Search results for: nonlocal boundary condition

Authors: Zdeněk Veselý, Milan Honner, Jiří Mach

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The aim of the performed work is to establish the 2D and 3D model of direct unsteady task of sample heat treatment by moving source employing computer model on the basis of finite element method. The complex boundary condition on heat loaded sample surface is the essential feature of the task. Computer model describes heat treatment of the sample during heat source movement over the sample surface. It is started from the 2D task of sample cross section as a basic model. Possibilities of extension from 2D to 3D task are discussed. The effect of the addition of third model dimension on the temperature distribution in the sample is showed. Comparison of various model parameters on the sample temperatures is observed. Influence of heat source motion on the depth of material heat treatment is shown for several velocities of the movement. Presented computer model is prepared for the utilization in laser treatment of machine parts.

Keywords: computer simulation, unsteady model, heat treatment, complex boundary condition, moving heat source

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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: Zainab A. Bu Sinnah, David I. Graham

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The Lattice Boltzmann Method has been developed and used to simulate both steady and unsteady fluid flow problems such as turbulent flows, multiphase flow and flows in the vascular system. As an example, the study of blood flow and its properties can give a greater understanding of atherosclerosis and the flow parameters which influence this phenomenon. The blood flow in the vascular system is driven by a pulsating pressure gradient which is produced by the heart. As a very simple model of this, we simulate plane channel flow under periodic forcing. This pulsatile flow is essentially the standard Poiseuille flow except that the flow is driven by the periodic forcing term. Moment boundary conditions, where various moments of the particle distribution function are specified, are applied at solid walls. We used a second-order single relaxation time model and investigated grid convergence using two distinct approaches. In the first approach, we fixed both Reynolds and Womersley numbers and varied relaxation time with grid size. In the second approach, we fixed the Womersley number and relaxation time. The expected second-order convergence was obtained for the second approach. For the first approach, however, the numerical method converged, but not necessarily to the appropriate analytical result. An explanation is given for these observations.

Keywords: Lattice Boltzmann method, single relaxation time, pulsatile flow, moment based boundary condition

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Authors: Exa Heydemans, Jessica Sjah, Dwinanti Rika Marthanty

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This paper presents numerical simulations using an open boundary algorithm with modified dynamic boundary condition (mDBC) for weakly compressible smoothed particle hydrodynamics models from particle-based code Dualsphysics. The problems of piping erosion in dams and dikes are aimed for studying the algorithm. The case 2D model of unsteady fluid flow past around a fixed cylinder is simulated, where various values of Reynold’s numbers (Re40, Re60, Re80, and Re100) and different model’s resolution are considered. A constant velocity with different values of viscosity for generating various Reynold’s numbers and different numbers of particles over a cylinder for the resolution are modeled. The interaction between solid particles of the cylinder and fluid particles is concerned. The cylinder is affected by the hydrodynamics force caused by the flow of fluid particles. The solid particles of the cylinder are the observation points to obtain force and pressure due to the hydrodynamics forces. As results of the simulation, which is to show the capability to model 2D unsteady with various Reynold’s numbers, the pressure coefficient, drag coefficient, lift coefficient, and Strouhal number are compared to the previous work from literature.

Keywords: hydrodynamics, internal erosion, dualsphysics, viscous fluid flow

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Authors: Sharfi Dirar, Shihab Elhaj, Ahmed El Fatih

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Computational fluid dynamics were used to simulate and study the heated water boiler tube for both normal and rifled tube with a refinement of the mesh to check the convergence. The operation condition was taken from GARRI power station and used in a boundary condition accordingly. The result indicates the rifled tube has higher heat transfer efficiency than the normal tube.

Keywords: boiler tube, convergence check, normal tube, rifled tube

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Authors: Gaokai Liu

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The distribution of material grain sizes reflects the strength, fracture, corrosion and other properties, and the grain size can be acquired via the grain boundary. In recent years, the automatic grain boundary detection is widely required instead of complex experimental operations. In this paper, an effective solution is applied to acquire the grain boundary of material images. First, the initial superpixel segmentation result is obtained via a superpixel approach. Then, a region merging method is employed to merge adjacent regions based on certain similarity criterions, the experimental results show that the merging strategy improves the superpixel segmentation result on material datasets.

