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Finite Element Solution of the Two-dimensional Incompressible Navier-Stokes Equations Using MATLAB
Get PDFThe Navier–Stokes equations are fundamental in fluid mechanics. The finite element method has become a popular method for the solution of the Navier-Stokes equations. In this paper, the Galerkin finite element method was used to solve the Navier-Stokes equations for two-dimensional steady flow of Newtonian and incompressible fluid with no body forces using MATLAB. The method was applied to the lid-driven cavity problem. The eight-noded rectangular element was used for the formulation of element equations. The velocity components were located at all of 8 nodes and the pressure variable is located at 4 corner of the element. From location of velocity components and pressure, it is obvious that this element consists of 16 unknowns for velocities and 4 unknowns for pressure. As a result, the unknown variables for velocities and pressure are 20 per each element. The quadratic interpolation functions represent velocity components while bilinear interpolation function represents pressure. Finite element codes were developed for implementation. The numerical results were compared with benchmark results from the literature
Stability and Bifurcation Analysis of a Delayed Three Species Food Chain Model with Crowley-Martin Response Function
Get PDFIn this paper we have studied the dynamical behaviors of three species prey-predator system. The interaction between prey and middle-predator is Crowley-Martin type functional response. Positivity and boundedness of the system are discussed. Stability analysis of the equilibrium points is presented. Permanence and Hopf-bifurcation of the system are analyzed under some conditions. The effect of discrete time-delay is studied, where the delay may be regarded as the gestation period of the super-predator. The direction and the stability criteria of the bifurcating periodic solutions are determined with the help of the normal form theory and the center manifold theorem. Extensive numerical simulations are carried out to validate our analytical findings. Implications of our analytical and numerical findings are discussed critically
On Chaplygin’s Method For First Order Neutral Differential Equation
Get PDFIn this paper we discuss the existence of a solution of a first order neutral differential equation with piecewise constant argument. We extend the method of Chaplygin’s sequence to obtain two sided bounds for the solution. These bounds are in the form of sequences of functions which are solutions of associated linear neutral differential equations with piecewise constant argument. This construction of monotonic sequences of upper and lower functions approximate, with increasing accuracy, the desired solution of the neutral differential equation with piecewise constant argument. Further we show that these sequences converge uniformly and monotonically to the unique solution of the equation.The error estimate obtained is better than the corresponding one for ordinary differential equations
Approximate Analytical Solutions of Space-Fractional Telegraph Equations by Sumudu Adomian Decomposition Method
Get PDFThe main goal in this work is to establish a new and efficient analytical scheme for space fractional telegraph equation (FTE) by means of fractional Sumudu decomposition method (SDM). The fractional SDM gives us an approximate convergent series solution. The stability of the analytical scheme is also studied. The approximate solutions obtained by SDM show that the approach is easy to implement and computationally very much attractive. Further, some numerical examples are presented to illustrate the accuracy and stability for linear and nonlinear cases
Soret Effect on Transient MHD Convective Flow past a Semi-infinite Vertical Porous Plate with Heat Sink and Chemical Reaction
Get PDFThis problem concerns with an analytical study of heat and mass transfer on unsteady MHD convective flow past a semi-infinite porous vertical plate in presence of thermal diffusion, heat sink and chemical reaction. A uniform magnetic field is imposed transversely to the plate. The governing equations are solved by perturbation technique. The expressions for the velocity, temperature and concentration fields as well as transport properties are obtained in non-dimensional form. The influence of the physical parameters like magnetic field parameter, Schmidt number, Prandtl number, heat sink parameter, chemical reaction parameter and Soret number on these fields is discussed through graphs and tables. It is found that the presence of thermal diffusion enhances the fluid motion
Generalized Sylvester Polynomials of in Several Variables
Get PDFThis study deals with some new properties for the Generalized Sylvester polynomials in several variables. Some properties of these polynomials were given. We also derive an application giving certain families of bilateral generating functions for the Generalized Sylvester polynomials in several variables. At the end, we discuss some special cases
Assessing potential climate change impacts on irrigation requirements of major crops in the brazos headwaters Basin, Texas
No full textIn order for the agricultural sector to be sustainable, farming practices and management strategies need to be informed by site-specific information regarding potential climate change impacts on irrigation requirements and water budget components of different crops. Such information would allow managers and producers to select cropping systems that ensure efficient use of water resources and crop productivity. The major challenge in understanding the link between cropping systems and climate change is the uncertainty of how the climate would change in the future and lack of understanding how different crops would respond to those changes. This study analyzed the potential impact of climate change on irrigation requirements of four major crops (cotton, corn, sorghum, and winter wheat) in the Brazos Headwaters Basin, Texas. The irrigation requirement of crops was calculated for the baseline period (1980-2010) and three projected