Search results for: Linear fredholm equations

Authors: Da-Hye Kim, Won-Hyung Park, In-Ho Yun, Jeong Cheol Kim, Sang-Youn Kim

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This paper presents an authoring tool which makes a user easily and intuitively design vibrotactile sensation. A mobile hardware platform powered by ANDROID, a multi-purpose haptic driver and a linear resonance actuator are used to implement the system of the presented authoring tool. The tool allows users to easily and simply create a vibrotactile sensation by drawing vibrotactile images and to feel the sensation by rubbing drawn images on the touch screen of a mobile device. The tool supports a graphical interface for designing, editing and playing vibrotactile images as well as a pre-defined file format for save and open.

Keywords: authoring tool, mobile device, vibrotactile pattern, vibrotactile sensation

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Authors: M. Zarebnia, R. Parvaz

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In this paper the Kuramoto-Sivashinsky equation is solved numerically by collocation method. The solution is approximated as a linear combination of septic B-spline functions. Applying the Von-Neumann stability analysis technique, we show that the method is unconditionally stable. The method is applied on some test examples, and the numerical results have been compared with the exact solutions. The global relative error and L∞ in the solutions show the efficiency of the method computationally.

Keywords: Kuramoto-Sivashinsky equation, Septic B-spline, Collocation method, Finite difference.

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Authors: Y. Heyrani Birak, R. Hizaji, J. Shahkarami

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Reinforced Concrete (RC) deep beams are special structural elements because of their geometry and behavior under loads. For example, assumption of strain- stress distribution is not linear in the cross section. These types of beams may have simple supports or fixed supports. A lot of research works have been conducted on simply supported deep beams, but little study has been done in the fixed-end RC deep beams behavior. Recently, using of fixed-ended deep beams has been widely increased in structures. In this study, the behavior of fixed-ended deep beams is investigated, and the important parameters in capacity of this type of beams are mentioned.

Keywords: Deep beam, capacity, reinforced concrete, fixed-ended.

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Authors: Irakli V. Gugushvili, Nickolay M. Evstigneev

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Numerical integration of initial boundary problem for advection equation in 3 ℜ is considered. The method used is  conditionally stable semi-Lagrangian advection scheme with high order interpolation on unstructured mesh. In order to increase time step integration the BFECC method with limiter TVD correction is used. The method is adopted on parallel graphic processor unit environment using NVIDIA CUDA and applied in Navier-Stokes solver. It is shown that the calculation on NVIDIA GeForce 8800  GPU is 184 times faster than on one processor AMDX2 4800+ CPU. The method is extended to the incompressible fluid dynamics solver. Flow over a Cylinder for 3D case is compared to the experimental data.

Keywords: Advection equations, CUDA technology, Flow overthe 3D Cylinder, Incompressible Pressure Projection Solver, Parallel computation.

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Authors: Javier Rivas, Olga Gimeno, Maria Carbajo, Teresa Borralho

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The elimination of ranitidine (a pharmaceutical compound) has been carried out in the presence of UV-C radiation. After some preliminary experiments, it has been experienced the no influence of the gas nature (air or oxygen) bubbled in photolytic experiments. From simple photolysis experiments the quantum yield of this compound has been determined. Two photolytic approximation has been used, the linear source emission in parallel planes and the point source emission in spherical planes. The quantum yield obtained was in the proximity of 0.05 mol Einstein-1 regardless of the method used. Addition of free radical promoters (hydrogen peroxide) increases the ranitidine removal rate while the use of photocatalysts (TiO2) negatively affects the process.

Keywords: Quantum yield, photolysis, ranitidine, watertreatment.

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Authors: A. Seleem, M. Mortada, M. El Morsi, M. Younan

Abstract:

Diffusion stills have been effective in water desalination. The present work represents a model of the distillation process by using vertical single-effect diffusion stills. A semianalytical model has been developed to model the process. A software computer code using Engineering Equation Solver EES software has been developed to solve the equations of the developed model. An experimental setup has been constructed, and used for the validation of the model. The model is also validated against former literature results. The results obtained from the present experimental test rig, and the data from the literature, have been compared with the results of the code to find its best range of validity. In addition, a parametric analysis of the system has been developed using the model to determine the effect of operating conditions on the system's performance. The dominant parameters that affect the productivity of the still are the hot plate temperature that ranges from (55- 90°C) and feed flow rate in range of (0.00694-0.0211 kg/m2-s).