Keywords: grain boundary detection, image segmentation, material images, region merging

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Authors: A. M. Gheitaghy, H. Saffari, G. Q. Zhang

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Numerical approach based on the electrical simulation method is proposed to solve a nonlinear transient heat conduction problem with nonlinear boundary for a spherical body. This problem represents a strong nonlinearity in both the governing equation for temperature dependent thermal property and the boundary condition for combined convective and radiative cooling. By analysing the equivalent electrical model using the electrical circuit simulation program HSPICE, transient temperature and heat flux distributions at sphere can be obtained easily and fast. The solutions clearly illustrate the effect of the radiation-conduction parameter Nrc, the Biot number and the linear coefficient of temperature dependent conductivity and heat capacity. On comparing the results with corresponding numerical solutions, the accuracy and efficiency of this computational method are found to be good.

Keywords: convective and radiative boundary, electrical simulation method, nonlinear heat conduction, spherical coordinate

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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: Gary Miller, Andriy Didenko, David Allison

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The boundary of a region in the plane shrinks according to its curvature. A simple algorithm based upon this motion by curvature performed by a spreadsheet simulates the evaporation/dissipation behavior of oil spill boundaries.

Keywords: mathematical modeling, oil, evaporation, dissipation, boundary

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Authors: S. Zenhari, M. R. Hematiyan, A. Khosravifard, M. R. Feizi

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The boundary element method (BEM) and the method of fundamental solutions (MFS) are well-known fundamental solution-based methods for solving a variety of problems. Both methods are boundary-type techniques and can provide accurate results. In comparison to the finite element method (FEM), which is a domain-type method, the BEM and the MFS need less manual effort to solve a problem. The aim of this study is to compare the accuracy and reliability of the BEM and the MFS. This comparison is made for 2D potential and elasticity problems with different boundary and loading conditions. In the comparisons, both convex and concave domains are considered. Both linear and quadratic elements are employed for boundary element analysis of the examples. The discretization of the problem domain in the BEM, i.e., converting the boundary of the problem into boundary elements, is relatively simple; however, in the MFS, obtaining appropriate locations of collocation and source points needs more attention to obtain reliable solutions. The results obtained from the presented examples show that both methods lead to accurate solutions for convex domains, whereas the BEM is more suitable than the MFS for concave domains.

Keywords: boundary element method, method of fundamental solutions, elasticity, potential problem, convex domain, concave domain

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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: Mohammadreza Akbari, Pooya Soleimani Besheli, Reza Khalili, Davood Domiri Danji

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In this conference, our aims are accuracy, capabilities and power at solving of the complicated non-linear partial differential. Our purpose is to enhance the ability to solve the mentioned nonlinear differential equations at basic science and engineering field and similar issues with a simple and innovative approach. As we know most of engineering system behavior in practical are nonlinear process (especially basic science and engineering field, etc.) and analytical solving (no numeric) these problems are difficult, complex, and sometimes impossible like (Fluids and Gas wave, these problems can't solve with numeric method, because of no have boundary condition) accordingly in this symposium we are going to exposure an innovative approach which we have named it Akbari-Ganji's Method or AGM in engineering, that can solve sets of coupled nonlinear differential equations (ODE, PDE) with high accuracy and simple solution and so this issue will emerge after comparing the achieved solutions by Numerical method (Runge-Kutta 4th). Eventually, AGM method will be proved that could be created huge evolution for researchers, professors and students in whole over the world, because of AGM coding system, so by using this software we can analytically solve all complicated linear and nonlinear partial differential equations, with help of that there is no difficulty for solving all nonlinear differential equations. Advantages and ability of this method (AGM) as follow: (a) Non-linear Differential equations (ODE, PDE) are directly solvable by this method. (b) In this method (AGM), most of the time, without any dimensionless procedure, we can solve equation(s) by any boundary or initial condition number. (c) AGM method always is convergent in boundary or initial condition. (d) Parameters of exponential, Trigonometric and Logarithmic of the existent in the non-linear differential equation with AGM method no needs Taylor expand which are caused high solve precision. (e) AGM method is very flexible in the coding system, and can solve easily varieties of the non-linear differential equation at high acceptable accuracy. (f) One of the important advantages of this method is analytical solving with high accuracy such as partial differential equation in vibration in solids, waves in water and gas, with minimum initial and boundary condition capable to solve problem. (g) It is very important to present a general and simple approach for solving most problems of the differential equations with high non-linearity in engineering sciences especially at civil engineering, and compare output with numerical method (Runge-Kutta 4th) and Exact solutions.

