Search results for: Boussinesq equation

Authors: Lamia Bourdache, Amar Djema

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The effect of non-Newtonian property (power law index n) on traveling waves of thin layer of power law fluid flowing over an inclined plane is investigated. For this, a simplified second-order two-equation model (SM) is used. The complete model is second-order four-equation (CM). It is derived by combining the weighted residual integral method and the lubrication theory. This is due to the fact that at the beginning of the instability waves, a very small number of waves is observed. Using a suitable set of test functions, second order terms are eliminated from the calculus so that the model is still accurate to the second order approximation. Linear, spatial, and temporal stabilities are studied. For travelling waves, a particular type of wave form that is steady in a moving frame, i.e., that travels at a constant celerity without changing its shape is studied. This type of solutions which are characterized by their celerity exists under suitable conditions, when the widening due to dispersion is balanced exactly by the narrowing effect due to the nonlinearity. Changing the parameter of celerity in some range allows exploring the entire spectrum of asymptotic behavior of these traveling waves. The (SM) model is converted into a three dimensional dynamical system. The result is that the model exhibits bifurcation scenarios such as heteroclinic, homoclinic, Hopf, and period-doubling bifurcations for different values of the power law index n. The influence of the non-Newtonian parameter on the nonlinear development of these travelling waves is discussed. It is found at the end that the qualitative characters of bifurcation scenarios are insensitive to the variation of the power law index.

Keywords: inclined plane, nonlinear stability, non-Newtonian, thin film

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Authors: Barenten Suciu

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Classical matrix calculus and Routh-Hurwitz stability conditions, applied to the snake-like motion of the conical wheel axle, lead to the conclusion that the hunting mode is inherently unstable, and its natural frequency is a complex number. In order to analytically solve such a complicated vibration model, either the inertia terms were neglected, in the model designated as geometrical, or restrictions on the creep coefficients and yawing diameter were imposed, in the so-called dynamical model. Here, an alternative solution is proposed to solve the hunting mode, based on the observation that the bullet train wheel axle is equipped with cylindrical wheels. One argues that for such wheel treads, the geometrical hunting is irrelevant, since its natural frequency becomes nil, but the dynamical hunting is significant since its natural frequency reduces to a real number. Moreover, one illustrates that the geometrical simplification of the wheel causes the stabilization of the hunting mode, since the characteristic quartic equation, derived for conical wheels, reduces to a quadratic equation of positive coefficients, for cylindrical wheels. Quite simple analytical expressions for the damping ratio and natural frequency are obtained, without applying restrictions into the model of contact. Graphs of the time-depending hunting lateral perturbation, including the maximal and inflexion points, are presented both for the critically-damped and the over-damped wheel axles.

Keywords: bullet train, creep, cylindrical wheels, damping, dynamical hunting, stability, vibration analysis

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Authors: Ahmad Fahim Nasiry, Shigeo Honma

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We examine two-dimensional oil displacement by water in a petroleum reservoir. The pore fluid is immiscible, and the porous media is homogenous and isotropic in the horizontal direction. Buckley-Leverett theory and a combination of Laplacian and Darcy’s law are used to study the fluid flow through porous media, and the Laplacian that defines the dispersion and diffusion of fluid in the sand using heavy oil is discussed. The reservoir is homogenous in the horizontal direction, as expressed by the partial differential equation. Two main factors which are observed are the water saturation and pressure distribution in the reservoir, and they are evaluated for predicting oil recovery in two dimensions by a physical and mathematical simulation model. We review the numerical simulation that solves difficult partial differential reservoir equations. Based on the numerical simulations, the saturation and pressure equations are calculated by the iterative alternating direction implicit method and the iterative alternating direction explicit method, respectively, according to the finite difference assumption. However, to understand the displacement of oil by water and the amount of water dispersion in the reservoir better, an interpolated contour line of the water distribution of the five-spot pattern, that provides an approximate solution which agrees well with the experimental results, is also presented. Finally, a computer program is developed to calculate the equation for pressure and water saturation and to draw the pressure contour line and water distribution contour line for the reservoir.

Keywords: numerical simulation, immiscible, finite difference, IADI, IDE, waterflooding

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Authors: Carlos Teodoro, Oscar Bautista

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In this work, we analyze theoretically the mass transport in a time-periodic electroosmotic flow through a parallel flat plate microchannel under different periodic functions of the applied external electric field. The microchannel connects two reservoirs having different constant concentrations of an electro-neutral solute, and the zeta potential of the microchannel walls are assumed to be uniform. The governing equations that allow determining the mass transport in the microchannel are given by the Poisson-Boltzmann equation, the modified Navier-Stokes equations, where the Debye-Hückel approximation is considered (the zeta potential is less than 25 mV), and the species conservation. These equations are nondimensionalized and four dimensionless parameters appear which control the mass transport phenomenon. In this sense, these parameters are an angular Reynolds, the Schmidt and the Péclet numbers, and an electrokinetic parameter representing the ratio of the half-height of the microchannel to the Debye length. To solve the mathematical model, first, the electric potential is determined from the Poisson-Boltzmann equation, which allows determining the electric force for various periodic functions of the external electric field expressed as Fourier series. In particular, three different excitation wave forms of the external electric field are assumed, a) sawteeth, b) step, and c) a periodic irregular functions. The periodic electric forces are substituted in the modified Navier-Stokes equations, and the hydrodynamic field is derived for each case of the electric force. From the obtained velocity fields, the species conservation equation is solved and the concentration fields are found. Numerical calculations were done by considering several binary systems where two dilute species are transported in the presence of a carrier. It is observed that there are different angular frequencies of the imposed external electric signal where the total mass transport of each species is the same, independently of the molecular diffusion coefficient. These frequencies are called crossover frequencies and are obtained graphically at the intersection when the total mass transport is plotted against the imposed frequency. The crossover frequencies are different depending on the Schmidt number, the electrokinetic parameter, the angular Reynolds number, and on the type of signal of the external electric field. It is demonstrated that the mass transport through the microchannel is strongly dependent on the modulation frequency of the applied particular alternating electric field. Possible extensions of the analysis to more complicated pulsation profiles are also outlined.

