Physics Commons^™

Reducing Food Scarcity: The Benefits Of Urban Farming, S.A. Claudell, Emilio Mejia

Journal of Nonprofit Innovation

Urban farming can enhance the lives of communities and help reduce food scarcity. This paper presents a conceptual prototype of an efficient urban farming community that can be scaled for a single apartment building or an entire community across all global geoeconomics regions, including densely populated cities and rural, developing towns and communities. When deployed in coordination with smart crop choices, local farm support, and efficient transportation then the result isn’t just sustainability, but also increasing fresh produce accessibility, optimizing nutritional value, eliminating the use of ‘forever chemicals’, reducing transportation costs, and fostering global environmental benefits.

Imagine Doris, who is …

Computational Models To Detect Radiation In Urban Environments: An Application Of Signal Processing Techniques And Neural Networks To Radiation Data Analysis, Jose Nicolas Gachancipa

Beyond: Undergraduate Research Journal

Radioactive sources, such as uranium-235, are nuclides that emit ionizing radiation, and which can be used to build nuclear weapons. In public areas, the presence of a radioactive nuclide can present a risk to the population, and therefore, it is imperative that threats are identified by radiological search and response teams in a timely and effective manner. In urban environments, such as densely populated cities, radioactive sources may be more difficult to detect, since background radiation produced by surrounding objects and structures (e.g., buildings, cars) can hinder the effective detection of unnatural radioactive material. This article presents a computational model …

Accurate Spectral Algorithms For Solving Variable-Order Fractional Percolation Equations, M. A. Abdelkawy

Applications and Applied Mathematics: An International Journal (AAM)

A high accurate spectral algorithm for one-dimensional variable-order fractional percolation equations (VO-FPEs) is considered.We propose a shifted Legendre Gauss-Lobatto collocation (SL-GLC) method in conjunction with shifted Chebyshev Gauss-Radau collocation (SC-GR-C) method to solve the proposed problem. Firstly, the solution and its space fractional derivatives are expanded as shifted Legendre polynomials series. Then, we determine the expansion coefficients by reducing the VO-FPEs and its conditions to a system of ordinary differential equations (SODEs) in time. The numerical approximation of SODEs is achieved by means of the SC-GR-C method. The under-study’s problem subjected to the Dirichlet or non-local boundary conditions is presented …

Local Non-Similar Solution Of Powell-Eyring Fluid Flow Over A Vertical Flat Plate, Hemangini Shukla, Hema C. Surati, M. G. Timol

Applications and Applied Mathematics: An International Journal (AAM)

Our objective is to obtain the non-similarity solution of non-Newtonian fluid for Powell-Eyring model by a local non-similarity method. Here, free stream velocity is considered in power-law form (𝑈=𝑥^m). The governing equations are transformed using non-similar transformations and derived equations are treated as ordinary differential equations. Non-similar solutions are obtained for different values of power-law index 𝑚 and stream-wise location 𝜉. Influence of various parameters on velocity and temperature field are presented graphically using MATLAB bvp4c solver.

Derivation Of Direct Explicit Integrators Of Rk Type For Solving Class Of Seventh-Order Ordinary Differential Equations, Mohammed S. Mechee, Jawad K. Mshachal

Karbala International Journal of Modern Science

The main contribution of this work is the development of direct explicit methods of Runge-Kutta (RK) type for solving class of seventh-order ordinary differential equations (ODEs) to improve computational efficiency. For this purpose, we have generalized RK, RKN, RKD, RKT, RKFD and RKM methods for solving class of first-, second-, third-, fourth-, and fifth-order ODEs. Using Taylor expansion approach, we have derived the algebraic equations of the order conditions for the proposed RKM integrators up to the tenth-order. Based on these order conditions, two RKM methods of fifth- and sixth-order with four- and five-stage are derived. The zero stability of …

Numerical Solution Of 3rd Order Ode Using Fdm: On A Moving Surface In Mhd Flow Of Sisko Fluid, Manisha Patel, Jayshri Patel, M. G. Timol

Applications and Applied Mathematics: An International Journal (AAM)

A Similarity group theoretical technique is used to transform the governing nonlinear partial differential equations of two dimensional MHD boundary layer flow of Sisko fluid into nonlinear ordinary differential equations. Then the resulting third order nonlinear ordinary differential equation with corresponding boundary conditions is linearised by Quasi linearization method. Numerical solution of the linearised third order ODE is obtained using Finite Difference method (FDM). Graphical presentation of the solution is given.