Keywords: Analytical Model, Solar Distillation, Sustainable Water Systems, Vertical Diffusion Still.

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Authors: V.P.Subramanyam Rallabandi, S.K.Sett

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An unsupervised classification algorithm is derived by modeling observed data as a mixture of several mutually exclusive classes that are each described by linear combinations of independent non-Gaussian densities. The algorithm estimates the data density in each class by using parametric nonlinear functions that fit to the non-Gaussian structure of the data. This improves classification accuracy compared with standard Gaussian mixture models. When applied to textures, the algorithm can learn basis functions for images that capture the statistically significant structure intrinsic in the images. We apply this technique to the problem of unsupervised texture classification and segmentation.

Keywords: Gaussian Mixture Model, Independent Component Analysis, Segmentation, Unsupervised Classification.

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Authors: Radouane Elbahjaoui, Hamid El Qarnia

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Melting of Paraffin Wax (P116) dispersed with Al₂O₃ nanoparticles in a rectangular latent heat storage unit (LHSU) is numerically investigated. The storage unit consists of a number of vertical and identical plates of nano-enhanced phase change material (NEPCM) separated by rectangular channels in which heat transfer fluid flows (HTF: Water). A two dimensional mathematical model is considered to investigate numerically the heat and flow characteristics of the LHSU. The melting problem was formulated using the enthalpy porosity method. The finite volume approach was used for solving equations. The effects of nanoparticles’ volumetric fraction and the Reynolds number on the thermal performance of the storage unit were investigated.

Keywords: Nano-enhanced phase change material, phase change material, nanoparticles, latent heat storage unit, melting.

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Authors: J. Kala, J. Melcher, M. Škaloud, Z. Kala

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In the paper, the results of sensitivity analysis of the influence of initial imperfections on the web stress state of a thinwalled girder are presented. The results of the study corroborate a very good and effective agreement of experiments with theory. Most input random quantities were found experimentally. The change of sensitivity coefficients in dependence on working load value is analysed. The stress was analysed by means of a geometrically and materially non-linear solution by applying the program ANSYS. This research study offers important background for theoretical studies of stability problems, post-critical effects and limit states of thin-walled steel structures.

Keywords: Buckling, Fatigue, Imperfection, Steel, Sensitivity analysis.

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Authors: Mohd Amaluddin Yusoff

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In this paper, we consider the design of pulse shaping filter using orthogonal Hermite-Rodriguez basis functions. The pulse shaping filter design problem has been formulated and solved as a quadratic programming problem with linear inequality constraints. Compared with the existing approaches reported in the literature, the use of Hermite-Rodriguez functions offers an effective alternative to solve the constrained filter synthesis problem. This is demonstrated through a numerical example which is concerned with the design of an equalization filter for a digital transmission channel.

Keywords: channel equalization filter, Hermite-Rodriguez, pulseshaping filter, quadratic programming.

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Authors: O. A. Apampa, Y. A. Jimoh, K. A. Olonade

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The need to save time and cost of soil testing at the planning stage of road work has necessitated developing predictive models. This study proposes a model for predicting the dry density of lateritic soils stabilized with corn cob ash (CCA) and blended cement - CCA. Lateritic soil was first stabilized with CCA at 1.5, 3.0, 4.5 and 6% of the weight of soil and then stabilized with the same proportions as replacement for cement. Dry density, specific gravity, maximum degree of saturation and moisture content were determined for each stabilized soil specimen, following standard procedure. Polynomial equations containing alpha and beta parameters for CCA and blended CCA-cement were developed. Experimental values were correlated with the values predicted from the Matlab curve fitting tool, and the Solver function of Microsoft Excel 2010. The correlation coefficient (R2) of 0.86 was obtained indicating that the model could be accepted in predicting the maximum dry density of CCA stabilized soils to facilitate quick decision making in roadworks.

Keywords: Corn cob ash, lateritic soil, stabilization, maximum dry density, moisture content.

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Authors: Cha’o-Kuang Chen, Ching-Chang Cho

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This paper investigates the natural convection heat transfer performance in a complex-wavy-wall cavity filled with power-law fluid. In performing the simulations, the continuity, Cauchy momentum and energy equations are solved subject to the Boussinesq approximation using a finite volume method. The simulations focus specifically on the effects of the flow behavior index in the power-law model and the Rayleigh number on the flow streamlines, isothermal contours and mean Nusselt number within the cavity. The results show that pseudoplastic fluids have a better heat transfer performance than Newtonian or dilatant fluids. Moreover, it is shown that for Rayleigh numbers greater than Ra=10³, the mean Nusselt number has a significantly increase as the flow behavior index is decreased.