Keywords: electroosmotic flow, mass transport, oscillatory flow, species separation

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Authors: Kwan U. Kim, Jin Sim, Ryong Jin Jang, Sung Duk Kim

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108 years have passed since a great number of physicists explained astronomical and physical phenomena by solving geodesic equations in Schwarzschild metric. However, when solving the geodesic equations in Schwarzschild metric, they did not correctly solve one branch of the component of space among spatial and temporal components of four-dimensional force and did not come up with physical laws correctly by means of physical analysis from the results obtained by solving the geodesic equations. In addition to it, they did not treat the astronomical and physical phenomena in a physical way based on the correct physical laws obtained from the solution of the geodesic equations in Schwarzschild metric. Therefore, some former scholars mentioned that Einstein’s theoretical basis of the general theory of relativity was obscure and incorrect, but they have not given a correct physical solution to the problems. Furthermore, since the general theory of relativity has not given a quantitative solution to obscure and incorrect problems, the generalization of gravitational theory has not been successfully completed yet, although the former scholars thought of it and tried to do it. In order to solve the problems it is necessary to explore the obscure and incorrect problems in general theory of relativity based on the physical laws and to find out the methodology of solving the problems. Therefore, first of all, as the first step for achieving the purpose, the right solution of the geodesic equation in Schwarzschild metric has been presented. Next, the correct physical laws found by making a physical analysis of the results have been presented, the obscure and incorrect problems have been shown, and an analysis of them has been made based on the physical laws. In addition, the experimental verification of the physical laws found by us has been made.

Keywords: equivalence principle, general relativity, geometrodynamics, Schwarzschild, Poincaré

Procedia PDF Downloads 78

Authors: Kwan U. Kim, Jin Sim, Ryong Jin Jang, Sung Duk Kim

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108 years have passed since a great number of physicists explained astronomical and physical phenomena by solving geodesic equations in the Schwarzschild metric. However, when solving the geodesic equations in Schwarzschild metric, they did not correctly solve one branch of the component of space among spatial and temporal components of four-dimensional force and did not come up with physical laws correctly by means of physical analysis from the results obtained by solving the geodesic equations. In addition, they did not treat the astronomical and physical phenomena in a physical way based on the correct physical laws obtained from the solution of the geodesic equations in the Schwarzschild metric. Therefore, some former scholars mentioned that Einstein’s theoretical basis of a general theory of relativity was obscure and incorrect, but they did not give a correct physical solution to the problems. Furthermore, since the general theory of relativity has not given a quantitative solution to obscure and incorrect problems, the generalization of gravitational theory has not yet been successfully completed, although former scholars have thought of it and tried to do it. In order to solve the problems, it is necessary to explore the obscure and incorrect problems in a general theory of relativity based on the physical laws and to find out the methodology for solving the problems. Therefore, as the first step toward achieving this purpose, the right solution of the geodesic equation in the Schwarzschild metric has been presented. Next, the correct physical laws found by making a physical analysis of the results have been presented, the obscure and incorrect problems have been shown, and an analysis of them has been made based on the physical laws. In addition, the experimental verification of the physical laws found by us has been made.

Keywords: equivalence principle, general relativity, geometrodynamics, Schwarzschild, Poincaré

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Authors: J.R.S.S. Kumara, M.A.R.M. Fernando, S.Venkatesh, D.K. Jayaratne

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Protection of heritage monuments against lightning has become extremely important as far as their historical values are concerned. When such structures are large and tall, the risk of lightning initiated from both cloud and ground can be high. This paper presents a lightning risk analysis of three giant stupas in Anuradhapura era (fourth century BC onwards) in Sri Lanka. The three stupas are Jethawaaramaya (269-296 AD), Abayagiriya (88-76 BC) and Ruwanweliseya (161-137 BC), the third, fifth and seventh largest ancient structures in the world. These stupas are solid brick structures consisting of a base, a near hemispherical dome and a conical spire on the top. The ancient stupas constructed with a dielectric crystal on the top and connected to the ground through a conducting material, was considered as the hypothesis for their original lightning protection technique. However, at present, all three stupas are protected with Franklin rod type air termination systems located on top of the spire. First, a risk analysis was carried out according to IEC 62305 by considering the isokeraunic level of the area and the height of the stupas. Then the standard protective angle method and rolling sphere method were used to locate the possible touching points on the surface of the stupas. The study was extended to estimate the critical current which could strike on the unprotected areas of the stupas. The equations proposed by (Uman 2001) and (Cooray2007) were used to find the striking distances. A modified version of rolling sphere method was also applied to see the effects of upward leaders. All these studies were carried out for two scenarios: with original (i.e. ancient) lightning protection system and with present (i.e. new) air termination system. The field distribution on the surface of the stupa in the presence of a downward leader was obtained using finite element based commercial software COMSOL Multiphysics for further investigations of lightning risks. The obtained results were analyzed and compared each other to evaluate the performance of ancient and new lightning protection methods and identify suitable methods to design lightning protection systems for stupas. According to IEC standards, all three stupas with new and ancient lightning protection system has Level IV protection as per protection angle method. However according to rolling sphere method applied with Uman’s equation protection level is III. The same method applied with Cooray’s equation always shows a high risk with respect to Uman’s equation. It was found that there is a risk of lightning strikes on the dome and square chamber of the stupa, and the corresponding critical current values were different with respect to the equations used in the rolling sphere method and modified rolling sphere method.

