Search results for: method of lines (MOL)

Authors: Amir Asadi, Karim Habib, Robert J. Moon, Kyriaki Kalaitzidou

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There has been considerable interest in cellulose nanomaterials (CN) as polymer and polymer composites reinforcement due to their high specific modulus and strength, low density and toxicity, and accessible hydroxyl side groups that can be readily chemically modified. The focus of this study is making lightweight composites for better fuel efficiency and lower CO2 emission in auto industries with no compromise on mechanical performance using a scalable technique that can be easily integrated in sheet molding compound (SMC) manufacturing lines. Light weighting will be achieved by replacing part of the heavier components, i.e. glass fibers (GF), with a small amount of cellulose nanocrystals (CNC) in short GF/epoxy composites made using SMC. CNC will be introduced as coating of the GF rovings prior to their use in the SMC line. The employed coating method is similar to the fiber sizing technique commonly used and thus it can be easily scaled and integrated to industrial SMC lines. This will be an alternative route to the most techniques that involve dispersing CN in polymer matrix, in which the nanomaterials agglomeration limits the capability for scaling up in an industrial production. We have demonstrated that incorporating CNC as a coating on GF surface by immersing the GF in CNC aqueous suspensions, a simple and scalable technique, increases the interfacial shear strength (IFSS) by ~69% compared to the composites produced by uncoated GF, suggesting an enhancement of stress transfer across the GF/matrix interface. As a result of IFSS enhancement, incorporation of 0.17 wt% CNC in the composite results in increases of ~10% in both elastic modulus and tensile strength, and 40 % and 43 % in flexural modulus and strength respectively. We have also determined that dispersing 1.4 and 2 wt% CNC in the epoxy matrix of short GF/epoxy SMC composites by sonication allows removing 10 wt% GF with no penalty on tensile and flexural properties leading to 7.5% lighter composites. Although sonication is a scalable technique, it is not quite as simple and inexpensive as coating the GF by passing through an aqueous suspension of CNC. In this study, the above findings are integrated to 1) investigate the effect of CNC content on mechanical properties by passing the GF rovings through CNC aqueous suspension with various concentrations (0-5%) and 2) determine the optimum ratio of the added CNC to the removed GF to achieve the maximum possible weight reduction with no cost on mechanical performance of the SMC composites. The results of this study are of industrial relevance, providing a path toward producing high volume lightweight and mechanically enhanced SMC composites using cellulose nanomaterials.

Keywords: cellulose nanocrystals, light weight polymer-matrix composites, mechanical properties, sheet molding compound (SMC)

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Authors: N. Senu, I. A. Kasim, F. Ismail, N. Bachok

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In this paper zero-dissipative explicit Runge-Kutta method is derived for solving second-order ordinary differential equations with periodical solutions. The phase-lag and dissipation properties for Runge-Kutta (RK) method are also discussed. The new method has algebraic order three with dissipation of order infinity. The numerical results for the new method are compared with existing method when solving the second-order differential equations with periodic solutions using constant step size.

Keywords: dissipation, oscillatory solutions, phase-lag, Runge-Kutta methods

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Authors: Chui Ka Shing

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This case study research attempts to examine the use of the Bar Model Method approach in learning and teaching mathematics in a primary school in Hong Kong. The objectives of the study are to find out to what extent (a) the Bar Model Method approach enhances the construction of students’ mathematics concepts, and (b) the school-based mathematics curriculum development with adopting the Bar Model Method approach. This case study illuminates the effectiveness of using the Bar Model Method to solve mathematics problems from Primary 1 to Primary 6. Some effective pedagogies and assessments were developed to strengthen the use of the Bar Model Method across year levels. Suggestions including school-based curriculum development for using Bar Model Method and further study were discussed.

Keywords: bar model method, curriculum development, mathematics education, problem solving

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Authors: Yang Zhong, Heng Liu

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The decoupling method and the modified Naiver method are combined for accurate bending analysis of rectangular thick plates with all edges clamped supported. The basic governing equations for Mindlin plates are first decoupled into independent partial differential equations which can be solved separately. Using modified Navier method, the analytic solution of rectangular thick plate with all edges clamped supported is then derived. The solution method used in this paper leave out the complicated derivation for calculating coefficients and obtain the solution to problems directly. Numerical comparisons show the correctness and accuracy of the results at last.