Keywords: Non-Newtonian fluid, Power-law fluid, Natural convection, Heat transfer enhancement, Cavity, Wavy wall.

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Authors: Phavanee Narataruksa, Karn Pana-Suppamassadu, Sabaithip TungkamaniRungrote Kokoo, Prayut Jiamrittiwong

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The major focus of this work was to characterize hydrodynamics in a packed-bed with and without static mixer by using Computational Fluid Dynamic (CFD). The commercial software: COMSOL MULTIPHYSICSTM Version 3.3 was used to simulate flow fields of mixed-gas reactants i.e. CO and H2. The packed-bed was a single tube with the inside diameter of 0.8 cm and the length of 1.2 cm. The static mixer was inserted inside the tube. The number of twisting elements was 1 with 0.8 cm in diameter and 1.2 cm in length. The packed-bed with and without static mixer were both packed with approximately 700 spherical structures representing catalyst pellets. Incompressible Navier-Stokes equations were used to model the gas flow inside the beds at steady state condition, in which the inlet Reynolds Number (Re) was 2.31. The results revealed that, with the insertion of static mixer, the gas was forced to flow radially inward and outward between the central portion of the tube and the tube wall. This could help improving the overall performance of the packed-bed, which could be utilized for heterogeneous catalytic reaction such as reforming and Fischer- Tropsch reactions.

Keywords: Packed Bed, Static Mixer, Computational Fluid Dynamic (CFD).

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Authors: Swarniv Chandra, Sibarjun Das, Agniv Chandra, Basudev Ghosh, Apratim Jash

Abstract:

Using the quantum hydrodynamic (QHD) model the nonlinear properties of ion-acoustic waves in are lativistically degenerate quantum plasma is investigated by deriving a nonlinear Spherical Kadomtsev–Petviashvili (SKP) equation using the standard reductive perturbation method equation. It was found that the electron degeneracy parameter significantly affects the linear and nonlinear properties of ion-acoustic waves in quantum plasma.

Keywords: Kadomtsev-Petviashvili equation, Ion-acoustic Waves, Relativistic Degeneracy, Quantum Plasma, Quantum Hydrodynamic Model.

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Authors: S. Sarumathi, N. Shanthi, S. Vidhya

Abstract:

In the present world, predicting rainfall is considered to be an essential and also a challenging task. Normally, the climate and rainfall are presumed to have non-linear as well as intricate phenomena. For predicting accurate rainfall, we necessitate advanced computer modeling and simulation. When there is an enhanced understanding of the spatial and temporal distribution of precipitation then it becomes enrichment to applications such as hydrologic, climatic and ecological. Conversely, there may be some kind of challenges occur in the community due to some application which results in the absence of consistent precipitation observation in remote and also emerging region. This survey paper provides a multifarious collection of methodologies which are epitomized by various researchers for predicting the rainfall. It also gives information about some technique to forecast rainfall, which is appropriate to all methods like numerical, traditional and statistical.

Keywords: Satellite Image, Segmentation, Feature Extraction, Classification, Clustering, Precipitation Estimation.

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Authors: Rajkishore Prasad, Hiroshi Saruwatari, Kiyohiro Shikano

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This paper describes Independent Component Analysis (ICA) based fixed-point algorithm for the blind separation of the convolutive mixture of speech, picked-up by a linear microphone array. The proposed algorithm extracts independent sources by non- Gaussianizing the Time-Frequency Series of Speech (TFSS) in a deflationary way. The degree of non-Gaussianization is measured by negentropy. The relative performances of algorithm under random initialization and Null beamformer (NBF) based initialization are studied. It has been found that an NBF based initial value gives speedy convergence as well as better separation performance

Keywords: Blind signal separation, independent component analysis, negentropy, convolutive mixture.

