Search results for: exact solutions of the Einstein equations

Authors: Raphael Zanella, Todd A. Oliver, Karl W. Schulz

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This work deals with the finite element approximation of axisymmetric compressible flows with swirl velocity. We are interested in problems where the flow, while weakly dependent on the azimuthal coordinate, may have a strong azimuthal velocity component. We describe the approximation of the compressible Navier-Stokes equations with H1-conformal spaces of axisymmetric functions. The weak formulation is implemented in a C++ solver with explicit time marching. The code is first verified with a convergence test on a manufactured solution. The verification is completed by comparing the numerical and analytical solutions in a Poiseuille flow case and a Taylor-Couette flow case. The code is finally applied to the problem of a swirling subsonic air flow in a plasma torch geometry.

Keywords: axisymmetric problem, compressible Navier-Stokes equations, continuous finite elements, swirling flow

Procedia PDF Downloads 148

Authors: Debajyoti Choudhuri, Ratan Kumar Giri, Shesadev Pradhan

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The perturbed nonlinear Schrodinger equation involving the p-biharmonic and the p-Laplacian operators involving a real valued parameter and a continuous real valued potential function defined over the N- dimensional Euclidean space has been considered. By the variational technique, an existence result pertaining to a nontrivial solution to this non-linear partial differential equation has been proposed. Further, by the Concentration lemma, the concentration of solutions to the same problem defined on the set consisting of those elements where the potential function vanishes as the real parameter approaches to infinity has been addressed.

Keywords: p-Laplacian, p-biharmonic, elliptic PDEs, Concentration lemma, Sobolev space

Procedia PDF Downloads 210

Authors: T. Bouchabchoub, A. Bendahmane, A. Haouriqui, N. Attou

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This paper presents simulation results of Forex predicting model equations in order to give approximately a prevision of interest rates. First, Hall-Taylor (HT) equations have been used with Taylor rule (TR) to adapt them to European and American Forex Markets. Indeed, initial Taylor Rule equation is conceived for all Forex transactions in every States: It includes only one equation and six parameters. Here, the model has been used with Hall-Taylor equations, initially including twelve equations which have been reduced to only three equations. Analysis has been developed on the following base macroeconomic variables: Real change rate, investment wages, anticipated inflation, realized inflation, real production, interest rates, gap production and potential production. This model has been used to specifically study the impact of an inflation shock on macroeconomic director interest rates.

Keywords: interest rate, Forex, Taylor rule, production, European Central Bank (ECB), Federal Reserve System (FED).

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Authors: Balgaisha Mukanova, Tolkyn Mirgalikyzy

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Theory of interpretation of electromagnetic fields studied in the electrical prospecting with direct current is mainly developed for the case of a horizontal surface observation. However in practice we often have to work in difficult terrain surface. Conducting interpretation without the influence of topography can cause non-existent anomalies on sections. This raises the problem of studying the impact of different shapes of ground surface relief on the results of electrical prospecting's research. This research examines the numerical solutions of the direct problem of electrical prospecting for two-dimensional and three-dimensional media, taking into account the terrain. The problem is solved using the method of integral equations. The density of secondary currents on the relief surface is obtained.

Keywords: ground surface relief, method of integral equations, numerical method, electromagnetic

Procedia PDF Downloads 334

Authors: Amit Bhunia, Mohit Kumar Singh, Maryam Al Huwayz, Mohamed Henini, Shouvik Datta

