Search results for: quantum kinetic equation

Authors: Reza Mohammadi, Mahdieh Sahebi

Abstract:

We develop a method based on polynomial quintic spline for numerical solution of fourth-order non-homogeneous parabolic partial differential equation with variable coefficient. By using polynomial quintic spline in off-step points in space and finite difference in time directions, we obtained two three level implicit methods. Stability analysis of the presented method has been carried out. We solve four test problems numerically to validate the derived method. Numerical comparison with other methods shows the superiority of presented scheme.

Keywords: Fourth-order parabolic equation, variable coefficient, polynomial quintic spline, off-step points, stability analysis.

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Authors: Teerapon Pirom, Ura Pancharoen

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Amoxicillin is an antibiotic which is widely used to treat various infections in both human beings and animals. However, when amoxicillin is released into the environment, it is a major problem. Amoxicillin causes bacterial resistance to these drugs and failure of treatment with antibiotics. Liquid membrane is of great interest as a promising method for the separation and recovery of the target ions from aqueous solutions due to the use of carriers for the transport mechanism, resulting in highly selectivity and rapid transportation of the desired metal ions. The simultaneous processes of extraction and stripping in a single unit operation of liquid membrane system are very interesting. Therefore, it is practical to apply liquid membrane, particularly the HFSLM for industrial applications as HFSLM is proved to be a separation process with lower capital and operating costs, low energy and extractant with long life time, high selectivity and high fluxes compared with solid membranes. It is a simple design amenable to scaling up for industrial applications. The extraction and recovery for (Amoxicillin) through the hollow fiber supported liquid membrane (HFSLM) using aliquat336 as a carrier were explored with the experimental data. The important variables affecting on transport of amoxicillin viz. extractant concentration and operating time were investigated. The highest AMOX- extraction percentages of 85.35 and Amoxicillin stripping of 80.04 were achieved with the best condition at 6 mmol/L [aliquat336] and operating time 100 min. The extraction reaction order (n) and the extraction reaction rate constant (kf) were found to be 1.00 and 0.0344 min-1, respectively.

Keywords: Aliquat336, amoxicillin, HFSLM, kinetic.

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Authors: A.R. Ismail, M. R. A. Rani, Z. K. M. Makhbul, M. J. M. Nor, M. N. A. Rahman

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The environmental factors such as temperature and relative humidity are very contribute to the effect of comfort, health, performance and worker productivity. To ensure an ergonomics work environment, it is possible to require a specific attention especially in industries. The aim of this study is to show the effect of temperature and relative humidity on worker productivity in automotive industry by taking a workstation in an automotive plant as the location to conduct the study. From the analysis of the data, there were relationship between temperature and relative humidity on worker productivity. Mathematical equation to represent the relationship between temperatures and relative humidity on the production rate is modelled. From the equation model, the production rate for the workstation can be predicted base on the value of temperature and relative humidity.

Keywords: WBGT, Relative Humidity, Comfort, Productivity.

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Authors: Abdurrahim Dal, Tuncay Karaçay

Abstract:

Dynamics of a rotor supported by air bearings is strongly depends on the pressure distribution between the rotor and the bearing. In this study, internal pressure in air bearings is numerical and experimental analyzed for different radial clearances. Firstly the pressure distribution between rotor and bearing is modeled using Reynold's equation and this model is solved numerically. The rotor-bearing system is also modeled in four degree of freedom and it is simulated for different radial clearances. Then, in order to validate numerical results, a test rig is designed and the rotor bearing system is run under the same operational conditions. Pressure signals of left and right bearings are recorded. Internal pressure variations are compared for numerical and experimental results for different radial clearances.

Keywords: Air bearing, internal pressure, Reynold’s equation, rotor.

