Search results for: waves equations

Authors: Andriy Didenko, Zanin Kavazovic

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Engineering students often have certain difficulties in mastering major theoretical concepts in mathematical courses such as differential equations. Student projects were proposed to motivate students’ learning and can be used as a tool to promote students’ interest in the material. Authors propose a student project that includes the use of Microsoft Excel. This instructional tool is often overlooked by both educators and students. An integral component of the experimental part of such a project is the exploration of an interactive spreadsheet. The aim is to assist engineering students in better understanding of Euler’s method. This method is employed to numerically solve first order differential equations. At first, students are invited to select classic equations from a list presented in a form of a drop-down menu. For each of these equations, students can select and modify certain key parameters and observe the influence of initial condition on the solution. This will give students an insight into the behavior of the method in different configurations as solutions to equations are given in numerical and graphical forms. Further, students could also create their own equations by providing functions of their own choice and a variety of initial conditions. Moreover, they can visualize and explore the impact of the length of the time step on the convergence of a sequence of numerical solutions to the exact solution of the equation. As a final stage of the project, students are encouraged to develop their own spreadsheets for other numerical methods and other types of equations. Such projects promote students’ interest in mathematical applications and further improve their mathematical and programming skills.

Keywords: student project, Euler's method, spreadsheet, engineering education

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Authors: K. T. Sun, Y. H. Tai, H. W. Yang, H. T. Lin

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This paper presented the technique of robot control by event-related potentials (ERPs) of brain waves. Based on the proposed technique, severe physical disabilities can free browse outside world. A specific component of ERPs, N2P3, was found and used to control the movement of robot and the view of camera on the designed brain-computer interface (BCI). Users only required watching the stimuli of attended button on the BCI, the evoked potentials of brain waves of the target button, N2P3, had the greatest amplitude among all control buttons. An experimental scene had been constructed that the robot required walking to a specific position and move the view of camera to see the instruction of the mission, and then completed the task. Twelve volunteers participated in this experiment, and experimental results showed that the correct rate of BCI control achieved 80% and the average of execution time was 353 seconds for completing the mission. Four main contributions included in this research: (1) find an efficient component of ERPs, N2P3, for BCI control, (2) embed robot's viewpoint image into user interface for robot control, (3) design an experimental scene and conduct the experiment, and (4) evaluate the performance of the proposed system for assessing the practicability.

Keywords: severe physical disabilities, robot control, event-related potentials (ERPs), brain-computer interface (BCI), brain waves

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Authors: Gaspar J. Machado, Stéphane Clain, Raphael Loubère

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The goal of the present work is to numerically study steady-state nonlinear hyperbolic equations in the context of the finite volume framework. We will consider the unidimensional Burgers' equation as the reference case for the scalar situation and the unidimensional Euler equations for the vectorial situation. We consider two approaches to solve the nonlinear equations: a time marching algorithm and a direct steady-state approach. We first develop the necessary and sufficient conditions to obtain the existence and unicity of the solution. We treat regular examples and solutions with a steady shock and to provide very-high-order finite volume approximations we implement a method based on the MOOD technology (Multi-dimensional Optimal Order Detection). The main ingredient consists in using an 'a posteriori' limiting strategy to eliminate non physical oscillations deriving from the Gibbs phenomenon while keeping a high accuracy for the smooth part.

Keywords: Euler equations, finite volume, MOOD, steady-state

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Authors: Fakhreddin Abedi, Wah June Leong

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Exponential stability of stochastic differential equations with non trivial solutions is provided in terms of Lyapunov functions. The main result of this paper establishes that, under certain hypotheses for the dynamics f(.) and g(.), practical exponential stability in probability at the small neighborhood of the origin is equivalent to the existence of an appropriate Lyapunov function. Indeed, we establish exponential stability of stochastic differential equation when almost all the state trajectories are bounded and approach a sufficiently small neighborhood of the origin. We derive sufficient conditions for exponential stability of stochastic differential equations. Finally, we give a numerical example illustrating our results.

Keywords: exponential stability in probability, stochastic differential equations, Lyapunov technique, Ito's formula

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Authors: Md. Moniruzzaman

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The energy of ocean waves across a large part of the earth is inexhaustible. The whole world will benefit if this endless energy can be used in an easy way. The coastal countries will easily be able to meet their own energy needs. The purpose of this article is to use the infinite energy of the ocean wave in a simple way. i.e. a method of efficient use of wave energy. The paper starts by discussing various forces acting on a floating object and, afterward, about the method. And then a calculation for a 73.39MW hydropower from the tidal wave. Used some sketches/pictures. Finally, the conclusion states the possibilities and advantages.