Keywords: Stupa, heritage, lightning protection, rolling sphere method, protection level

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Authors: Sidrah Ahmed

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The river and lakes flows are modeled mathematically by shallow water equations that are depth-averaged Reynolds Averaged Navier-Stokes equations under Boussinesq approximation. The temperature stratification dynamics influence the water quality and mixing characteristics. It is mainly due to the atmospheric conditions including air temperature, wind velocity, and radiative forcing. The experimental observations are commonly taken along vertical scales and are not sufficient to estimate small turbulence effects of temperature variations induced characteristics of shallow flows. Wind shear stress over the water surface influence flow patterns, heat fluxes and thermodynamics of water bodies as well. Hence it is crucial to couple temperature gradients with shallow water model to estimate the atmospheric effects on flow patterns. The Ripa system has been introduced to study ocean currents as a variant of shallow water equations with addition of temperature variations within the flow. Ripa model is a hyperbolic system of partial differential equations because all the eigenvalues of the system’s Jacobian matrix are real and distinct. The time steps of a numerical scheme are estimated with the eigenvalues of the system. The solution to Riemann problem of the Ripa model is composed of shocks, contact and rarefaction waves. Solving Ripa model with Riemann initial data with the central schemes is difficult due to the eigen structure of the system.This works presents the comparison of four different finite difference schemes for the numerical solution of Riemann problem for Ripa model. These schemes include Lax-Friedrichs, Lax-Wendroff, MacCormack scheme and a higher order finite difference scheme with WENO method. The numerical flux functions in both dimensions are approximated according to these methods. The temporal accuracy is achieved by employing TVD Runge Kutta method. The numerical tests are presented to examine the accuracy and robustness of the applied methods. It is revealed that Lax-Freidrichs scheme produces results with oscillations while Lax-Wendroff and higher order difference scheme produce quite better results.

Keywords: finite difference schemes, Riemann problem, shallow water equations, temperature gradients

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Authors: H. Khanfari, M. Johari Fard

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Dealing with carbonate reservoirs can be mind-boggling for the reservoir engineers due to various digenetic processes that cause a variety of properties through the reservoir. A good estimation of the reservoir heterogeneity which is defined as the quality of variation in rock properties with location in a reservoir or formation, can better help modeling the reservoir and thus can offer better understanding of the behavior of that reservoir. Most of reservoirs are heterogeneous formations whose mineralogy, organic content, natural fractures, and other properties vary from place to place. Over years, reservoir engineers have tried to establish methods to describe the heterogeneity, because heterogeneity is important in modeling the reservoir flow and in well testing. Geological methods are used to describe the variations in the rock properties because of the similarities of environments in which different beds have deposited in. To illustrate the heterogeneity of a reservoir vertically, two methods are generally used in petroleum work: Dykstra-Parsons permeability variations (V) and Lorenz coefficient (L) that are reviewed briefly in this paper. The concept of Lorenz is based on statistics and has been used in petroleum from that point of view. In this paper, we correlated the statistical-based Lorenz method to a petroleum concept, i.e. Kozeny-Carman equation and derived the straight line plot of Lorenz graph for a homogeneous system. Finally, we applied the two methods on a heterogeneous field in South Iran and discussed each, separately, with numbers and figures. As expected, these methods show great departure from homogeneity. Therefore, for future investment, the reservoir needs to be treated carefully.

Keywords: carbonate reservoirs, heterogeneity, homogeneous system, Dykstra-Parsons permeability variations (V), Lorenz coefficient (L)

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Authors: Nargis Ali

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Since the modest fashion market is growing in the UK, there is still little understanding and more concerns found among researchers and marketers about Muslim consumers. Therefore, the present study is designed to explore critical factors influencing Muslim women’s intention to purchase clothing and to identify the differences in the purchase intention of ethnic minority groups in the UK. The conceptual framework is designed using the theory of planned behavior and social identity theory. In order to satisfy the research objectives, a structured online questionnaire was published on Facebook from 20 November to 21 March. As a result, 1087 usable questionnaires were received and used to assess the proposed model fit through structural equation modeling. Results revealed that social media does influence the purchase intention of Muslim women. Muslim women search for stylish clothes that provide comfort during summer while they prefer soft and subdued colors. Furthermore, religious knowledge and religious practice, and fashion uniqueness strongly influence their purchase intention, while hybrid identity is negatively related to the purchase intention of Muslim women. This research contributes to the literature linked to Muslim consumers at a time when the UK's large retailers were seeking to attract Muslim consumers through modestly designed outfits. Besides, it will be helpful to formulate or revise product and marketing strategies according to UK’s Muslim women’s tastes and needs.

Keywords: fashion uniqueness, hybrid identity, religiosity, social media, social identity theory, structural equation modeling, theory of planned behavior

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Authors: A. K. Borah, A. K. Singh

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In this paper we deal building blocks of the computer simulation of the multiphase flows. Whole simulation procedure can be viewed as two super procedures; The implementation of VOF method and the solution of Navier Stoke’s Equation. Moreover, a sequential code for a Navier Stoke’s solver has been studied.

Keywords: Bi-conjugate gradient stabilized (Bi-CGSTAB), ILUT function, krylov subspace, multifluid flows preconditioner, simple algorithm

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Authors: Tarek Sabri Duzan

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Knowledge of the magnitude of Geo-pressures (Pore, Fracture & Over-burden pressures) is vital especially during drilling, completions, stimulations, Enhance Oil Recovery. Many times problems, like lost circulation could have been avoided if techniques for calculating Geo-pressures had been employed in the well planning, mud weight plan, and casing design. In this paper, we focused on the relationships between Geo-pressures and wave velocities (P-Wave (Vp) and S-wave (Vs)) in shallow Libyan carbonate reservoir in the western part of the Sirte Basin (Dahra F-Area). The data used in this report was collected from four new wells recently drilled. Those wells were scattered throughout the interested reservoir as shown in figure-1. The data used in this work are bulk density, Formation Mult -Tester (FMT) results and Acoustic wave velocities. Furthermore, Eaton Method is the most common equation used in the world, therefore this equation has been used to calculate Fracture pressure for all wells using dynamic Poisson ratio calculated by using acoustic wave velocities, FMT results for pore pressure, Overburden pressure estimated by using bulk density. Upon data analysis, it has been found that there is a linear relationship between Geo-pressures (Pore, Fracture & Over-Burden pressures) and wave velocities ratio (Vp/Vs). However, the relationship was not clear in the high-pressure area, as shown in figure-10. Therefore, it is recommended to use the output relationship utilizing the new seismic data for shallow carbonate reservoir to predict the Geo-pressures for future oil operations. More data can be collected from the high-pressure zone to investigate more about this area.

