Abstract: In this paper, there is an implementation, verification, and graphical demonstration of a software application, which can be used swiftly over different preliminary orbit determination methods. A passive orbit determination method is used in this study to determine the location of a satellite or a flying body. It is named a passive orbit determination because it depends on observation without the use of any aids (radio and laser) installed on satellite. In order to understand how these methods work and how their output is accurate when compared with available verification data, the built models help in knowing the different inputs used with each method. Output from the different orbit determination methods (Gibbs, Lambert, and Gauss) will be compared with each other and verified by the data obtained from Satellite Tool Kit (STK) application. A modified model including all of the orbit determination methods using the same input will be introduced to investigate different models output (orbital parameters) for the same input (azimuth, elevation, and time). Simulation software is implemented using MATLAB. A Graphical User Interface (GUI) application named OrDet is produced using the GUI of MATLAB. It includes all the available used inputs and it outputs the current Classical Orbital Elements (COE) of satellite under observation. Produced COE are then used to propagate for a complete revolution and plotted on a 3-D view. Modified model which uses an adapter to allow same input parameters, passes these parameters to the preliminary orbit determination methods under study. Result from all orbit determination methods yield exactly the same COE output, which shows the equality of concept in determination of satellite’s location, but with different numerical methods.
Abstract: Volterra integro-differential equations appear in many models for real life phenomena. Since analytical solutions for this type of differential equations are hard and at times impossible to attain, engineers and scientists resort to numerical solutions that can be made as accurately as possible. Conventionally, numerical methods for ordinary differential equations are adapted to solve Volterra integro-differential equations. In this paper, numerical solution for solving Volterra integro-differential equation using extended trapezoidal method is described. Formulae for the integral and differential parts of the equation are presented. Numerical results show that the extended method is suitable for solving first order Volterra integro-differential equations.
Abstract: In this paper, we present a simple effective numerical geometric method to estimate the divergence of a vector field over a curved surface. The conservation law is an important principle in physics and mathematics. However, many well-known numerical methods for solving diffusion equations do not obey conservation laws. Our presented method in this paper combines the divergence theorem with a generalized finite difference method and obeys the conservation law on discrete closed surfaces. We use the similar method to solve the Cahn-Hilliard equations on evolving spherical surfaces and observe stability results in our numerical simulations.
Abstract: The diffusion-reaction equations are important Partial Differential Equations in mathematical biology, material science, physics, and so on. However, finding efficient numerical methods for diffusion-reaction systems on curved surfaces is still an important and difficult problem. The purpose of this paper is to present a convergent geometric method for solving the reaction-diffusion equations on closed surfaces by an O(r)-LTL configuration method. The O(r)-LTL configuration method combining the local tangential lifting technique and configuration equations is an effective method to estimate differential quantities on curved surfaces. Since estimating the Laplace-Beltrami operator is an important task for solving the reaction-diffusion equations on surfaces, we use the local tangential lifting method and a generalized finite difference method to approximate the Laplace-Beltrami operators and we solve this reaction-diffusion system on closed surfaces. Our method is not only conceptually simple, but also easy to implement.
Abstract: Apple bruise damage from harvesting, handling, transporting and sorting is considered to be the major source of reduced fruit quality, resulting in loss of profits for the entire fruit industry. The three factors which can physically cause fruit bruising are vibration, compression load and impact, the latter being the most common source of bruise damage. Therefore, prediction of the level of damage, stress distribution and deformation of the fruits under external force has become a very important challenge. In this study, experimental and numerical methods were used to better understand the impact caused when an apple is dropped from different heights onto a plastic surface and a conveyor belt. Results showed that the extent of fruit damage is significantly higher for plastic surface, being dependent on the height. In order to support the development of a biomimetic electronic device for the determination of fruit damage, the mechanical properties of the apple fruit were determined using mechanical tests. Preliminary results showed different values for the Young’s modulus according to the zone of the apple tested. Along with the mechanical characterization of the apple fruit, the development of the first two prototypes is discussed and the integration of the results obtained to construct the final element model of the apple is presented. This work will help to reduce significantly the bruise damage of fruits or vegetables during the entire processing which will allow the introduction of exportation destines and consequently an increase in the economic profits in this sector.