Keywords: anchor, electricity, floating object, pump, ship city, wave energy

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Authors: Zahid Ullah, Atlas Khan

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This research endeavors to explore the regularity properties associated with a specific class of equations, namely extremely degenerate elliptic equations. These equations hold significance in understanding complex physical systems like porous media flow, with applications spanning various branches of mathematics. The focus is on unraveling and analyzing regularity results to gain insights into the smoothness of solutions for these highly degenerate equations. Elliptic equations, fundamental in expressing and understanding diverse physical phenomena through partial differential equations (PDEs), are particularly adept at modeling steady-state and equilibrium behaviors. However, within the realm of elliptic equations, the subset of extremely degenerate cases presents a level of complexity that challenges traditional analytical methods, necessitating a deeper exploration of mathematical theory. While elliptic equations are celebrated for their versatility in capturing smooth and continuous behaviors across different disciplines, the introduction of degeneracy adds a layer of intricacy. Extremely degenerate elliptic equations are characterized by coefficients approaching singular behavior, posing non-trivial challenges in establishing classical solutions. Still, the exploration of extremely degenerate cases remains uncharted territory, requiring a profound understanding of mathematical structures and their implications. The motivation behind this research lies in addressing gaps in the current understanding of regularity properties within solutions to extremely degenerate elliptic equations. The study of extreme degeneracy is prompted by its prevalence in real-world applications, where physical phenomena often exhibit characteristics defying conventional mathematical modeling. Whether examining porous media flow or highly anisotropic materials, comprehending the regularity of solutions becomes crucial. Through this research, the aim is to contribute not only to the theoretical foundations of mathematics but also to the practical applicability of mathematical models in diverse scientific fields.

Keywords: elliptic equations, extremely degenerate, regularity results, partial differential equations, mathematical modeling, porous media flow

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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

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Authors: Abdul Wajid Ali

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Supersonic flight promises speed, but the design of the air inlet faces an obstacle: shock waves. They prevent air flow in the mixed compression ports, which reduces engine performance. Our research investigates this using supersonic wind tunnels and schlieren imaging to reveal the complex dance between shock waves and airflow. The findings show clear patterns of shock wave formation influenced by internal/external pressure surfaces. We looked at the boundary layer, the slow-moving air near the inlet walls, and its interaction with shock waves. In addition, the study emphasizes the dependence of the shock wave behaviour on the Mach number, which highlights the need for adaptive models. This knowledge is key to optimizing the combined compression inputs, paving the way for more powerful and efficient supersonic vehicles. Future engineers can use this knowledge to improve existing designs and explore innovative configurations for next-generation ultrasonic applications.

Keywords: oblique shock formation, boundary layer interaction, schlieren images, double wedge surface

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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: Trilok Mathur, Shivi Agarwal

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This paper deals with the solutions of fuzzy-fractional-order Riccati equations under Caputo-type fuzzy fractional derivatives. The Caputo-type fuzzy fractional derivatives are defined based on Hukuhura difference and strongly generalized fuzzy differentiability. The Laplace-Adomian-Pade method is used for solving fractional Riccati-type initial value differential equations of fractional order. Moreover, we also displayed some examples to illustrate our methods.

Keywords: Caputo-type fuzzy fractional derivative, Fractional Riccati differential equations, Laplace-Adomian-Pade method, Mittag Leffler function

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Authors: Y. N. Reddy

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The class of differential-difference equations which have characteristics of both classes, i.e., delay/advance and singularly perturbed behaviour is known as singularly perturbed differential-difference equations. The expression ‘positive shift’ and ‘negative shift’ are also used for ‘advance’ and ‘delay’ respectively. In general, an ordinary differential equation in which the highest order derivative is multiplied by a small positive parameter and containing at least one delay/advance is known as singularly perturbed differential-difference equation. Singularly perturbed differential-difference equations arise in the modelling of various practical phenomena in bioscience, engineering, control theory, specifically in variational problems, in describing the human pupil-light reflex, in a variety of models for physiological processes or diseases and first exit time problems in the modelling of the determination of expected time for the generation of action potential in nerve cells by random synaptic inputs in dendrites. In this paper, we envisage the use of Liouville Green Transformation to find the solution of singularly perturbed differential difference equations. First, using Taylor series, the given singularly perturbed differential difference equation is approximated by an asymptotically equivalent singularly perturbation problem. Then the Liouville Green Transformation is applied to get the solution. Several model examples are solved, and the results are compared with other methods. It is observed that the present method gives better approximate solutions.

