Search results for: sediment continuity equation

Authors: Phuoc Si Nguyen

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Infinite impulse response (IIR) filters can be designed from an analogue low pass prototype by using frequency transformation in the s-domain and bilinear z-transformation with pre-warping frequency; this method is known as frequency transformation from the s-domain to the z-domain. This paper will introduce a new method to transform an IIR digital filter to another type of IIR digital filter (low pass, high pass, band pass, band stop or narrow band) using a technique based on inverse bilinear z-transformation and inverse matrices. First, a matrix equation is derived from inverse bilinear z-transformation and Pascal’s triangle. This Low Pass Digital to Digital Filter Pascal Matrix Equation is used to transform a low pass digital filter to other digital filter types. From this equation and the inverse matrix, a Digital to Digital Filter Pascal Matrix Equation can be derived that is able to transform any IIR digital filter. This paper will also introduce some specific matrices to replace the inverse matrix, which is difficult to determine due to the larger size of the matrix in the current method. This will make computing and hand calculation easier when transforming from one IIR digital filter to another in the digital domain.

Keywords: bilinear z-transformation, frequency transformation, inverse bilinear z-transformation, IIR digital filters

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Authors: Asal Pournaghshband

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This paper presents the development of a finite element model to study the large deflection behavior of restrained stainless steel cellular beams at elevated temperature. Cellular beams are widely used for efficient utilization of raw materials to facilitate long spans with faster construction resulting sustainable design solution that can enhance the performance and merit of any construction project. However, their load carrying capacity is less than the equivalent beams without opening due to developing shear-moment interaction at the openings. In structural frames due to elements continuity, such beams are restrained by their adjoining members which has a substantial effect on beams behavior in fire. Stainless steel has also become integral part of the build environment due to its excellent corrosion resistance, whole life-cycle costs, and sustainability. This paper reports the numerical investigations into the effect of structural continuity on the thermo-mechanical performance of restrained steel beams with circle and elongated circle shapes of web opening in fire. The numerical model is firstly validated using existing numerical results from the literature, and then employed to perform a parametric study. The structural continuity is evaluated through the application of different levels of axial restraints on the response of carbon steel and stainless steel cellular beam in fire. The transit temperature for stainless steel cellular beam is shown to be less affected by the level of axial stiffness than the equivalent carbon steel cellular beam. Overall, it was established that whereas stainless steel cellular beams show similar stages of behavior of carbon steel cellular beams in fire, they are capable of withstanding higher temperatures prior to the onset of catenary action in large deflection, despite the higher thermal expansion of stainless steel material.

Keywords: axial restraint, catenary action, cellular beam, fire, numerical modeling, stainless steel, transit temperature

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Authors: M. Karami Khorramabadi, A. R. Nezamabadi

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This paper studies free vibration of functionally graded beams Subjected to Axial Load that is simply supported at both ends lies on a continuous elastic foundation. The displacement field of beam is assumed based on Engesser-Timoshenko beam theory. The Young's modulus of beam is assumed to be graded continuously across the beam thickness. Applying the Hamilton's principle, the governing equation is established. Resulting equation is solved using the Euler's Equation. The effects of the constituent volume fractions and foundation coefficient on the vibration frequency are presented. To investigate the accuracy of the present analysis, a compression study is carried out with a known data.

Keywords: functionally graded beam, free vibration, elastic foundation, Engesser-Timoshenko beam theory

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Authors: M. Budakoglu, M. Karaman, D. Kiran, Z. Doner, B. Zeytuncu, B. Tanç, M. Kumral

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Lake Acıgöl is one of the large saline lacustrine environment in Turkey. Eleven trace metals (Cr, Mn, Fe, Al, Co, Ni, Cu, Zn, Cd, Pb and As) in 9 surface and subsurface sediment samples from the Lake Acıgöl were analyzed with the bulk and sequential extraction analysis methods by ICP-MS to obtain the metal distribution patterns in this extreme environment. Five stepped sequential extraction technique (1- exchangeable, 2- bond to carbonates, 3- bond to iron and manganese oxides/hydroxides, 4- bond to organic matter and sulphides, and 5- residual fraction incorporated into clay and silicate mineral lattices) was used to characterize the various forms of metals in the <63μ size sediments. The metal contents (ppm) and their percentages for each extraction step were reported and compared with the results obtained from the total digestion. Results indicate that sum of the four fraction are in good agreement with the total digestion results of Ni, Cd, As, Zn, Cu and Fe with the satisfactory recoveries (94.04–109.0%) and the method used is reliable and repeatable for these elements. It was found that there were high correlations between Fe vs. Ni loads in the fraction of F2 and F4 with R2= 0,91 and 0,81, respectively. Comparison of totally 135 chemical analysis results in three sampling location and for 5 fraction between Fe-Co, Co-Ni and Fe-Ni element couples were presented elevated correlations with R2=0,98, 0,92 and 0,91, respectively.