Keywords: new approach, AGM, sets of coupled nonlinear differential equation, exact solutions, numerical

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Authors: Azad Mohammed Ali Saber, Lanja Saeed Omer

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The present study deals with numerical method (FE) and experimental investigations on the vibration behavior of carbon fiber-polyester laminated plates. Finite element simulation is done using APDL (Ansys Parametric Design Language) macro codes software version 19. Solid185 layered structural element, including eight nodes, is adopted in this analysis. The experimental work is carried out using (Hand Layup method) to fabricate different layers and orientation angles of composite laminate plates. Symmetric samples include four layers (00/900)s and six layers (00/900/00)s, (00/00/900)s. Antisymmetric samples include one layer (00), (450), two layers (00/900), (-450/450), three layers (00/900/00), four layers (00/900)2, (-450/450)2, five layers (00/900)2.5, and six layers (00/900)3, (-450/450)3. An experimental investigation is carried out using a modal analysis technique with a Fast Fourier Transform Analyzer (FFT), Pulse platform, impact hammer, and accelerometer to obtain the frequency response functions. The influences of different parameters such as the number of layers, aspect ratio, modulus ratio, ply orientation, and different boundary conditions on the dynamic behavior of the CFRPs are studied, where the 1st, 2nd, and 3rd natural frequencies are observed to be the minimum for cantilever boundary condition (CFFF) and the maximum for full clamped boundary condition (CCCC). Experimental results show that the natural frequencies of laminated plates are significantly reliant on the type of boundary conditions due to the restraint effect at the edges. Good agreement is achieved among the finite element and experimental results. All results indicate that any increase in aspect ratio causes a decrease in the natural frequency of the CFRPs plate, while any increase in the modulus ratio or number of layers causes an increase in the fundamental natural frequency of vibration.

Keywords: vibration, composite materials, finite element, APDL ANSYS

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Authors: Win-Jin Chang, Haw-Long Lee, Yu-Ching Yang

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Atomic finite element simulation is applied to investigate the vibration frequency of a single-layer gamma graphyne with an attached mass for the CCCC, SSSS, CFCF, SFSF boundary conditions using the commercial code ANSYS. The fundamental frequencies of the graphyne sheet are compared with the results of the previous study. The results of the comparison are very good in all considered cases. The attached mass causes a shift in the resonant frequency of the graphyne. The frequencies of the single-layer gamma graphyne with an attached mass for different boundary conditions are obtained, and the order based on the boundary condition is CCCC >SSSS > CFCF> SFSF. The highest frequency shift is obtained when the attached mass is located at the center of the graphyne sheet. This is useful for the design of a highly sensitive graphyne-based mass sensor.

Keywords: graphyne, finite element analysis, vibration analysis, frequency shift

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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: 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: Muhammad Sufian Jusoh, Mesliza Mohamed

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In this paper, we investigate the existence of positive solutions for a Dirichlet second order boundary value problem by applying the Krasnosel'skii fixed point theorem on compression and expansion of cones.

Keywords: Krasnosel'skii fixed point theorem, positive solutions, Dirichlet boundary value problem, Dirichlet second order boundary problem

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Authors: Dur-E- Shahwar

Abstract:

Much attention has been given to ‘bridging the gap’ between neuroscience and educational practice. In order to gain a better understanding of the nature of this gap and of possibilities to enable the linking process, we have taken a boundary perspective on these two fields and the brain-based learning approach, focusing on boundary-spanning actors, boundary objects, and boundary work. In 26 semi-structured interviews, neuroscientists and education professionals were asked about their perceptions in regard to the gap between science and practice and the role they play in creating, managing, and disrupting this boundary. Neuroscientists and education professionals often hold conflicting views and expectations of both brain-based learning and of each other. This leads us to argue that there are increased prospects for a neuro-scientifically informed learning practice if science and practice work together as equal stakeholders in developing and implementing neuroscience research.