Keywords: difference equations, differential equations, singular perturbations, boundary layer

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Authors: Ghoutia Naima Sabri, Tayeb Benouaz

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The interaction between wave and electron cyclotron movement when the electron passes through a layer of resonance at a fixed frequency results an Electron Cyclotron (EC) absorption in Tokamak plasma and dependent magnetic field. This technique is the principle of additional heating (ECRH) and the generation of non-inductive current drive (ECCD) in modern fusion devices. In this paper we are interested by the problem of EC absorption which used a microscopic description of kinetic theory treatment versus the propagation which used the cold plasma description. The power absorbed depends on the optical depth which in turn depends on coefficient of absorption and the order of the excited harmonic for O-mode or X-mode. There is another possibility of heating by dissipation of Alfven waves, based on resonance of cold plasma waves, the shear Alfven wave (SW) and the compressional Alfven wave (FW). Once the (FW) power is coupled to (SW), it stays on the magnetic surface and dissipates there, which cause the heating of bulk plasmas.

Keywords: electron cyclotron, heating, plasma, tokamak

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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: 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: João Madureira, Ricardo Lagido, Inês Sousa, Fraunhofer Portugal

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Surf is an increasingly popular sport and its performance evaluation is often qualitative. This work aims at using a smartphone to collect and analyze the GPS and inertial sensors data in order to obtain quantitative metrics of the surfing performance. Two approaches are compared for detection of wave rides, computing the number of waves rode in a surfing session, the starting time of each wave and its duration. The first approach is based on computing the velocity from the Global Positioning System (GPS) signal and finding the velocity thresholds that allow identifying the start and end of each wave ride. The second approach adds information from the Inertial Measurement Unit (IMU) of the smartphone, to the velocity thresholds obtained from the GPS unit, to determine the start and end of each wave ride. The two methods were evaluated using GPS and IMU data from two surfing sessions and validated with similar metrics extracted from video data collected from the beach. The second method, combining GPS and IMU data, was found to be more accurate in determining the number of waves, start time and duration. This paper shows that it is feasible to use smartphones for quantification of performance metrics during surfing. In particular, detection of the waves rode and their duration can be accurately determined using the smartphone GPS and IMU.

Keywords: inertial measurement unit (IMU), global positioning system (GPS), smartphone, surfing performance

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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

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Authors: Anand Kumar Yadav

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Purpose – The purpose of this paper is to investigate the fluctuation of amplitude ratios of various transmitted and reflected waves. Design/methodology/approach – The reflection and transmission of plane waves on the interface between an orthotropic hygro-thermo-elastic half-space (OHTHS) and a viscous-fluid half-space (VFHS) were investigated in this study with reference to coupled hygro-thermo-elasticity. Findings – The interface, where y = 0, is struck by the principal (P) plane waves as they travel through the VFHS. Two waves are reflected in VFHS, and four waves are transmitted in OHTHS as a result namely longitudinal displacement, Pwave − , thermal diffusion TDwave − and moisture diffusion mDwave − and shear vertical SV wave. Expressions for the reflection and transmitted coefficient are developed for the incidence of a hygrothermal plane wave. It is noted that these ratios are graphically displayed and are observed under the influence of coupled hygro-thermo-elasticity. Research limitations/implications – There isn't much study on the model under consideration, which combines OHTHS and VFHS with coupled hygro-thermo-elasticity, according to the existing literature Practical implications – The current model can be applied in many different areas, such as soil dynamics, nuclear reactors, high particle accelerators, earthquake engineering, and other areas where linked hygrothermo-elasticity is important. In a range of technical and geophysical settings, wave propagation in a viscous fluid-thermoelastic medium with various characteristics, such as initial stress, magnetic field, porosity, temperature, etc., gives essential information regarding the presence of new and modified waves. This model may prove useful in modifying earthquake estimates for experimental seismologists, new material designers, and researchers. Social implications – Researchers may use coupled hygro-thermo-elasticity to categories the material, where the parameter is a new indication of its ability to conduct heat in interaction with diverse materials. Originality/value – The submitted text is the sole creation of the team of writers, and all authors equally contributed to its creation.

Keywords: hygro-thermo-elasticity, viscous fluid, reflection coefficient, transmission coefficient, moisture concentration

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Authors: Ehsan Kadkhodaie, Shahin Parvar, Soroush Senemar, Mostafa Shriat, Abdolrasoul Malekpour

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The role of oil in supra distribution transformers is so critical and, several standards in determining the quality of oil have been offered. So far, moisture, viscosity and insulation protection of the oil have been measured based on mechanical and chemical methods and systems such as kart fisher, falling ball and TDM 4000 that most of these techniques are destructive and have many problems such as pollution. In this study, due to the properties of oil and also physical behavior of ultrasound wave new method was designed to in the determination of oil indicators including viscosity and moisture. The results show the oil viscosity can be found from the relationship μ = 42.086/√EE and moisture from (PLUS+) = −15.65 (PPM) + 26040 relationship.