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We report [https://arxiv.org/abs/2107.13518] experimental detection and control of Schrodinger’s Cat like macroscopically large, quantum coherent state of a two-component Bose-Einstein condensate of spatially indirect electron-hole pairs or excitons using a resonant tunneling diode of III-V Semiconductors. This provides access to millions of excitons as qubits to allow efficient, fault-tolerant quantum computation. In this work, we measure phase-coherent periodic oscillations in photo-generated capacitance as a function of an applied voltage bias and light intensity over a macroscopically large area. Periodic presence and absence of splitting of excitonic peaks in the optical spectra measured by photocapacitance point towards tunneling induced variations in capacitive coupling between the quantum well and quantum dots. Observation of negative ‘quantum capacitance’ due to a screening of charge carriers by the quantum well indicates Coulomb correlations of interacting excitons in the plane of the sample. We also establish that coherent resonant tunneling in this well-dot heterostructure restricts the available momentum space of the charge carriers within this quantum well. Consequently, the electric polarization vector of the associated indirect excitons collective orients along the direction of applied bias and these excitons undergo Bose-Einstein condensation below ~100 K. Generation of interference beats in photocapacitance oscillation even with incoherent white light further confirm the presence of stable, long-range spatial correlation among these indirect excitons. We finally demonstrate collective Rabi oscillations of these macroscopically large, ‘multipartite’, two-level, coupled and uncoupled quantum states of excitonic condensate as qubits. Therefore, our study not only brings the physics and technology of Bose-Einstein condensation within the reaches of semiconductor chips but also opens up experimental investigations of the fundamentals of quantum physics using similar techniques. Operational temperatures of such two-component excitonic BEC can be raised further with a more densely packed, ordered array of QDs and/or using materials having larger excitonic binding energies. However, fabrications of single crystals of 0D-2D heterostructures using 2D materials (e.g. transition metal di-chalcogenides, oxides, perovskites etc.) having higher excitonic binding energies are still an open challenge for semiconductor optoelectronics. As of now, these 0D-2D heterostructures can already be scaled up for mass production of miniaturized, portable quantum optoelectronic devices using the existing III-V and/or Nitride based semiconductor fabrication technologies.

Keywords: exciton, Bose-Einstein condensation, quantum computation, heterostructures, semiconductor Physics, quantum fluids, Schrodinger's Cat

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Authors: Bhavya Tripathi, Bhupendra Kumar Sharma

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In blood, the concentration of red blood cell varies with the arterial diameter. In the case of narrow arteries, red blood cells concentrate around the center of the artery and there exists a cell-free plasma layer near the arterial wall due to Fahraeus-Lindqvist effect. Due to non- uniformity of the fluid in the narrow arteries, it is preferable to consider the two-phase model of the blood flow. In the present article, coupled nonlinear differential equations have been developed for momentum, energy and concentration of two phase model of the blood flow assuming the Newtonian fluid in both central core and cell free plasma layer and the exact solutions have been found for the problem. For having an adequate insight into the stenosed arterial two-phase blood flow, major components of the flow as flow resistance, total flow rate, and wall shear stress have been estimated for different values of magnetic and radiation parameter. Results show that the increase in the effects of magnetic field decreases the velocity of both cores as well as plasma regions. This result can be helpful to control the blood flow in narrow arteries during surgical process. Temperature of core as well plasma regions decrease as value of radiation parameter increases. The present result is implemented in the form of radiation therapy which is very helpful for cancer patients.

Keywords: two phase blood flow, radiation, magnetohydrodynamics (MHD), stenosis

Procedia PDF Downloads 171

Authors: O. M. Bamigbola, A. A. Ibrahim

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Analysis of real life problems often results in linear systems of equations for which solutions are sought. The method to employ depends, to some extent, on the properties of the coefficient matrix. It is not always feasible to solve linear systems of equations by direct methods, as such the need to use an iterative method becomes imperative. Before an iterative method can be employed to solve a linear system of equations there must be a guaranty that the process of solution will converge. This guaranty, which must be determined a priori, involve the use of some criterion expressible in terms of the entries of the coefficient matrix. It is, therefore, logical that the convergence criterion should depend implicitly on the algebraic structure of such a method. However, in deference to this view is the practice of conducting convergence analysis for Gauss-Seidel iteration on a criterion formulated based on the algebraic structure of Jacobi iteration. To remedy this anomaly, the Gauss-Seidel iteration was studied for its algebraic structure and contrary to the usual assumption, it was discovered that some property of the iteration matrix of Gauss-Seidel method is only diagonally dominant in its first row while the other rows do not satisfy diagonal dominance. With the aid of this structure we herein fashion out an improved version of Gauss-Seidel iteration with the prospect of enhancing convergence and robustness of the method. A numerical section is included to demonstrate the validity of the theoretical results obtained for the improved Gauss-Seidel method.