Keywords: Mindlin plates, decoupling method, modified Navier method, bending rectangular plates

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Authors: Azizakhanim Maharramli

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The gradual transition from entrenched traditional technology and organization of construction production to innovative additive construction technology inevitably meets technological, technical, organizational, labour, and, finally, social difficulties. Therefore, the chosen nodal method will lead to the elimination of the above difficulties, combining some of the usual methods of construction and the myth in world practice that the labour force is subjected to a strong stream of reduction. The nodal method of additive technology will create favourable conditions for the optimal degree of distribution of labour across facilities due to the consistent performance of homogeneous work and the introduction of additive technology and traditional technology into construction production.

Keywords: parallel method, sequential method, stream method, combined method, nodal method

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Authors: Mahacine Amrani

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A simple and rapid method for the determination of alcohol in gasoline-alcohol mixtures using density measurements is described. The method can determine a minimum of 1% of alcohol by volume. The precision of the method is ± 3%.The method is more useful for field test in the quality assessment of alcohol blended fuels.

Keywords: gasoline-alcohol, mixture, alcohol determination, density, measurement, Morocco

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Authors: Kaarour Abdelkrim, Ouardi Okkacha, Meskine Mohamed

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In this study, the υ_4 fundamental band of 12CD4 molecule has been studied by infrared spectroscopy with high resolution. Using XTDS and SPEVIEW software and the tensor formalism developed by ICB (laboratoire interdisciplinaire de Bourgogne) to several lines have been assigned and fitted with a standard deviation acceptable. This analysis allowed us to calculate several parameters of the molecule 12 CD4.

Keywords: XTDS, SPEVIEW, tetrahedral tensorial formalism, rovibrational band

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Authors: Melusi Khumalo, Anastacia Dlamini

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In this paper, we consider a numerical solution for nonlinear Fredholm integral equations of the second kind. We work with uniform mesh and use the Lagrange polynomials together with the Galerkin finite element method, where the weight function is chosen in such a way that it takes the form of the approximate solution but with arbitrary coefficients. We implement the finite element method to the nonlinear Fredholm integral equations of the second kind. We consider the error analysis of the method. Furthermore, we look at a specific example to illustrate the implementation of the finite element method.

Keywords: finite element method, Galerkin approach, Fredholm integral equations, nonlinear integral equations

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Authors: Cao Bin, Yuan Yi, Wang Qiang, Amor Abdelkader, Ali Reza Kamali, Diogo Montalvão

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The study of the electrodynamic behavior of non-ferrous particles in time-varying magnetic fields is a promising area of research with wide applications, including recycling of non-ferrous metals, mechanical transmission, and space debris. The key technology for recovering non-ferrous metals is eddy current separation (ECS), which utilizes the eddy current force and torque to separate non-ferrous metals. ECS has several advantages, such as low energy consumption, large processing capacity, and no secondary pollution, making it suitable for processing various mixtures like electronic scrap, auto shredder residue, aluminum scrap, and incineration bottom ash. Improving the separation efficiency of mixtures with different particle sizes in ECS can create significant social and economic benefits. Our previous study investigated the influence of particle size on separation efficiency by combining numerical simulations and separation experiments. Pearson correlation analysis found a strong correlation between the eddy current force in simulations and the repulsion distance in experiments, which confirmed the effectiveness of our simulation model. The interaction effects between particle size and material type, rotational speed, and magnetic pole arrangement were examined. It offer valuable insights for the design and optimization of eddy current separators. The underlying mechanism behind the effect of particle size on separation efficiency was discovered by analyzing eddy current and field gradient. The results showed that the magnitude and distribution heterogeneity of eddy current and magnetic field gradient increased with particle size in eddy current separation. Based on this, we further found that increasing the curvature of magnetic field lines within particles could also increase the eddy current force, providing a optimized method to improving the separation efficiency of fine particles. By combining the results of the studies, a more systematic and comprehensive set of optimization guidelines can be proposed for mixtures with different particle size ranges. The separation efficiency of fine particles could be improved by increasing the rotational speed, curvature of magnetic field lines, and electrical conductivity/density of materials, as well as utilizing the eddy current torque. When designing an ECS, the particle size range of the target mixture should be investigated in advance, and the suitable parameters for separating the mixture can be fixed accordingly. In summary, these results can guide the design and optimization of ECS, and also expand the application areas for ECS.

