Search results for: morphotropic phase boundary (MPB)

Authors: Ajay R, Rammohan B, Sridhar K S S, Gurusharan N

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The objective of the work is to develop a numerical method to solve the inverse mode shape problem by determining the cross-sectional area of a structure for the desired mode shape via the vibration response study of the humerus bone, which is in the form of a cantilever beam with anisotropic material properties. The humerus bone is the long bone in the arm that connects the shoulder to the elbow. The mode shape is assumed to be a higher-order polynomial satisfying a prescribed set of boundary conditions to converge the numerical algorithm. The natural frequency and the mode shapes are calculated for different boundary conditions to find the cross-sectional area of humerus bone from Eigenmode shape with the aid of the inverse mode shape algorithm. The cross-sectional area of humerus bone validates the mode shapes of specific boundary conditions. The numerical method to solve the inverse mode shape problem is validated in the biomedical application by finding the cross-sectional area of a humerus bone in the human arm.

Keywords: Cross-sectional area, Humerus bone, Inverse mode shape problem, Mode shape

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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: Abid Boudiar

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We propose a simple model to obtain an exact expression of Tc/(Tc,max) for the temperature-doping phase diagram of superconducting cuprates. We showed that our model predicted most phase diagram scenario. We found the exact special doping points p(opt), p(qcp) and an accurate E(g,max). Some other properties such as the stripes length 100.1°A and the energy gap in cuprates chain
6meV can also be calculated exactly. Another interesting consequence of this simple picture is the new magic numbers and the ability to express everything using a (Tc,p) diagram via the golden ratio.

Keywords: superconducting cuprates, phase, pseudogap, hole doping, strips, golden ratio, soliton

Procedia PDF Downloads 446

Authors: J. S. Kim, N. P. Hong

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In this paper, a CMOS vector modulator designed for wireless backhaul system based on 802.11ac is presented. A poly phase filter and sign select switches yield two orthogonal signal paths. Two variable gain amplifiers with strongly reduced phase shift of only ±5 ° are used to weight these paths. It has a phase control range of 360 ° and a gain range of -10 dB to 10 dB. The current drawn from a 1.2 V supply amounts 20.4 mA. Using a 0.13 mm technology, the chip die area amounts 1.47x0.75 mm².

Keywords: CMOS, phase shifter, backhaul, 802.11ac

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Authors: András Rövid, Takeshi Hashimoto

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The paper focuses on the problem of the point correspondence matching in stereo images. The proposed matching algorithm is based on the combination of simpler methods such as normalized sum of squared differences (NSSD) and a more complex phase correlation based approach, by considering the noise and other factors, as well. The speed of NSSD and the preciseness of the phase correlation together yield an efficient approach to find the best candidate point with sub-pixel accuracy in stereo image pairs. The task of the NSSD in this case is to approach the candidate pixel roughly. Afterwards the location of the candidate is refined by an enhanced phase correlation based method which in contrast to the NSSD has to run only once for each selected pixel.

Keywords: stereo matching, sub-pixel accuracy, phase correlation, SVD, NSSD

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Authors: Nima Shafaghi, Gunay Anlaş, C. Can Aydiner

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A realistic understanding of martensitic phase transition under complex stress states is key for accurately describing the mechanical behavior of shape memory alloys (SMAs). Particularly regarding the sharply changing stress fields at the tip of a crack, the size, nature and shape of transformed zones are of great interest. There is significant variation among various analytical models in their predictions of the size and shape of the transformation zone. As the fully transformed region remains inside a very small boundary at the tip of the crack, experimental validation requires microscopic resolution. Here, the crack tip vicinity of NiTi compact tension specimen has been monitored in situ with microscopic image correlation with 20x magnification. With nominal 15 micrometer grains and 0.2 micrometer per pixel optical resolution, the strains at the crack tip are mapped with intra-grain detail. The transformation regions are then deduced using an equivalent strain formulation.