Keywords: linear algebraic system, Gauss-Seidel iteration, algebraic structure, convergence

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Authors: Davood Yazdani Cherati, Hussein Hashemi Senejani

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In this paper, a convenient analytical solution for a system of coupled differential equations, derived from thermo-hydro-mechanical analysis of three-phase porous media such as unsaturated soils is developed. This kind of analysis can be used in various fields such as geothermal energy systems and seepage of leachate from buried municipal and domestic waste in geomaterials. Initially, a system of coupled differential equations, including energy, mass, and momentum conservation equations is considered, and an analytical method called AGM is employed to solve the problem. The method is straightforward and comprehensible and can be used to solve various nonlinear partial differential equations (PDEs). Results indicate the accuracy of the applied method for solving nonlinear partial differential equations.

Keywords: AGM, analytical solution, porous media, thermo-hydro-mechanical, unsaturated soils

Procedia PDF Downloads 194

Authors: Jessada Tariboon

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In this article, using distribution kernel, we study the nonlinear equations with n-dimensional telegraph operator iterated k-times.

Keywords: telegraph operator, elementary solution, distribution kernel, nonlinear equations

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Authors: Alireza Abbasi Moshaii, Shaghayegh Nasiri, Mehdi Tale Masouleh

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The main purpose of this study is static analysis of two three-degree of freedom parallel mechanisms: 3-RCC and 3-RRS. Geometry of these mechanisms is expressed and static equilibrium equations are derived for the whole chains. For these mechanisms due to the equal number of equations and unknowns, the solution is as same as 3-RCC mechanism. Mathematical software is used to solve the equations. In order to prove the results obtained from solving the equations of mechanisms, their CAD model has been simulated and their static is analysed in ADAMS software. Due to symmetrical geometry of the mechanisms, the force and external torque acting on the end-effecter have been considered asymmetric to prove the generality of the solution method. Finally, the results of both softwares, for both mechanisms are extracted and compared as graphs. The good achieved comparison between the results indicates the accuracy of the analysis.

Keywords: robotic, static analysis, 3-RCC, 3-RRS

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Authors: Nia Mair Fry, Matthew Profit, Chenfeng Li

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This work focuses on the development and implementation of a fully implicit-implicit, coupled mechanical deformation and porous flow, finite element software tool. The fully implicit software accurately predicts classical fundamental analytical solutions such as the Terzaghi consolidation problem. Furthermore, it can capture other analytical solutions less well known in the literature, such as Gibson’s sedimentation rate problem and Coussy’s problems investigating wellbore stability for poroelastic rocks. The mechanical volume strains are transferred to the porous flow governing equation in an implicit framework. This will overcome some of the many current industrial issues, which use explicit solvers for the mechanical governing equations and only implicit solvers on the porous flow side. This can potentially lead to instability and non-convergence issues in the coupled system, plus giving results with an accountable degree of error. The specification of a fully monolithic implicit-implicit coupled porous media code sees the solution of both seepage-mechanical equations in one matrix system, under a unified time-stepping scheme, which makes the problem definition much easier. When using an explicit solver, additional input such as the damping coefficient and mass scaling factor is required, which are circumvented with a fully implicit solution. Further, improved accuracy is achieved as the solution is not dependent on predictor-corrector methods for the pore fluid pressure solution, but at the potential cost of reduced stability. In testing of this fully monolithic porous media code, there is the comparison of the fully implicit coupled scheme against an existing staggered explicit-implicit coupled scheme solution across a range of geotechnical problems. These cases include 1) Biot coefficient calculation, 2) consolidation theory with Terzaghi analytical solution, 3) sedimentation theory with Gibson analytical solution, and 4) Coussy well-bore poroelastic analytical solutions.

Keywords: coupled, implicit, monolithic, porous media

Procedia PDF Downloads 101

Authors: Reza Alikhani

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This research focuses on the establishment of horizontal cooperation among companies to enhance their operational efficiency and competitiveness. The study proposes an approach to horizontal collaboration, called coalition configuration, which involves partnering companies sharing distribution centers in a network design problem. The paper investigates which coalition should be formed in each distribution center to minimize the total cost of the network. Moreover, potential uncertainties, such as operational and disruption risks, are considered during the collaborative design phase. To address this problem, a two-stage robust optimization model for collaborative distribution network design under surging demand and facility disruptions is presented, along with a column-and-constraint generation algorithm to obtain exact solutions tailored to the proposed formulation. Extensive numerical experiments are conducted to analyze solutions obtained by the model in various scenarios, including decisions ranging from fully centralized to fully decentralized settings, collaborative versus non-collaborative approaches, and different amounts of uncertainty budgets. The results show that the coalition formation mechanism proposes some solutions that are competitive with the savings of the grand coalition. The research also highlights that collaboration increases network flexibility and resilience while reducing costs associated with demand and capacity uncertainties.