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Authors: Mohammad M. Toufigh, Ahad Ouria

Abstract:

This paper presents an analytical method to solve governing consolidation parabolic partial differential equation (PDE) for inelastic porous Medium (soil) with consideration of variation of equation coefficient under cyclic loading. Since under cyclic loads, soil skeleton parameters change, this would introduce variable coefficient of parabolic PDE. Classical theory would not rationalize consolidation phenomenon in such condition. In this research, a method based on time space mapping to a virtual time space along with superimposing rule is employed to solve consolidation of inelastic soils in cyclic condition. Changes of consolidation coefficient applied in solution by modification of loading and unloading duration by introducing virtual time. Mapping function is calculated based on consolidation partial differential equation results. Based on superimposing rule a set of continuous static loads in specified times used instead of cyclic load. A set of laboratory consolidation tests under cyclic load along with numerical calculations were performed in order to verify the presented method. Numerical solution and laboratory tests results showed accuracy of presented method.

Keywords: Mapping, Consolidation, Inelastic porous medium, Cyclic loading, Superimposing rule.

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Authors: Xin Luo, Jin Huang, Chuan-Long Wang

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The mechanical quadrature methods for solving the boundary integral equations of the anisotropic Darcy-s equations with Dirichlet conditions in smooth domains are presented. By applying the collectively compact theory, we prove the convergence and stability of approximate solutions. The asymptotic expansions for the error show that the methods converge with the order O (h3), where h is the mesh size. Based on these analysis, extrapolation methods can be introduced to achieve a higher convergence rate O (h5). An a posterior asymptotic error representation is derived in order to construct self-adaptive algorithms. Finally, the numerical experiments show the efficiency of our methods.

Keywords: Darcy's equation, anisotropic, mechanical quadrature methods, extrapolation methods, a posteriori error estimate.

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Authors: Fuziyah Ishak, Siti Norazura Ahmad

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Volterra integro-differential equations appear in many models for real life phenomena. Since analytical solutions for this type of differential equations are hard and at times impossible to attain, engineers and scientists resort to numerical solutions that can be made as accurately as possible. Conventionally, numerical methods for ordinary differential equations are adapted to solve Volterra integro-differential equations. In this paper, numerical solution for solving Volterra integro-differential equation using extended trapezoidal method is described. Formulae for the integral and differential parts of the equation are presented. Numerical results show that the extended method is suitable for solving first order Volterra integro-differential equations.

Keywords: Accuracy, extended trapezoidal method, numerical solution, Volterra integro-differential equations.

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Authors: V. Ghadamyari, F. Samadi, F. Kowsary

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An inverse geometry problem is solved to predict an unknown irregular boundary profile. The aim is to minimize the objective function, which is the difference between real and computed temperatures, using three different versions of Conjugate Gradient Method. The gradient of the objective function, considered necessary in this method, obtained as a result of solving the adjoint equation. The abilities of three versions of Conjugate Gradient Method in predicting the boundary profile are compared using a numerical algorithm based on the method. The predicted shapes show that due to its convergence rate and accuracy of predicted values, the Powell-Beale version of the method is more effective than the Fletcher-Reeves and Polak –Ribiere versions.

Keywords: Boundary elements, Conjugate Gradient Method, Inverse Geometry Problem, Sensitivity equation.

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Authors: M. Akbari, S. Sadodin

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In this paper, the melting of a semi-infinite body as a result of a moving laser beam has been studied. Because the Fourier heat transfer equation at short times and large dimensions does not have sufficient accuracy; a non-Fourier form of heat transfer equation has been used. Due to the fact that the beam is moving in x direction, the temperature distribution and the melting pool shape are not asymmetric. As a result, the problem is a transient threedimensional problem. Therefore, thermophysical properties such as heat conductivity coefficient, density and heat capacity are functions of temperature and material states. The enthalpy technique, used for the solution of phase change problems, has been used in an explicit finite volume form for the hyperbolic heat transfer equation. This technique has been used to calculate the transient temperature distribution in the semi-infinite body and the growth rate of the melt pool. In order to validate the numerical results, comparisons were made with experimental data. Finally, the results of this paper were compared with similar problem that has used the Fourier theory. The comparison shows the influence of infinite speed of heat propagation in Fourier theory on the temperature distribution and the melt pool size.