Keywords: Lake Acigol, sequancial extraction, recent lake sediment, geochemical speciation of heavy metals

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Authors: Gautam Kumar Saharia, Sagardeep Talukdar, Riki Dutta, Sudipta Nandy

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The physics informed neural network (PINN) method opens up an approach for numerically solving nonlinear partial differential equations leveraging fast calculating speed and high precession of modern computing systems. We construct the PINN based on strong universal approximation theorem and apply the initial-boundary value data and residual collocation points to weekly impose initial and boundary condition to the neural network and choose the optimization algorithms adaptive moment estimation (ADAM) and Limited-memory Broyden-Fletcher-Golfard-Shanno (L-BFGS) algorithm to optimize learnable parameter of the neural network. Next, we improve the PINN with a weighted loss function to obtain both the bright and dark soliton solutions of Fokas-Lenells equation (FLE). We find the proposed scheme of adjustable weight coefficients into PINN has a better convergence rate and generalizability than the basic PINN algorithm. We believe that the PINN approach to solve the partial differential equation appearing in nonlinear optics would be useful to study various optical phenomena.

Keywords: deep learning, optical Soliton, neural network, partial differential equation

Procedia PDF Downloads 126

Authors: Ajith Kumar S., Sankaran Namboothiri, Sankrish J., SarathKumar S., S. Anil Lal

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A numerical analysis of flow over a heated circular cylinder is done in this paper. The governing equations, Navier-Stokes, and energy equation within the Boussinesq approximation along with continuity equation are solved using hybrid FEM-FVM technique. The density gradient created due to the heating of the cylinder will induce buoyancy force, opposite to the direction of action of acceleration due to gravity, g. In the present work, the flow direction and the direction of buoyancy force are taken as same (vertical flow configuration), so that the buoyancy force accelerates the mean flow past the cylinder. The relative dominance of the buoyancy force over the inertia force is characterized by the Richardson number (Ri), which is one of the parameter that governs the flow dynamics and heat transfer in this analysis. It is well known that above a certain value of Reynolds number, Re (ratio of inertia force over the viscous forces), the unsteady Von Karman vortices can be seen shedding behind the cylinder. The shedding wake patterns could be seriously altered by heating/cooling the cylinder. The non-dimensional shedding frequency called the Strouhal number is found to be increasing as Ri increases. The aerodynamic force coefficients CL and CD are observed to change its value. In the present vertical configuration of flow over the cylinder, as Ri increases, shedding frequency gets increased and suddenly drops down to zero at a critical value of Richardson number. The unsteady vortices turn to steady standing recirculation bubbles behind the cylinder after this critical Richardson number. This phenomenon is well known in literature as "Breakdown of the Karman Vortex Street". It is interesting to see the flow structures on further increase in the Richardson number. On further heating of the cylinder surface, the size of the recirculation bubble decreases without loosing its symmetry about the horizontal axis passing through the center of the cylinder. The separation angle is found to be decreasing with Ri. Finally, we observed a second critical Richardson number, after which the the flow will be attached to the cylinder surface without any wake behind it. The flow structures will be symmetrical not only about the horizontal axis, but also with the vertical axis passing through the center of the cylinder. At this stage, there will be a "single plume" emanating from the rear stagnation point of the cylinder. We also observed the transition of the plume is a strong function of the Richardson number.

Keywords: drag reduction, flow over circular cylinder, flow control, mixed convection flow, vortex shedding, vortex breakdown

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Authors: Asmat Siddiqui, Noor Us Saher

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Heavy metal contamination in the marine environment is a global issue, and in past decades, this problem has intensified due to an increase in urbanization and industrialization, especially in developing countries. Marine sediments act as a preliminary indicator of heavy metal contamination in the coastal and estuarine environment, which has adverse effects on biota as well as in the marine system. The aim of the current study was to evaluate the contamination status, enrichment, and flux of heavy metals in two monitoring years from coastal sediments of Pakistan. A total of 74 sediment samples were collected from seven coastal areas of Pakistan in two monitoring years, 2001-03 (MY-I) and 2011-13 (MY-II). The geochemical properties (grain size analysis, organic contents and eight heavy metals, i.e. Fe, Zn, Cu, Cr, Ni, Co, Pb, and Cd) of all sediment samples were analyzed. A significant increase in Fe, Ni and Cr concentrations detected between the years, whereas no significant differences were exhibited in Cu, Zn, Co, Pb and Cd concentrations. The extremely high enrichment (>50) of Cu, Zn, Pb and Cd were scrutinized in both monitoring years. The annual deposition flux of heavy metals ranged from 0.63 to 66.44 and 0.78 to 68.27 tons per year in MY-I and MY-II, respectively, with the lowest flux evaluated for Cd and highest for Zn in both monitoring years. A significant increase (p <0.05) was observed in the burial flux of Cr and Ni during the last decade in coastal sediments. The use of geo-indicators is helpful to assess the contamination analysis for management and conservation of the marine environment.