periods: 2020s (2011-2030), 2055s (2046-2065), and 2090s (2080-2099). Daily climate predictions from 15 general circulation models (GCMs) under three greenhouse gas (GHG) emission scenarios (B1, A1B, and A2) were generated for three future periods using the Long Ashton Research Station-Weather Generator (LARS-WG) statistical downscaling model. Grid-based (55 grids at ~38 km resolution) irrigation water requirements (IRRs) and other water budget components of each crop were calculated using the Irrigation Management System (IManSys) model. Future period projection results show that evapotranspiration (ET) and IRR will increase for all crops, while precipitation is projected to decrease compared with the baseline period. On average, precipitation meets only 25-32% of the ET demand, depending on crop type. In general, projections from almost all GCMs show an increase in IRR for all crops for the three future periods under the three GHG emission scenarios. Irrigation requirement prediction uncertainty between GCMs was consistently greater in July and August for corn, cotton, and sorghum regardless of period and emission scenario. However, for winter wheat, greater uncertainties between GCMs were observed during April and May. Irrigation requirements show significant variations across spatial locations. There was no consistent spatial trend in changes of IRR for the four crops. A unit change in precipitation is projected to affect IRR differently depending on the crop type
Assessing the spatiotemporal distributions of evapotranspiration in the Three Gorges Reservoir Region of China using remote sensing data
No full textEvapotranspiration (ET) is a critical component of the global hydrological cycle, and it has a large impact on water resource management as it affects the availability of freshwater resources. It is important to understand the hydrological cycle for the water resources planning and management. This study used Moderate Resolution Imaging Spectroradiometer (MODIS) satellite derived ET, and potential evapotranspiration (PET) and Tropical Rainfall Measuring Mission (TRMM) satellite derived precipitation datasets to assess the spatial and temporal distributions of ET, PET, and precipitation during the study period at Three Gorges Reservoir (TGR) region. Based on the topographic variations and land-use/land-cover distributions, the study region which includes five counties of Hubei Province and nineteen counties of Chongqing Municipality was divided into four study zones. The ET and precipitation data were evaluated using in situ observations. The ET, PET, and precipitation data were compared to analyze the spatial and long-term (2001-2016) temporal distributions of average annual ET, PET, and precipitation, and to understand the relationships between them in the study region. The results showed that each selected zone had highest ET at the counties with the Yangtze River passing through whereas lowest at the counties which were located away from the river. Results also showed increasing trends in ET and PET from south-west to north-east in the study region. Analysis showed TGR had a significant impact on spatial and temporal distributions of ET and PET in the study region. Therefore, this study helps to understand the impact of TGR on spatial and temporal distributions of ET and PET during and after the construction
Gender differences in the evaluation of aggravating and mitigating circumstances: the mediating role of attributional complexity\u3csup\u3e*\u3c/sup\u3e
No full textAt the penalty phase of a capital trial, jurors endorse and weigh aggravators and mitigators. The purpose of the current studies was to examine how gender differences in attributional complexity relate to endorsements of aggravators and mitigators. In Study 1, undergraduate participants read definitions of aggravators and mitigators and rated the extent to which circumstances were aggravating or mitigating. In Study 2, a death qualified community sample read a trial summary, rated the extent to which aggravators and mitigators were present in the case, reported whether mitigators outweighed aggravators, and rendered a sentence. Results indicated that gender differences in mitigator endorsement were mediated by attributional complexity, and that gender differences in sentencing decisions were serially mediated by attributional complexity, mitigator endorsement, and aggravator and mitigator weighing
Understanding Crime Control Theater: Do Sample Type, Gender, and Emotions Relate to Support for Crime Control Theater Policies?
No full textPolicies such as America’s Missing: Broadcast Emergency Response Alerts, safe haven laws, Megan’s law, and three-strikes laws have provided the public with a feeling of safety and security. However, research has provided evidence that disputes their effectiveness. These types of laws and policies have become known as “crime control theater” (CCT) because they appear to be effective, serve the public’s best interests, and provide a crime control purpose but are largely ineffective and have unintended negative consequences. Using self-affirmation and emotion theory, this study examines potential explanations as to why individuals might support CCT policies. It also investigates whether support differs based on relevant characteristics (e.g., gender, sample type, and preexisting beliefs about policy effectiveness). Results suggest that females and Amazon Mechanical Turk (MTurk) workers tend to support CCT policies more than males and college students. Further, the relationship between gender and support was mediated by anticipatory guilt, and this effect was stronger for individuals who did not believe in the effectiveness of the policy. Results suggest that individuals who believe the policy is effective will support it more than those who do not, regardless of their anticipated guilt. In contrast, those who doubt the policy only support it if they anticipate feeling guilty; this effect is stronger for women. Results can help explain why people support policies that are largely ineffective and suggest that relevance to the issue can help explain why some groups are more supportive than others