Keywords: language learning, explore, educational practices, mentalist, practice

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Authors: Shivani Saini

Abstract:

The effect of vertical throughflow on the onset of convection in Rivlin-Ericksen Elastico-Viscous nanofluid with convective boundary condition is investigated. The flow is stimulated with modified Darcy model under the assumption that the nanoparticle volume fraction is not actively managed on the boundaries. The heat conservation equation is formulated by introducing the convective term of nanoparticle flux. A linear stability analysis based upon normal mode is performed, and an approximate solution of eigenvalue problems is obtained using the Galerkin weighted residual method. Investigation of the dependence of the Rayleigh number on various viscous and nanofluid parameter is performed. It is found that through flow and nanofluid parameters hasten the convection while capacity ratio, kinematics viscoelasticity, and Vadasz number do not govern the stationary convection. Using the convective component of nanoparticle flux, critical wave number is the function of nanofluid parameters as well as the throughflow parameter. The obtained solution provides important physical insight into the behavior of this model.

Keywords: Darcy model, nanofluid, porous layer, throughflow

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Authors: Sagardeep Talukdar, Riki Dutta, Gautam Kumar Saharia, Sudipta Nandy

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In non-linear optics, the Fokas-Lenells equation (FLE) is a well-known integrable equation that describes how ultrashort pulses move across the optical fiber. It admits localized wave solutions, just like any other integrable equation. We apply the Hirota bilinearization method to obtain the soliton solution of FLE. The proposed bilinearization makes use of an auxiliary function. We apply the method to FLE with a vanishing boundary condition, that is, to obtain a bright soliton solution. We have obtained bright 1-soliton and 2-soliton solutions and propose a scheme for obtaining an N-soliton solution. We have used an additional parameter that is responsible for the shift in the position of the soliton. Further analysis of the 2-soliton solution is done by asymptotic analysis. In the non-vanishing boundary condition, we obtain the dark 1-soliton solution. We discover that the suggested bilinearization approach, which makes use of the auxiliary function, greatly simplifies the process while still producing the desired outcome. We think that the current analysis will be helpful in understanding how FLE is used in nonlinear optics and other areas of physics.

Keywords: asymptotic analysis, fokas-lenells equation, hirota bilinearization method, soliton

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Authors: Huei Chu Weng

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This paper presents a study on the effect of second-order slip on forced convection through a long isoflux heated or cooled planar microchannel. The fully developed solutions of flow and thermal fields are analytically obtained on the basis of the second-order Maxwell-Burnett slip and local heat flux boundary conditions. Results reveal that when the average flow velocity increases or the wall heat flux amount decreases, the role of thermal creep becomes more insignificant, while the effect of second-order slip becomes larger. The second-order term in the Deissler slip boundary condition is found to contribute a positive velocity slip and then to lead to a lower pressure drop as well as a lower temperature rise for the heated-wall case or to a higher temperature rise for the cooled-wall case. These findings are contrary to predictions made by the Karniadakis slip model.

Keywords: microfluidics, forced convection, thermal creep, second-order boundary conditions

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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: Mohamed Houas, Maamar Benbachir

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In this paper, under weak assumptions, we study the existence and uniqueness of solutions for a nonlinear fractional boundary value problem. New existence and uniqueness results are established using Banach contraction principle. Other existence results are obtained using scheafer and krasnoselskii's fixed point theorem. At the end, some illustrative examples are presented.