Keywords: coastal contamination, enrichment factor, geo-indicator, heavy metal flux

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Authors: Katarina Lazarević, Mirjana Todosijević, Tijana Vulević, Natalija Momirović, Ranka Erić

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Due to increasing demand, climate change, and world population growth, natural resources are getting exploit fast. One of the most important natural resources is soil, which is susceptible to degradation. Erosion as one of the forms of land degradation is also one of the most global environmental problems. Ecosystem services are often defined as benefits that nature provides to humankind. Soil, as the foundation of basic ecosystem functions, provides benefits to people, erosion control, water infiltration, food, fuel, fibers… This research is using the ecosystem approach as a strategy for natural resources management for promoting sustainability and conservation. The research was done on the Topčiderska River basin (Belgrade, Serbia). The InVEST Sediment Delivery Ratio model was used, to quantify erosion intensity with a spatial distribution output map of overland sediment generation and delivery to the stream. InVEST SDR, a spatially explicit model, is using a method based on the concept of hydrological connectivity and (R) USLE model. This, combined with socio-economic and law and policy analysis, gives a full set of information to decision-makers helping them to successfully manage and deliver sustainable ecosystems.

Keywords: ecosystem services, InVEST model, soil erosion, sustainability

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Authors: Yvonne Ayerki Lamptey

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The expanding informal sector in developing countries and in Ghana in particular from the 1980s has now been aggravated by the growing population and downsizing in both the public and private sectors, with displaced workers finding alternative livelihoods in the informal sector. Youth and graduate unemployment also swell the numbers and further promote the continuity of the sector. Formal workers and institutions facilitate the growth and complicate demarcations between informality within the formal and informal sectors. In spite of its growth and increasing importance, the informal economy does not feature in policy debates and has often been neglected by the Ghana government. The phenomenon has evolved with modernity into myriad unimaginable forms. Indeed, actors within the sector often clash with the interventions provided by policy makers - because neither the operatives nor the activities they perform can be clearly defined. This study uses in-depth interviews to explore the behavioural nature of the informal workers in Ghana to understand how the operatives describe and perceive the sector, and to identify the factors that influence their drive to stay within the sector. This paper concludes that the operatives clearly distinguish between the formal and informal sectors and identify the characteristics and conditions that constitute the informal sector. Other workers are trapped between formality and informality. The findings also enumerate the push and pull factors contributing to the growth of the sector.

Keywords: informal employment, informal sector, informal work, informality

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Authors: Hamed A. El-Serehy, Khaled A. Al-Rasheid, Fahad A. Al-Misned

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The composition and distribution of the benthic meiofauna assemblages of the Egyptian coasts along the Red Sea are described in relation to abiotic variables. Sediment samples were collected seasonally from twelve stations chosen along the northern part of the Red Sea to observe the meiofaunal community structure, its temporal distribution and horizontal fluctuation in relation to environmental conditions of the Red Sea marine ecosystem. The meiofaunal assemblage in the area of study was well diversified including 140 taxa. The temperature, salinity, pH, dissolved oxygen, and redox potential were measured at the time of collection. The water content of the sediments, total organic matters and chlorophyll a values were determined, and sediment samples were subjected to granulometric analysis. A total of 10 meiofauna taxa were identified, with the meiofauna being primarily represented by nematodes (on annual average from 42% to 84%), harpacticoids, polycheates and ostracodes; and the meiofauna abundances ranging from 41- to 167 ind. / 10 cm2. The meiofaunal population density fluctuated seasonally with a peak of 192.52 ind. / 10 cm2 during summer at station II. The vertical zonation in the distribution of meiofaunal community was significantly correlated with interstitial water, chlorophyll a and total organic matter values. The present study indicates that the existing of well diversified meiofaunal group which can serve as food for higher trophic levels in the Red Sea interstitial environment.

Keywords: benthos, diversity, meiofauna, Red Sea

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Authors: Alexandra Leukauf, Alexander Schirrer, Emir Talic

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Numerical computation of wave propagation in a large domain usually requires significant computational effort. Hence, the considered domain must be truncated to a smaller domain of interest. In addition, special boundary conditions, which absorb the outward travelling waves, need to be implemented in order to describe the system domains correctly. In this work, the linear one dimensional wave equation is approximated by utilizing the Fourier Galerkin approach. Furthermore, the artificial boundaries are realized with absorbing boundary conditions. Within this work, a systematic work flow for setting up the wave problem, including the absorbing boundary conditions, is proposed. As a result, a convenient modal system description with an effective absorbing boundary formulation is established. Moreover, the truncated model shows high accuracy compared to the global domain.