Keywords: digital image correlation, fracture, martensitic phase transition, mode I, NiTi, transformation zone

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Authors: Aliaksei Patsekha, Michael Hohenberger, Harald Raupenstrauch

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An effective emergency response to accidents with chemical, biological, radiological, nuclear, or explosive materials (CBRNE) that represent highly dynamic situations needs immediate actions within limited time, information and resources. The aim of the study is to provide the foundation for division of unsafe area into risk zones according to the impact of hazardous parameters (heat radiation, thermal dose, overpressure, chemical concentrations). A decision on the boundary values for three risk zones is based on the vulnerability analysis that covered a variety of accident scenarios containing the release of a toxic or flammable substance which either evaporates, ignites and/or explodes. Critical values are selected for the boundary definition of the Red, Orange and Yellow risk zones upon the examination of harmful effects that are likely to cause injuries of varying severity to people and different levels of damage to structures. The obtained results provide the basis for creating a comprehensive real-time risk map for a decision support at CBRNE operations.

Keywords: boundary values, CBRNE threats, decision making process, hazardous effects, vulnerability analysis, risk zones

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Authors: Walter Sebron, Hans Tschürtz, Peter Krebs

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The choice of applicable analysis methods in safety or systems engineering depends on the depth of knowledge about a system, and on the respective lifecycle phase. However, the analysis method chain still shows gaps as it should support system analysis during the lifecycle of a system from a rough concept in pre-project phase until end-of-life. This paper’s goal is to discuss an analysis method, the VISSE Shell Model Analysis (VISMA) method, which aims at closing the gap in the early system lifecycle phases, like the conceptual or pre-project phase, or the project start phase. It was originally developed to aid in the definition of the system boundary of electronic system parts, like e.g. a control unit for a pump motor. Furthermore, it can be also applied to non-electronic system parts. The VISMA method is a graphical sketch-like method that stratifies a system and its parts in inner and outer shells, like the layers of an onion. It analyses a system in a two-step approach, from the innermost to the outermost components followed by the reverse direction. To ensure a complete view of a system and its environment, the VISMA should be performed by (multifunctional) development teams. To introduce the method, a set of rules and guidelines has been defined in order to enable a proper shell build-up. In the first step, the innermost system, named system under consideration (SUC), is selected, which is the focus of the subsequent analysis. Then, its directly adjacent components, responsible for providing input to and receiving output from the SUC, are identified. These components are the content of the first shell around the SUC. Next, the input and output components to the components in the first shell are identified and form the second shell around the first one. Continuing this way, shell by shell is added with its respective parts until the border of the complete system (external border) is reached. Last, two external shells are added to complete the system view, the environment and the use case shell. This system view is also stored for future use. In the second step, the shells are examined in the reverse direction (outside to inside) in order to remove superfluous components or subsystems. Input chains to the SUC, as well as output chains from the SUC are described graphically via arrows, to highlight functional chains through the system. As a result, this method offers a clear and graphical description and overview of a system, its main parts and environment; however, the focus still remains on a specific SUC. It helps to identify the interfaces and interfacing components of the SUC, as well as important external interfaces of the overall system. It supports the identification of the first internal and external hazard causes and causal chains. Additionally, the method promotes a holistic picture and cross-functional understanding of a system, its contributing parts, internal relationships and possible dangers within a multidisciplinary development team.

Keywords: analysis methods, functional safety, hazard identification, system and safety engineering, system boundary definition, system safety

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Authors: Ebenezer Obaloluwa Olaniyi

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In this paper, an intelligent system has been designed to grade apple based on either its defective or healthy for production in food processing. This paper is segmented into two different phase. In the first phase, the image processing techniques were employed to extract the necessary features required in the apple. These techniques include grayscale conversion, segmentation where a threshold value is chosen to separate the foreground of the images from the background. Then edge detection was also employed to bring out the features in the images. These extracted features were then fed into the neural network in the second phase of the paper. The second phase is a classification phase where neural network employed to classify the defective apple from the healthy apple. In this phase, the network was trained with back propagation and tested with feed forward network. The recognition rate obtained from our system shows that our system is more accurate and faster as compared with previous work.