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Authors: S.F. Tsen, M. Zamin Jumaat

Abstract:

The characteristic bending strength (MOR) and mean modulus of elasticity (MOE) of tropical hardwood red seraya (Shorea spp.) plywood were determined using European Standard EN310 and EN789. The thickness of the test specimen was 4.0mm, 7.0mm, 9.0mm, 12.0mm and 15.0mm. The experiment found that the MOR of red seraya plywood in EN310 is about 12% to 20% and 7% to 24% higher than EN789 whereas MOE were about 28% to 41% and 30% to 36% lower than those obtained from EN 789 for test specimens parallel and perpendicular to the grain direction. The linear regression shows that MOR and MOE for EN789 is about 0.8 times less and 1.5 times more than EN310. The experiment also found that the MOR and MOE of EN310 and EN789 also depend on the wood species that used in the experiment.

Keywords: Bending strength, Modulus of elasticity, EN310, EN789

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Authors: Nahid Ghasemi, Morteza Sohrabi, Yasan Soleymani

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The quantified residence time distribution (RTD) provides a numerical characterization of mixing in a reactor, thus allowing the process engineer to better understand mixing performance of the reactor.This paper discusses computational studies to investigate flow patterns in a two impinging streams cyclone reactor(TISCR) . Flow in the reactor was modeled with computational fluid dynamics (CFD). Utilizing the Eulerian- Lagrangian approach, implemented in FLUENT (V6.3.22), particle trajectories were obtained by solving the particle force balance equations. From simulation results obtained at different Δts, the mean residence time (tm) and the mean square deviation (σ2) were calculated. a good agreement can be observed between predicted and experimental data. Simulation results indicate that the behavior of complex reactor systems can be predicted using the CFD technique with minimum data requirement for validation.

Keywords: Impinging streams reactor, Residence timedistribution, CFD, Eulerian-Lagrangian approach

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Authors: Tze Sian Pui, Tushar Bansal, Patthara Kongsuphol, Sunil K. Arya

Abstract:

We present a label-free biosensor based on electrochemical impedance spectroscopy for the detection of proinflammatory cytokine Tumor Necrosis Factor (TNF-α). Secretion of TNF-α has been correlated to the onset of various diseases including rheumatoid arthritis, Crohn-s disease etc. Gold electrodes were patterned on a silicon substrate and self assembled monolayer of dithiobis-succinimidyl propionate was used to develop the biosensor which achieved a detection limit of ~57fM. A linear relationship was also observed between increasing TNF-α concentrations and chargetransfer resistance within a dynamic range of 1pg/ml – 1ng/ml.

Keywords: Tumor necrosis factor, electrochemical impedance spectroscopy, label free, self assembled monolayer

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Authors: Dowluru Ravi Kumar, Bhima Prabhakara Rao

Abstract:

Propagation of solitons in single-mode birefringent fibers is considered under the presence of third-order dispersion (TOD). The behavior of two neighboring solitons and their interaction is investigated under the presence of third-order dispersion with different group velocity dispersion (GVD) parameters. It is found that third-order dispersion makes the resultant soliton to deviate from its ideal position and increases the interaction between adjacent soliton pulses. It is also observed that this deviation due to third-order dispersion is considerably small when the optical pulse propagates at wavelengths relatively far from the zerodispersion. Modified coupled nonlinear Schrödinger-s equations (CNLSE) representing the propagation of optical pulse in single mode fiber with TOD are solved using split-step Fourier algorithm. The results presented in this paper reveal that the third-order dispersion can substantially increase the interaction between the solitons, but large group velocity dispersion reduces the interaction between neighboring solitons.

Keywords: Birefringence, Group velocity dispersion, Polarization mode dispersion, Soliton interaction, Third order dispersion.

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Authors: Mohammad Hadi Bordbar, Timo Hyppänen

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The radiative exchange method is introduced as a numerical method for the simulation of radiative heat transfer in an absorbing, emitting and isotropically scattering media. In this method, the integro-differential radiative balance equation is solved by using a new introduced concept for the exchange factor. Even though the radiative source term is calculated in a mesh structure that is coarser than the structure used in computational fluid dynamics, calculating the exchange factor between different coarse elements by using differential integration elements makes the result of the method close to that of integro-differential radiative equation. A set of equations for calculating exchange factors in two and threedimensional Cartesian coordinate system is presented, and the method is used in the simulation of radiative heat transfer in twodimensional rectangular case and a three-dimensional simple cube. The result of using this method in simulating different cases is verified by comparing them with those of using other numerical radiative models.

Keywords: Exchange factor, Numerical simulation, Thermal radiation.