Keywords: absorbing boundary conditions, boundary control, Fourier Galerkin approach, modal approach, wave equation

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Authors: Avinash Nayak, Debopam Das

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The current work implements the variational principle to find the optimum initial perturbation that provides maximum growth in an impulsively blocked channel flow. The conventional method for studying temporal stability has always been through modal analysis. In most of the transient flows, this modal analysis is still followed with the quasi-steady assumption, i.e. change in base flow is much slower compared to perturbation growth rate. There are other studies where transient analysis on time dependent flows is done by formulating the growth of perturbation as an initial value problem. But the perturbation growth is sensitive to the initial condition. This study intends to find the initial perturbation that provides the maximum growth at a later time. Here, the expression of base flow for blocked channel is derived and the formulation is based on the two dimensional perturbation with stream function representing the perturbation quantity. Hence, the governing equation becomes the Orr-Sommerfeld equation. In the current context, the cost functional is defined as the ratio of disturbance energy at a terminal time 'T' to the initial energy, i.e. G(T) = ||q(T)||2/||q(0)||2 where q is the perturbation and ||.|| defines the norm chosen. The above cost functional needs to be maximized against the initial perturbation distribution. It is achieved with the constraint that perturbation follows the basic governing equation, i.e. Orr-Sommerfeld equation. The corresponding adjoint equation is derived and is solved along with the basic governing equation in an iterative manner to provide the initial spatial shape of the perturbation that provides the maximum growth G (T). The growth rate is plotted against time showing the development of perturbation which achieves an asymptotic shape. The effects of various parameters, e.g. Reynolds number, are studied in the process. Thus, the study emphasizes on the usage of optimal perturbation and its growth to understand the stability characteristics of time dependent flows. The assumption of quasi-steady analysis can be verified against these results for the transient flows like impulsive blocked channel flow.

Keywords: blocked channel flow, calculus of variation, hydrodynamic stability, optimal perturbation

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Authors: S. S. Abas, Y. M. Yatim

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In this paper the unsteady, slender, symmetric dry patch in an infinitely wide and thin liquid film of Newtonian fluid draining under gravity down an inclined plane in the presence of strong surface-tension effect is considered. A similarity transformation, named a travelling-wave similarity solution is used to reduce the governing partial differential equation into the ordinary differential equation which is then solved numerically using a shooting method. The introduction of surface-tension effect on the flow leads to a fourth-order ordinary differential equation. The solution obtained predicts that the dry patch has a quartic shape and the free surface has a capillary ridge near the contact line which decays in an oscillatory manner far from it.

Keywords: dry patch, Newtonian fluid, similarity solution, surface-tension effect, travelling-wave, unsteady thin-film flow

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Authors: Kaoutar Lamrini Uahabi, Mohamed Atounti

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In the present work, we consider one category of curves denoted by L(p, k, r, n). These curves are continuous arcs which are trajectories of roots of the trinomial equation zn = αzk + (1 − α), where z is a complex number, n and k are two integers such that 1 ≤ k ≤ n − 1 and α is a real parameter greater than 1. Denoting by L the union of all trinomial curves L(p, k, r, n) and using the box counting dimension as fractal dimension, we will prove that the dimension of L is equal to 3/2.

Keywords: feasible angles, fractal dimension, Minkowski sausage, trinomial curves, trinomial equation

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Authors: Muhammad Bilal Ameen, M. Zubair Akbar Qureshi

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The current investigation of two-dimensional hybrid nanofluid flows with two coaxial parallel disks has been presented. Consider the hybrid nanofluid has been taken as steady-state. Consider the coaxial disks that have been porous. Consider the heat equation to examine joule heating and viscous dissipation effects. Nonlinear partial differential equations have been solved numerically. For shear stress and heat transfer, results are tabulated. Hybrid nanoparticles and Eckert numbers are increasing for heat transfer. Entropy generation is expanded with radiation parameters Eckert, Reynold, Prandtl, and Peclet numbers. A set of ordinary differential equations is obtained to utilize the capable transformation variables. The numerical solution of the continuity, momentum, energy, and entropy generation equations is obtaining using the command bvp4c of Matlab as a solver. To explore the impact of main parameters like suction/infusion, Prandtl, Reynold, Eckert, Peclet number, and volume fraction parameters, various graphs have been plotted and examined. It is concluded that a convectional nanofluid is highly compared by entropy generation with the boundary layer of hybrid nanofluid.