Keywords: bulk density, formation mult-tester (FMT) results, acoustic wave, carbonate shalow reservoir, d/jfield velocities

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Authors: Jyh Sheen, Yong-Lin Wang

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This research dedicates to find a different measurement procedure of microwave dielectric properties of ceramic materials with high dielectric constants. For the composite of ceramic dispersed in the polymer matrix, the dielectric constants of the composites with different concentrations can be obtained by various mixture equations. The other development of mixture rule is to calculate the permittivity of ceramic from measurements on composite. To do this, the analysis method and theoretical accuracy on six basic mixture laws derived from three basic particle shapes of ceramic fillers have been reported for dielectric constants of ceramic less than 40 at microwave frequency. Similar researches have been done for other well-known mixture rules. They have shown that both the physical curve matching with experimental results and low potential theory error are important to promote the calculation accuracy. Recently, a modified of mixture equation for high dielectric constant ceramics at microwave frequency has also been presented for strontium titanate (SrTiO3) which was selected from five more well known mixing rules and has shown a good accuracy for high dielectric constant measurements. However, it is still not clear the accuracy of this modified equation for other high dielectric constant materials. Therefore, the five more well known mixing rules are selected again to understand their application to other high dielectric constant ceramics. The other high dielectric constant ceramic, TiO2 with dielectric constant 100, was then chosen for this research. Their theoretical error equations are derived. In addition to the theoretical research, experimental measurements are always required. Titanium dioxide is an interesting ceramic for microwave applications. In this research, its powder is adopted as the filler material and polyethylene powder is like the matrix material. The dielectric constants of those ceramic-polyethylene composites with various compositions were measured at 10 GHz. The theoretical curves of the five published mixture equations are shown together with the measured results to understand the curve matching condition of each rule. Finally, based on the experimental observation and theoretical analysis, one of the five rules was selected and modified to a new powder mixture equation. This modified rule has show very good curve matching with the measurement data and low theoretical error. We can then calculate the dielectric constant of pure filler medium (titanium dioxide) by those mixing equations from the measured dielectric constants of composites. The accuracy on the estimating dielectric constant of pure ceramic by various mixture rules will be compared. This modified mixture rule has also shown good measurement accuracy on the dielectric constant of titanium dioxide ceramic. This study can be applied to the microwave dielectric properties measurements of other high dielectric constant ceramic materials in the future.

Keywords: microwave measurement, dielectric constant, mixture rules, composites

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Authors: D. T. Chabalala, J. M. Ndambuki, M. F. Ilunga

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Sedimentation includes the processes of erosion, transportation, deposition, and the compaction of sediment. Sedimentation in reservoir results in a decrease in water storage capacity, downstream problems involving aggregation and degradation, blockage of the intake, and change in water quality. A study was conducted in Caledon River catchment in the upstream of Welbedacht Reservoir located in the South Eastern part of Free State province, South Africa. The aim of this research was to investigate and develop a model for an Integrated Catchment Modelling of Sedimentation processes and management for the Welbedacht reservoir. Revised Universal Soil Loss Equation (RUSLE) was applied to determine sources of sediment at different areas of the catchment. The model has been also used to determine the impact of changes from management practice on erosion generation. The results revealed that the main sources of sediment in the watershed are cultivated land (273 ton per hectare), built up and forest (103.3 ton per hectare), and grassland, degraded land, mining and quarry (3.9, 9.8 and 5.3 ton per hectare) respectively. After application of soil conservation practices to developed Revised Universal Soil Loss Equation model, the results revealed that the total average annual soil loss in the catchment decreased by 76% and sediment yield from cultivated land decreased by 75%, while the built up and forest area decreased by 42% and 99% respectively. Thus, results of this study will be used by government departments in order to develop sustainable policies.

Keywords: Welbedacht reservoir, sedimentation, RUSLE, Caledon River

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Authors: Triveni Gogoi, Rima Chatterjee

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Shear wave velocity (Vs) estimation is an important approach in the seismic exploration and characterization of a hydrocarbon reservoir. There are varying methods for prediction of S-wave velocity, if recorded S-wave log is not available. But all the available methods for Vs prediction are empirical mathematical models. Shear wave velocity can be estimated using P-wave velocity by applying Castagna’s equation, which is the most common approach. The constants used in Castagna’s equation vary for different lithologies and geological set-ups. In this study, multiple regression analysis has been used for estimation of S-wave velocity. The EMERGE module from Hampson-Russel software has been used here for generation of S-wave log. Both single attribute and multi attributes analysis have been carried out for generation of synthetic S-wave log in Upper Assam basin. Upper Assam basin situated in North Eastern India is one of the most important petroleum provinces of India. The present study was carried out using four wells of the study area. Out of these wells, S-wave velocity was available for three wells. The main objective of the present study is a prediction of shear wave velocities for wells where S-wave velocity information is not available. The three wells having S-wave velocity were first used to test the reliability of the method and the generated S-wave log was compared with actual S-wave log. Single attribute analysis has been carried out for these three wells within the depth range 1700-2100m, which corresponds to Barail group of Oligocene age. The Barail Group is the main target zone in this study, which is the primary producing reservoir of the basin. A system generated list of attributes with varying degrees of correlation appeared and the attribute with the highest correlation was concerned for the single attribute analysis. Crossplot between the attributes shows the variation of points from line of best fit. The final result of the analysis was compared with the available S-wave log, which shows a good visual fit with a correlation of 72%. Next multi-attribute analysis has been carried out for the same data using all the wells within the same analysis window. A high correlation of 85% has been observed between the output log from the analysis and the recorded S-wave. The almost perfect fit between the synthetic S-wave and the recorded S-wave log validates the reliability of the method. For further authentication, the generated S-wave data from the wells have been tied to the seismic and correlated them. Synthetic share wave log has been generated for the well M2 where S-wave is not available and it shows a good correlation with the seismic. Neutron porosity, density, AI and P-wave velocity are proved to be the most significant variables in this statistical method for S-wave generation. Multilinear regression method thus can be considered as a reliable technique for generation of shear wave velocity log in this study.