Keywords: image processing, neural network, apple, intelligent system

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Authors: Duanlei Yuan, Guangchao Yan, Zhanqing Chen, Xian Cheng

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This paper mainly focuses on the problem that high voltage circuit breaker’s closing and opening operation at random phase brings harmful electromagnetic transient effects on the power system. To repress the negative transient effects, a 35 kV SF6 phase-control circuit breaker equipped with electromagnetic force driving actuator is designed in this paper. Based on the constructed mathematical and structural models, the static magnetic field distribution and dynamic properties of the under loading actuator are simulated. The prototype of 35 kV SF6 phase-control circuit breaker is developed based on theories analysis and simulation. Tests are carried on to verify the operating reliability of the prototype. The developed circuit breaker can control its operating speed intelligently and switches with phase selection. Results of the tests and simulation prove that the phase-control circuit breaker is feasible for industrial applications.

Keywords: phase-control, circuit breaker, electromagnetic force driving actuator, tests and simulation

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Authors: Asmaa Zaraq

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In the present work we report X-ray powder diffraction measurements of SrCaCoTeO6 and SrCaNiTeO6, at different temperatures. The crystal structures at room temperature of both compounds are determined; and results showing the existence of high-temperature phase transitions in them are presented. Both compounds have double perovskite structure with 1:1 ordered arrangement of the B site cations. At room temperature their symmetries are described with the P21/n space group, that correspond to the (a+b-b-) tilt system. The evolution with temperature of the structure of both compounds shows the presence of three phase transitions: a continuous one, at 450 and 500 K, a discontinuous one, at 700 and 775 K, and a continuous one at 900 and 950 K for SrCaCoTeO6 and SrCaNiTeO6, respectively with the following phase-transition sequence: P21/n → I2/m → I4/m → Fm-3m.

Keywords: double perovskites, caracterisation DRX, transition de phase

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Authors: Avijit Datta

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We have presented a phase control scheme in population transfer using chirped laser fields. A chirped pulse can do population transfer from one level to another level via adiabatic rapid passage accessible by one photon dipole transition. We propose to use a pair of phase-locked chirped pulses of the same frequency w(t) instead of a singly chirped-pulse frequency w(t). Simultaneous action of phase controlled interference in addition to rapid adiabatic passages due to chirped pulses lead to phase control over this population transfer dynamics. We have demonstrated the proposed phase control scheme over the population distribution from the initial level X(v=0,j=0) to C(v=2,j=1) level of hydrogen molecule using a pair of phase-locked and similarly chirped laser pulses. We have extended this two-level system to three-level 1+1 ladder system of hydrogen molecule from X level to final J(v=2,j=2) level via C intermediate level using two pairs of laser pulses having frequencies w(t) and w'(t) respectively and obtained laudable control over the population distribution among three levels. We also have presented some results of interference effects of w₁(t) and its third harmonics w₃(t).

Keywords: phase control, population transfer, chirped laser pulses, rapid adiabatic passage, laser-molecule interaction

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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: M. S. Gadala, Khaled Ahmed, Elasadig Mahdi

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In this paper, we introduced a gradient-based inverse solver to obtain the missing boundary conditions based on the readings of internal thermocouples. The results show that the method is very sensitive to measurement errors, and becomes unstable when small time steps are used. The artificial neural networks are shown to be capable of capturing the whole thermal history on the run-out table, but are not very effective in restoring the detailed behavior of the boundary conditions. Also, they behave poorly in nonlinear cases and where the boundary condition profile is different. GA and PSO are more effective in finding a detailed representation of the time-varying boundary conditions, as well as in nonlinear cases. However, their convergence takes longer. A variation of the basic PSO, called CRPSO, showed the best performance among the three versions. Also, PSO proved to be effective in handling noisy data, especially when its performance parameters were tuned. An increase in the self-confidence parameter was also found to be effective, as it increased the global search capabilities of the algorithm. RPSO was the most effective variation in dealing with noise, closely followed by CRPSO. The latter variation is recommended for inverse heat conduction problems, as it combines the efficiency and effectiveness required by these problems.