Keywords: entropy generation, hybrid nano fluid, heat transfer, porous disks

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Authors: Saidu Ibrahim, Winston M. W. Shakantu

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The problem of construction material waste remains unresolved, as a significant percentage of the materials delivered to some project sites end up as waste which might result in additional project cost. Cost overrun is a problem which affects 90% of the completed projects in the world. The argument on how to eliminate it has been on-going for the past 70 years, but there is neither substantial improvement nor significant solution for mitigating its detrimental effects. Research evidence has proposed various construction cost overruns and material-waste management approaches; nonetheless, these studies failed to give a clear indication on the framework and the equation for managing construction material waste and cost overruns. Hence, this research aims to develop a conceptual framework and a mathematical equation for managing material waste and cost overrun in the construction industry. The paper adopts the desktop methodological approach. This involves comparing the causes of material waste and those of cost overruns from the literature to determine the possible relationship. The review revealed a relationship between material waste and cost overrun that; increase in material waste would result to a corresponding increase in the amount of cost overrun at both the pre-contract and the post contract stages of a project. It was found from the equation that achieving an effective construction material waste management must ensure a “Good Quality-of-Planning, Estimating, and Design Management” and a “Good Quality- of-Construction, Procurement and Site Management”; a decrease in “Design Complexity” which would reduce “Material Waste” and subsequently reduce the amount of cost overrun by 86.74%. The conceptual framework and the mathematical equation developed in this study are recommended to the professionals of the construction industry.

Keywords: conceptual framework, cost overrun, material waste, project stags

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Authors: Joshua N. Edokpayi, John O. Odiyo, Titus A. M. Msagati, Elizabeth O. Popoola

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Polycyclic aromatic hydrocarbons (PAHs) are very toxic and persistent environmental contaminants. This study was undertaken to assess the concentrations and possible sources of 16 PAHs classified by the United State Environmental Protection Agency as priority pollutants in Mvudi and Nzhelele Rivers and sediments. Effluents from Thohoyandou wastewater treatment plant and Siloam waste stabilization ponds were also investigated. Diagnostic ratios were used to evaluate the possible sources of PAHs. PAHs in the water samples were extracted using 1:1 dichloromethane and n-hexane mixtures, while those in the sediment samples were extracted with 1:1 acetone and dichloromethane using ultrasonication method. The extracts were purified using SPE technique and reconstituted in n-hexane before analyses with GC-TOF-MS. The results obtained indicate the prevalence of high molecular weight PAHs in all the samples. PAHs concentrations in water and sediment samples from all the sampling sites were in the range of 13.174-26.382 mg/L and 27.10-55.93 mg/kg, respectively. Combustion of biomass was identified as the major possible source of PAHs. Effluents from wastewater treatment facilities were also considered as major anthropogenic contributions to the levels of PAHs determined in both river waters and sediments. Mvudi and Nzhelele Rivers show moderate to high contamination level of PAHs.

Keywords: polycyclic aromatic hydrocarbon, rivers, sediments, wastewater effluents

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Authors: Liqin Zhi, Lin Xu, Wenxia Wei, Yaqi Cai

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Recently, replacing some of the methyl groups in polydimethylsiloxanes with other functional groups has been extensively explored to obtain modified polymethylsiloxanes with special properties that enable new industrial applications. Fluorinated polysiloxanes, one type of these modified polysiloxanes, are based on a siloxane backbone with fluorinated groups attached to the side chains of polysiloxanes. As a commercially significant material, poly[methyl(trifluoropropyl)siloxane] (PMTFPS) has sufficient fluorine content to be useful as a fuel-and oil-resistant elastomer, which combines both the chemical and solvent resistance of fluorocarbons and the wide temperature range applicability of organosilicones. PMTFPS products can be used in many applications in which resistance to fuel, oils and hydrocarbon solvents is required, including use as lubricants in bearings, sealants, and elastomers for aerospace and automotive fuel systems. Fluorinated methylsiloxanes, a type of modified methylsiloxane, include tris(trifluoropropyl)trimethylcyclotrisiloxane (D3F) and tetrakis(trifluoropropyl)tetramethylcyclotetrasiloxane (D4F), both of which contain trifluoropropyl groups in the side chains of cyclic methylsiloxanes. D3F, as an important monomer in the manufacture of PMTFPS, is often present as an impurity in PMTFPS. In addition, the synthesis of PMTFPS from D3F could form other fluorinated methylsiloxanes with low molecular weights (such as D4F). The yearly demand and production volumes of D3F increased rapidly all over world. Fluorinated methylsiloxanes might be released into the environment via different pathways during the production and application of PMTFPS. However, there is a lack of data concerning the emission, environmental occurrence and potential environmental impacts of fluorinated methylsiloxanes. Here, we report fluorinated methylsiloxanes (D3F and D4F) in surface water and sediment samples collected near a fluorinated methylsiloxane manufacturing plant in Weihai, China. The concentrations of D3F and D4F in surface water ranged from 3.29 to 291 ng/L and from 7.02 to 168 ng/L, respectively. The concentrations of D3F and D4F in sediment ranged from 11.8 to 5478 ng/g and from 17.2 to 6277 ng/g, respectively. In simulation experiment, the half-lives of D3F and D4F at different pH values (5.2, 6.4, 7.2, 8.3 and 9.2) varied from 80.6 to 154 h and from 267 to 533 h respectively. CF₃(CH₂)₂MeSi(OH)₂ was identified as one of the main hydrolysis products of fluorinated methylsiloxanes. It was also detected in the river samples at concentrations of 72.1-182.9 ng/L. In addition, the slow rearrangement of D3F (spiked concentration = 500 ng/L) to D4F (concentration = 11.0-22.7 ng/L) was also found during 336h hydrolysis experiment.