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Authors: E. Abedi, A. Ahmadi Nadooshan, S. Salehi

Abstract:

Modeling and vibration of a flexible link manipulator with tow flexible links and rigid joints are investigated which can include an arbitrary number of flexible links. Hamilton principle and finite element approach is proposed to model the dynamics of flexible manipulators. The links are assumed to be deflection due to bending. The association between elastic displacements of links is investigated, took into account the coupling effects of elastic motion and rigid motion. Flexible links are treated as Euler-Bernoulli beams and the shear deformation is thus abandoned. The dynamic behavior due to flexibility of links is well demonstrated through numerical simulation. The rigid-body motion and elastic deformations are separated by linearizing the equations of motion around the rigid body reference path. Simulation results are shown on for both position and force trajectory tracking tasks in the presence of varying parameters and unknown dynamics remarkably well. The proposed method can be used in both dynamic simulation and controller design.

Keywords: Flexible manipulator, flexible link, dynamicmodeling, end point.

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Authors: Farzin Salmasi

Abstract:

Energy dissipation in drops has been investigated by physical models. After determination of effective parameters on the phenomenon, three drops with different heights have been constructed from Plexiglas. They have been installed in two existing flumes in the hydraulic laboratory. Several runs of physical models have been undertaken to measured required parameters for determination of the energy dissipation. Results showed that the energy dissipation in drops depend on the drop height and discharge. Predicted relative energy dissipations varied from 10.0% to 94.3%. This work has also indicated that the energy loss at drop is mainly due to the mixing of the jet with the pool behind the jet that causes air bubble entrainment in the flow. Statistical model has been developed to predict the energy dissipation in vertical drops denotes nonlinear correlation between effective parameters. Further an artificial neural networks (ANNs) approach was used in this paper to develop an explicit procedure for calculating energy loss at drops using NeuroSolutions. Trained network was able to predict the response with R2 and RMSE 0.977 and 0.0085 respectively. The performance of ANN was found effective when compared to regression equations in predicting the energy loss.

Keywords: Air bubble, drop, energy loss, hydraulic jump, NeuroSolutions

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Authors: Takashi Shimizu, Tomoaki Hashimoto

Abstract:

Recently, crystal growth technologies have made progress by the requirement for the high quality of crystal materials. To control the crystal growth dynamics actively by external forces is useuful for reducing composition non-uniformity. In this study, a control method based on model predictive control using thermal inputs is proposed for crystal growth dynamics of semiconductor materials. The control system of crystal growth dynamics considered here is governed by the continuity, momentum, energy, and mass transport equations. To establish the control method for such thermal fluid systems, we adopt model predictive control known as a kind of optimal feedback control in which the control performance over a finite future is optimized with a performance index that has a moving initial time and terminal time. The objective of this study is to establish a model predictive control method for crystal growth dynamics of semiconductor materials.

Keywords: Model predictive control, optimal control, crystal growth, process control.

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Authors: Wenyu Song, Bingxi Li, Zhongbin Fu, Bo Zhang

Abstract:

Although water only takes a little percentage in the total mass of soil, it indeed plays an important role to the strength of structure. Moisture transfer can be carried out by many different mechanisms which may involve heat and mass transfer, thermodynamic phase change, and the interplay of various forces such as viscous, buoyancy, and capillary forces. The continuum models are not well suited for describing those phenomena in which the connectivity of the pore space or the fracture network, or that of a fluid phase, plays a major role. However, Lattice Boltzmann methods (LBMs) are especially well suited to simulate flows around complex geometries. Lattice Boltzmann methods were initially invented for solving fluid flows. Recently, fluid with multicomponent and phase change is also included in the equations. By comparing the numerical result with experimental result, the Lattice Boltzmann methods with phase change will be optimized.

Keywords: Frozen soil, Lattice Boltzmann method, Phase change, Test rig.

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Authors: B. Bagheri Nakhjavanlo, T. S. Ellis, P.Raoofi, Sh.ziari

Abstract:

This paper presents an application of level sets for the segmentation of abdominal and thoracic aortic aneurysms in CTA datasets. An important challenge in reliably detecting aortic is the need to overcome problems associated with intensity inhomogeneities. Level sets are part of an important class of methods that utilize partial differential equations (PDEs) and have been extensively applied in image segmentation. A kernel function in the level set formulation aids the suppression of noise in the extracted regions of interest and then guides the motion of the evolving contour for the detection of weak boundaries. The speed of curve evolution has been significantly improved with a resulting decrease in segmentation time compared with previous implementations of level sets, and are shown to be more effective than other approaches in coping with intensity inhomogeneities. We have applied the Courant Friedrichs Levy (CFL) condition as stability criterion for our algorithm.