Keywords: Castagna's equation, multi linear regression, multi attribute analysis, shear wave logs

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Authors: W. Meron Mebrahtu, R. Absi

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Velocity distribution in turbulent open-channel flows is organized in a complex manner. This is due to the large spatial and temporal variability of fluid motion resulting from the free-surface turbulent flow condition. This phenomenon is complicated further due to the complex geometry of channels and the presence of solids transported. Thus, several efforts were made to understand the phenomenon and obtain accurate mathematical models that are suitable for engineering applications. However, predictions are inaccurate because oversimplified assumptions are involved in modeling this complex phenomenon. Therefore, the aim of this work is to study velocity distribution profiles and obtain simple, more accurate, and predictive mathematical models. Particular focus will be made on the acceptable simplification of the general transport equations and an accurate representation of eddy viscosity. Wide rectangular open-channel seems suitable to begin the study; other assumptions are smooth-wall, and sediment-free flow under steady and uniform flow conditions. These assumptions will allow examining the effect of the bottom wall and the free surface only, which is a necessary step before dealing with more complex flow scenarios. For this flow condition, two ordinary differential equations are obtained for velocity profiles; from the Reynolds-averaged Navier-Stokes (RANS) equation and equilibrium consideration between turbulent kinetic energy (TKE) production and dissipation. Then different analytic models for eddy viscosity, TKE, and mixing length were assessed. Computation results for velocity profiles were compared to experimental data for different flow conditions and the well-known linear, log, and log-wake laws. Results show that the model based on the RANS equation provides more accurate velocity profiles. In the viscous sublayer and buffer layer, the method based on Prandtl’s eddy viscosity model and Van Driest mixing length give a more precise result. For the log layer and outer region, a mixing length equation derived from Von Karman’s similarity hypothesis provides the best agreement with measured data except near the free surface where an additional correction based on a damping function for eddy viscosity is used. This method allows more accurate velocity profiles with the same value of the damping coefficient that is valid under different flow conditions. This work continues with investigating narrow channels, complex geometries, and the effect of solids transported in sewers.

Keywords: accuracy, eddy viscosity, sewers, velocity profile

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Authors: Mihaly Homostrei, Tamas Simon, Dorottya Schnider

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The topic of oscillation in physics is one of the key ideas which is usually taught based on the concept of harmonic oscillation. It can be an interesting activity to deal with a frictional oscillator in advanced high school classes or in university courses. Its mechanics are investigated in this research, which shows that the motion of the frictional oscillator is more complicated than a simple harmonic oscillator. The physics of the applied model in this study seems to be interesting and useful for undergraduate students. The study presents a well-known physical system, which is mostly discussed theoretically in high school and at the university. The ideal frictional oscillator is normally used as an example of harmonic oscillatory motion, as its theory relies on the constant coefficient of sliding friction. The structure of the system is simple: a rod with a homogeneous mass distribution is placed on two rotating identical cylinders placed at the same height so that they are horizontally aligned, and they rotate at the same angular velocity, however in opposite directions. Based on this setup, one could easily show that the equation of motion describes a harmonic oscillation considering the magnitudes of the normal forces in the system as the function of the position and the frictional forces with a constant coefficient of frictions are related to them. Therefore, the whole description of the model relies on simple Newtonian mechanics, which is available for students even in high school. On the other hand, the phenomenon of the described frictional oscillator does not seem to be so straightforward after all; experiments show that the simple harmonic oscillation cannot be observed in all cases, and the system performs a much more complex movement, whereby the rod adjusts itself to a non-harmonic oscillation with a nonzero stable amplitude after an unconventional damping effect. The stable amplitude, in this case, means that the position function of the rod converges to a harmonic oscillation with a constant amplitude. This leads to the idea of a more complex model which can describe the motion of the rod in a more accurate way. The main difference to the original equation of motion is the concept that the frictional coefficient varies with the relative velocity. This dependence on the velocity was investigated in many different research articles as well; however, this specific problem could demonstrate the key concept of the varying friction coefficient and its importance in an interesting and demonstrative way. The position function of the rod is described by a more complicated and non-trivial, yet more precise equation than the usual harmonic oscillation description of the movement. The study discusses the structure of the measurements related to the frictional oscillator, the qualitative and quantitative derivation of the theory, and the comparison of the final theoretical function as well as the measured position-function in time. The project provides useful materials and knowledge for undergraduate students and a new perspective in university physics education.

Keywords: friction, frictional coefficient, non-harmonic oscillator, physics education

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Authors: Johnson Audu, Faisal Fairag

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In a bounded subset of R^d, d=2 or 3, we consider the Darcy-Forchheimer power model with the exponent 1 < m ≤ 2 for a single-phase strong-inertia fluid flow in a porous medium. Under necessary compatibility condition, and some mild regularity assumptions on the interior and the boundary data, we prove the existence and uniqueness of solution (u, p) in L^(m+1 ) (Ω)^d X (W^(1,(m+1)/m) (Ω)^d ⋂L_0^2 (Ω)^d) and its stability.

Keywords: porous media, power law, strong inertia, nonlinear, monotone type

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Authors: Nada Abdelsadig Moahamed Saied

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Female Genital Mutilation (FGM) and other similar traditional cultural practices pose a significant problem for Sudanese society. Such actions are severe and seriously detrimental to people's health since they are based on false social perceptions. To address these problems, numerous institutions and organizations were compelled to act rapidly. Female circumcision, or FGM, is one of the riskiest practices. It is referred to as the excision of the genitalia. Any surgeries involving the total or partial removal of the external female genitalia for non-medical reasons fall under this category. The results of FGM can vary depending on the kind and degree of the operation. These can be categorized as short-term, mid-term, or long-term issues. Infections, including the Human, blood, discomfort, and difficulty urinating are the immediate effects. FGM is defined by the World Health Organization (WHO) as practices that purposefully damage or modify female genital organs for non-medical purposes. It often takes place between the ages of one and fifteen. The girl's right to decide on important choices affecting her sexual and reproductive health is violated because the act is usually performed without her consent and frequently against her will. UNICEF, the United Nations International Children's Emergency Fund, aggressively combats the issue of FGM in Sudan. Numerous programs were started by NGOs to stop the practice. To our knowledge, no scientific study has been conducted to evaluate the effects of such social marketing techniques on simulating and comprehending society’s feelings surrounding FGM. This study proposes the development of a structural equation model aiming to determine the impact of awareness programs on people’s intentions to adopt the behavior of abandoning FGM based on theoretical models of behavior change. The model incorporates all the relevant factors that contribute to FGM and possible strategic actions to tackle this problem. The theoretical backdrop for FGM is presented in the next section, which also explains the practice's history, justifications, and potential treatments. The methodology section that follows describes the structural equation model. The proposed model, which compiles all the pertinent elements into a single image, is presented in the fourth part. Finally, conclusions are reached, and suggestions for further research are made.