Keywords: fluorinated methylsiloxanes, environmental matrices, hydrolysis, sediment

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Authors: Adriano Valdes-Gomez, Francisco Javier Sevilla

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We devise a numerical algorithm to simulate the diffusion of a Brownian particle restricted to the surface of a three-dimensional sphere when the particle is under the effects of an external potential that is coupled linearly. It is obtained using elementary geometry, yet, it converges, in the weak sense, to the solutions to the Smoluchowski equation. Rotations on the sphere, which are the analogs of linear displacements in euclidean spaces, are calculated using algebraic operations and then by a proper scaling, which makes the algorithm efficient and quite simple, especially to what may be the short-time propagator approach. Our findings prove that the global effects of curvature are taken into account in both dynamic and stationary processes, and it is not restricted to work in configuration space, neither restricted to the overdamped limit. We have generalized it successfully to simulate the Kramers or the Ornstein-Uhlenbeck process, where it is necessary to work directly in phase space, and it may be adapted to other two dimensional surfaces with non-constant curvature.

Keywords: diffusion on the sphere, Fokker-Planck equation on the sphere, non equilibrium processes on the sphere, numerical methods for diffusion on the sphere

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Authors: Shangerganesh Lingeshwaran

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In this presentation, we have performed numerical simulations for a reaction-diffusion equation with various nonlinear density-dependent diffusion operators and proliferation functions. The mathematical model represented by parabolic partial differential equation is considered to study the invasion of gliomas (the most common type of brain tumors) and to describe the growth of cancer cells and response to their treatment. The unknown quantity of the given reaction-diffusion equation is the density of cancer cells and the mathematical model based on the proliferation and migration of glioma cells. A standard Galerkin finite element method is used to perform the numerical simulations of the given model. Finally, important observations on the each of nonlinear diffusion functions and proliferation functions are presented with the help of computational results.

Keywords: glioma invasion, nonlinear diffusion, reaction-diffusion, finite eleament method

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Authors: Gautam Kumar Saharia, Sagardeep Talukdar, Riki Dutta, Sudipta Nandy

Abstract:

The physics-informed neural network (PINN) method opens up an approach for numerically solving nonlinear partial differential equations leveraging fast calculating speed and high precession of modern computing systems. We construct the PINN based on a strong universal approximation theorem and apply the initial-boundary value data and residual collocation points to weekly impose initial and boundary conditions to the neural network and choose the optimization algorithms adaptive moment estimation (ADAM) and Limited-memory Broyden-Fletcher-Golfard-Shanno (L-BFGS) algorithm to optimize learnable parameter of the neural network. Next, we improve the PINN with a weighted loss function to obtain both the bright and dark soliton solutions of the Fokas-Lenells equation (FLE). We find the proposed scheme of adjustable weight coefficients into PINN has a better convergence rate and generalizability than the basic PINN algorithm. We believe that the PINN approach to solve the partial differential equation appearing in nonlinear optics would be useful in studying various optical phenomena.

Keywords: deep learning, optical soliton, physics informed neural network, partial differential equation

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Authors: S. O. Oyamakin, A. U. Chukwu

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Richard's growth equation being a generalized logistic growth equation was improved upon by introducing an allometric parameter using the hyperbolic sine function. The integral solution to this was called hyperbolic Richard's growth model having transformed the solution from deterministic to a stochastic growth model. Its ability in model prediction was compared with the classical Richard's growth model an approach which mimicked the natural variability of heights/diameter increment with respect to age and therefore provides a more realistic height/diameter predictions using the coefficient of determination (R2), Mean Absolute Error (MAE) and Mean Square Error (MSE) results. The Kolmogorov-Smirnov test and Shapiro-Wilk test was also used to test the behavior of the error term for possible violations. The mean function of top height/Dbh over age using the two models under study predicted closely the observed values of top height/Dbh in the hyperbolic Richard's nonlinear growth models better than the classical Richard's growth model.

Keywords: height, Dbh, forest, Pinus caribaea, hyperbolic, Richard's, stochastic

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Authors: Changqiao Wu, Guoqing Ding, Xin Chen

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In this paper, ways of modeling dynamic measurement systems are discussed. Specially, for linear system with single-input single-output, it could be modeled with shallow neural network. Then, gradient based optimization algorithms are used for searching the proper coefficients. Besides, method with normal equation and second order gradient descent are proposed to accelerate the modeling process, and ways of better gradient estimation are discussed. It shows that the mathematical essence of the learning objective is maximum likelihood with noises under Gaussian distribution. For conventional gradient descent, the mini-batch learning and gradient with momentum contribute to faster convergence and enhance model ability. Lastly, experimental results proved the effectiveness of second order gradient descent algorithm, and indicated that optimization with normal equation was the most suitable for linear dynamic models.