Abstract: The development of numerical analysis and its
application to geomechanics problems have provided geotechnical
engineers with extremely powerful tools. One of the most important
problems in geotechnical engineering is the slope stability
assessment. It is a very difficult task due to several aspects such the
nature of the problem, experimental consideration, monitoring,
controlling, and assessment. The main objective of this paper is to
perform a comparative numerical study between the following
methods: The Limit Equilibrium (LEM), Finite Element (FEM),
Limit Analysis (LAM) and Distinct Element (DEM). The comparison
is conducted in terms of the safety factors and the critical slip
surfaces. Through the results, we see the feasibility to analyse slope
stability by many methods.
Abstract: The fluid-structure coupling is a natural phenomenon which reflects the effects of two continuums: fluid and structure of different types in the reciprocal action on each other, involving knowledge of elasticity and fluid mechanics. The solution for such problems is based on the relations of continuum mechanics and is mostly solved with numerical methods. It is a computational challenge to solve such problems because of the complex geometries, intricate physics of fluids, and complicated fluid-structure interactions. The way in which the interaction between fluid and solid is described gives the largest opportunity for reducing the computational effort. In this paper, a problem of fluid structure interaction is investigated with two-way coupling method. The formulation Arbitrary Lagrangian-Eulerian (ALE) was used, by considering a dynamic grid, where the solid is described by a Lagrangian formulation and the fluid by a Eulerian formulation. The simulation was made on the ANSYS software.
Abstract: In this work, we propose an algorithm developed under Python language for the modeling of ordinary scalar Bessel beams and their discrete superpositions and subsequent calculation of optical forces exerted over dielectric spherical particles. The mathematical formalism, based on the generalized Lorenz-Mie theory, is implemented in Python for its large number of free mathematical (as SciPy and NumPy), data visualization (Matplotlib and PyJamas) and multiprocessing libraries. We also propose an approach, provided by a synchronized Software as Service (SaaS) in cloud computing, to develop a user interface embedded on a mobile application, thus providing users with the necessary means to easily introduce desired unknowns and parameters and see the graphical outcomes of the simulations right at their mobile devices. Initially proposed as a free Android-based application, such an App enables data post-processing in cloud-based architectures and visualization of results, figures and numerical tables.
Abstract: This paper addresses a cutting edge method of
business demand forecasting, based on an empirical probability
function when the historical behavior of the data is random.
Additionally, it presents error determination based on the numerical
method technique ‘propagation of errors.’ The methodology was
conducted characterization and process diagnostics demand planning
as part of the production management, then new ways to predict its
value through techniques of probability and to calculate their mistake
investigated, it was tools used numerical methods. All this based on
the behavior of the data. This analysis was determined considering
the specific business circumstances of a company in the sector of
communications, located in the city of Bogota, Colombia. In
conclusion, using this application it was possible to obtain the
adequate stock of the products required by the company to provide its
services, helping the company reduce its service time, increase the
client satisfaction rate, reduce stock which has not been in rotation
for a long time, code its inventory, and plan reorder points for the
replenishment of stock.