Keywords: social marketing, policy-making, behavioral change, female genital mutilation, culture

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Authors: Einav Srulovici, Michal Grinstein-Weiss, George Knafl, Linda Beeber, Shawn Kneipp, Barbara Mark

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Background: The asset-building theoretical framework (ABTF) is acknowledged as the most complete framework thus far for depicting the relationships between asset accumulation (the stock of a household’s saved resources available for future investment) and health outcomes. Although the ABTF takes into consideration the reciprocal relationship between asset accumulation and health, no ABTF based study has yet examined this relationship. Therefore, the purpose of this study was to test the ABTF and psychological distress, focusing on the reciprocal relationship between assets accumulation and psychological distress. Methods: The study employed longitudinal data from 6,295 families from the 2001 and 2007 Panel Study of Income Dynamics data sets. Structural equation modeling (SEM) was used to test the reciprocal relationship between asset accumulation and psychological distress. Results: In general, the data displayed a good fit to the model. The longitudinal SEM found that asset accumulation significantly increased with a decreased in psychological distress over time, while psychological distress significantly increased with an increase in asset accumulation over time, confirming the existence of the hypothesized reciprocal relationship. Conclusions: Individuals who are less psychological distressed might have more energy to engage in activities, such as furthering their education or obtaining better jobs that are in turn associated with greater asset accumulation, while those who have greater assets may invest those assets in riskier investments, resulting in increased psychological distress. The confirmation of this reciprocal relationship highlights the importance of conducting longitudinal studies and testing the reciprocal relationship between asset accumulation and other health outcomes.

Keywords: asset-building theoretical framework, psychological distress, structural equation modeling, reciprocal relationship

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Authors: Sarah Mueller-Saegebrecht, André Brendler

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Business model innovation (BMI) as an intentional change of an existing business model (BM) or the design of a new BM is essential to a firm's development in dynamic markets. The relevance of BMI is also evident in the ongoing COVID-19 pandemic, in which start-ups, in particular, are affected by limited access to resources. However, first studies also show that they react faster to the pandemic than established firms. A strategy to successfully handle such threatening dynamic changes represents BMI. Entrepreneurship literature shows how and when firms should utilize BMI in times of crisis and which barriers one can expect during the BMI process. Nevertheless, research merging BMI barriers and crises is still underexplored. Specifically, further knowledge about antecedents and the effect of moderators on the BMI process is necessary for advancing BMI research. The addressed research gap of this study is two-folded: First, foundations to the subject on how different crises impact BM change intention exist, yet their analysis lacks the inclusion of barriers. Especially, entrepreneurship literature lacks knowledge about the individual perception of BMI barriers, which is essential to predict managerial reactions. Moreover, internal BMI barriers have been the focal point of current research, while external BMI barriers remain virtually understudied. Second, to date, BMI research is based on qualitative methodologies. Thus, a lack of quantitative work can specify and confirm these qualitative findings. By focusing on the crisis context, this study contributes to BMI literature by offering a first quantitative attempt to embed BMI barriers into a structural equation model. It measures managers' perception of BMI development and implementation barriers in the BMI process, asking the following research question: How does a manager's perception of BMI barriers influence BMI development and implementation in times of crisis? Two distinct research streams in economic literature explain how individuals react when perceiving a threat. "Prospect Theory" claims that managers demonstrate risk-seeking tendencies when facing a potential loss, and opposing "Threat-Rigidity Theory" suggests that managers demonstrate risk-averse behavior when facing a potential loss. This study quantitively tests which theory can best predict managers' BM reaction to a perceived crisis. Out of three in-depth interviews in the German chemical industry, 60 past BMIs were identified. The participating start-up managers gave insights into their start-up's strategic and operational functioning. After, each interviewee described crises that had already affected their BM. The participants explained how they conducted BMI to overcome these crises, which development and implementation barriers they faced, and how severe they perceived them, assessed on a 5-point Likert scale. In contrast to current research, results reveal that a higher perceived threat level of a crisis harms BM experimentation. Managers seem to conduct less BMI in times of crisis, whereby BMI development barriers dampen this relation. The structural equation model unveils a mediating role of BMI implementation barriers on the link between the intention to change a BM and the concrete BMI implementation. In conclusion, this study confirms the threat-rigidity theory.

Keywords: barrier perception, business model innovation, business model innovation barriers, crises, prospect theory, start-ups, structural equation model, threat-rigidity theory

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Authors: T. Nakpun, T. Kanjanarach, T. Kittisopee

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Turnover of community pharmacist can affect continuity of patient care and most importantly the quality of care and also the costs of a pharmacy. It was hypothesized that organizational resources, job characteristics, and social supports had direct effect on pharmacist turnover intention, and indirect effect on pharmacist turnover intention via pharmacist engagement. This research aimed to study influencing factors on pharmacist engagement and pharmacist turnover intention by testing the proposed structural hypothesized model to explain the relationship among organizational resources, job characteristics, and social supports that effect on pharmacist turnover intention and pharmacist engagement in Thai community pharmacists. A cross sectional study design with self-administered questionnaire was conducted in 209 Thai community pharmacists. Data were analyzed using Structural Equation Modeling technique with analysis of a moment structures AMOS program. The final model showed that only organizational resources had significant negative direct effect on pharmacist turnover intention (β =-0.45). Job characteristics and social supports had significant positive relationship with pharmacist engagement (β = 0.44, and 0.55 respectively). Pharmacist engagement had significant negative relationship with pharmacist turnover intention (β = - 0.24). Thus, job characteristics and social supports had significant negative indirect effect on turnover intention via pharmacist engagement (β =-0.11 and -0.13, respectively). The model fit the data well (χ2/ degree of freedom (DF) = 2.12, the goodness of fit index (GFI)=0.89, comparative fit index (CFI) = 0.94 and root mean square error of approximation (RMSEA) = 0.07). This study can be concluded that organizational resources were the most important factor because it had direct effect on pharmacist turnover intention. Job characteristics and social supports were also help decrease pharmacist turnover intention via pharmacist engagement.