Keywords: dynamic system modeling, neural network, normal equation, second order gradient descent

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Authors: Kamel Al-Khaled

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A comparative study of the Sinc-Galerkin and Sinc-Collocation methods for solving the Kuramoto-Sivashinsky equation is given. Both approaches depend on using Sinc basis functions. Firstly, a numerical scheme using Sinc-Galerkin method is developed to approximate the solution of Kuramoto-Sivashinsky equation. Sinc approximations to both derivatives and indefinite integrals reduces the solution to an explicit system of algebraic equations. The error in the solution is shown to converge to the exact solution at an exponential. The convergence proof of the solution for the discrete system is given using fixed-point iteration. Secondly, a combination of a Crank-Nicolson formula in the time direction, with the Sinc-collocation in the space direction is presented, where the derivatives in the space variable are replaced by the necessary matrices to produce a system of algebraic equations. The methods are tested on two examples. The demonstrated results show that both of the presented methods more or less have the same accuracy.

Keywords: Sinc-Collocation, nonlinear PDEs, numerical methods, fixed-point

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Authors: Priyanka Ghosh, Priti Kumar Roy

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Every year a considerable number of people die due to methyl alcohol poisoning, in which most of them die even before proper treatment. This work gives a simple and cheap first aid to those affected individuals by the administration of activated charcoal. In this article, we emphasise on the adsorption capability of activated charcoal for the treatment of poisoning and use an impulsive differential equation to study the effect of activated charcoal during adsorption. We also investigate the effects of various parameters on the adsorption which are incorporated in the model system.

Keywords: activated charcoal, adsorption, impulsive differential equation, methanol poisoning

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Authors: Jiradeach Kalayaruan, Tosawat Seetawan

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This paper studied the energy of the nature systems by looking at the overall image throughout the universe. The energy of the nature systems was developed from the Einstein’s energy equation. The researcher used the new ideas called even 2n and odd 3n light dimension energy states systems, which were developed from Einstein’s relativity energy theory equation. In this study, the major methodology the researchers used was the basic principle ideas or beliefs of some religions such as Buddhism, Christianity, Hinduism, Islam, or Tao in order to get new discoveries. The basic beliefs of each religion - Nivara, God, Ether, Atman, and Tao respectively, were great influential ideas on the researchers to use them greatly in the study to form new ideas from philosophy. Since the philosophy of each religion was alive with deep insight of the physical nature relative energy, it connected the basic beliefs to light dimension energy states systems. Unfortunately, Einstein’s original relative energy equation showed only even 2n light dimension energy states systems (if n = 1,…,∞). But in advance ideas, the researchers multiplied light dimension energy by Einstein’s original relative energy equation and get new idea of theoritical physics in odd 3n light dimension energy states systems (if n = 1,…,∞). Because from basic principle ideas or beliefs of some religions philosophy of each religion, you had to add the media light dimension energy into Einstein’s original relative energy equation. Consequently, the simple meaning picture in deep insight showed that you could touch light dimension energy of Nivara, God, Ether, Atman, and Tao by light dimension energy. Since light dimension energy was transferred by Nivara, God, Ether, Atman and Tao, the researchers got the new equation of odd 3n light dimension energy states systems. Moreover, the researchers expected to be able to solve overview problems of all light dimension energy in all nature relative energy, which are developed from Eistein’s relative energy equation.The finding of the study was called 'super nature relative energy' ( in odd 3n light dimension energy states systems (if n = 1,…,∞)). From the new ideas above you could do the summation of even 2n and odd 3n light dimension energy states systems in all of nature light dimension energy states systems. In the future time, the researchers will expect the new idea to be used in insight theoretical physics, which is very useful to the development of quantum mechanics, all engineering, medical profession, transportation, communication, scientific inventions, and technology, etc.

Keywords: 2n light dimension energy states systems effect, Ether, even 2n light dimension energy states systems, nature relativity, Nivara, odd 3n light dimension energy states systems, perturbation points energy, relax point energy states systems, stress perturbation energy states systems effect, super relative energy

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Authors: Alireza Abdikian

Abstract:

By assuming a quantum relativistic degenerate electron-positron (e-p) plasma media, the nonlinear acoustic solitary propagation in the presence of the stationary ions for neutralizing the plasma background of bounded cylindrical geometry was investigated. By using the standard reductive perturbation technique with cooperation the quantum hydrodynamics model for the e-p fluid, the spherical Kadomtsev-Petviashvili equation was derived for small but finite amplitude waves and was given the solitary wave solution for the parameters relevant for dense astrophysical objects such as white dwarf stars. By using a suitable coordinate transformation and using improved F-expansion technique, the SKP equation can be solved analytically. The numerical results reveal that the relativistic effects lead to propagate the electrostatic bell shape structures and by increasing the relativistic effects, the amplitude and the width of the e-p acoustic solitary wave will decrease.

