolaroa (Satkhira). Murarikati, Keralkata, Jallabad, Jugikhali and Helatala of Kolaroa showed high As in the soils and groundwater. Similarly, high soil and water As were found in Aliabad, Kaijuri and Majchar (Faridpur) areas. The high As containing areas may be considered as arsenic hot spots. Arsenic content in the deep tube well water was also high in the Kolaroa area. In the hot spot areas, the level of As ...
This article presents an inexact optimal hybrid conjugate gradient (CG) method for solving symmet... more This article presents an inexact optimal hybrid conjugate gradient (CG) method for solving symmetric nonlinear systems. The method is a convex combination of the optimal Dai–Liao (DL) and the extended three-term Polak–Ribiére–Polyak (PRP) CG methods. However, two different formulas for selecting the convex parameter are derived by using the conjugacy condition and also by combining the proposed direction with the default Newton direction. The proposed method is again derivative-free, therefore the Jacobian information is not required throughout the iteration process. Furthermore, the global convergence of the proposed method is shown using some appropriate assumptions. Finally, the numerical performance of the method is demonstrated by solving some examples of symmetric nonlinear problems and comparing them with some existing symmetric nonlinear equations CG solvers.
Objectives: To analyze the reasons for treatment by Traditional Bone Setters(TBS) and the frequen... more Objectives: To analyze the reasons for treatment by Traditional Bone Setters(TBS) and the frequency of complications in patients treated by traditional bone setters in our setup. Study Design: Descriptive case series. Place and Duration of Study: District HeadquarterHospital (DHQ) Temargarah & Lady Reading Hospital Peshawar and, Ghurki Trust TeachingHospital, Lahore from Dec 2014 to Nov 2015. Material and Methods: Patients of either genderor all ages received in outpatient department or accident and emergency of DHQ Temargarah,Lady Reading Hospital Peshawar and Ghurki Trust Teaching Hospital, Lahore with history oftrauma followed by treatment by local bonesetters were included in our study. After properhistory, examinations and investigations, appropriate treatment were given and complicationswere noted. Results: We received a total of 267 patients who were treated by Traditional bonesetters.186 were males and 81 were females. Age ranges from 1.5 years to 87 years. In majorityAdvice...
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.
In Silico Mutagenesis Based Remodeling of SARs-CoV-1 Peptide (ATLQAIAS) to Inhibit SARs-CoV-2: Structural-dynamics and Free Energy Calculations
Background:The prolific spread of COVID-19 caused by a novel coronavirus (SARS-CoV-2) from its ep... more Background:The prolific spread of COVID-19 caused by a novel coronavirus (SARS-CoV-2) from its epicenter in Wuhan, China, to every nook and cranny of the world after December 2019, jeopardize the prevailing health system in the world and has raised serious concerns about human safety. To date efforts are continuing to design small molecule inhibitor, vaccines and many other therapeutic options are practiced but their final therapeutic potential is still to be tested. Using the old drug or vaccine or peptides could aid this process to avoid such long experimental procedure. Results:Hence, here we have repurposed a small peptide (ATLQAIAS) from the previous study which reported the inhibitory effects of this peptide. We used in silico mutagenesis approach to design more peptides from the native wild peptide, which revealed that substitutions (T2W, T2Y, L3R and A5W) could increase the binding affinity of the peptide towards the 3CLpro. Furthermore, using MD simulation and free energy c...
Inspired by the large number of applications for symmetric nonlinear equations, this article will... more Inspired by the large number of applications for symmetric nonlinear equations, this article will suggest two optimal choices for the modified Polak–Ribiére–Polyak (PRP) conjugate gradient (CG) method by minimizing the measure function of the search direction matrix and combining the proposed direction with the default Newton direction. In addition, the corresponding PRP parameters are incorporated with the Li and Fukushima approximate gradient to propose two robust CG-type algorithms for finding solutions for large-scale systems of symmetric nonlinear equations. We have also demonstrated the global convergence of the suggested algorithms using some classical assumptions. Finally, we demonstrated the numerical advantages of the proposed algorithms compared to some of the existing methods for nonlinear symmetric equations.
The outbreak of the recent coronavirus (SARS-CoV-2), which causes a severe pneumonia infection, f... more The outbreak of the recent coronavirus (SARS-CoV-2), which causes a severe pneumonia infection, first identified in Wuhan, China, imposes significant risks to public health. Around the world, researchers are continuously trying to identify small molecule inhibitors or vaccine candidates by targeting different drug targets. The SARs-CoV-2 macrodomain-I, which helps in viral replication and hijacking the host immune system, is also a potential drug target. Hence, this study targeted viral macrodomain-I by using drug similarity, virtual screening, docking and re-docking approaches. A total of 64,043 compounds were screened, and potential hits were identified based on the docking score and interactions with the key residues. The top six hits were subjected to molecular dynamics simulation and Free energy calculations and repeated three times each. The per-residue energy decomposition analysis reported that these compounds significantly interact with Asp22,
In this paper, a new hybrid conjugate gradient method for solving monotone nonlinear equations is... more In this paper, a new hybrid conjugate gradient method for solving monotone nonlinear equations is introduced. The scheme is a combination of the Fletcher-Reeves (FR) and Polak-Ribiére-Polyak (PRP) conjugate gradient methods with the Solodov and Svaiter projection strategy. Using suitable assumptions, the global convergence of the scheme with monotone line search is provided. Lastly, a numerical experiment was used to enumerate the suitability of the proposed scheme for large-scale problems.
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.
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