Search results for: Dirichlet second order boundary problem

Authors: Mircea Ivanescu, Nirvana Popescu, Decebal Popescu, Dorin Popescu

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This paper addresses the control problem of a class of hyper-redundant arms. In order to avoid discrepancy between the mathematical model and the actual dynamics, the dynamic model with uncertain parameters of this class of manipulators is inferred. A procedure to design a feedback controller which stabilizes the uncertain system has been proposed. A PD boundary control algorithm is used in order to control the desired position of the manipulator. This controller is easy to implement from the point of view of measuring techniques and actuation. Numerical simulations verify the effectiveness of the presented methods. In order to verify the suitability of the control algorithm, a platform with a 3D flexible manipulator has been employed for testing. Experimental tests on this platform illustrate the applications of the techniques developed in the paper.

Keywords: distributed model, flexible manipulator, observer, robot control

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Authors: Parveen Kumar, J. K. Juneja, Chandra Prakash, K. K. Raina

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A series of polycrystalline ferroelectric ceramics with compositional formula Ba0.80-xSmxPb0.20Ti0.90Zr0.10O3 with x varying from 0 to 0.01 in the steps of 0.0025 has been prepared by solid state reaction method. The dielectric constant and tangent loss was measured as a function of frequency from 100Hz to 1MHz at different temperatures (200-500oC). The electrical behavior was then investigated using complex impedance spectroscopy (CIS) technique. From the CIS study, it has been found that there is a contribution of both grain and grain boundary in the electrical behavior of such ceramics. Grain and grain boundary resistivity and capacitance were calculated at different temperature using CIS technique. The present paper is about the discussion of grain and grain boundary contribution towards the electrical properties of Sm modified BaTiO3 based ceramics at high temperature.

Keywords: grain, grain boundary, impedance, dielectric

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Authors: David Ming Liu, Benjamin Hirsch, Bashir Aden

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Syndromic surveillance is to detect or predict disease outbreaks through the analysis of medical sources of data. Using social media data like tweets to do syndromic surveillance becomes more and more popular with the aid of open platform to collect data and the advantage of microblogging text and mobile geographic location features. In this paper, a Syndromic Surveillance Framework is presented with machine learning kernel using tweets data analytics. Influenza and the three cities Abu Dhabi, Al Ain and Dubai of United Arabic Emirates are used as the test disease and trial areas. Hospital cases data provided by the Health Authority of Abu Dhabi (HAAD) are used for the correlation purpose. In our model, Latent Dirichlet allocation (LDA) engine is adapted to do supervised learning classification and N-Fold cross validation confusion matrix are given as the simulation results with overall system recall 85.595% performance achieved.

Keywords: Syndromic surveillance, Tweets, Machine Learning, data mining, Latent Dirichlet allocation (LDA), Influenza

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Authors: N. M. Arifin, S. P. M. Isa, R. Nazar, N. Bachok, F. M. Ali, I. Pop

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In this paper, the steady forced convection boundary layer flow of a Casson fluid past a moving permeable semi-infinite flat plate beneath a uniform free stream is investigated. The mathematical problem reduces to a pair of noncoupled ordinary differential equations by similarity transformation, which is then solved numerically using the shooting method. Both the cases when the plate moves into or out of the origin are considered. Effects of the non-Newtonian (Casson) parameter, moving parameter, suction or injection parameter and Eckert number on the flow and heat transfer characteristics are thoroughly examined. Dual solutions are found to exist for each value of the governing parameters.

Keywords: forced convection, Casson fluids, moving flat plate, boundary layer

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Authors: Reza Mohammadi

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Using quartic spline, we develop a method for numerical solution of singularly perturbed two-point boundary-value problems. The purposed method is fourth-order accurate and applicable to problems both in singular and non-singular cases. The convergence analysis of the method is given. The resulting linear system of equations has been solved by using a tri-diagonal solver. We applied the presented method to test problems which have been solved by other existing methods in references, for comparison of presented method with the existing methods. Numerical results are given to illustrate the efficiency of our methods.