Keywords: Electron-positron plasma, Acoustic solitary wave, Relativistic plasmas, the spherical Kadomtsev-Petviashvili equation

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Authors: Arash Jafari, Mehdi Taghaddosi, Azin Parvin

Abstract:

In the paper, our purpose is to enhance the ability to solve a nonlinear differential equation which is about the motion of an incompressible fluid flow going down of an inclined plane without thermal effect with a simple and innovative approach which we have named it new method. Comparisons are made amongst the Numerical, new method, and HPM methods, and the results reveal that this method is very effective and simple and can be applied to other nonlinear problems. It is noteworthy that there are some valuable advantages in this way of solving differential equations, and also most of the sets of differential equations can be answered in this manner which in the other methods they do not have acceptable solutions up to now. A summary of the excellence of this method in comparison to the other manners is as follows: 1) Differential equations are directly solvable by this method. 2) Without any dimensionless procedure, we can solve equation(s). 3) It is not necessary to convert variables into new ones. According to the afore-mentioned assertions which will be proved in this case study, the process of solving nonlinear equation(s) will be very easy and convenient in comparison to the other methods.

Keywords: viscos fluid, incompressible fluid flow, inclined plane, nonlinear phenomena

Procedia PDF Downloads 283

Authors: Ranju Chowdhury, Santosh K. Sarkar

Abstract:

Trace element accumulation potential of ten mangrove species in individual plant tissues (leaves, bark and root/pneumatophore) along with host sediments was carried out at 2 study sites of diverse environmental stresses of Indian Sundarban Wetland, a UNESCO world heritage site. The study was undertaken with the following objectives: (i) to investigate the extent of accumulation and the distribution of trace metals in plant tissues (ii) to determine whether sediment trace metal levels are correlated with trace metal levels in tissues and (iii) to find out the suitable candidate for phytoremediation species. Mangrove sediments showed unique potential in many- fold increase for most trace metals than plant tissues due to their inherent physicochemical properties. The concentrations of studied 11 trace elements (expressed in µg g -1) showed wide range of variations in host sediment with the following descending order: Fe (2865.31-3019.62) > Mn (646.04- 648.47 > Cu (35.03- 41.55) > Zn (32.51- 36.33) > Ni (34.4- 36.60) > Cr (27.5- 29.54) > Pb (11.6- 20.34) > Co (6.79- 8.55) > As (3.22- 4.41) > Cd (0.19- 0.22) > Hg (0.06- 0.07). The ranges of concentration of trace metals (expressed in µg g -1) for As, Cd, Co, Cr, Cu, Fe, Hg, Mn, Ni, Pb and Zn in plant tissues were 0.006- 0.31, 0.02- 2.97, 0.10- 4.80, 0.13- 6.49, 4.46- 48.30, 9.20- 938.13, 0.02- 0.13, 9.8- 1726.24, 5.41- 11.34, 0.04 - 7.64, 3.81- 52.20 respectively. Among all trace elements, Cd and Zn were highly bioaccumulated in Excoecaria agallocha (2.97 and 52.20 µg g -1 respectively). The bio- concentration factor (BCF) showed its maximum value (15.5) in E. agallocha for Cd, suggesting that it can be considered as a high-efficient plant for trace metal bioaccumulation. Therefore, phytoremediation could be extensively used for the removal of the toxic contaminants for sustainable management of Sundarban coastal regions.

Keywords: Indian Sundarban, mangroves, phytoremediation, trace elements

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Authors: Rajkumar N. Ingle

Abstract:

In this paper, the existence of a solution of nonlinear functional random differential equations of the first order is proved under caratheodory condition. The study of the functional random differential equation has got importance in the random analysis of the dynamical systems of universal phenomena. Objectives: Nonlinear functional random differential equation is useful to the scientists, engineers, and mathematicians, who are engaged in N.F.R.D.E. analyzing a universal random phenomenon, govern by nonlinear random initial value problems of D.E. Applications of this in the theory of diffusion or heat conduction. Methodology: Using the concepts of probability theory, functional analysis, generally the existence theorems for the nonlinear F.R.D.E. are prove by using some tools such as fixed point theorem. The significance of the study: Our contribution will be the generalization of some well-known results in the theory of Nonlinear F.R.D.E.s. Further, it seems that our study will be useful to scientist, engineers, economists and mathematicians in their endeavors to analyses the nonlinear random problems of the universe in a better way.

Keywords: Random Fixed Point Theorem, functional random differential equation, N.F.R.D.E., universal random phenomenon

Procedia PDF Downloads 501