Keywords: oil, viscosity, moisture, ultrasonic waves

Procedia PDF Downloads 581

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: Akram Boubakri, Fethi Choubeni, Tan Hoa Vuong, Jacques David

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The control of electromagnetic waves is a key aim of several researches over the past decade. In this regard, Metamaterials have shown a strong ability to manipulate the electromagnetic waves on a subwavelength scales thanks to its unconventional properties that are not available in natural materials such as negative refraction index, super imaging and invisibility cloaking. Metalenses were used to avoid some drawbacks presented by conventional lenses since focusing with conventional lenses suffered from the limited resolution because they were only able to focus the propagating wave component. Nevertheless, Metalenses were able to go beyond the diffraction limit and enhance the resolution not only by collecting the propagating waves but also by restoring the amplitude of evanescent waves that decay rapidly when going far from the source and that contains the finest details of the image. Metasurfaces have many mechanical advantages over three-dimensional metamaterial structures especially the ease of fabrication and a smaller required volume. Those structures have been widely used for antenna performance improvement and to build flat metalenses. In this work, we showed that a well-designed metasurface lens operating at the frequency of 5.9GHz, has efficiently enhanced the radiation characteristics of a patch antenna and can be used for WLAN applications (IEEE 802.11 a). The proposed metasurface lens is built with a geometrically modified unit cells which lead to a change in the response of the lens at different position and allow the control of the wavefront beam of the incident wave thanks to the gradient refractive index.

Keywords: focusing, gradient index, metasurface, metalens, WLAN Applications

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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

Procedia PDF Downloads 640

Authors: Ahmed A. El-Gindy, Elham S. El-Nashar, Abdallah Nafaa, Sameh El-Kafrawy

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The generation of energy from marine energy became one of the most preferable resources since it is a clean source and friendly to environment. Egypt has long shores along Mediterranean with important cities that need energy resources with significant wave energy. No detailed studies have been done on wave energy distribution in the Egyptian waters. The objective of this paper is to assess the energy wave power available in the Egyptian waters for the choice of the most suitable devices to be used in this area. This paper deals the characteristics and power of the offshore waves in the Egyptian waters. Since the field observations of waves are not frequent and need much technical work, the European Centre for Medium-Range Weather Forecasts (ECMWF) interim reanalysis data in Mediterranean, with a grid size 0.75 degree, which is a relatively course grid, are considered in the present study for preliminary assessment of sea waves characteristics and power. The used data covers the period from 2012 to 2014. The data used are significant wave height (swh), mean wave period (mwp) and wave direction taken at six hourly intervals, at seven chosen stations, and at grid points covering the Egyptian waters. The wave power (wp) formula was used to calculate energy flux. Descriptive statistical analysis including monthly means and standard deviations of the swh, mwp, and wp. The percentiles of wave heights and their corresponding power are done, as a tool of choice of the best technology suitable for the site. The surfer is used to show spatial distributions of wp. The analysis of data at chosen 7 stations determined the potential of wp off important Egyptian cities. Offshore of Al Saloum and Marsa Matruh, the highest wp occurred in January and February (16.93-18.05) ± (18.08-22.12) kw/m while the lowest occurred in June and October (1.49-1.69) ± (1.45-1.74) kw/m. In front of Alexandria and Rashid, the highest wp occurred in January and February (16.93-18.05) ± (18.08-22.12) kw/m while the lowest occurred in June and September (1.29-2.01) ± (1.31-1.83) kw/m. In front of Damietta and Port Said, the highest wp occurred in February (14.29-17.61) ± (21.61-27.10) kw/m and the lowest occurred in June (0.94-0.96) ± (0.71-0.72) kw/m. In winter, the probabilities of waves higher than 0.8 m in percentage were, at Al Saloum and Marsa Matruh (76.56-80.33) ± (11.62-12.05), at Alexandria and Rashid (73.67-74.79) ± (16.21-18.59) and at Damietta and Port Said (66.28-68.69) ± (17.88-17.90). In spring, the percentiles were, at Al Saloum and Marsa Matruh, (48.17-50.92) ± (5.79-6.56), at Alexandria and Rashid, (39.38-43.59) ± (9.06-9.34) and at Damietta and Port Said, (31.59-33.61) ± (10.72-11.25). In summer, the probabilities were, at Al Saloum and Marsa Matruh (57.70-66.67) ± (4.87-6.83), at Alexandria and Rashid (59.96-65.13) ± (9.14-9.35) and at Damietta and Port Said (46.38-49.28) ± (10.89-11.47). In autumn, the probabilities were, at Al Saloum and Marsa Matruh (58.75-59.56) ± (2.55-5.84), at Alexandria and Rashid (47.78-52.13) ± (3.11-7.08) and at Damietta and Port Said (41.16-42.52) ± (7.52-8.34).