Keywords: second-order ordinary differential equation, singularly-perturbed, quartic spline, convergence analysis

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Authors: Suleiman Bashir Adamu, Lawan Sani Taura

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We study the role of boundary conditions via -symmetric quantum mechanics, where denotes parity operator and denotes time reversal operator. Using the one-dimensional Schrödinger Hamiltonian for a free particle in an infinite square well, we introduce symmetric boundary conditions. We find solutions of the 1D Klein-Gordon equation for a free particle in an infinite square well with Hermitian boundary and symmetry boundary conditions, where in both cases the energy eigenvalues and eigenfunction, respectively, are obtained.

Keywords: Eigenvalues, Eigenfunction, Hamiltonian, Klein- Gordon equation, PT-symmetric quantum mechanics

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Authors: M. Eskandarighadi, C. R. McGann

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It is observed from past experiences of earthquakes that local site conditions can significantly affect the strong ground motion characteristicssuch as frequency content, amplitude, and duration of seismic waves. The most common method for investigating site response is one-dimensional seismic site response analysis. The infinite horizontal length of the model and the homogeneous characteristic of the soil are crucial assumptions of this method. One boundary condition that can be used in the sides is tying the sides horizontally for vertical 1D wave propagation. However, 1D analysis cannot account for the 2D nature of wave propagation in the condition where the soil profile is not fully horizontal or has heterogeneity within layers. Therefore, 2D seismic site response analysis can be used to take all of these limitations into account for a better understanding of local site conditions. Different types of boundary conditions can be appliedin 2D site response models, such as tied boundary condition, massive columns, and free-field boundary condition. The tied boundary condition has been used in 1D analysis, which is useful for 1D wave propagation. Employing two massive columns at the sides is another approach for capturing the 2D nature of wave propagation. Free-field boundary condition can simulate the free-field motion that would exist far from the domain of interest. The goal for free-field boundary condition is to minimize the unwanted reflection from sides. This research focuses on the comparison between these methods with examples and discusses the details and limitations of each of these boundary conditions.

Keywords: boundary condition, free-field, massive columns, opensees, site response analysis, wave propagation

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Authors: Chinh Phuong Do

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Dynamic analysis of slope under seismic condition requires the elimination of spurious reflection at the bounded domain. This paper studies the performances of wave transmitting boundaries, including the standard viscous boundary and the viscoelastic boundary to the material point method (MPM) framework. First, analytical derivations of these non-reflecting conditions particularly to the implicit MPM are presented. Then, a number of benchmark and geotechnical examples will be shown. Overall, the results agree well with analytical solutions, indicating the ability to accurately simulate the radiation at the bounded domain.

Keywords: dynamic analysis, implicit, MPM, non-reflecting boundary

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Authors: Sidi Yang, Haiyi Zhang

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Twitter is a microblogging platform, where millions of users daily share their attitudes, views, and opinions. Using a probabilistic Latent Dirichlet Allocation (LDA) topic model to discern the most popular topics in the Twitter data is an effective way to analyze a large set of tweets to find a set of topics in a computationally efficient manner. Sentiment analysis provides an effective method to show the emotions and sentiments found in each tweet and an efficient way to summarize the results in a manner that is clearly understood. The primary goal of this paper is to explore text mining, extract and analyze useful information from unstructured text using two approaches: LDA topic modelling and sentiment analysis by examining Twitter plain text data in English. These two methods allow people to dig data more effectively and efficiently. LDA topic model and sentiment analysis can also be applied to provide insight views in business and scientific fields.

Keywords: text mining, Twitter, topic model, sentiment analysis

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Authors: Arturo Ayala-Hernandez, Humberto Hijar

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We propose a new alternative method for imposing fluid-solid boundary conditions in simulations of Multiparticle Collision Dynamics. Our method is based on the introduction of an explicit potential force acting between the fluid particles and a surface representing a solid boundary. We show that our method can be used in simulations of plane Poiseuille flows. Important quantities characterizing the flow and the fluid-solid interaction like the slip coefficient at the solid boundary and the effective viscosity of the fluid, are measured in terms of the set of independent parameters defining the numerical implementation. We find that our method can be used to simulate the correct hydrodynamic flow within a wide range of values of these parameters.