Keywords: eddy current separation, particle size, numerical simulation, metal recovery

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Authors: Jiankang Wang, Hongyang Yu

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This paper proposes a portable online 3D modeling method. The method first utilizes a depth camera to collect data and compresses the depth data using a frame-by-frame lossless data compression method. The color image is encoded using the H.264 encoding format. After the cloud obtains the color image and depth image, a 3D modeling method based on bundlefusion is used to complete the 3D modeling. The results of this study indicate that this method has the characteristics of portability, online, and high efficiency and has a wide range of application prospects.

Keywords: 3D reconstruction, bundlefusion, lossless compression, depth image

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Authors: Haijie Li, Xuping Zhang

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This paper presents a computationally efficient method for the modeling of robot manipulators with flexible links and joints. This approach combines the Discrete Time Transfer Matrix Method with the Finite Segment Method, in which the flexible links are discretized by a number of rigid segments connected by torsion springs; and the flexibility of joints are modeled by torsion springs. The proposed method avoids the global dynamics and has the advantage of modeling non-uniform manipulators. Experiments and simulations of a single-link flexible manipulator are conducted for verifying the proposed methodologies. The simulations of a three-link robot arm with links and joints flexibility are also performed.

Keywords: flexible manipulator, transfer matrix method, linearization, finite segment method

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Authors: Ahmed Guerine, Ali El Hafidi, Bruno Martin, Philippe Leclaire

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In this paper, we propose a method for the dynamic response of multi-storey structures with uncertain-but-bounded parameters. The effectiveness of the proposed method is demonstrated by a numerical example of three-storey structures. This equation is integrated numerically using Newmark’s method. The numerical results are obtained by the proposed method. The simulation accounting the interval analysis method results are compared with a probabilistic approach results. The interval analysis method provides a mean curve that is between an upper and lower bound obtained from the probabilistic approach.

Keywords: multi-storey structure, dynamic response, interval analysis method, random parameters

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Authors: Dalita G. S. M. Cavalcante, Elton A. P. dos Reis, Andressa S. Gomes, Caroline S. Danna, Leandra Ernest Kerche-Silva, Eidi Yoshihara, Aldo E. Job

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In order to minimize environmental impacts, a composite was developed from mixture of leather shavings (LE) with natural rubber (NR), which patent is already deposited. The new material created can be used in applications such as floors e heels for shoes. Besides these applications, the aim is to use this new material for the production of products for the textile industry, such as boots, gloves and bags. But the question arises, as to biocompatibility of this new material. This is justified because the structure of the leather shavings has chrome. The trivalent chromium is usually not toxic, but the hexavalent chromium can be highly toxic and genotoxic for living beings, causing damage to the DNA molecule and contributing to the formation of cancer. Based on this, the objective of this study is evaluate the possible genotoxic effects of the new composite, using as system - test two cell lines (MRC-5 and CHO-K1) by comet assay. For this, the production of the composite was performed in three proportions: for every 100 grams of NR was added 40 (E40), 50 (E50) or 60 (E60) grams of LE. The latex was collected from the rubber tree (Hevea brasiliensis). For vulcanization of the NR, activators and accelerators were used. The two cell lines were exposed to the new composite in its three proportions using elution method, that is, cells exposed to liquid extracts obtained from the composite for 24 hours. For obtaining the liquid extract, each sample of the composite was crushed into pieces and mixed with an extraction solution. The quantification of total chromium and hexavalent chromium in the extracts were performed by Optical Emission Spectrometry by Inductively Coupled Plasma (ICP-OES). The levels of DNA damage in cells exposed to both extracts were monitored by alkaline version of the comet assay. The results of the quantification of metals in ICP-OES indicated the presence of total chromium in different extracts, but were not detected presence of hexavalent chromium in any extract. Through the comet assay were not found DNA damage of the CHO-K1 cells exposed to both extracts. As for MRC-5, was found a significant increase in DNA damage in cells exposed to E50 and E60. Based on the above data, it can be asserted that the extracts obtained from the composite were highly genotoxic for MRC-5 cells. These biological responses do not appear to be related to chromium metal, since there was a predominance of trivalent chromium in the extracts, indicating that during the production process of the new composite, there was no formation of hexavalent chromium. In conclusion it can infer that the leather shavings containing chromium can be reused, thereby reducing the environmental impacts of this waste. Already on the composite indicates to its incorporation in applications that do not aim at direct contact with the human skin, and it is suggested the chain of composite production be studied, in an attempt to make it biocompatible so that it may be safely used by the textile industry.