Keywords: logistics, warehouse sharing, robust facility location, collaboration for resilience

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Authors: Lizhou Chen, Abdelhamid Belgaid, Assem Elsayed, Xiaoming Yang

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Compression index is essential in foundation settlement calculation. The traditional method for determining compression index is consolidation test which is expensive and time consuming. Many researchers have used regression methods to develop empirical equations for predicting compression index from soil properties. Based on a large number of compression index data collected from consolidation tests, the accuracy of some popularly empirical equations were assessed. It was found that primary compression index is significantly overestimated in some equations while it is underestimated in others. The sensitivity analyses of soil parameters including water content, liquid limit and void ratio were performed. The results indicate that the compression index obtained from void ratio is most accurate. The ANOVA (analysis of variance) demonstrates that the equations with multiple soil parameters cannot provide better predictions than the equations with single soil parameter. In other words, it is not necessary to develop the relationships between compression index and multiple soil parameters. Meanwhile, it was noted that secondary compression index is approximately 0.7-5.0% of primary compression index with an average of 2.0%. In the end, the proposed prediction equations using power regression technique were provided that can provide more accurate predictions than those from existing equations.

Keywords: compression index, clay, settlement, consolidation, secondary compression index, soil parameter

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Authors: Bidzina Matsaberidze, Anna Sikharulidze, Gia Sirbiladze, Bezhan Ghvaberidze

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In the modern world emergency management decision support systems are actively used by state organizations, which are interested in extreme and abnormal processes and provide optimal and safe management of supply needed for the civil and military facilities in geographical areas, affected by disasters, earthquakes, fires and other accidents, weapons of mass destruction, terrorist attacks, etc. Obviously, these kinds of extreme events cause significant losses and damages to the infrastructure. In such cases, usage of intelligent support technologies is very important for quick and optimal location-transportation of emergency service in order to avoid new losses caused by these events. Timely servicing from emergency service centers to the affected disaster regions (response phase) is a key task of the emergency management system. Scientific research of this field takes the important place in decision-making problems. Our goal was to create an expert knowledge-based intelligent support system, which will serve as an assistant tool to provide optimal solutions for the above-mentioned problem. The inputs to the mathematical model of the system are objective data, as well as expert evaluations. The outputs of the system are solutions for Fuzzy Multi-Objective Emergency Location-Transportation Problem (FMOELTP) for disasters’ regions. The development and testing of the Intelligent Support System were done on the example of an experimental disaster region (for some geographical zone of Georgia) which was generated using a simulation modeling. Four objectives are considered in our model. The first objective is to minimize an expectation of total transportation duration of needed products. The second objective is to minimize the total selection unreliability index of opened humanitarian aid distribution centers (HADCs). The third objective minimizes the number of agents needed to operate the opened HADCs. The fourth objective minimizes the non-covered demand for all demand points. Possibility chance constraints and objective constraints were constructed based on objective-subjective data. The FMOELTP was constructed in a static and fuzzy environment since the decisions to be made are taken immediately after the disaster (during few hours) with the information available at that moment. It is assumed that the requests for products are estimated by homeland security organizations, or their experts, based upon their experience and their evaluation of the disaster’s seriousness. Estimated transportation times are considered to take into account routing access difficulty of the region and the infrastructure conditions. We propose an epsilon-constraint method for finding the exact solutions for the problem. It is proved that this approach generates the exact Pareto front of the multi-objective location-transportation problem addressed. Sometimes for large dimensions of the problem, the exact method requires long computing times. Thus, we propose an approximate method that imposes a number of stopping criteria on the exact method. For large dimensions of the FMOELTP the Estimation of Distribution Algorithm’s (EDA) approach is developed.