Keywords: community pharmacist, influencing factor, turnover intention, work engagement

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Authors: Ehsan Pegah, Huabei Liu

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Determination of the internal friction angle (φ) in natural soil deposits is an important issue in geotechnical engineering. The main objective of this study was to examine the evaluation of this parameter in overconsolidated granular soil deposits by using the P-wave velocity and the anisotropic components of S-wave velocity (i.e., both the vertical component (SV) and the horizontal component (SH) of S-wave). To this end, seventeen pairs of P-wave and S-wave seismic refraction profiles were carried out at three different granular sites in Iran using non-invasive seismic wave methods. The acquired shot gathers were processed, from which the P-wave, SV-wave and SH-wave velocities were derived. The reference values of φ and overconsolidation ratio (OCR) in the soil deposits were measured through laboratory tests. By assuming cross-anisotropy of the soils, the P-wave and S-wave velocities were utilized to develop an equation for calculating the coefficient of lateral earth pressure at-rest (K₀) based on the theory of elasticity for a cross-anisotropic medium. In addition, to develop an equation for OCR estimation in granular geomaterials in terms of SH/SV velocity ratios, a general regression analysis was performed on the resulting information from this research incorporated with the respective data published in the literature. The calculated K₀ values coupled with the estimated OCR values were finally employed in the Mayne and Kulhawy formula to evaluate φ in granular soil deposits. The results showed that reliable values of φ could be estimated based on the seismic wave velocities. The findings of this study may be used as the appropriate approaches for economic and non-invasive determination of in-situ φ in granular soil deposits using the surface seismic surveys.

Keywords: angle of internal friction, overconsolidation ratio, granular soils, P-wave velocity, SV-wave velocity, SH-wave velocity

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Authors: K. Meera Saheb, K. Krishna Bhaskar

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Complex structures used in many fields of engineering are made up of simple structural elements like beams, plates etc. These structural elements, sometimes carry concentrated masses at discrete points, and when subjected to severe dynamic environment tend to vibrate with large amplitudes. The frequency amplitude relationship is very much essential in determining the response of these structural elements subjected to the dynamic loads. For Timoshenko beams, the effects of shear deformation and rotary inertia are to be considered to evaluate the fundamental linear and nonlinear frequencies. A commonly used method for solving vibration problem is energy method, or a finite element analogue of the same. In the present Coupled Displacement Field method the number of undetermined coefficients is reduced to half when compared to the famous Rayleigh Ritz method, which significantly simplifies the procedure to solve the vibration problem. This is accomplished by using a coupling equation derived from the static equilibrium of the shear flexible structural element. The prime objective of the present paper here is to study, in detail, the effect of a central concentrated mass on the large amplitude free vibrations of uniform shear flexible beams. Accurate closed form expressions for linear frequency parameter for uniform shear flexible beams with a central concentrated mass was developed and the results are presented in digital form.

Keywords: coupled displacement field, coupling equation, large amplitude vibrations, moderately thick plates

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Authors: Jill Round

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In the economic system, the financial sector plays a crucial role as an intermediary between market participants, other financial institutions, and customers. Financial institutions such as banks have to make decisions to satisfy the demands of all the participants by keeping abreast of regulatory change. In recent years, progress has been made regarding frameworks, development of rules, standards, and processes to manage risks in the banking sector. The increasing focus of regulators and policymakers placed on risk management, corporate governance, and the organization’s culture is of special interest as it requires a well-resourced risk controlling function, compliance function, and internal audit function. In the past years, the relevance of these functions that make up the so-called Three Lines of Defense has moved from the backroom to the boardroom. The approach of the model can vary based on the various organizational characteristics. Due to the intense regulatory requirements, organizations operating in the financial sector have more mature models. In less regulated industries there is more cloudiness about what tasks are allocated where. All parties strive to achieve their objectives through the effective management of risks and serve the identical stakeholders. Today, the Three Lines of Defense model is used throughout the world. The research looks at trends and emerging issues in the professions of the Three Lines of Defense within the banking sector. The answers are believed to helping to explain the increasing regulatory requirements for the banking sector. While the number of supervisory practices increases the risk management requirements intensify and demand more regulatory compliance at the same time. The Structural Equation Modeling (SEM) is applied by making use of conducted surveys in the research field. It aims to describe (i) the theoretical model regarding the applicable linearity relationships, (ii) the causal relationship between multiple predictors (exogenous) and multiple dependent variables (endogenous), (iii) taking into consideration the unobservable variables and (iv) the measurement errors. The surveys conducted on the research field suggest that the observable variables are caused by various latent variables. The SEM consists of the 1) measurement model and the 2) structural model. There is a detectable correlation regarding the cause-effect relationship among the performed supervisory practices and the increasing scope of regulation. Supervisory practices reinforce the regulatory density. In the past, controls were placed after supervisory practices were conducted or incidents occurred. In further research, it is of interest to examine, whether risk management is proactive, reactive to incidents and supervisory practices or can be both at the same time.