Keywords: Multiparticle Collision Dynamics, fluid-solid, boundary conditions, molecular dynamics

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Authors: Reza Mohammadi

Abstract:

Using quartic spline, we develop a method for numerical solution of singularly perturbed two-point boundary-value problems. The purposed method is fourth-order accurate and applicable to problems both in singular and non-singular cases. The convergence analysis of the method is given. The resulting linear system of equations has been solved by using a tri-diagonal solver. We applied the presented method to test problems which have been solved by other existing methods in references, for comparison of presented method with the existing methods. Numerical results are given to illustrate the efficiency of our methods.

Keywords: second-order ordinary differential equation, singularly-perturbed, quartic spline, convergence analysis

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Authors: Ranjith Maniyeri, Ahamed C. Saleel

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Two-dimensional fluid flow over a stationary circular cylinder is one of the bench mark problem in the field of fluid-structure interaction in computational fluid dynamics (CFD). Motivated by this, in the present work, a two-dimensional computational model is developed using an improved version of immersed boundary method which combines the feedback forcing scheme of the virtual boundary method with Peskin’s regularized delta function approach. Lagrangian coordinates are used to represent the cylinder and Eulerian coordinates are used to describe the fluid flow. A two-dimensional Dirac delta function is used to transfer the quantities between the sold to fluid domain. Further, continuity and momentum equations governing the fluid flow are solved using fractional step based finite volume method on a staggered Cartesian grid system. The developed code is validated by comparing the values of drag coefficient obtained for different Reynolds numbers with that of other researcher’s results. Also, through numerical simulations for different Reynolds numbers flow behavior is well captured. The stability analysis of the improved version of immersed boundary method is tested for different values of feedback forcing coefficients.

Keywords: Feedback Forcing Scheme, Finite Volume Method, Immersed Boundary Method, Navier-Stokes Equations

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Authors: M. Abir Hossain, M. Shahjada Tarafder

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This paper deals with the analysis of potential flow past two-dimensional body by discretizing the body into panels where the Laplace equation was applied to each panel. The Laplace equation was solved at each panel by applying the boundary conditions. The boundary condition was applied at each panel to mathematically formulate the problem and then convert the problem into a computer-solvable problem. Kutta condition was applied at both the leading and trailing edges to see whether the condition is satisfied or not. Another approach that is applied for the analysis is Vortex Lattice Method (VLM). A vortex ring is considered at each control point. Using the Biot-Savart Law the strength at each control point is calculated and hence the pressure differentials are measured. For the comparison of the analytic result with the experimental result, different NACA section hydrofoil is used. The analytic result of NACA 0012 and NACA 0015 are compared with the experimental result of Abbott and Doenhoff and found significant conformity with the achieved result.

Keywords: Kutta condition, Law of Biot-Savart, pressure differentials, potential flow, vortex lattice method

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Authors: Mrinal Jana, Geetanjali Panda

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In this paper a methodology is developed to solve a nonlinear fractional programming problem in which the coefficients of the objective function and constraints are interval parameters. This model is transformed into a general optimization problem and relation between the original problem and the transformed problem is established. Finally the proposed methodology is illustrated through a numerical example.

Keywords: fractional programming, interval valued function, interval inequalities, partial order relation

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Authors: Imen Debbabi, Hédi BelHadjSalah

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The Improved Element Free Galerkin (IEFG) method is presented to treat the steady states and the transient heat transfer problems. As a result of a combination between the Improved Moving Least Square (IMLS) approximation and the Element Free Galerkin (EFG) method, the IEFG's shape functions don't have the Kronecker delta property and the penalty method is used to impose the Dirichlet boundary conditions. In this paper, two heat transfer problems, transient and steady states, are studied to improve the efficiency of this meshfree method for 2D heat transfer problems. The performance of the IEFG method is shown using the comparison between numerical and analytic results.

Keywords: meshfree methods, the Improved Moving Least Square approximation (IMLS), the Improved Element Free Galerkin method (IEFG), heat transfer problems

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Authors: Si Abdallah Mayouf

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In this work, the effects of the wavy surface on free convection heat transfer boundary layer flow between two parallel wavy plates have been studied numerically. The two plates are considered at a constant temperature. The equations and the boundary conditions are discretized by the finite difference scheme and solved numerically using the Gauss-Seidel algorithm. The important parameters in this problem are the amplitude of the wavy surfaces and the distance between the two wavy plates. Results are presented as velocity profiles, temperature profiles and local Nusselt number according to the important parameters.