Keywords: Non-Fourier, Enthalpy technique, Melt pool, Radiational boundary condition

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Authors: Yiqin Lin, Liang Bao, Yimin Wei

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In this paper we study numerical methods for solving Sylvester matrix equations of the form AX +XBT +CDT = 0. A new projection method is proposed. The union of Krylov subspaces in A and its inverse and the union of Krylov subspaces in B and its inverse are used as the right and left projection subspaces, respectively. The Arnoldi-like process for constructing the orthonormal basis of the projection subspaces is outlined. We show that the approximate solution is an exact solution of a perturbed Sylvester matrix equation. Moreover, exact expression for the norm of residual is derived and results on finite termination and convergence are presented. Some numerical examples are presented to illustrate the effectiveness of the proposed method.

Keywords: Arnoldi process, Krylov subspace, Iterative method, Sylvester equation, Dissipative matrix.

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Authors: Omer K. Jasim, Safia Abbas, El-Sayed M. El-Horbaty, Abdel-Badeeh M. Salem

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Cloud computing technology is very useful in present day to day life, it uses the internet and the central remote servers to provide and maintain data as well as applications. Such applications in turn can be used by the end users via the cloud communications without any installation. Moreover, the end users’ data files can be accessed and manipulated from any other computer using the internet services. Despite the flexibility of data and application accessing and usage that cloud computing environments provide, there are many questions still coming up on how to gain a trusted environment that protect data and applications in clouds from hackers and intruders. This paper surveys the “keys generation and management” mechanism and encryption/decryption algorithms used in cloud computing environments, we proposed new security architecture for cloud computing environment that considers the various security gaps as much as possible. A new cryptographic environment that implements quantum mechanics in order to gain more trusted with less computation cloud communications is given.

Keywords: Cloud Computing, Cloud Encryption Model, Quantum Key Distribution.

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Authors: Arti Vaish, Harish Parthasarathy

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The scalar wave equation for a potential in a curved space time, i.e., the Laplace-Beltrami equation has been studied in this work. An action principle is used to derive a finite element algorithm for determining the modes of propagation inside a waveguide of arbitrary shape. Generalizing this idea, the Maxwell theory in a curved space time determines a set of linear partial differential equations for the four electromagnetic potentials given by the metric of space-time. Similar to the Einstein-s formulation of the field equations of gravitation, these equations are also derived from an action principle. In this paper, the expressions for the action functional of the electromagnetic field have been derived in the presence of gravitational field.

Keywords: General theory of relativity, electromagnetism, metric tensor, Maxwells equations, test functions, finite element method.

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Authors: R. Rajeshkannan, M. Rajasimman, N. Rajamohan

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In this study, the sorption of Malachite green (MG) on Hydrilla verticillata biomass, a submerged aquatic plant, was investigated in a batch system. The effects of operating parameters such as temperature, adsorbent dosage, contact time, adsorbent size, and agitation speed on the sorption of Malachite green were analyzed using response surface methodology (RSM). The proposed quadratic model for central composite design (CCD) fitted very well to the experimental data that it could be used to navigate the design space according to ANOVA results. The optimum sorption conditions were determined as temperature - 43.5oC, adsorbent dosage - 0.26g, contact time - 200min, adsorbent size - 0.205mm (65mesh), and agitation speed - 230rpm. The Langmuir and Freundlich isotherm models were applied to the equilibrium data. The maximum monolayer coverage capacity of Hydrilla verticillata biomass for MG was found to be 91.97 mg/g at an initial pH 8.0 indicating that the optimum sorption initial pH. The external and intra particle diffusion models were also applied to sorption data of Hydrilla verticillata biomass with MG, and it was found that both the external diffusion as well as intra particle diffusion contributes to the actual sorption process. The pseudo-second order kinetic model described the MG sorption process with a good fitting.