Keywords: cell line, chrome, genotoxicity, leather, natural rubber

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Authors: Somaya Adwan, Rasha Majed, Lamya'a Majed, Hamzah Arof

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In order to produce images with whole body parts, X-ray of different portions of the body parts is assembled using image stitching methods. A new method for image stitching that exploits mutually feature based method and direct based method to identify and merge pairs of X-ray medical images is presented in this paper. The performance of the proposed method based on this hybrid approach is investigated in this paper. The ability of the proposed method to stitch and merge the overlapping pairs of images is demonstrated. Our proposed method display comparable if not superior performance to other feature based methods that are mentioned in the literature on the standard databases. These results are promising and demonstrate the potential of the proposed method for further development to tackle more advanced stitching problems.

Keywords: image stitching, direct based method, panoramic image, X-ray

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Authors: Chutamas Thepmalee, Aussara Panya, Mutita Junking, Jatuporn Sujjitjoon, Nunghathai Sawasdee, Pa-Thai Yenchitsomanus

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Cholangiocarcinoma (CCA) is an aggressive malignancy of bile duct epithelial cells in which the standard treatments, including surgery, radiotherapy, chemotherapy, and targeted therapy are partially effective. Many solid tumors including CCA escape host immune responses by creating tumor microenvironment and generating immunosuppressive cytokines such as interleukin-10 (IL-10) and transforming growth factor-β (TGF-β). These cytokines can inhibit dendritic cell (DC) differentiation and function, leading to decreased activation and response of effector CD4+ and CD8+ T cells for cancer cell elimination. To overcome the effects of these immunosuppressive cytokines and to increase ability of DC to activate effector CD4+ and CD8+ T cells, we generated self-differentiated DCs (SD-DCs) with down-regulation of IL-10 and TGF-β receptors for activation of effector CD4+ and CD8+ T cells. Human peripheral blood monocytes were initially transduced with lentiviral particles containing the genes encoding GM-CSF and IL-4 and then secondly transduced with lentiviral particles containing short-hairpin RNAs (shRNAs) to knock-down mRNAs of IL-10 and TGF-β receptors. The generated SD-DCs showed up-regulation of MHC class II (HLA-DR) and co-stimulatory molecules (CD40 and CD86), comparable to those of DCs generated by convention method. Suppression of IL-10 and TGF-β receptors on SD-DCs by specific shRNAs significantly increased levels of IFN-γ and also increased cytolytic activity of DC-activated effector T cells against CCA cell lines (KKU-213 and KKU-100), but it had little effect to immortalized cholangiocytes (MMNK-1). Thus, SD-DCs with down-regulation of IL-10 and TGF-β receptors increased activation of effector T cells, which is a recommended method to improve DC function for the preparation of DC-activated effector T cells for adoptive T-cell therapy.

Keywords: cholangiocarcinoma, IL-10 receptor, self-differentiated dendritic cells, TGF-β receptor

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Authors: M. O. Olayiwola

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Numerical solutions of the generalized Burger-Fisher are obtained using a Modified Variational Iteration Method (MVIM) with minimal computational efforts. The computed results with this technique have been compared with other results. The present method is seen to be a very reliable alternative method to some existing techniques for such nonlinear problems.