Solitary And Periodic Exact Solutions Of The Viscosity-Capillarity Van Der Waals Gas Equations, Emad A. Az-Zo’Bi

Applications and Applied Mathematics: An International Journal (AAM)

Periodic and soliton solutions are derived for the (1+1)-dimensional van der Waals gas system in the viscosity-capillarity regularization form. The system is handled via the e-^φ(ξ) -expansion method. The obtained solutions have been articulated by the hyperbolic, trigonometric, exponential and rational functions with arbitrary constants. Mathematical analysis and numerical graphs are provided for some solitons, periodic and kink solitary wave solutions to visualize the dynamics of equations. Obtained results reveal that the method is very influential and effective tool for solving nonlinear partial differential equations in applied mathematics.

Numerical Treatment For The Flow Of Casson Fluid And Heat Transfer Model Over An Unsteady Stretching Surface In The Presence Of Internal Heat Generation/Absorption And Thermal Radiation, Mohammed M. Babatin

Applications and Applied Mathematics: An International Journal (AAM)

Several important industrial and engineering problems are very difficult to solve analytically since they are high nonlinear. The Chebyshev spectral collocation method possesses an ability to predict the solution behavior for a system of high nonlinear ordinary differential equations. This method which is based on differentiated Chebyshev polynomials is introduced to obtain an approximate solution to the system of ordinary differential equations which physically describe the flow and heat transfer problem of an unsteady Casson fluid model taking into consideration both heat generation and radiation effects in the temperature equation. Based on the spectral collocation method, the obtained solution is …

Quasi-Linearization Method With Rational Legendre Collocation Method For Solving Mhd Flow Over A Stretching Sheet With Variable Thickness And Slip Velocity Which Embedded In A Porous Medium, M. M. Khader

Applications and Applied Mathematics: An International Journal (AAM)

The quasi-linearization method (QLM) and the rational Legendre functions are introduced here to present the numerical solution for the Newtonian fluid flow past an impermeable stretching sheet which embedded in a porous medium with a power-law surface velocity, variable thickness and slip velocity. Firstly, due to the high nonlinearity which yielded from the ordinary differential equation which describes the proposed physical problem, we construct a sequence of linear ODEs by using the QLM, hence the resulted equations become a system of linear algebraic equations. The comparison with the available results in the literature review proves that the obtained results via …

Numerical Studies For Mhd Flow And Gradient Heat Transport Past A Stretching Sheet With Radiation And Heat Production Via Dtm, Khadijah M. Abualnaja

Applications and Applied Mathematics: An International Journal (AAM)

This paper presents a numerically study for the effect of the internal heat generation, magnetic field and thermal radiation effects on the flow and gradient heat transfer of a Newtonian fluid over a stretching sheet. By using a similarity transformation, the governing PDEs can be transformed into a coupled non-linear system of ODEs with variable coefficients. Numerical solutions for these equations subject to appropriate boundary conditions are obtained by using the differential transformation method (DTM). The effects of various physical parameters such as viscosity parameter, the suction parameter, the radiation parameter, internal heat generation or absorption parameter and the Prandtl …

Interactions Of Thermoelastic Beam In Modified Couple Stress Theory, Rajneesh Kumar, Shaloo Devi

Applications and Applied Mathematics: An International Journal (AAM)

This paper is concerned with the study of thermoelastic beam in modified couple stress theory. The governing equations of motion for modified couple stress theory and heat conduction equation for non-Fourier (non-classical process) are investigated to model the vibrations in a homogeneous isotropic thin beam in a closed form by employing the Euler Bernoulli beam theory. The generalized theories of thermoelasticity with one and two relaxation times are used to model the problem. Both ends of the beam are simply supported. The Laplace transform technique applied to solve the system of equations which are written in dimensionless form. A general …

Numerical Solution Of Fractional Integro-Differential Equations With Nonlocal Conditions, M. Jani, D. Bhatta, S. Javadi

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we present a numerical method for solving fractional integro-differential equations with nonlocal boundary conditions using Bernstein polynomials. Some theoretical considerations regarding fractional order derivatives of Bernstein polynomials are discussed. The error analysis is carried out and supported with some numerical examples. It is shown that the method is simple and accurate for the given problem.