Keywords: Response surface methodology, Hydrilla verticillata, malachite green, adsorption, central composite design

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Authors: Djemai Bara, Mohamed Faouzi Mahboub, Djamila Bennaceur-Doumaz

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In this work, the role of the preformed plasma created on the front face of a target, irradiated by a high intensity short pulse laser, in the framework of ion acceleration process, modeled by Target Normal Sheath Acceleration (TNSA) mechanism, is studied. This plasma is composed of cold ions governed by fluid equations and non-thermal & trapped with densities represented by a "Cairns-Gurevich" equation. The self-similar solution of the equations shows that electronic trapping and the presence of non-thermal electrons in the pre-plasma are both responsible in ion acceleration as long as the proportion of energetic electrons is not too high. In the case where the majority of electrons are energetic, the electrons are accelerated directly by the ponderomotive force of the laser without the intermediate of an accelerating plasma wave.

Keywords: Cairns-Gurevich Equation, ion acceleration, plasma expansion, pre-plasma.

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Authors: Tan K. B., Norhashidah Hj. M. Ali

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In this article, we aim to discuss the formulation of two explicit group iterative finite difference methods for time-dependent two dimensional Burger-s problem on a variable mesh. For the non-linear problems, the discretization leads to a non-linear system whose Jacobian is a tridiagonal matrix. We discuss the Newton-s explicit group iterative methods for a general Burger-s equation. The proposed explicit group methods are derived from the standard point and rotated point Crank-Nicolson finite difference schemes. Their computational complexity analysis is discussed. Numerical results are given to justify the feasibility of these two proposed iterative methods.

Keywords: Standard point Crank-Nicolson (CN), Rotated point Crank-Nicolson (RCN), Explicit Group (EG), Explicit Decoupled Group (EDG).

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Authors: Zhenying Hong, Guangwei Yuan, Xuedong Fu, Shulin Yang

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In this paper, the typical exponential method, diamond difference and modified time discrete scheme is researched for self adaptive time step. The second-order time evolution scheme is applied to time-dependent spherical neutron transport equation by discrete ordinates method. The numerical results show that second-order time evolution scheme associated exponential method has some good properties. The time differential curve about neutron current is more smooth than that of exponential method and diamond difference and modified time discrete scheme.

Keywords: Exponential method, diamond difference, modified time discrete scheme, second-order time evolution scheme.

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Authors: Pranav Ravikumar, Arunabha Bera, Vijay K. Mehra, Anand Kumar

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This paper solves the Non Linear Schrodinger Equation using the Split Step Fourier method for modeling an optical fiber. The model generates a complex wave of optical pulses and using the results obtained two graphs namely Loss versus Wavelength and Dispersion versus Wavelength are generated. Taking Chromatic Dispersion and Polarization Mode Dispersion losses into account, the graphs generated are compared with the graphs formulated by JDS Uniphase Corporation which uses standard values of dispersion for optical fibers. The graphs generated when compared with the JDS Uniphase Corporation plots were found to be more or less similar thus verifying that the model proposed is right. MATLAB software was used for doing the modeling.

Keywords: Modulation, Non Linear Schrodinger Equation, Optical fiber, Split Step Fourier Method.

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Authors: Punit Kumar, Niraj Kumar

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The influence of transverse surface roughness on EHL characteristics has been investigated numerically using an extensive set of full EHL line contact simulations for shear-thinning lubricants under pure sliding condition. The shear-thinning behavior of lubricant is modeled using Carreau viscosity equation along with Doolittle-Tait equation for lubricant compressibility. The surface roughness is assumed to be sinusoidal and it is present on the stationary surface. It is found that surface roughness causes sharp pressure peaks along with reduction in central and minimum film thickness. With increasing amplitude of surface roughness, the minimum film thickness decreases much more rapidly as compared to the central film thickness.

Keywords: EHL, Carreau, Shear-thinning, Surface Roughness, Amplitude, Wavelength.