Keywords: inverse analysis, function specification, neural net works, particle swarm, run-out table

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Authors: Abdelhadi Elharfi

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A problem of boundary feedback (exponential) stabilization of an overhead crane model represented by a PDE is considered. For any $r>0$, the exponential stability at the desired decay rate $r$ is solved in semi group setting by a collocated-type stabiliser of a target system combined with a term involving the solution of an appropriate PDE.

Keywords: feedback stabilization, semi group and generator, overhead crane system

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Authors: Elyas Shivanian

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In this paper, the spectral meshless radial point interpolation (SMRPI) technique is applied to the Cauchy problems of two-dimensional elliptic PDEs in doubly connected domains. It is obtained the unknown data on the inner boundary of the domain while overspecified boundary data are imposed on the outer boundary of the domain by using the SMRPI. Shape functions, which are constructed through point interpolation method using the radial basis functions, help us to treat problem locally with the aim of high order convergence rate. In this way, localization in SMRPI can reduce the ill-conditioning for Cauchy problem. Furthermore, we improve previous results and it is revealed the SMRPI is more accurate and stable by adding strong perturbations.

Keywords: cauchy problem, doubly connected domain, radial basis function, shape function

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Authors: Perumalsamy Muthiah, Murugesan Thanapalan

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The remains of cheese production contain nutritional value added proteins viz., α-Lactalbumin, β-Lactoglobulin representing 80- 90% of the total volume of milk entering the process. Although several possibilities for cheese-whey exploitation have been assayed, approximately half of world cheese-whey production is not treated but is discarded as effluent. It is necessary to develop an effective and environmentally benign extraction process for the recovery of value added cheese whey proteins. Recently aqueous two phase system (ATPS) have emerged as potential separation process, particularly in the field of biotechnology due to the mild conditions of the process, short processing time, and ease of scale-up. In order to design an ATPS process for the recovery of cheese whey proteins, development of phase diagram and the effect of system parameters such as pH, types and the concentrations of the phase forming components, temperature, etc., on the partitioning of proteins were addressed in order to maximize the recovery of proteins. Some of the practical problems encountered in the application of aqueous two-phase systems for the recovery of Cheese whey proteins were also discussed.

Keywords: aqueous two-phase system, phase diagram, extraction, cheese whey

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Authors: Hamed Zolfaghari, Mojtaba Kord

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After feasibility study the design phase is started and the rest of other phases are highly dependent on this phase. forecasting the duration of design phase could do a miracle and would save a lot of time. This study provides a fast and accurate Machine learning (ML) and optimization framework, which allows a quick duration estimation of project design phase, hence improving operational efficiency and competitiveness of a design construction company. 3 data sets of three years composed of daily time spent for different design projects are used to train and validate the ML models to perform multiple projects. Our study concluded that Artificial Neural Network (ANN) performed an accuracy of 0.94.

Keywords: time estimation, machine learning, Artificial neural network, project design phase

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Authors: Huei Chu Weng, Chien-Hung Liu

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This paper presents a study on the effect of second-order slip and jump on forced convection through a long isothermally heated or cooled planar microchannel. The fully developed solutions of thermal flow fields are analytically obtained on the basis of the second-order Maxwell-Burnett slip and Smoluchowski jump boundary conditions. Results reveal that the second-order term in the Karniadakis slip boundary condition is found to contribute a negative velocity slip and then to lead to a higher pressure drop as well as a higher fluid temperature for the heated-wall case or to a lower fluid temperature for the cooled-wall case. These findings are contrary to predictions made by the Deissler model. In addition, the role of second-order slip becomes more significant when the Knudsen number increases.