Keywords: epsilon-constraint method, estimation of distribution algorithm, fuzzy multi-objective combinatorial programming problem, fuzzy multi-objective emergency location/transportation problem

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Authors: Shahroz Khan, Osman Taha Şen

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In automotive brake systems, brake noise has been a major problem, and brake squeal is one of the critical ones which is an instability issue. The brake squeal produces an audible sound at high frequency that is irritating to the human ear. To study this critical problem, first a nonlinear mathematical model with three degree of freedom is developed. This model consists of a point mass that simulates the brake pad and a sliding surface that simulates the brake rotor. The model exposes kinematic and clearance nonlinearities, but no friction nonlinearity. In the formulation, the friction coefficient is assumed to be constant and the friction force does not change direction. The nonlinear governing equations of the model are first obtained, and numerical solutions are sought for different cases. Second, a computational model for the squeal problem is developed with a commercial software, and computational solutions are obtained with two different types of contact cases (solid-to-solid and sphere-to-plane). This model consists of three rigid bodies and several elastic elements that simulate the key characteristics of a brake system. The response obtained from this model is compared with numerical solutions in time and frequency domain.

Keywords: contact force, nonlinearities, brake squeal, vehicle brake

Procedia PDF Downloads 227

Authors: Elvis Adam Alhassan, Kaiyu Tian, Akos Konadu, Ernest Zamanah, Michael Jackson Adjabui, Ibrahim Justice Musah, Esther Agyeiwaa Owusu, Emmanuel K. A. Agyeman

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In this paper, how to solve simultaneous equations using the Elvis improved method is shown. The Elvis improved method says; to make one variable in the first equation the subject; make the same variable in the second equation the subject; equate the results and simplify to obtain the value of the unknown variable; put the value of the variable found into one equation from the first or second steps and simplify for the remaining unknown variable. The difference between our Elvis improved method and the substitution method is that: with Elvis improved method, the same variable is made the subject in both equations, and the two resulting equations equated, unlike the substitution method where one variable is made the subject of only one equation and substituted into the other equation. After describing the Elvis improved method, findings from 100 secondary students and the views of 5 secondary tutors to demonstrate the effectiveness of the method are presented. The study's purpose is proved by hypothetical examples.

Keywords: simultaneous equations, substitution method, elimination method, graphical method, Elvis improved method

Procedia PDF Downloads 88

Authors: Esmaeil Bahmyari

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The natural frequency analysis of the functionally graded (FG) rotating cylindrical shells subjected to thermal loads is studied based on the three-dimensional elasticity theory. The temperature-dependent assumption of the material properties is graded in the thickness direction, which varies based on the simple power law distribution. The governing equations and the appropriate boundary conditions, which include the effects of initial thermal stresses, are derived employing Hamilton’s principle. The initial thermo-mechanical stresses are obtained by the thermo-elastic equilibrium equation’s solution. As an efficient and accurate numerical tool, the differential quadrature method (DQM) is adopted to solve the thermo-elastic equilibrium equations, free vibration equations and natural frequencies are obtained. The high accuracy of the method is demonstrated by comparison studies with those existing solutions in the literature. Ultimately, the parametric studies are performed to demonstrate the effects of boundary conditions, temperature rise, material graded index, the thickness-to-length and the aspect ratios for the rotating cylindrical shells on the natural frequency.

Keywords: free vibration, DQM, elasticity theory, FG shell, rotating cylindrical shell

Procedia PDF Downloads 54

Authors: H. Ozbasaran

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IPN and IPE sections, which are commonly used European I shapes, are widely used in steel structures as cantilever beams to support overhangs. A considerable number of studies exist on calculating lateral torsional buckling load of I sections. However, most of them provide series solutions or complex closed-form equations. In this paper, a simple equation is presented to calculate lateral torsional buckling load of IPN and IPE section cantilever beams. First, differential equation of lateral torsional buckling is solved numerically for various loading cases. Then a parametric study is conducted on results to present an equation for lateral torsional buckling load of European IPN and IPE beams. Finally, results obtained by presented equation are compared to differential equation solutions and finite element model results. ABAQUS software is utilized to generate finite element models of beams. It is seen that the results obtained from presented equation coincide with differential equation solutions and ABAQUS software results. It can be suggested that presented formula can be safely used to calculate critical lateral torsional buckling load of European IPN and IPE section cantilevers.