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Authors: Chien-Hua Lee, Cheng-Yi Chen

Abstract:

The stability test problem for homogeneous large-scale perturbed bilinear time-delay systems subjected to constrained inputs is considered in this paper. Both nonlinear uncertainties and interval systems are discussed. By utilizing the Lyapunove equation approach associated with linear algebraic techniques, several delay-independent criteria are presented to guarantee the robust stability of the overall systems. The main feature of the presented results is that although the Lyapunov stability theorem is used, they do not involve any Lyapunov equation which may be unsolvable. Furthermore, it is seen the proposed schemes can be applied to solve the stability analysis problem of large-scale time-delay systems.

Keywords: homogeneous bilinear system, constrained input, time-delay, uncertainty, transient response, decay rate.

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Authors: Constantin Z. Leshan

Abstract:

Hole Vacuum theory is based on discontinuous spacetime that contains vacuum holes. Vacuum holes can explain gravitation, some laws of quantum mechanics and allow teleportation of matter. All massive bodies emit a flux of holes which curve the spacetime; if we increase the concentration of holes, it leads to length contraction and time dilation because the holes do not have the properties of extension and duration. In the limited case when space consists of holes only, the distance between every two points is equal to zero and time stops - outside of the Universe, the extension and duration properties do not exist. For this reason, the vacuum hole is the only particle in physics capable of describing gravitation using its own properties only. All microscopic particles must 'jump' continually and 'vibrate' due to the appearance of holes (impassable microscopic 'walls' in space), and it is the cause of the quantum behavior. Vacuum holes can explain the entanglement, non-locality, wave properties of matter, tunneling, uncertainty principle and so on. Particles do not have trajectories because spacetime is discontinuous and has impassable microscopic 'walls' due to the simple mechanical motion is impossible at small scale distances; it is impossible to 'trace' a straight line in the discontinuous spacetime because it contains the impassable holes. Spacetime 'boils' continually due to the appearance of the vacuum holes. For teleportation to be possible, we must send a body outside of the Universe by enveloping it with a closed surface consisting of vacuum holes. Since a material body cannot exist outside of the Universe, it reappears instantaneously in a random point of the Universe. Since a body disappears in one volume and reappears in another random volume without traversing the physical space between them, such a transportation method can be called teleportation (or Hole Teleportation). It is shown that Hole Teleportation does not violate causality and special relativity due to its random nature and other properties. Although Hole Teleportation has a random nature, it can be used for colonization of extrasolar planets by the help of the method called 'random jumps': after a large number of random teleportation jumps, there is a probability that the spaceship may appear near a habitable planet. We can create vacuum holes experimentally using the method proposed by Descartes: we must remove a body from the vessel without permitting another body to occupy this volume.

Keywords: Border of the universe, causality violation, perfect isolation, quantum jumps.

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Authors: Hassan Manouzi, Taous-Meriem Laleg-Kirati

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In this paper we study mathematically the eigenvalue problem for stochastic elliptic partial differential equation of Wick type. Using the Wick-product and the Wiener-Itô chaos expansion, the stochastic eigenvalue problem is reformulated as a system of an eigenvalue problem for a deterministic partial differential equation and elliptic partial differential equations by using the Fredholm alternative. To reduce the computational complexity of this system, we shall use a decomposition method using the Wiener-Itô chaos expansion. Once the approximation of the solution is performed using the finite element method for example, the statistics of the numerical solution can be easily evaluated.

Keywords: Eigenvalue problem, Wick product, SPDEs, finite element, Wiener-Itô chaos expansion.

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Authors: Stephen Kirkup

Abstract:

This paper discusses the implementation of the boundary element method (BEM) on an Excel spreadsheet and how it can be used in teaching vector calculus and simulation. There are two separate spreadheets, within which Laplace equation is solved by the BEM in two dimensions (LIBEM2) and axisymmetric three dimensions (LBEMA). The main algorithms are implemented in the associated programming language within Excel, Visual Basic for Applications (VBA). The BEM only requires a boundary mesh and hence it is a relatively accessible method. The BEM in the open spreadsheet environment is demonstrated as being useful as an aid to teaching and learning. The application of the BEM implemented on a spreadsheet for educational purposes in introductory vector calculus and simulation is explored. The development of assignment work is discussed, and sample results from student work are given. The spreadsheets were found to be useful tools in developing the students’ understanding of vector calculus and in simulating heat conduction.