Effect Of Damping And Thermal Gradient On Vibrations Of Orthotropic Rectangular Plate Of Variable Thickness, U. S. Rana, Robin Robin

Applications and Applied Mathematics: An International Journal (AAM)

In this present paper, damped vibrations of an orthotropic rectangular plate resting on elastic foundation with thermal gradient is modeled, considering variable thickness of plate. Following Le`vy approach, the governed equation of motion is solved numerically using quintic spline technique with clamped and simply supported edges. The effect of damping parameter and thermal gradient together with taper constant, density parameter and elastic foundation parameter on the natural frequencies of vibration for the first three modes of vibration are depicted through Tables and Figures, and mode shapes have been computed for fixed value of plate parameter. It has been observed that …

Damping In Microscale Modified Couple Stress Thermoelastic Circular Kirchhoff Plate Resonators, Rajneesh Kumar, Shaloo Devi, Veena Sharma

Applications and Applied Mathematics: An International Journal (AAM)

The vibrations of circular plate in modified couple stress thermoelastic medium using Kirchhoff- Love plate theory has been presented. The basic equations of motion and heat conduction equation for Lord Shulman (L-S, 1967) theory are written with the help of Kirchhoff-Love plate theory. The thermoelastic damping of micro beam resonators is studied by applying normal mode analysis method. The solutions for the free vibrations of plates under clamped, simply supported and free boundary conditions are obtained. The analytical expressions for thermoelastic damping of vibration and frequency shift are obtained for generalized couple stress thermoelastic and coupled thermoelastic plates. Numerical results …

Non-Newtonian Prandtl Fluid Over Stretching Permeable Surface, N. R. Jain, M. G. Timol

Applications and Applied Mathematics: An International Journal (AAM)

An analysis is made of the velocity and temperature distribution in the flow of a viscous incompressible fluid caused by the stretching permeable surface which issues in the Prandtl fluid. Parandtl fluid is a pseudoplastic visco-inelastic non-Newtonian fluid. The governing partial differential equations are reduced to ordinary differential equations using deductive group transformation and similarity solution is derived. Numerical solutions to the reduced non-linear similarity equations are then obtained by adopting shooting method using the Nachtsheim-Swigert iteration technique. The results of the numerical solution are then presented graphically in the form of velocity and temperature profiles. The corresponding skin friction …

Approximate Solutions For The Flow And Heat Transfer Due To A Stretching Sheet Embedded In A Porous Medium With Variable Thickness, Variable Thermal Conductivity And Thermal Radiation Using Laguerre Collocation Method, M. M. Khader, Ahmed M. Megahed

Applications and Applied Mathematics: An International Journal (AAM)

In this article, a numerical approach is given for studying the flow of a Newtonian fluid over an impermeable stretching sheet embedded in a porous medium with a power law surface velocity and variable thickness in the presence of thermal radiation. The flow is caused by a non-linear stretching of a sheet. Thermal conductivity of the fluid is assumed to vary linearly with temperature. The governing PDEs are transformed into a system of coupled non-linear ODEs which are using appropriate boundary conditions for various physical parameters. The proposed method is based on replacement of the unknown function by truncated series …

Laminar Boundary Layer Flow Of Sisko Fluid, Manisha Patel, Jayshri Patel, M. G. Timol

Applications and Applied Mathematics: An International Journal (AAM)

The problem of steady two dimensional laminar boundary layer flow of non-Newtonian fluid is analyzed in the present paper. Sisko fluid model, one of the various fluid models of non- Newtonian fluid, is considered for stress-strain relationship. Similarity and numerical solutions obtained for the defined flow problem.

Global Optimized Isothermal And Nonlinear Models Of Earth’S Standard Atmosphere, Nihad E. Daidzic, Ph.D.,

International Journal of Aviation, Aeronautics, and Aerospace

Both, a global isothermal temperature model and a nonlinear quadratic temperature model of the ISA was developed and presented here. Constrained optimization techniques in conjunction with the least-square-root approximations were used to design best-fit isothermal models for ISA pressure and density changes up to 47 geopotential km for NLPAM, and 86 orthometric km for ISOAM respectively. The mass of the dry atmosphere and the relevant fractional-mass scale heights have been computed utilizing the very accurate eight-point Gauss-Legendre numerical quadrature for both ISOAM and NLPAM. Both, the ISOAM and the NLPAM represent viable alternatives to ISA in many practical applications and …