Keywords: cantilever, IPN, IPE, lateral torsional buckling

Procedia PDF Downloads 517

Authors: Arun Goel

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Prediction of maximum local scour is necessary for the safety and economical design of the bridges. A number of equations have been developed over the years to predict local scour depth using laboratory data and a few pier equations have also been proposed using field data. Most of these equations are empirical in nature as indicated by the past publications. In this paper, attempts have been made to compute local depth of scour around bridge pier in dimensional and non-dimensional form by using linear regression, simple regression and SVM (Poly and Rbf) techniques along with few conventional empirical equations. The outcome of this study suggests that the SVM (Poly and Rbf) based modeling can be employed as an alternate to linear regression, simple regression and the conventional empirical equations in predicting scour depth of bridge piers. The results of present study on the basis of non-dimensional form of bridge pier scour indicates the improvement in the performance of SVM (Poly and Rbf) in comparison to dimensional form of scour.

Keywords: modeling, pier scour, regression, prediction, SVM (Poly and Rbf kernels)

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Authors: Jerry Hu

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Let G = (V, E) with V = {1, 2, ..., k} be a graph, the k positive integers a₁, a₂, ..., ak are G-wise relatively prime if (aᵢ, aⱼ ) = 1 for {i, j} ∈ E. We use an inductive approach to give an asymptotic formula for the number of k-tuples of integers that are G-wise relatively prime. An exact formula is obtained for the probability that k positive integers are G-wise relatively prime. As a corollary, we also provide an exact formula for the probability that k positive integers have exactly r relatively prime pairs.

Keywords: graph, independent set, G-wise relatively prime, probability

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Authors: M. Y. Waziri, M. A. Aliyu

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The paper proposes an approach to improve the performance of Broyden’s method for solving systems of nonlinear equations. In this work, we consider the information from two preceding iterates rather than a single preceding iterate to update the Broyden’s matrix that will produce a better approximation of the Jacobian matrix in each iteration. The numerical results verify that the proposed method has clearly enhanced the numerical performance of Broyden’s Method.

Keywords: mulit-step Broyden, nonlinear systems of equations, computational efficiency, iterate

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Authors: Alibakhsh Kasaeian, Mohammad Sameti, Zahra Noori, Mona Rastgoo Bahambari

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Nowadays, the parabolic trough solar collector technology has become the most promising large-scale technology among various solar thermal generations. In this paper, a detailed numerical heat transfer model for a parabolic trough collector with nanofluid is presented based on the finite difference approach for which a MATLAB code was developed. The model was used to simulate the performance of a parabolic trough solar collector’s linear receiver, called a heat collector element (HCE). In this model, the heat collector element of the receiver was discretized into several segments in axial directions and energy balances were used for each control volume. All the heat transfer correlations, the thermodynamic equations and the optical properties were considered in details and the set of algebraic equations were solved simultaneously using iterative numerical solutions. The modeling assumptions and limitations are also discussed, along with recommendations for model improvement.

Keywords: heat transfer, nanofluid, numerical analysis, trough

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Authors: Paschal A. Ochang, Emmanuel C. Oji

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The Duffing’s Equation is a second order system that is very important because they are fundamental to the behaviour of higher order systems and they have applications in almost all fields of science and engineering. In the biological area, it is useful in plant stem dependence and natural frequency and model of the Brain Crash Analysis (BCA). In Engineering, it is useful in the study of Damping indoor construction and Traffic lights and to the meteorologist it is used in the prediction of weather conditions. However, most Problems in real life that occur are non-linear in nature and may not have analytical solutions except approximations or simulations, so trying to find an exact explicit solution may in general be complicated and sometimes impossible. Therefore we aim to find out if it is possible to obtain one analytical fixed point to the non-linear ordinary equation using fixed point analytical method. We started by exposing the scope of the Duffing’s equation and other related works on it. With a major focus on the fixed point and fixed point iterative scheme, we tried different iterative schemes on the Duffing’s Equation. We were able to identify that one can only see the fixed points to a Damped Duffing’s Equation and not to the Undamped Duffing’s Equation. This is because the cubic nonlinearity term is the determining factor to the Duffing’s Equation. We finally came to the results where we identified the stability of an equation that is damped, forced and second order in nature. Generally, in this research, we approximate the solution of Duffing’s Equation by converting it to a system of First and Second Order Ordinary Differential Equation and using Fixed Point Iterative approach. This approach shows that for different versions of Duffing’s Equations (damped), we find fixed points, therefore the order of computations and running time of applied software in all fields using the Duffing’s equation will be reduced.