Keywords: Boundary element method, laplace equation, vector calculus, simulation, education.

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Authors: Karandeep Singh, Baibing Li

Abstract:

Traffic density, an indicator of traffic conditions, is one of the most critical characteristics to Intelligent Transport Systems (ITS). This paper investigates recursive traffic density estimation using the information provided from inductive loop detectors. On the basis of the phenomenological relationship between speed and density, the existing studies incorporate a state space model and update the density estimate using vehicular speed observations via the extended Kalman filter, where an approximation is made because of the linearization of the nonlinear observation equation. In practice, this may lead to substantial estimation errors. This paper incorporates a suitable transformation to deal with the nonlinear observation equation so that the approximation is avoided when using Kalman filter to estimate the traffic density. A numerical study is conducted. It is shown that the developed method outperforms the existing methods for traffic density estimation.

Keywords: Density estimation, Kalman filter, speed-densityrelationship, Traffic surveillance.

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Authors: Amir Hossein Daei Sorkhabi, Farid Vakili Tahami

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In this paper, creep constitutive equations of base (Parent) and weld materials of the weldment for cold-drawn 304L stainless steel have been obtained experimentally. For this purpose, test samples have been generated from cold drawn bars and weld material according to the ASTM standard. The creep behavior and properties have been examined for these materials by conducting uniaxial creep tests. Constant temperatures and constant load uni-axial creep tests have been carried out at two high temperatures, 680 and 720 oC, subjected to constant loads, which produce initial stresses ranging from 240 to 360 MPa. The experimental data have been used to obtain the creep constitutive parameters using numerical optimization techniques.

Keywords: Creep, Constitutive equation, Cold-drawn 304L stainless steel, Weld, Base material

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Authors: Madiha Tariq, Hena Rabbani

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Recently, cavity-optomechanics becomes an extensive research field that has manipulated the mechanical effects of light for coupling of the optical field with other physical objects specifically with regards to dynamical localization. We investigate the dynamical localization (both in momentum and position space) for a vibrational mirror in a Fabry-Pérot cavity driven by a single mode optical field and a transverse probe field. The weak probe field phenomenon results in classical chaos in phase space and spatio temporal dynamics in position |ψ(x)²| and momentum space |ψ(p)²| versus time show quantum localization in both momentum and position space. Also, we discuss the parametric dependencies of dynamical localization for a designated set of parameters to be experimentally feasible. Our work opens an avenue to manipulate the other optical phenomena and applicability of proposed work can be prolonged to turn-able laser sources in the future.

Keywords: Dynamical localization, cavity optomechanics, hamiltonian chaos, probe field.

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Authors: Zebiri Chemseddine, Benabdelaziz Fatiha

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The effect of a chiral bianisotropic substrate on the complex resonant frequency of a rectangular microstrip resonator has been studied on the basis of the integral equation formulation. The analysis is based on numerical resolution of the integral equation using Galerkin procedure for moment method in the spectral domain. This work aim first to study the effect of the chirality of a bianisotopic substrate upon the resonant frequency and the half power bandwidth, second the effect of a magnetic anisotropy via an asymptotic approach for very weak substrate upon the resonant frequency and the half power bandwidth has been investigated. The obtained results are compared with previously published work [11-9], they were in good agreement.

Keywords: Microstrip antenna, bianisotropic media, resonant frequency, moment method.