Keywords: caputo derivative, boundary value problem, fixed point theorem, local conditions

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Authors: Guohua Tu, Zhi Fu, Zhiwei Hu, Neil D Sandham, Jianqiang Chen

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Tripping of boundary-layers from laminar to turbulent flow, which may be necessary in specific practical applications, requires high amplitude disturbances to be introduced into the boundary layers without large drag penalties. As a possible improvement on fixed trip devices, a technique based on vortex shedding for enhancing supersonic flow transition is demonstrated in the present paper for a Mach 1.5 boundary layer. The compressible Navier-Stokes equations are solved directly using a high-order (fifth-order in space and third-order in time) finite difference method for small-scale cylinders suspended transversely near the wall. For cylinders with proper diameter and mount location, asymmetry vortices shed within the boundary layer are capable of tripping laminar-turbulent transition. Full three-dimensional simulations showed that transition was enhanced. A parametric study of the size and mounting location of the cylinder is carried out to identify the most effective setup. It is also found that the vortex shedding can be suppressed by some factors such as wall effect.

Keywords: boundary layer instability, boundary layer transition, vortex shedding, supersonic flows, flow control

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Authors: Sudipto Sarkar, Anamika Paul

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Pseudoplastic (n<1, n is the power index) fluids have great importance in food, pharmaceutical and chemical process industries which require a lot of attention. Unfortunately, due to its complex flow behavior inadequate research works can be found even in laminar flow regime. A practical problem is solved in the present research work by numerical simulation where we tried to control the vortex shedding from a square cylinder using a horizontal splitter plate placed at the downstream flow region. The position of the plate is at the centerline of the cylinder with varying distance from the cylinder to calculate the critical gap-ratio. If the plate is placed inside this critical gap, the vortex shedding from the cylinder suppressed completely. The Reynolds number considered here is in unsteady laminar vortex shedding regime, Re = 100 (Re = U∞a/ν, where U∞ is the free-stream velocity of the flow, a is the side of the cylinder and ν is the maximum value of kinematic viscosity of the fluid). Flow behavior has been studied for three different gap-ratios (G/a = 2, 2.25 and 2.5, where G is the gap between cylinder and plate) and for a fluid with three different flow behavior indices (n =1, 0.8 and 0.5). The flow domain is constructed using Gambit 2.2.30 and this software is also used to generate the mesh and to impose the boundary conditions. For G/a = 2, the domain size is considered as 37.5a × 16a with 316 × 208 grid points in the streamwise and flow-normal directions respectively after a thorough grid independent study. Fine and equal grid spacing is used close to the geometry to capture the vortices shed from the cylinder and the boundary layer developed over the flat plate. Away from the geometry meshes are unequal in size and stretched out. For other gap-ratios, proportionate domain size and total grid points are used with similar kind of mesh distribution. Velocity inlet (u = U∞), pressure outlet (Neumann condition), symmetry (free-slip boundary condition) at upper and lower domain boundary conditions are used for the simulation. Wall boundary condition (u = v = 0) is considered both on the cylinder and the splitter plate surfaces. Discretized forms of fully conservative 2-D unsteady Navier Stokes equations are then solved by Ansys Fluent 14.5. SIMPLE algorithm written in finite volume method is selected for this purpose which is a default solver inculcate in Fluent. The results obtained for Newtonian fluid flow agree well with previous works supporting Fluent’s usefulness in academic research. A thorough analysis of instantaneous and time-averaged flow fields are depicted both for Newtonian and pseudoplastic fluid flow. It has been observed that as the value of n reduces the stretching of shear layers also reduce and these layers try to roll up before the plate. For flow with high pseudoplasticity (n = 0.5) the nature of vortex shedding changes and the value of critical gap-ratio reduces. These are the remarkable findings for laminar periodic vortex shedding regime in pseudoplastic flow environment.

Keywords: CFD, pseudoplastic fluid flow, wake-boundary layer interactions, critical gap-ratio

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Authors: Mohammad Mojtahedpoor

Abstract:

In this paper, it has been studied the method of optimal design of the supersonic nozzle. It could make viscous axisymmetric nozzles that the quality of their outlet flow is quite desired. In this method, it is optimized the divergent nozzle, at first. The initial divergent nozzle contour is designed through the method of characteristics and adding a suitable boundary layer to the inviscid contour. After that, it is made a proper grid and then simulated flow by the numerical solution and AUSM+ method by using the operation boundary condition. At the end, solution outputs are investigated and optimized. The numerical method has been validated with experimental results. Also, in order to evaluate the effectiveness of the present method, the nozzles compared with the previous studies. The comparisons show that the nozzles obtained through this method are sufficiently better in some conditions, such as the flow uniformity, size of the boundary layer, and obtained an axial length of the nozzle. Designing the convergent nozzle part affects by flow uniformity through changing its axial length and input diameter. The results show that increasing the length of the convergent part improves the output flow uniformity.