Keywords: burger-fisher, modified variational iteration method, lagrange multiplier, Taylor’s series, partial differential equation

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Authors: Omolola A. Tajelawi, Hari L. Garbharran

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Revenue leakages are one of the major challenges manufacturers face in production processes, as most of the input materials that should emanate as products from the lines are lost as waste. Rather than generating income from material input which is meant to end-up as products, losses are further incurred as costs in order to manage waste generated. In addition, due to the lack of a clear view of the flow of resources on the lines from input to output stage, acquiring information on the true cost of waste generated have become a challenge. This has therefore given birth to the conceptualization and implementation of waste minimization strategies by several manufacturing industries. This paper reviews the principles and applications of three environmental management accounting tools namely Activity-based Costing (ABC), Life-Cycle Assessment (LCA) and Material Flow Cost Accounting (MFCA) in the manufacturing industry and their effectiveness in curbing revenue leakages. The paper unveils the strengths and limitations of each of the tools; beaming a searchlight on the tool that could allow for optimal resource utilization, transparency in production process as well as improved cost efficiency. Findings from this review reveal that MFCA may offer superior advantages with regards to the provision of more detailed information (both in physical and monetary terms) on the flow of material inputs throughout the production process compared to the other environmental accounting tools. This paper therefore makes a case for the adoption of MFCA as a viable technique for the identification and reduction of waste in production processes, and also for effective decision making by production managers, financial advisors and other relevant stakeholders.

Keywords: MFCA, environmental management accounting, resource efficiency, waste reduction, revenue losses

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Authors: Mohammad Ahmad, Dayalan Kasilingam

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In this paper, a spectral domain implementation of the fast multipole method is presented. It is shown that the aggregation, translation, and disaggregation stages of the fast multipole method (FMM) can be performed using the spectral domain (SD) analysis. The spectral domain fast multipole method (SD-FMM) has the advantage of eliminating the near field/far field classification used in conventional FMM formulation. The study focuses on the application of SD-FMM to one-dimensional (1D) and two-dimensional (2D) electric field integral equation (EFIE). The case of perfectly conducting strip, circular and square cylinders are numerically analyzed and compared with the results from the standard method of moments (MoM).

Keywords: electric field integral equation, fast multipole method, method of moments, wave scattering, spectral domain

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Authors: Alkaben Patel

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The proposed RP-HPLC method is easy, rapid, economical, precise and accurate stability indicating RP-HPLC method for simultaneous estimation of Astorvastatin and Methylcobalamine in their combined dosage form has been developed.The separation was achieved by LC-20 AT C18(250mm*4.6mm*2.6mm)Colum and water (pH 3.5): methanol 70:30 as mobile phase, at a flow rate of 1ml/min. wavelength of this dosage form is 215nm.The drug is related to stress condition of hydrolysis, oxidation, photolysis and thermal degradation.

Keywords: RP- HPLC, atorvastatin, methylcobalamine, method, development, validation

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Authors: Yasir Ali, Farhatullah

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The present study was conducted to estimate the genetic variability, heritability and genetic advance in six parental lines and their 56 genotypes derived from five introgressed brassica populations on the basis of morphological and biochemical traits. The experiment was laid out in a randomized complete block design with two replications at The University of Agriculture Peshawar-Pakistan during growing season of 2015-2016. The ANOVA of all traits of F5:6 populations showed highly significant differences (P ≤ 0.01) for all morphological and biochemical traits. Among F5:6 populations, the genotype 2(526) was earlier in flowering (108.65 days), and genotype 14(485) was earlier in maturity (170 days). Tallest plants (182.5 cm), largest main raceme (91.5 cm) and maximum number of pods (80.5) on main raceme were recorded for genotype 17(34). Maximum primary branches plant-1(6.2) and longest pods (10.26 cm) were recorded for genotype 15, while genotype 16(171) had more seeds pod⁻¹ (22) and gave maximum yield plant-1 (30.22 g). The maximum 100-seed weight (0.60 g) was observed for genotype 10(506) while high protein content (22.61%) was recorded for genotype 4(99). Maximum oil content (54.08 %) and low linoleic acid (7.07 %) were produced by genotype (12(138) and low glucosinolate (59.01 µMg⁻¹) was recorded for genotype 21(113). The genotype 27(303) having high oleic acid content (51.73 %) and genotype 1(209) gave low erucic acid (35.97 %). Among the F5:6 populations moderate to high heritability observed for all morphological and biochemical traits coupled with high genetic advance. Cluster analysis grouped the 56 F5:6 populations along their parental lines into seven different groups. Each group was different from the other group on the basis of morphological and biochemical traits. Moreover all the F5:6 populations showed sufficient variability. Genotypes 10(506) and 16(171) were superior for high seed yield⁻¹, 100-seeds weight, and seed pod⁻¹ and are recommended for future breeding program.