Abstract: The problem of toughening in brittle materials
reinforced by fibers is complex, involving all of the mechanical
properties of fibers, matrix and the fiber/matrix interface, as well as
the geometry of the fiber. Development of new numerical methods
appropriate to toughening simulation and analysis is necessary. In
this work, we have performed simulations and analysis of toughening
in brittle matrix reinforced by randomly distributed fibers by means
of the discrete elements method. At first, we put forward a
mechanical model of toughening contributed by random fibers. Then
with a numerical program, we investigated the stress, damage and
bridging force in the composite material when a crack appeared in the
brittle matrix. From the results obtained, we conclude that: (i) fibers
of high strength and low elasticity modulus are beneficial to
toughening; (ii) fibers of relatively high elastic modulus compared to
the matrix may result in substantial matrix damage due to spalling
effect; (iii) employment of high-strength synthetic fibers is a good
option for toughening. We expect that the combination of the discrete
element method (DEM) with the finite element method (FEM) can
increase the versatility and efficiency of the software developed. The
present work can guide the design of ceramic composites of high
performance through the optimization of the parameters.
Abstract: Numerical studies were conducted using Lattice
Boltzmann Method (LBM) to study the natural convection in a square
cavity in the presence of roughness. An algorithm based on a single
relaxation time Bhatnagar-Gross-Krook (BGK) model of Lattice
Boltzmann Method (LBM) was developed. Roughness was
introduced on both the hot and cold walls in the form of sinusoidal
roughness elements. The study was conducted for a Newtonian fluid
of Prandtl number (Pr) 1.0. The range of Ra number was explored
from 10^3 to 10^6 in a laminar region. Thermal and hydrodynamic
behavior of fluid was analyzed using a differentially heated square
cavity with roughness elements present on both the hot and cold wall.
Neumann boundary conditions were introduced on horizontal walls
with vertical walls as isothermal. The roughness elements were at the
same boundary condition as corresponding walls. Computational
algorithm was validated against previous benchmark studies
performed with different numerical methods, and a good agreement
was found to exist. Results indicate that the maximum reduction in
the average heat transfer was 16.66 percent at Ra number 10^5.
Abstract: In this paper, groundwater seepage into Amirkabir
tunnel has been estimated using analytical and numerical methods for
14 different sections of the tunnel. Site Groundwater Rating (SGR)
method also has been performed for qualitative and quantitative
classification of the tunnel sections. The obtained results of above
mentioned methods were compared together. The study shows
reasonable accordance with results of the all methods unless for two
sections of tunnel. In these two sections there are some significant
discrepancies between numerical and analytical results mainly
originated from model geometry and high overburden. SGR and the
analytical and numerical calculations, confirm high concentration of
seepage inflow in fault zones. Maximum seepage flow into tunnel has
been estimated 0.425 lit/sec/m using analytical method and 0.628
lit/sec/m using numerical method occured in crashed zone. Based on
SGR method, six sections of 14 sections in Amirkabir tunnel axis are
found to be in "No Risk" class that is supported by the analytical and
numerical seepage value of less than 0.04 lit/sec/m.
Abstract: Numerical methods like binomial and trinomial trees and finite difference methods can be used to price a wide range of options contracts for which there are no known analytical solutions. American options are the most famous of that kind of options. Besides numerical methods, American options can be valued with the approximation formulas, like Bjerksund-Stensland formulas from 1993 and 2002. When the value of American option is approximated by Bjerksund-Stensland formulas, the computer time spent to carry out that calculation is very short. The computer time spent using numerical methods can vary from less than one second to several minutes or even hours. However to be able to conduct a comparative analysis of numerical methods and Bjerksund-Stensland formulas, we will limit computer calculation time of numerical method to less than one second. Therefore, we ask the question: Which method will be most accurate at nearly the same computer calculation time?
Abstract: In this paper, steady-state ampacity (current carrying capacity) evaluation of underground power cable system by using analytical and numerical methods for different conditions (depth of cable, spacing between phases, soil thermal resistivity, ambient temperature, wind speed), for two system voltage level were used 132 and 380 kV. The analytical method or traditional method that was used is based on the thermal analysis method developed by Neher-McGrath and further enhanced by International Electrotechnical Commission (IEC) and published in standard IEC 60287. The numerical method that was used is finite element method and it was recourse commercial software based on finite element method.