Keywords: nozzle, supersonic, optimization, characteristic method, CFD

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Authors: Thanin Sitthiwirattham, Jiraporn Reunsumrit

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We study the existence of positive solutions to the three points difference summation boundary value problem. We show the existence of at least one positive solution if f is either superlinear or sublinear by applying the fixed point theorem due to Krasnoselskii in cones.

Keywords: positive solution, boundary value problem, fixed point theorem, cone

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Authors: Takuya Suzuki, Atsushi Shirai, Takashi Seki

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Acupuncture therapy is one of the treatments in traditional Chinese medicine. Recently, some reports have shown the effectiveness of acupuncture. However, its full acceptance has been hindered by the lack of understanding on mechanism of the therapy. Acupuncture applied to Zusanli (ST-36) enhances blood flow volume in superior mesenteric artery (SMA), yielding peripheral vascular resistance – regulated blood flow of SMA dominated by the parasympathetic system and inhibition of sympathetic system. In this study, a lumped-parameter approximation model of blood flow in the systemic arteries was developed. This model was extremely simple, consisting of the aorta, carotid arteries, arteries of the four limbs and SMA, and their peripheral vascular resistances. Here, the individual artery was simplified to a tapered tube and the resistances were modelled by a linear resistance. We numerically investigated contribution of the peripheral vascular resistance of SMA to the systemic blood distribution using this model. In addition to the upstream end of the model, which correlates with the left ventricle, two types of boundary condition were applied; mean left ventricular pressure which correlates with blood pressure (BP) and mean cardiac output which corresponds to cardiac index (CI). We examined it to reproduce the experimentally obtained hemodynamic change, in terms of the ratio of the aforementioned hemodynamic parameters from their initial values before the acupuncture, by regulating the peripheral vascular resistances and the upstream boundary condition. First, only the peripheral vascular resistance of SMA was changed to show contribution of the resistance to the change in blood flow volume in SMA, expecting reproduction of the experimentally obtained change. It was found, however, this was not enough to reproduce the experimental result. Then, we also changed the resistances of the other arteries together with the value given at upstream boundary. Here, the resistances of the other arteries were changed simultaneously in the same amount. Consequently, we successfully reproduced the hemodynamic change to find that regulation of the upstream boundary condition to the value experimentally obtained after the stimulation is necessary for the reproduction, though statistically significant changes in BP and CI were not observed in the experiment. It is generally known that sympathetic and parasympathetic tones take part in regulation of whole the systemic circulation including the cardiac function. The present result indicates that stimulation to ST-36 could induce vasodilation of peripheral circulation of SMA and vasoconstriction of that of other arteries. In addition, it implies that experimentally obtained small changes in BP and CI induced by the acupuncture may be involved in the therapeutic response.

Keywords: acupuncture, hemodynamics, lumped-parameter approximation, modeling, systemic vascular resistance

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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: Aziz Sezgin

Abstract:

We consider the problem of stabilization of an unstable heat equation in a 2-D, 3-D and generally n-D domain by deriving a generalized backstepping boundary control design methodology. To stabilize the systems, we design boundary backstepping controllers inspired by the 1-D unstable heat equation stabilization procedure. We assume that one side of the boundary is hinged and the other side is controlled for each direction of the domain. Thus, controllers act on two boundaries for 2-D domain, three boundaries for 3-D domain and ”n” boundaries for n-D domain. The main idea of the design is to derive ”n” controllers for each of the dimensions by using ”n” kernel functions. Thus, we obtain ”n” controllers for the ”n” dimensional case. We use a transformation to change the system into an exponentially stable ”n” dimensional heat equation. The transformation used in this paper is a generalized Volterra/Fredholm type with ”n” kernel functions for n-D domain instead of the one kernel function of 1-D design.

Keywords: backstepping, boundary control, 2-D, 3-D, n-D heat equation, distributed parameter systems

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