Keywords: free convection, wavy surface, parallel plates, fluid dynamics

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Authors: Ching-Shoei Chiang

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The Malfatti’s Problem is to ask for fitting 3 circles into a right triangle such that they are tangent to each other, and each circle is also tangent to a pair of the triangle’s side. This problem has been extended to any triangle (called general Malfatti’s Problem). Furthermore, the problem has been extended to have 1+2+…+n circles, we call it extended general Malfatti’s problem, these circles whose tangency graph, using the center of circles as vertices and the edge connect two circles center if these two circles tangent to each other, has the structure as Pascal’s triangle, and the exterior circles of these circles tangent to three sides of the triangle. In the extended general Malfatti’s problem, there are closed-form solutions for n=1, 2, and the problem becomes complex when n is greater than 2. In solving extended general Malfatti’s problem (n>2), we initially give values to the radii of all circles. From the tangency graph and current radii, we can compute angle value between two vectors. These vectors are from the center of the circle to the tangency points with surrounding elements, and these surrounding elements can be the boundary of the triangle or other circles. For each circle C, there are vectors from its center c to its tangency point with its neighbors (count clockwise) pi, i=0, 1,2,..,n. We add all angles between cpi to cp(i+1) mod (n+1), i=0,1,..,n, call it sumangle(C) for circle C. Using sumangle(C), we can reduce/enlarge the radii for all circles in next iteration, until sumangle(C) is equal to 2πfor all circles. With a similar idea, this paper proposed an algorithm to find the radii of circles whose tangency has the structure of Pascal’s triangle, and the exterior circles of these circles are tangent to the unit Realeaux Triangle.

Keywords: Malfatti’s problem, geometric constraint solver, computer-aided geometric design, circle packing, data visualization

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Authors: Pradeepa Teegala, Ramreddy Chitteti

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This article analyzes the mixed convection flow of chemically reacting micropolar fluid over a truncated cone embedded in non-Darcy porous medium with convective boundary condition. In addition, heat generation/absorption and Joule heating effects are taken into consideration. The similarity solution does not exist for this complex fluid flow problem, and hence non-similarity transformations are used to convert the governing fluid flow equations along with related boundary conditions into a set of nondimensional partial differential equations. Many authors have been applied the spectral quasi-linearization method to solve the ordinary differential equations, but here the resulting nonlinear partial differential equations are solved for non-similarity solution by using a recently developed method called the spectral quasi-linearization method (SQLM). Comparison with previously published work on special cases of the problem is performed and found to be in excellent agreement. The effect of pertinent parameters namely, Biot number, mixed convection parameter, heat generation/absorption, Joule heating, Forchheimer number, chemical reaction, micropolar and magnetic field on physical quantities of the flow are displayed through graphs and the salient features are explored in detail. Further, the results are analyzed by comparing with two special cases, namely, vertical plate and full cone wherever possible.

Keywords: chemical reaction, convective boundary condition, joule heating, micropolar fluid, mixed convection, spectral quasi-linearization method

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Authors: Shunichi Ohmori, Sirawadee Arunyanart, Kazuho Yoshimoto

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We consider a periodic review inventory control problem of minimizing production cost, inventory cost, and lost-sales under demand uncertainty, in which product demands are not specified exactly and it is only known to belong to a given uncertainty set, yet the constraints must hold for possible values of the data from the uncertainty set. We propose a robust optimization formulation for obtaining lowest cost possible and guaranteeing the feasibility with respect to range of order quantity and inventory level under demand uncertainty. Our formulation is based on the adaptive robust counterpart, which suppose order quantity is affine function of past demands. We derive certainty equivalent problem via second-order cone programming, which gives 'not too pessimistic' worst-case.

Keywords: robust optimization, inventory control, supply chain managment, second-order programming

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Authors: K. Manmi, Q. X. Wang

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This paper investigates microbubble dynamics subject to ultrasound in a weakly viscous fluid near a rigid boundary. The phenomenon is simulated using a boundary integral method. The weak viscous effects are incorporated into the model through the normal stress balance across the bubble surface. The model agrees well with the Rayleigh-Plesset equation for a spherical bubble for several cycles. The effects of the fluid viscosity in the bubble dynamics are analyzed, including jet development, centroid movement and bubble volume.