Keywords: Image segmentation, Level-sets, Local fitting binary, Thoracic aorta.

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Authors: Mansour Nikpour, Mohd Zin kandar, Mohsen Ghasemi, Hossein Fallah

Abstract:

Over half of the total electricity consumption is used in buildings. Air-conditioning and electric lighting are the two main resources of electricity consumption in high rise buildings. One way to reduce electricity consumption would be to limit heat gain into buildings, therefore reduce the demand for air-conditioning during hot summer months especially in hot regions. On the other hand natural daylight can be used to reduce the use of electricity for artificial lighting. In this paper effective factors on minimizing heat gain and achieving required day light were reviewed .As daylight always accompanied by solar heat gain. Also interactions between heat gain and daylight were discussed through previous studies and equations which are related to heat gain and day lighting especially in high rise buildings. As a result importance of building-s form and its component on energy consumption in buildings were clarified.

Keywords: High rise buildings, energy demand, day lighting, heat gain.

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Authors: Alaa A. Osman, Amgad M. Bayoumy, Ismail El baialy, Osama E. Abdellatif, Essam E. Khallil

Abstract:

In this paper, a numerical simulation of a finned store separating from a wing-pylon configuration has been studied and validated. A dynamic unstructured tetrahedral mesh approach is accomplished by using three grid sizes to numerically solving the discretized three dimensional, inviscid and compressible Euler equations. The method used for computations of separation of an external store assuming quasi-steady flow condition. Computations of quasi-steady flow have been directly coupled to a six degree-offreedom (6DOF) rigid-body motion code to generate store trajectories. The pressure coefficients at four different angular cuts and time histories of various trajectory parameters and wing pressure distribution during the store separation are compared for every grid size with published experimental data.

Keywords: CFD Modelling, Quasi-steady Flow, Moving-body Trajectories, Transonic Store Separation, Moving-body Trajectories.

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Authors: Fred Lacy

Abstract:

A superconductor has the ability to conduct electricity perfectly and exclude magnetic fields from its interior. In order to understand electromagnetic characteristics of superconductors, their material properties need to be examined. To facilitate this understanding, a theoretical model based on concepts of electromagnetics is presented to explain the electrical and magnetic properties of superconductors. The permittivity response is the key aspect of the model and it describes the electrical resistance response and why it vanishes at the material’s critical temperature. The model also explains the behavior of magnetic fields and why they cannot exist inside superconducting materials. The theoretical concepts and equations associated with this model are used to demonstrate that they are sufficient in describing the behavior of both type I and type II (or high temperature) superconductors. This model is also able to explain why superconductors behave differently than perfect conductors. As a result, examining the permittivity response and understanding electromagnetic field theory provides insight into the major aspects associated with superconducting materials.

Keywords: Ampere’s law, permittivity, permeability, resistivity, Schrödinger wave equation.

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Authors: Z. Hormozi Moghaddam, M. Mokhtari-Dizaji, M. Movahedin, M. E. Ravari

Abstract:

Mechanical index (MI) is used for quantifying acoustic cavitation and the relationship between acoustic pressure and the frequency. In this study, modeling of the MI was applied to provide treatment protocol and to understand the effective physical processes on reproducibility of stem cells. The acoustic pressure and MI equations are modeled and solved to estimate optimal MI for 28, 40, 150 kHz and 1 MHz frequencies. Radial and axial acoustic pressure distribution was extracted. To validate the results of the modeling, the acoustic pressure in the water and near field depth was measured by a piston hydrophone. Results of modeling and experiments show that the model is consistent well to experimental results with 0.91 and 0.90 correlation of coefficient (p<0.05) for 1 MHz and 40 kHz. Low intensity ultrasound with 0.40 MI is more effective on the proliferation rate of the spermatogonial stem cells during the seven days of culture, in contrast, high MI has a harmful effect on the spermatogonial stem cells. This model provides proper treatment planning in vitro and in vivo by estimating the cavitation phenomenon.

Keywords: Ultrasound, mechanical index, modeling, stem cell.

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