Abstract: The primary objective of this paper is to study the thermal effects of the electric arc on the breaker apparatus contacts for forecasting and improving the contact durability. We will propose a model which takes account of the main influence factors on the erosion contacts. This phenomenon is very complicated because the amount of ejected metal is not necessarily constituted by the whole melted metal bath but this depends on the balance of forces on the contact surface. Consequently, to calculate the metal ejection coefficient, we propose a method which consists in comparing the experimental results with the calculated ones. The proposed model estimates the mass lost by vaporization, by droplets ejection and by the extraction mechanism of liquid or solid metal. In the one-dimensional geometry, to calculate of the contact heating, we used Green’s function which expresses the point source and allows the transition to the surface source. However, for the two- dimensional model we used explicit and implicit numerical methods. The results are similar to those found by Wilson’s experiments.
Abstract: Induction heating computer simulation is a powerful tool for process design and optimization, induction coil design, equipment selection, as well as education and business presentations. The authors share their vast experience in the practical use of computer simulation for different induction heating and heat treating processes. In this paper treated with mathematical modeling and numerical simulation of induction heating furnaces with axisymmetric geometries for the numerical solution, we propose finite element methods combined with boundary (FEM) for the electromagnetic model using COMSOL® Multiphysics Software. Some numerical results for an industrial furnace are shown with high frequency.
Abstract: This paper presents an evolutionary method for designing
electronic circuits and numerical methods associated with
monitoring systems. The instruments described here have been used
in studies of weather and climate changes due to global warming, and
also in medical patient supervision. Genetic Programming systems
have been used both for designing circuits and sensors, and also for
determining sensor parameters. The authors advance the thesis that
the software side of such a system should be written in computer
languages with a strong mathematical and logic background in order
to prevent software obsolescence, and achieve program correctness.
Abstract: In this paper we study numerical methods for solving Sylvester matrix equations of the form AX +XBT +CDT = 0. A new projection method is proposed. The union of Krylov subspaces in A and its inverse and the union of Krylov subspaces in B and its inverse are used as the right and left projection subspaces, respectively. The Arnoldi-like process for constructing the orthonormal basis of the projection subspaces is outlined. We show that the approximate solution is an exact solution of a perturbed Sylvester matrix equation. Moreover, exact expression for the norm of residual is derived and results on finite termination and convergence are presented. Some numerical examples are presented to illustrate the effectiveness of the proposed method.
Abstract: Behavior of dams against the seismic loads has been
studied by many researchers. Most of them proposed new numerical
methods to investigate the dam safety. In this paper, to study the
effect of nonlinear parameters of concrete in gravity dams, a twodimensional
approach was used including the finite element method,
staggered method and smeared crack approach. Effective parameters
in the models are physical properties of concrete such as modulus of
elasticity, tensile strength and specific fracture energy. Two different
models were used in foundation (mass-less and massed) in order to
determine the seismic response of concrete gravity dams. Results
show that when the nonlinear analysis includes the dam- foundation
interaction, the foundation-s mass, flexibility and radiation damping
are important in gravity dam-s response.
Abstract: In this article, the flow behavior around a NACA 0012 airfoil which is oscillating with different Reynolds numbers and in various amplitudes has been investigated numerically. Numerical simulations have been performed with ANSYS software. First, the 2- D geometry has been studied in different Reynolds numbers and angles of attack with various numerical methods in its static condition. This analysis was to choose the best turbulent model and comparing the grids to have the optimum one for dynamic simulations. Because the analysis was to study the blades of wind turbines, the Reynolds numbers were not arbitrary. They were in the range of 9.71e5 to 22.65e5. The angle of attack was in the range of -41.81° to 41.81°. By choosing the forward wind speed as the independent parameter, the others like Reynolds and the amplitude of the oscillation would be known automatically. The results show that the SST turbulent model is the best choice that leads the least numerical error with respect the experimental ones. Also, a dynamic stall phenomenon is more probable at lower wind speeds in which the lift force is less.