Keywords: microbubble dynamics, bubble jetting, viscous effect, boundary integral method

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Authors: Thorsten Herrmann, Alexander Laukemann, Hansgeorg Binz, Daniel Roth

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For the analysis of already identified and existing problems, the pertinent literature provides a comprehensive collection of approaches as well as methods in order to analyze the problems in detail. But coming up with problems, which are assets worth pursuing further, is often challenging. However, the importance of well-formulated problem ideas and their influence of subsequent creative processes are incontestable and proven. In order to meet the covered challenges, the Institute for Engineering Design and Industrial Design (IKTD) developed the Emoji Method. This paper presents the Emoji Method, which support designers to generate problem ideas in a structured way. Considering research findings from knowledge management and innovation management, research into emojis and emoticons reveal insights by means of identifying and formulating problem ideas within the early design phase. The simple application and the huge supporting potential of the Emoji Method within the early design phase are only few of the many successful results of the conducted evaluation. The Emoji Method encourages designers to identify problem ideas and describe them in a structured way in order to start focused with generating solution ideas for the revealed problem ideas.

Keywords: emojis, problem ideas, innovation management, knowledge management

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Authors: Carlos A. Vega-Posada, Jeisson Alejandro Higuita-Villa, Julio C. Saldarriaga-Molina

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This paper presents a simplified analytical approach to conduct elastic stability and second-order lateral stiffness analyses of beam-column elements (i.e., piles) with generalized end-boundary conditions embedded on a homogeneous or non-homogeneous Pasternak foundation. The solution is derived using the well-known Differential Transformation Method (DTM), and it consists simply of solving a system of two linear algebraic equations. Using other conventional approaches to solve the governing differential equation of the proposed element can be cumbersome and the solution challenging to implement, especially when the non-homogeneity of the soil is considered. The proposed formulation includes the effects of i) any rotational or lateral transverse spring at the ends of the pile, ii) any external transverse load acting along the pile, iii) soil non-homogeneity, and iv) the second-parameter of the elastic foundation (i.e., shear layer connecting the springs at the top). A parametric study is conducted to investigate the effects of different modulus of subgrade reactions, degrees of non-homogeneities, and intermediate end-boundary conditions on the pile response. The same set of equations can be used to conduct both elastic stability and static analyses. Comprehensive examples are presented to show the simplicity and practicability of the proposed method.

Keywords: elastic stability, second-order lateral stiffness, soil-non-homogeneity, pile analysis

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Authors: Shubham Jaiswal

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In this study, the numerical solution of two-dimensional solute transport system in a homogeneous porous medium of finite-length is obtained. The considered transport system have the terms accounting for advection, dispersion and first-order decay with first-type boundary conditions. Initially, the aquifer is considered solute free and a constant input-concentration is considered at inlet boundary. The solution is describing the solute concentration in rectangular inflow-region of the homogeneous porous media. The numerical solution is derived using a powerful method viz., spectral collocation method. The numerical computation and graphical presentations exhibit that the method is effective and reliable during solution of the physical model with complicated boundary conditions even in the presence of reaction term.

Keywords: two-dimensional solute transport system, spectral collocation method, Chebyshev polynomials, Chebyshev differentiation matrix

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Authors: E. Sener, O. Isik, E. Eroglu, U. Sahin

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The main idea is to solve the system of Maxwell’s equations in accordance with the causality principle to get the energy quantities via Airy functions in a hollow rectangular waveguide. We used the evolutionary approach to electromagnetics that is an analytical time-domain method. The boundary-value problem for the system of Maxwell’s equations is reformulated in transverse and longitudinal coordinates. A self-adjoint operator is obtained and the complete set of Eigen vectors of the operator initiates an orthonormal basis of the solution space. Hence, the sought electromagnetic field can be presented in terms of this basis. Within the presentation, the scalar coefficients are governed by Klein-Gordon equation. Ultimately, in this study, time-domain waveguide problem is solved analytically in accordance with the causality principle. Moreover, the graphical results are visualized for the case when the energy and surplus of the energy for the time-domain waveguide modes are represented via airy functions.