Keywords: distribution of sea waves energy, Egyptian Mediterranean waters, waves characteristics, waves power

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Authors: M. Yusefzad

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Law of energy conservation is one of the fundamental laws of physics. Energy is conserved, and the total amount of energy is constant. It can be transferred from one object to another and changed from one state to another. However, in the case of wave interference, this law faces important contradictions. Based on the presented mathematical relationship in this paper, it seems that validity of this law depends on the path of energy wave, like light, in which it is located. In this paper, by using some fundamental concepts in physics like the constancy of the electromagnetic wave speed in a specific media and wave theory of light, it will be shown that law of energy conservation is not valid in every condition and in some circumstances, it is possible to increase energy of a system with a determined amount of energy without any input.

Keywords: power, law of energy conservation, electromagnetic wave, interference, Maxwell’s equations

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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 508

Authors: M. Abderrahmane Mograne, Didier Laux, Jean-Yves Ferrandis

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Rheological characterizations of complex liquids like polymer solutions present an important scientific interest for a lot of researchers in many fields as biology, food industry, chemistry. In order to establish master curves (elastic moduli vs frequency) which can give information about microstructure, classical rheometers or viscometers (such as Couette systems) are used. For broadband characterization of the sample, temperature is modified in a very large range leading to equivalent frequency modifications applying the Time Temperature Superposition principle. For many liquids undergoing phase transitions, this approach is not applicable. That is the reason, why the development of broadband spectroscopic methods around room temperature becomes a major concern. In literature many solutions have been proposed but, to our knowledge, there is no experimental bench giving the whole rheological characterization for frequencies about a few Hz (Hertz) to many MHz (Mega Hertz). Consequently, our goal is to investigate in a nondestructive way in very broadband frequency (A few Hz – Hundreds of MHz) rheological properties using longitudinal ultrasonic waves (L waves), a unique experimental bench and a specific container for the liquid: a test tube. More specifically, we aim to estimate the three viscosities (longitudinal, shear and bulk) and the complex elastic moduli (M*, G* and K*) respectively longitudinal, shear and bulk moduli. We have decided to use only L waves conditioned in two ways: bulk L wave in the liquid or guided L waves in the tube test walls. In this paper, we will present first results for very low frequencies using the ultrasonic tracking of a falling ball in the test tube. This will lead to the estimation of shear viscosity from a few mPa.s to a few Pa.s (Pascal second). Corrections due to the small dimensions of the tube will be applied and discussed regarding the size of the falling ball. Then the use of bulk L wave’s propagation in the liquid and the development of a specific signal processing in order to assess longitudinal velocity and attenuation will conduct to the longitudinal viscosity evaluation in the MHz frequency range. At last, the first results concerning the propagation, the generation and the processing of guided compressional waves in the test tube walls will be discussed. All these approaches and results will be compared to standard methods available and already validated in our lab.

Keywords: nondestructive measurement for liquid, piezoelectric transducer, ultrasonic longitudinal waves, viscosities

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Authors: Arcady Ponosov, Ramazan Kadiev

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Input-to-State Stability (ISS) is widely used in deterministic control theory but less known in the stochastic case. Roughly speaking, the theory explains when small perturbations of the right-hand sides of the system on the entire semiaxis cause only small changes in the solutions of the system, again on the entire semiaxis. This property is crucial in many applications. In the report, we explain how to define and study ISS for systems of linear stochastic differential equations with or without delays. The central result connects ISS with the property of Lyapunov stability. This relationship is well-known in the deterministic setting, but its stochastic version is new. As an application, a method of studying asymptotic Lyapunov stability for stochastic delay equations is described and justified. Several examples are provided that confirm the efficiency and simplicity of the framework.

Keywords: asymptotic stability, delay equations, operator methods, stochastic perturbations

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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: Mei-Hsiu Chi, Jyh-Yang Wu, Sheng-Gwo Chen

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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.

Keywords: closed surfaces, high-order approachs, numerical solutions, reaction-diffusion systems

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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 216

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 501