Keywords: damping, Duffing's equation, fixed point analysis, second order differential, stability analysis

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Authors: Kohei Inoue, Kenji Hara, Kiichi Urahama

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We describe a relationship between integral images and differential images. First, we derive a simple difference filter from conventional integral image. In the derivation, we show that an integral image and the corresponding differential image are related to each other by simultaneous linear equations, where the numbers of unknowns and equations are the same, and therefore, we can execute the integration and differentiation by solving the simultaneous equations. We applied the relationship to an image fusion problem, and experimentally verified the effectiveness of the proposed method.

Keywords: integral images, differential images, differential filters, image fusion

Procedia PDF Downloads 473

Authors: Anyeres N. Atehortua Jimenez, J. David Lambraño, Juan Carlos Muñoz

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Navier-Stokes equations (NSE), which describe the dynamics of a fluid, have an important application on modeling waves used for data inversion techniques as full waveform inversion (FWI). In this work a linearized version of NSE and its variables, neglecting deviatoric terms of stress tensor, is presented. In order to get a theoretical modeling of pressure p(x,t) and wave velocity profile c(x,t), a wave equation of visco-acoustic medium (VAE) is written. A change of variables p(x,t)=q(x,t)h(ρ), is made on the equation for the VAE leading to a well known Klein-Gordon equation (KGE) describing waves propagating in variable density medium (ρ) with dispersive term α^2(x). KGE is reduced to a Poisson equation and solved by proposing a specific function for α^2(x) accounting for the energy dissipation and dispersion. Finally, an integral form solution is derived for p(x,t), c(x,t) and kinematics variables like particle velocity v(x,t), displacement u(x,t) and bulk modulus function k_b(x,t). Further, it is compared this visco-acoustic formulation with another form broadly used in the geophysics; it is argued that this formalism is more general and, given its integral form, it may offer several advantages from the modern parallel computing point of view. Applications to minimize the errors in modeling for FWI applied to oils resources in geophysics are discussed.

Keywords: Navier-Stokes equations, modeling, visco-acoustic, inversion FWI

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Authors: Frederick Ferguson, Dehua Feng, Yang Gao

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No doubt, current CFD tools have a great many technical limitations, and active research is being done to overcome these limitations. Current areas of limitations include vortex-dominated flows, separated flows, and turbulent flows. In general, turbulent flows are unsteady solutions to the fluid dynamic equations, and instances of these solutions can be computed directly from the equations. One of the approaches commonly implemented is known as the ‘direct numerical simulation’, DNS. This approach requires a spatial grid that is fine enough to capture the smallest length scale of the turbulent fluid motion. This approach is called the ‘Kolmogorov scale’ model. It is of interest to note that the Kolmogorov scale model must be captured throughout the domain of interest and at a correspondingly small-time step. In typical problems of industrial interest, the ratio of the length scale of the domain to the Kolmogorov length scale is so great that the required grid set becomes prohibitively large. As a result, the available computational resources are usually inadequate for DNS related tasks. At this time in its development, DNS is not applicable to industrial problems. In this research, an attempt is made to develop a numerical technique that is capable of delivering DNS quality solutions at the scale required by the industry. To date, this technique has delivered preliminary results for both steady and unsteady, viscous and inviscid, compressible and incompressible, and for both high and low Reynolds number flow fields that are very accurate. Herein, it is proposed that the Integro-Differential Scheme (IDS) be applied to a set of vortex-shockwave interaction problems with the goal of investigating the nonstationary physics within the resulting interaction regions. In the proposed paper, the IDS formulation and its numerical error capability will be described. Further, the IDS will be used to solve the inviscid and viscous Burgers equation, with the goal of analyzing their solutions over a considerable length of time, thus demonstrating the unsteady capabilities of the IDS. Finally, the IDS will be used to solve a set of fluid dynamic problems related to flow that involves highly vortex interactions. Plans are to solve the following problems: the travelling wave and vortex problems over considerable lengths of time, the normal shockwave–vortex interaction problem for low supersonic conditions and the reflected oblique shock–vortex interaction problem. The IDS solutions obtained in each of these solutions will be explored further in efforts to determine the distributed density gradients and vorticity, as well as the Q-criterion. Parametric studies will be conducted to determine the effects of the Mach number on the intensity of vortex-shockwave interactions.