Keywords: airy functions, Klein-Gordon Equation, Maxwell’s equations, Surplus of energy, wave boundary operators

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Authors: Junling Li, Fang Meng, Yichun Zhang

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Image saliency detection has been long studied, while several challenging problems are still unsolved, such as detecting saliency inaccurately in complex scenes or suppressing salient objects in the image borders. In this paper, we propose a new saliency detection algorithm in order to solving these problems. We represent the image as a graph with superixels as nodes. By considering appearance similarity between the boundary and the background, the proposed method chooses non-saliency boundary nodes as background priors to construct the background probability model. The probability that each node belongs to the model is computed, which measures its similarity with backgrounds. Thus we can calculate saliency by the transformed probability as a metric. We compare our algorithm with ten-state-of-the-art salient detection methods on the public database. Experimental results show that our simple and effective approach can attack those challenging problems that had been baffling in image saliency detection.

Keywords: visual saliency, background probability, boundary knowledge, background priors

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Authors: M. Rezki, A. Belaidi

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This paper deals with a method of learning to solve a real problem in biomedical engineering from a technical study of muscle fatigue. Electromyography (EMG) is a technique for evaluating and recording the electrical activity produced by skeletal muscles (viewpoint: anatomical and physiological). EMG is used as a diagnostics tool for identifying neuromuscular diseases, assessing low-back pain and muscle fatigue in general. In order to study the EMG signal for detecting fatigue in a muscle, we have taken a real problem which touches the tramway conductor the handle bar. For the study, we have used a typical autonomous platform in order to get signals at real time. In our case study, we were confronted with complex problem to do our experiments in a tram. This type of problem is recurring among students. To teach our students the method to solve this kind of problem, we built a similar system. Through this study, we realized a lot of objectives such as making the equipment for simulation, the study of detection of muscle fatigue and especially how to manage a study of biomedical looking.

Keywords: EMG, health platform, conductor’s tram, muscle fatigue

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Authors: Roslinda Nazar, Ezad Hafidz Hafidzuddin, Norihan M. Arifin, Ioan Pop

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In this paper, the problem of steady laminar boundary layer flow and heat transfer over a permeable exponentially stretching/shrinking sheet with generalized slip velocity is considered. The similarity transformations are used to transform the governing nonlinear partial differential equations to a system of nonlinear ordinary differential equations. The transformed equations are then solved numerically using the bvp4c function in MATLAB. Dual solutions are found for a certain range of the suction and stretching/shrinking parameters. The effects of the suction parameter, stretching/shrinking parameter, velocity slip parameter, critical shear rate, and Prandtl number on the skin friction and heat transfer coefficients as well as the velocity and temperature profiles are presented and discussed.

Keywords: boundary layer, exponentially stretching/shrinking sheet, generalized slip, heat transfer, numerical solutions

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Authors: Yuan Yan Tang, Lina Yang, Hong Li

Abstract:

Harmonic model is a very important approximation for the image transform. The harmanic model converts an image into arbitrary shape; however, this mode cannot be described by any fixed functions in mathematics. In fact, it is represented by partial differential equation (PDE) with boundary conditions. Therefore, to develop an efficient method to solve such a PDE is extremely significant in the image transform. In this paper, a novel Integral Equation-Wavelet based method is presented, which consists of three steps: (1) The partial differential equation is converted into boundary integral equation and representation by an indirect method. (2) The boundary integral equation and representation are changed to plane integral equation and representation by boundary measure formula. (3) The plane integral equation and representation are then solved by a method we call wavelet collocation. Our approach has two main advantages, the shape of an image is arbitrary and the program code is independent of the boundary. The performance of our method is evaluated by numerical experiments.

Keywords: harmonic model, partial differential equation (PDE), integral equation, integral representation, boundary measure formula, wavelet collocation

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Authors: Alexander Norbach

Abstract:

The script in this paper describes the use of advanced simulation environment using electronic systems (Microcontroller, Operational Amplifiers, and FPGA). The simulation may be used for all dynamic systems with the diffusion and the ionisation behaviour also. By additionally required observer structure, the system works with parallel real-time simulation based on diffusion model and the state-space representation for other dynamics. The proposed deposited model may be used for electrodynamic effects, including ionising effects and eddy current distribution also. With the script and proposed method, it is possible to calculate the spatial distribution of the electromagnetic fields in real-time. For further purpose, the spatial temperature distribution may be used also. With upon system, the uncertainties, unknown initial states and disturbances may be determined. This provides the estimation of the more precise system states for the required system, and additionally, the estimation of the ionising disturbances that occur due to radiation effects. The results have shown that a system can be also developed and adopted specifically for space systems with the real-time calculation of the radiation effects only. Electronic systems can take damage caused by impacts with charged particle flux in space or radiation environment. In order to be able to react to these processes, it must be calculated within a shorter time that ionising radiation and dose is present. All available sensors shall be used to observe the spatial distributions. By measured value of size and known location of the sensors, the entire distribution can be calculated retroactively or more accurately. With the formation, the type of ionisation and the direct effect to the systems and thus possible prevent processes can be activated up to the shutdown. The results show possibilities to perform more qualitative and faster simulations independent of kind of systems space-systems and radiation environment also. The paper gives additionally an overview of the diffusion effects and their mechanisms. For the modelling and derivation of equations, the extended current equation is used. The size K represents the proposed charge density drifting vector. The extended diffusion equation was derived and shows the quantising character and has similar law like the Klein-Gordon equation. These kinds of PDE's (Partial Differential Equations) are analytically solvable by giving initial distribution conditions (Cauchy problem) and boundary conditions (Dirichlet boundary condition). For a simpler structure, a transfer function for B- and E- fields was analytically calculated. With known discretised responses g₁(k·Ts) and g₂(k·Ts), the electric current or voltage may be calculated using a convolution; g₁ is the direct function and g₂ is a recursive function. The analytical results are good enough for calculation of fields with diffusion effects. Within the scope of this work, a proposed model of the consideration of the electromagnetic diffusion effects of arbitrary current 'waveforms' has been developed. The advantage of the proposed calculation of diffusion is the real-time capability, which is not really possible with the FEM programs available today. It makes sense in the further course of research to use these methods and to investigate them thoroughly.

Keywords: advanced observer, electrodynamics, systems, diffusion, partial differential equations, solver

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Authors: Samuele Viaro, Pierre Ricco

Abstract:

Görtler instabilities generate in boundary layers from an unbalance between pressure and centrifugal forces caused by concave surfaces. Their spatial streamwise evolution influences transition to turbulence. It is therefore important to understand even the early stages where perturbations, still small, grow linearly and could be controlled more easily. This work presents a rigorous theoretical framework for compressible flows using the linearized unsteady boundary region equations, where only the streamwise pressure gradient and streamwise diffusion terms are neglected from the full governing equations of fluid motion. Boundary and initial conditions are imposed through an asymptotic analysis in order to account for the interaction of the boundary layer with free-stream turbulence. The resulting parabolic system is discretize with a second-order finite difference scheme. Realistic flow parameters are chosen from wind tunnel studies performed at supersonic and subsonic conditions. The Mach number ranges from 0.5 to 8, with two different radii of curvature, 5 m and 10 m, frequencies up to 2000 Hz, and vortex spanwise wavelengths from 5 mm to 20 mm. The evolution of the perturbation flow is shown through velocity, temperature, pressure profiles relatively close to the leading edge, where non-linear effects can still be neglected, and growth rate. Results show that a global stabilizing effect exists with the increase of Mach number, frequency, spanwise wavenumber and radius of curvature. In particular, at high Mach numbers curvature effects are less pronounced and thermal streaks become stronger than velocity streaks. This increase of temperature perturbations saturates at approximately Mach 4 flows, and is limited in the early stage of growth, near the leading edge. In general, Görtler vortices evolve closer to the surface with respect to a flat plate scenario but their location shifts toward the edge of the boundary layer as the Mach number increases. In fact, a jet-like behavior appears for steady vortices having small spanwise wavelengths (less than 10 mm) at Mach 8, creating a region of unperturbed flow close to the wall. A similar response is also found at the highest frequency considered for a Mach 3 flow. Larger vortices are found to have a higher growth rate but are less influenced by the Mach number. An eigenvalue approach is also employed to study the amplification of the perturbations sufficiently downstream from the leading edge. These eigenvalue results are compared with the ones obtained through the initial value approach with inhomogeneous free-stream boundary conditions. All of the parameters here studied have a significant influence on the evolution of the instabilities for the Görtler problem which is indeed highly dependent on initial conditions.

Keywords: compressible boundary layers, Görtler instabilities, receptivity, turbulence transition

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