Keywords: Brassicaceae, biochemical characterization, introgression, morphological characterization

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Authors: Soroosh Torabi, Brad Berron, Ren Xu, Christine Trinkle

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Microfluidics integrated with 3D cell culture is a powerful technology to mimic cellular environment, and can be used to study cell activities such as proliferation, migration and response to drugs. This technology has gained more attention in cancer studies over the past years, and many organ-on-a-chip systems have been developed to study cancer cell behaviors in an ex-vivo tumor microenvironment. However, there are still some barriers to adoption which include low throughput, complexity in 3D cell culture integration and limitations on non-optical analysis of cells. In this study, a user-friendly microfluidic multi-well plate was developed to mimic the in vivo tumor microenvironment. The microfluidic platform feeds multiple 3D cell culture sites at the same time which enhances the throughput of the system. The platform uses hydrophobic Cassie-Baxter surfaces created by microchannels to enable convenient loading of hydrogel/cell suspensions into the device, while providing barrier free placement of the hydrogel and cells adjacent to the fluidic path. The microchannels support convective flow and diffusion of nutrients to the cells and a removable lid is used to enable further chemical and physiological analysis on the cells. Different breast cancer cell lines were cultured in the device and then monitored to characterize nutrient delivery to the cells as well as cell invasion and proliferation. In addition, the drug response of breast cancer cell lines cultured in the device was compared to the response in xenograft models to the same drugs to analyze relevance of this platform for use in future drug-response studies.

Keywords: microfluidics, multi-well 3d cell culture, tumor microenvironment, tumor-on-a-chip

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Authors: Sumachaya Harnsukworapanich, Tetsuo Ichimori

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The apportionment method is used by many countries, to calculate the distribution of seats in political bodies. For example, this method is used in the United States (U.S.) to distribute house seats proportionally based on the population of the electoral district. Famous apportionment methods include the divisor methods called the Adams Method, Dean Method, Hill Method, Jefferson Method and Webster Method. Sometimes the results from the implementation of these divisor methods are unfair and include errors. Therefore, it is important to examine the optimization of this method by using a bias measurement to figure out precise and fair results. In this research we investigate the bias of divisor methods in the U.S. Houses of Representatives toward large and small states by applying the Stolarsky Mean Method. We compare the bias of the apportionment method by using two famous bias measurements: The Balinski and Young measurement and the Ernst measurement. Both measurements have a formula for large and small states. The Third measurement however, which was created by the researchers, did not factor in the element of large and small states into the formula. All three measurements are compared and the results show that our measurement produces similar results to the other two famous measurements.

Keywords: apportionment, bias, divisor, fair, measurement

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Authors: Scott A. Ochsner, Christopher M. Watkins, Apollo McOwiti, David L. Steffen Lauren B. Becnel, Neil J. McKenna

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Understanding signaling by nuclear receptors (NRs) requires an appreciation of their cognate ligand- and tissue-specific transcriptomes. While target gene regulation data are abundant in this field, they reside in hundreds of discrete publications in formats refractory to routine query and analysis and, accordingly, their full value to the NR signaling community has not been realized. One of the mandates of the Nuclear Receptor Signaling Atlas (NURSA) is to facilitate access of the community to existing public datasets. Pursuant to this mandate we are developing a freely-accessible community web resource, Transcriptomine, to bring together the sum total of available expression array and RNA-Seq data points generated by the field in a single location. Transcriptomine currently contains over 25,000,000 gene fold change datapoints from over 1200 contrasts relevant to over 100 NRs, ligands and coregulators in over 200 tissues and cell lines. Transcriptomine is designed to accommodate a spectrum of end users ranging from the bench researcher to those with advanced bioinformatic training. Visualization tools allow users to build custom charts to compare and contrast patterns of gene regulation across different tissues and in response to different ligands. Our resource affords an entirely new paradigm for leveraging gene expression data in the NR signaling field, empowering users to query gene fold changes across diverse regulatory molecules, tissues and cell lines, target genes, biological functions and disease associations, and that would otherwise be prohibitive in terms of time and effort. Transcriptomine will be regularly updated with gene lists from future genome-wide expression array and expression-sequencing datasets in the NR signaling field.