Keywords: microfluidics, forced convection, gas rarefaction, second-order boundary conditions

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Authors: Irina Peterburgsky

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Let T be a unit circumference of a complex plane, E be a Banach space, E* and E** be its conjugate and second conjugate, respectively. In general, a Hardy space Hp(E), p ≥1, where functions act from the open unit disk to E, could contain a function for which even weak nontangential (angular) boundary value in the space E** does not exist at any point of the unit circumference T (C. Grossetete.) The situation is "better" when certain restrictions to the Banach space of values are applied (more or less resembling a classical case of scalar-valued functions depending on constrains, as shown by R. Ryan.) This paper shows that, nevertheless, in the case of a Banach space of a general type, the following positive statement is true: Proposition. For any function f(z) from Hp(E), p ≥ 1, there exists a function F(eiθ) on the unit circumference T to E** whose Poisson (in the Pettis sense) is integral regains the function f(z) on the open unit disk. Some characteristics of the function F(eiθ) are demonstrated.

Keywords: hardy spaces, Banach space-valued function, boundary values, Pettis integral

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Authors: Imine Zakaria, Meftah Sidi Mohamed El Amine

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One of the most vital aerodynamic organs of a flying machine is the wing, which allows it to fly in the air efficiently. The flow around the wing is very sensitive to changes in the angle of attack. Beyond a value, there is a phenomenon of the boundary layer separation on the upper surface, which causes instability and total degradation of aerodynamic performance called a stall. However, controlling flow around an airfoil has become a researcher concern in the aeronautics field. There are two techniques for controlling flow around a wing to improve its aerodynamic performance: passive and active controls. Blowing and suction are among the active techniques that control the boundary layer separation around an airfoil. Their objective is to give energy to the air particles in the boundary layer separation zones and to create vortex structures that will homogenize the velocity near the wall and allow control. Blowing and suction have long been used as flow control actuators around obstacles. In 1904 Prandtl applied a permanent blowing to a cylinder to delay the boundary layer separation. In the present study, several numerical investigations have been developed to predict a turbulent flow around an aerodynamic profile. CFD code was used for several angles of attack in order to validate the present work with that of the literature in the case of a clean profile. The variation of the lift coefficient CL with the momentum coefficient

Keywords: CFD, control flow, lift, slot

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Authors: Haode Huo, Jingjing He, Rui Kang, Xuefei Guan

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This paper presents a study of Lamb wave damage diagnosis of composite delamination using instantaneous phase data. Numerical experiments are performed using the finite element method. Different sizes of delamination damages are modeled using finite element package ABAQUS. Lamb wave excitation and responses data are obtained using a pitch-catch configuration. Empirical mode decomposition is employed to extract the intrinsic mode functions (IMF). Hilbert–Huang Transform is applied to each of the resulting IMFs to obtain the instantaneous phase information. The baseline data for healthy plates are also generated using the same procedure. The size of delamination is correlated with the instantaneous phase change for damage diagnosis. It is observed that the unwrapped instantaneous phase of shows a consistent behavior with the increasing delamination size.

Keywords: delamination, lamb wave, finite element method, EMD, instantaneous phase

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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: Junling Li, Fang Meng, Yichun Zhang

Abstract:

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: Korosh Khorshidi, Mohammad Khodadadi

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In this paper, exact close form solution for out of plate free flexural vibration of moderately thick rectangular nanoplates are presented based on nonlocal modified trigonometric shear deformation theory, with assumptions of the Levy's type boundary conditions, for the first time. The aim of this study is to evaluate the effect of small-scale parameters on the frequency parameters of the moderately thick rectangular nano-plates. To describe the effects of small-scale parameters on vibrations of rectangular nanoplates, the Eringen theory is used. The Levy's type boundary conditions are combination of six different boundary conditions; specifically, two opposite edges are simply supported and any of the other two edges can be simply supported, clamped or free. Governing equations of motion and boundary conditions of the plate are derived by using the Hamilton’s principle. The present analytical solution can be obtained with any required accuracy and can be used as benchmark. Numerical results are presented to illustrate the effectiveness of the proposed method compared to other methods reported in the literature. Finally, the effect of boundary conditions, aspect ratios, small scale parameter and thickness ratios on nondimensional natural frequency parameters and frequency ratios are examined and discussed in detail.