Keywords: risk management, structural equation model, supervisory practice, three lines of defense

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Authors: Ranjeet Sable, Mahotsavi Patil, Aadesh Nimbalkar, Prajakta Palaskar, Ritu Sagar

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The exact amount of water used by various crops in different climatic conditions is necessary to step for design, planning, and management of irrigation schemes, water resources, scheduling of irrigation systems. Evaporation and transpiration are combinable called as evapotranspiration. Water loss from trees during photosynthesis is called as transpiration and when water gets converted into gaseous state is called evaporation. For calculation of correct evapotranspiration, we have to choose the method in such way that is should be suitable and require minimum climatic data also it should be applicable for wide range of climatic conditions. In hydrology, there are multiple correlations and regression is generally used to develop relationships between three or more hydrological variables by knowing the dependence between them. This research work includes the study of various methods for calculation of evapotranspiration and selects reasonable and suitable one Pune region (Maharashtra state). As field methods are very costly, time-consuming and not give appropriate results if the suitable climate is not maintained. Observation recorded at Pune metrological stations are used to calculate evapotranspiration with the help of Radiation Method (RAD), Modified Penman Method (MPM), Thornthwaite Method (THW), Blaney-Criddle (BCL), Christiansen Equation (CNM), Hargreaves Method (HGM), from which Hargreaves and Thornthwaite are temperature based methods. Performance of all these methods are compared with Modified Penman method and method which showing less variation with standard Modified Penman method (MPM) is selected as the suitable one. Evapotranspiration values are estimated on a monthly basis. Comparative analysis in this research used for selection for raw data-dependent methods in case of missing data.

Keywords: Blaney-Criddle, Christiansen equation evapotranspiration, Hargreaves method, precipitations, Penman method, water use efficiency

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Authors: Ayub Khan, Net Ram Garg, Geeta Jain

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In this paper, backstepping method is proposed to synchronize two fractional-order systems. The simulation results show that this method can effectively synchronize two chaotic systems.

Keywords: backstepping method, fractional order, synchronization, chaotic system

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Authors: Young Hee Geum

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We compare optimal quartic order method for the multiple zeros of nonlinear equations illustrating the basins of attraction. To construct basins of attraction effectively, we take a 600×600 uniform grid points at the origin of the complex plane and paint the initial values on the basins of attraction with different colors according to the iteration number required for convergence.

Keywords: basins of attraction, convergence, multiple-root, nonlinear equation

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Authors: Judith Stein, Elfriede Friedmann

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The injection of a drug into the vitreous body for the treatment of retinal diseases like wet aged-related macular degeneration (AMD) is the most common medical intervention worldwide. We develop mathematical models for drug transport in the vitreous body of a human eye to analyse the impact of different rheological models of the vitreous on drug distribution. In addition to the convection diffusion equation characterizing the drug spreading, we use porous media modeling for the healthy vitreous with a dense collagen network and include the steady permeating flow of the aqueous humor described by Darcy's law driven by a pressure drop. Additionally, the vitreous body in a healthy human eye behaves like a viscoelastic gel through the collagen fibers suspended in the network of hyaluronic acid and acts as a drug depot for the treatment of retinal diseases. In a completely liquefied vitreous, we couple the drug diffusion with the classical Navier-Stokes flow equations. We prove the global existence and uniqueness of the weak solution of the developed initial-boundary value problem describing the drug distribution in the healthy vitreous considering the permeating aqueous humor flow in the realistic three-dimensional setting. In particular, for the drug diffusion equation, results from the literature are extended from homogeneous Dirichlet boundary conditions to our mixed boundary conditions that describe the eye with the Galerkin's method using Cauchy-Schwarz inequality and trace theorem. Because there is only a small effective drug concentration range and higher concentrations may be toxic, the ability to model the drug transport could improve the therapy by considering patient individual differences and give a better understanding of the physiological and pathological processes in the vitreous.

Keywords: coupled PDE systems, drug diffusion, mixed boundary conditions, vitreous body

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Authors: Alper T. Celebi, Ali Beskok

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Electroosmotic (EO) slip flows in nanochannels are investigated using non-equilibrium molecular dynamics (MD) simulations, and the results are compared with analytical solution of Poisson-Boltzmann and Stokes (PB-S) equations with slip contribution. The ultimate objective of this study is to show that well-known continuum flow model can accurately predict the EO velocity profiles in nanochannels using the slip lengths and apparent viscosities obtained from force-driven flow simulations performed at various liquid-wall interaction strengths. EO flow of aqueous NaCl solution in silicon nanochannels are simulated under realistic electrochemical conditions within the validity region of Poisson-Boltzmann theory. A physical surface charge density is determined for nanochannels based on dissociations of silanol functional groups on channel surfaces at known salt concentration, temperature and local pH. First, we present results of density profiles and ion distributions by equilibrium MD simulations, ensuring that the desired thermodynamic state and ionic conditions are satisfied. Next, force-driven nanochannel flow simulations are performed to predict the apparent viscosity of ionic solution between charged surfaces and slip lengths. Parabolic velocity profiles obtained from force-driven flow simulations are fitted to a second-order polynomial equation, where viscosity and slip lengths are quantified by comparing the coefficients of the fitted equation with continuum flow model. Presence of charged surface increases the viscosity of ionic solution while the velocity-slip at wall decreases. Afterwards, EO flow simulations are carried out under uniform electric field for different liquid-wall interaction strengths. Velocity profiles present finite slips near walls, followed with a conventional viscous flow profile in the electrical double layer that reaches a bulk flow region in the center of the channel. The EO flow enhances with increased slip at the walls, which depends on wall-liquid interaction strength and the surface charge. MD velocity profiles are compared with the predictions from analytical solutions of the slip modified PB-S equation, where the slip length and apparent viscosity values are obtained from force-driven flow simulations in charged silicon nano-channels. Our MD results show good agreements with the analytical solutions at various slip conditions, verifying the validity of PB-S equation in nanochannels as small as 3.5 nm. In addition, the continuum model normalizes slip length with the Debye length instead of the channel height, which implies that enhancement in EO flows is independent of the channel height. Further MD simulations performed at different channel heights also shows that the flow enhancement due to slip is independent of the channel height. This is important because slip enhanced EO flow is observable even in micro-channels experiments by using a hydrophobic channel with large slip and high conductivity solutions with small Debye length. The present study provides an advanced understanding of EO flows in nanochannels. Correct characterization of nanoscale EO slip flow is crucial to discover the extent of well-known continuum models, which is required for various applications spanning from ion separation to drug delivery and bio-fluidic analysis.

Keywords: electroosmotic flow, molecular dynamics, slip length, velocity-slip

Procedia PDF Downloads 157