Keywords: target gene database, informatics, gene expression, transcriptomics

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Authors: Mei-Jie Xu, Yang Zhong

Abstract:

Based on the symplectic geometry method, the theory of Hamilton system can be applied in the analysis of problem solved using the theory of elasticity and in the solution of elliptic partial differential equations. With this technique, this paper derives the theoretical solution for a thick rectangular plate with four free edges supported on a Winkler foundation by variable separation method. In this method, the governing equation of thick plate was first transformed into state equations in the Hamilton space. The theoretical solution of this problem was next obtained by applying the method of variable separation based on the Hamilton system. Compared with traditional theoretical solutions for rectangular plates, this method has the advantage of not having to assume the form of deflection functions in the solution process. Numerical examples are presented to verify the validity of the proposed solution method.

Keywords: symplectic geometry method, Winkler foundation, thick rectangular plate, variable separation method, Hamilton system

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Authors: H. N. Agiza, M. A. Sohaly, M. A. Elfouly

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Parkinson's disease (PD) is a heterogeneous disorder with common age of onset, symptoms, and progression levels. In this paper we will solve analytically the PD model as a non-linear delay differential equation using the steps method. The step method transforms a system of delay differential equations (DDEs) into systems of ordinary differential equations (ODEs). On some numerical examples, the analytical solution will be difficult. So we will approximate the analytical solution using Picard method and Taylor method to ODEs.

Keywords: Parkinson's disease, step method, delay differential equation, two delays

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Authors: Alexander Matrosov, Guriy Shirunov

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A superposition method based on Lame's idea is used to get a general analytical solution to analyze a stress and strain state of a rectangular isotropjc elastic thick plate. The solution is built by using three solutions of the method of initial functions in the form of double trigonometric series. The results of bending of a thick plate under normal stress on its top face with two opposite sides clamped while others free of load are presented and compared with FEM modelling.

Keywords: general solution, method of initial functions, superposition method, thick isotropic plates

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Authors: Mahmood Otadi, Maryam Mosleh

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The hybrid differential equations have a wide range of applications in science and engineering. In this paper, the homotopy analysis method (HAM) is applied to obtain the series solution of the hybrid differential equations. Using the homotopy analysis method, it is possible to find the exact solution or an approximate solution of the problem. Comparisons are made between improved predictor-corrector method, homotopy analysis method and the exact solution. Finally, we illustrate our approach by some numerical example.

Keywords: fuzzy number, fuzzy ODE, HAM, approximate method

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Authors: Khosrow Maleknejad, Asyieh Ebrahimzadeh

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In this paper, the numerical solution of optimal control problem (OCP) for systems governed by Volterra integro-differential (VID) equation is considered. The method is developed by means of the Legendre wavelet approximation and collocation method. The properties of Legendre wavelet accompany with Gaussian integration method are utilized to reduce the problem to the solution of nonlinear programming one. Some numerical examples are given to confirm the accuracy and ease of implementation of the method.

Keywords: collocation method, Legendre wavelet, optimal control, Volterra integro-differential equation

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Authors: Cletus Abhulimen, L. A. Ukpebor

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In this paper, we construct a class of four-step third derivative exponential fitting integrator of order six for the numerical integration of stiff initial-value problems of the type: y’= f(x,y); y(x₀) =y₀. The implicit method has free parameters which allow it to be fitted automatically to exponential functions. For the purpose of effective implementation of the proposed method, we adopted the techniques of splitting the method into predictor and corrector schemes. The numerical analysis of the stability of the new method was discussed; the results show that the method is A-stable. Finally, numerical examples are presented, to show the efficiency and accuracy of the new method.

Keywords: third derivative four-step, exponentially fitted, a-stable, stiff differential equations

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Authors: Guettal Djaouida, Ziadi Abdelkader

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In this paper, we study a coupling of the Alienor method with the algorithm of Piyavskii-Shubert. The classical multidimensional global optimization methods involves great difficulties for their implementation to high dimensions. The Alienor method allows to transform a multivariable function into a function of a single variable for which it is possible to use efficient and rapid method for calculating the the global optimum. This simplification is based on the using of a reducing transformation called Alienor.

Keywords: global optimization, reducing transformation, α-dense curves, Alienor method, Piyavskii-Shubert algorithm

Procedia PDF Downloads 483