Implicit-Explicit Higher-Order Time Integration Schemes For Computations Of Structural Dynamics With Fluid-Structure Interaction, José C. Pedro, Mapundi K. Banda, Precious Sibanda

Applications and Applied Mathematics: An International Journal (AAM)

In this paper higher order implicit Runge-Kutta schemes are applied to fluid-structure interaction (FSI) simulations. A staggered approach with a structural predictor is applied to an FSI problem. The equations governing the dynamics of the structure are integrated in time by the Explicit Single Diagonal Implicit Runge-Kutta (ESDIRK) schemes and the arbitrary high order finite volume scheme is taken as the fluid solver. The performance of the ESDIRK scheme of order of convergence three to five is tested. Comparative studies with other time integration schemes which have been successfully applied to FSI problems are undertaken. Comparisons to test the performance …

Efficient General Computational Method For Estimation Of Standard Atmosphere Parameters, Nihad E. Daidzic Ph.D., Sc.D.

International Journal of Aviation, Aeronautics, and Aerospace

Knowledge of standard air temperature, pressure, density, speed of sound, and viscosity as a function of altitude is essential information in aircraft design, performance testing, pressure altimeter calibration, and several other aeronautical engineering and aviation science applications. A new efficient computational method for rapid calculations of standard atmospheric parameters up to 86 orthometric km is presented. Additionally, mass and weight of each standard atmospheric layer were calculated using a numerical integration method. The sum of all fractional masses and weights represents the total mass and weight of Earth’s atmosphere. The results obtained here agree well with measurements and models of …

A Contribution Toward Better Understanding Of Overbanking Tendency In Fixed-Wing Aircraft, Nihad E. Daidzic

Journal of Aviation Technology and Engineering

The phenomenon of overbanking tendency for a rigid-body, fixed-wing aircraft is investigated. Overbanking tendency is defined as a spontaneous, unbalanced rolling moment that keeps increasing an airplane’s bank angle in steep turns and must be arrested by opposite aileron action. As stated by the Federal Aviation Administration, the overbanking tendency may lead to a loss of control, especially in instrument meteorological conditions. It was found in this study that the speed differential over wing halves in horizontal turns indeed creates a rolling moment that achieves maximum values for bank angles between 45 and 55 degrees. However, this induced rolling moment …

Mhd Mixed Convective Flow Of Viscoelastic And Viscous Fluids In A Vertical Porous Channel, R. Sivaraj, B. R. Kumar, J. Prakash

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we analyze the problem of steady, mixed convective, laminar flow of two incompressible, electrically conducting and heat absorbing immiscible fluids in a vertical porous channel filled with viscoelastic fluid in one region and viscous fluid in the other region. A uniform magnetic field is applied in the transverse direction, the fluids rise in the channel driven by thermal buoyancy forces associated with thermal radiation. The equations are modeled using the fully developed flow conditions. An exact solution is obtained for the velocity, temperature, skin friction and Nusselt number distributions. The physical interpretation to these expressions is examined …

Finite Element Analysis In Porous Media For Incompressible Flow Of Contamination From Nuclear Waste, Abbas Al-Bayati, Saad A. Manaa, Ekhlass S. Ahmed

Applications and Applied Mathematics: An International Journal (AAM)

A non-linear parabolic system is used to describe incompressible nuclear waste disposal contamination in porous media, in which both molecular diffusion and dispersion are considered. The Galerkin method is applied for the pressure equation. For the brine, radionuclide and heat, a kind of partial upwind finite element scheme is constructed. Examples are included to demonstrate certain aspects of the theory and illustrate the capabilities of the kind of partial upwind finite element approach.

Effects Of Radiation And Variable Viscosity On Mhd Free Convective Flow And Mass Transfer Over A Stretching Sheet With Chemical Reaction, M. A. Seddeek, A. A. Almushigeh

Applications and Applied Mathematics: An International Journal (AAM)

A similarity solution is proposed for the analysis of steady free convection heat and mass transfer over a stretching sheet. The effect of radiation, chemical reaction and variable viscosity on hydromagnetic heat and mass transfer in the presence of magnetic field are investigated. The governing partial differential equations are transformed to the ordinary differential equations using similarity variables, and then solved numerically by means of the fourth-order Runge– Kutta method with shooting technique. A comparison with exact solution is performed and the results are found to be in excellent. Numerical results for the velocity, temperature and concentration as well as …