Keywords: vortex dominated flows, shockwave interactions, high Reynolds number, integro-differential scheme

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Authors: Nader Parsazadeh

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The variety of bed sediment load relationships, insufficient information and data, and the influence of river conditions make the selection of an optimum relationship for a given river extremely difficult. Hence, in order to select the best formulae, the bed load equations should be evaluated. The affecting factors need to be scrutinized, and equations should be verified. Also, re-evaluation may be needed. In this research, sediment bed load of Dez Dam at Tal-e Zang Station has been studied. After reviewing the available references, the most common formulae were selected that included Meir-Peter and Muller, using MS Excel to compute and evaluate data. Then, 52 series of already measured data at the station were re-measured, and the sediment bed load was determined. 1. The calculated bed load obtained by different equations showed a great difference with that of measured data. 2. r difference ratio from 0.5 to 2.00 was 0% for all equations except for Nilsson and Shields equations while it was 61.5 and 59.6% for Nilsson and Shields equations, respectively. 3. By reviewing results and discarding probably erroneous measured data measurements (by human or machine), one may use Nilsson Equation due to its r value higher than 1 as an effective equation for estimating bed load at Tal-e Zang Station in order to predict activities that depend upon bed sediment load estimate to be determined. Also, since only few studies have been conducted so far, these results may be of assistance to the operators and consulting companies.

Keywords: bed load, empirical relation ship, sediment, Tale Zang Station

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Authors: Serdal Pamuk, Irem Cay

Abstract:

Our model is based on the theory of reinforced random walks coupled with Michealis-Menten mechanisms which view endothelial cell receptors as the catalysts for transforming both tumor and macrophage derived tumor angiogenesis factor (TAF) into proteolytic enzyme which in turn degrade the basal lamina. The model consists of two main parts. First part has seven differential equations (DE’s) in one space dimension over the capillary, whereas the second part has the same number of DE’s in two space dimensions in the extra cellular matrix (ECM). We connect these two parts via some boundary conditions to move the cells into the ECM in order to initiate capillary formation. But, when does this movement begin? To address this question we estimate the thresholds that activate the transport equations in the capillary. We do this by using steady-state analysis of TAF equation under some assumptions. Once these equations are activated endothelial, pericyte and macrophage cells begin to move into the ECM for the initiation of angiogenesis. We do believe that our results play an important role for the mechanisms of cell migration which are crucial for tumor angiogenesis. Furthermore, we estimate the long time tendency of these three cells, and find that they tend to the transition probability functions as time evolves. We provide our numerical solutions which are in good agreement with our theoretical results.

Keywords: angiogenesis, capillary formation, mathematical analysis, steady-state, transition probability function

Procedia PDF Downloads 121

Authors: Davood Yazdani Cherati, Ali Pak, Mehrdad Jafarzadeh

Abstract:

This research contains the formulation of a two-dimensional analytical solution to transient heat, and moisture flow in a semi-infinite unsaturated soil environment under the influence of daily temperature changes. For this purpose, coupled energy conservation and mass fluid continuity equations governing hydrothermal behavior of unsaturated soil media are presented in terms of temperature and volumetric moisture content. In consideration of the soil environment as an infinite half-space and by linearization of the governing equations, Laplace–Fourier transformation is conducted to convert differential equations with partial derivatives (PDEs) to ordinary differential equations (ODEs). The obtained ODEs are solved, and the inverse transformations are calculated to determine the solution to the system of equations. Results indicate that heat variation induces moisture transport in both horizontal and vertical directions.

Keywords: analytical solution, heat conduction, hydrothermal analysis, laplace–fourier transformation, two-dimensional

Procedia PDF Downloads 186

Authors: Ömer Aktaş, Olga A. Suvorova, Oleg Tretyakov

Abstract:

The boundary value problem on non-canonical and arbitrary shaped contour is solved with a numerically effective method called Analytical Regularization Method (ARM) to calculate propagation parameters. As a result of regularization, the equation of first kind is reduced to the infinite system of the linear algebraic equations of the second kind in the space of L2. This equation can be solved numerically for desired accuracy by using truncation method. The parameters as cut-off wavenumber and cut-off frequency are used in waveguide evolutionary equations of electromagnetic theory in time-domain to illustrate the real-valued TM fields with lossy and lossless media.

Keywords: analytical regularization method, electromagnetic theory evolutionary equations of time-domain, TM Field

Procedia PDF Downloads 467