Keywords: exact solution, nonlocal modified sinusoidal shear deformation theory, out of plane vibration, moderately thick rectangular plate

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Authors: Avelino Marques, Diamantino Freitas

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Some important electroacoustic systems, like loudspeaker systems, exhibit a nonminimum phase behavior that poses considerable effort when applying advanced digital signal processing techniques, such as linear equalization. In this paper, the position and the number of zeros and poles of the inverse filter, FIR type or IIR type, designed using time domain techniques, are studied, compared and related to the nonminimum phase zeros of system to be equalized. Conclusions about the impact of the position of the system non-minimum phase zeros, on the length/order of the inverse filter and on the delay of the equalized system are outlined as a guide to previously decide which type of filter will be more adequate.

Keywords: loudspeaker systems, nonminimum phase system, FIR and IIR filter, delay

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Authors: Zahreddine Hafsi, Manoranjan Mishra , Sami Elaoud

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Ensuring the maximum recovery rate of oil from reservoir rocks is a challenging task that requires preliminary numerical analysis of different techniques used to enhance the recovery process. After conventional oil recovery processes and in order to retrieve oil left behind after the primary recovery phase, water flooding in one of several techniques used for enhanced oil recovery (EOR). In this research work, EOR via water flooding is numerically modeled, and hydrodynamic instabilities resulted from immiscible oil-water flow in reservoir rocks are investigated. An oil reservoir is a porous medium consisted of many fractures of tiny dimensions. For modeling purposes, the oil reservoir is considered as a collection of capillary tubes which provides useful insights into how fluids behave in the reservoir pore spaces. Equations governing oil-water flow in oil reservoir rocks are developed and numerically solved following a finite element scheme. Numerical results are obtained using Comsol Multiphysics software. The two phase Darcy module of COMSOL Multiphysics allows modelling the imbibition process by the injection of water (as wetting phase) into an oil reservoir. Van Genuchten, Brooks Corey and Levrett models were considered as retention models and obtained flow configurations are compared, and the governing parameters are discussed. For the considered retention models it was found that onset of instabilities viz. fingering phenomenon is highly dependent on the capillary pressure as well as the boundary conditions, i.e., the inlet pressure and the injection velocity.

Keywords: capillary pressure, EOR process, immiscible flow, numerical modelling

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Authors: Habtamu Garoma Debela, Gemechis File Duressa

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In this work, our primary interest is to provide ε-uniformly convergent numerical techniques for solving singularly perturbed semilinear boundary value problems with non-local boundary condition. These singular perturbation problems are described by differential equations in which the highest-order derivative is multiplied by an arbitrarily small parameter ε (say) known as singular perturbation parameter. This leads to the existence of boundary layers, which are basically narrow regions in the neighborhood of the boundary of the domain, where the gradient of the solution becomes steep as the perturbation parameter tends to zero. Due to the appearance of the layer phenomena, it is a challenging task to provide ε-uniform numerical methods. The term 'ε-uniform' refers to identify those numerical methods in which the approximate solution converges to the corresponding exact solution (measured to the supremum norm) independently with respect to the perturbation parameter ε. Thus, the purpose of this work is to develop, analyze, and improve the ε-uniform numerical methods for solving singularly perturbed problems. These methods are based on nonstandard fitted finite difference method. The basic idea behind the fitted operator, finite difference method, is to replace the denominator functions of the classical derivatives with positive functions derived in such a way that they capture some notable properties of the governing differential equation. A uniformly convergent numerical method is constructed via nonstandard fitted operator numerical method and numerical integration methods to solve the problem. The non-local boundary condition is treated using numerical integration techniques. Additionally, Richardson extrapolation technique, which improves the first-order accuracy of the standard scheme to second-order convergence, is applied for singularly perturbed convection-diffusion problems using the proposed numerical method. Maximum absolute errors and rates of convergence for different values of perturbation parameter and mesh sizes are tabulated for the numerical example considered. The method is shown to be ε-uniformly convergent. Finally, extensive numerical experiments are conducted which support all of our theoretical findings. A concise conclusion is provided at the end of this work.

Keywords: nonlocal boundary condition, nonstandard fitted operator, semilinear problem, singular perturbation, uniformly convergent

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Authors: Himanshu Singh, Rishi Kant, Shantanu Bhattacharya

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This paper adopts a top-down approach for mathematical modeling to predict the size reduction from micro to nano-scale through persistent etching. The process is simulated using a finite difference approach. Previously, various researchers have simulated the etching process for 1-D and 2-D substrates. It consists of two processes: 1) Convection-Diffusion in the etchant domain; 2) Chemical reaction at the surface of the particle. Since the process requires analysis along moving boundary, partial differential equations involved cannot be solved using conventional methods. In 1-D, this problem is very similar to Stefan's problem of moving ice-water boundary. A fixed grid method using finite volume method is very popular for modelling of etching on a one and two dimensional substrate. Other popular approaches include moving grid method and level set method. In this method, finite difference method was used to discretize the spherical diffusion equation. Due to symmetrical distribution of etchant, the angular terms in the equation can be neglected. Concentration is assumed to be constant at the outer boundary. At the particle boundary, the concentration of the etchant is assumed to be zero since the rate of reaction is much faster than rate of diffusion. The rate of reaction is proportional to the velocity of the moving boundary of the particle. Modelling of the above reaction was carried out using Matlab. The initial particle size was taken to be 50 microns. The density, molecular weight and diffusion coefficient of the substrate were taken as 2.1 gm/cm3, 60 and 10-5 cm2/s respectively. The etch-rate was found to decline initially and it gradually became constant at 0.02µ/s (1.2µ/min). The concentration profile was plotted along with space at different time intervals. Initially, a sudden drop is observed at the particle boundary due to high-etch rate. This change becomes more gradual with time due to declination of etch rate.

Keywords: particle size reduction, micromixer, FDM modelling, wet etching

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Authors: H. Ben Khlifa, W. Cheikhrouhou, R. M'nassri

Abstract:

The Orthorhombic Pr0.8Na0.2MnO3 ceramic was prepared in Polycrystalline form by a Pechini sol–gel method and its structural, magnetic, electrical, and dielectric properties were investigated experimentally. A structural study confirms that the sample is a single phase. Magnetic measurements show that the sample is a charge ordered Manganite. The sample undergoes two successive magnetic phase transitions with the variation of temperature: a charge ordering transition occurred at TCO = 212 K followed by a Paramagnetic (PM) to ferromagnetic (FM) transition around TC = 115 K. From an electrical point of view, a saturation region was marked in the conductivity as a function of Temperature s(T) curves at a specific temperature. The dc-conductivity (sdc) reaches a maximum value at 240 K. The obtained results are in good agreement with the temperature dependence of the average normalized change (ANC). We found that the conduction mechanism was governed by small polaron hopping (SPH) in the high-temperature region and by variable range hopping (VRH) in the low-temperature region. Complex impedance analysis indicates the presence of a non-Debye relaxation phenomenon in the system. Also, the compound was modeled by an electrical equivalent circuit. Then, the contribution of the grain boundary in the transport properties was confirmed.

Keywords: manganites, preparation methods, magnetization, magnetocaloric effect, electrical and dielectric

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