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Authors: Gopu Sreenivasulu, Bimlesh Kumar, Achanta Ramakrishna Rao

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To define or predict incipient motion in an alluvial channel, most of the investigators use a standard or modified form of Shields- diagram. Shields- diagram does give a process to determine the incipient motion parameters but an iterative one. To design properly (without iteration), one should have another equation for resistance. Absence of a universal resistance equation also magnifies the difficulties in defining the model. Neural network technique, which is particularly useful in modeling a complex processes, is presented as a tool complimentary to modeling incipient motion. Present work develops a neural network model employing the RBF network to predict the average velocity u and water depth y based on the experimental data on incipient condition. Based on the model, design curves have been presented for the field application.

Keywords: Incipient motion, Prediction error, Radial-Basisfunction, Sediment transport, Shields' diagram.

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Authors: Dara Singh, Keikhosrow Firouzbakhsh, Mohammad Taghi Ahmadian

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In this paper, conventional laser Keratoplasty surgeries in the human eye are studied. For this purpose, a validated 3D finite volume model of the human eye is introduced. In this model the fluid flow has also been considered. The discretized domain of the human eye incorporates a bio-heat transfer equation coupled with a Boussinesq equation. Both continuous and pulsed lasers have been modeled and the results are compared. Moreover, two different conventional surgical positions that are upright and recumbent are compared for these laser therapies. The simulation results show that in these conventional surgeries, the temperature rises above the critical values at the laser insertion areas. However, due to the short duration and the localized nature, the potential damages are restricted to very small regions and can be ignored. The conclusion is that the present day lasers are acceptably safe to the human eye.

Keywords: Eye, heat-transfer, keratoplasty laser, surgery.

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Authors: Gesine Hellwig

Abstract:

Functional imaging procedures for the non-invasive assessment of tissue microcirculation are highly requested, but require a mathematical approach describing the trans- and intercapillary passage of tracer particles. Up to now, two theoretical, for the moment different concepts have been established for tracer kinetic modeling of contrast agent transport in tissues: pharmacokinetic compartment models, which are usually written as coupled differential equations, and the indicator dilution theory, which can be generalized in accordance with the theory of lineartime- invariant (LTI) systems by using a convolution approach. Based on mathematical considerations, it can be shown that also in the case of an open two-compartment model well-known from functional imaging, the concentration-time course in tissue is given by a convolution, which allows a separation of the arterial input function from a system function being the impulse response function, summarizing the available information on tissue microcirculation. Due to this reason, it is possible to integrate the open two-compartment model into the system-theoretic concept of indicator dilution theory (IDT) and thus results known from IDT remain valid for the compartment approach. According to the long number of applications of compartmental analysis, even for a more general context similar solutions of the so-called forward problem can already be found in the extensively available appropriate literature of the seventies and early eighties. Nevertheless, to this day, within the field of biomedical imaging – not from the mathematical point of view – there seems to be a trench between both approaches, which the author would like to get over by exemplary analysis of the well-known model.

Keywords: Functional imaging, Tracer kinetic modeling, LTIsystem, Indicator dilution theory / convolution approach, Two-Compartment model.

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Authors: Barenten Suciu

Abstract:

In this work, effects of the friction and truncation on the dynamics of a double-cone gravitational motor, self-propelled on a straight V-shaped horizontal rail, are evaluated. Such mechanism has a variable radius of contact, and, on one hand, it is similar to a pulley mechanism that changes the potential energy into the kinetic energy of rotation, but on the other hand, it is similar to a pendulum mechanism that converts the potential energy of the suspended body into the kinetic energy of translation along a circular path. Movies of the self- propelled double-cones, made of S45C carbon steel and wood, along rails made of aluminum alloy, were shot for various opening angles of the rails. Kinematical features of the double-cones were estimated through the slow-motion processing of the recorded movies. Then, a kinematical model is derived under assumption that the distance traveled by the contact points on the rectilinear rails is identical with the distance traveled by the contact points on the truncated conical surface. Additionally, a dynamic model, for this particular contact problem, was proposed and validated against the experimental results. Based on such model, the traction force and the traction torque acting on the double-cone are identified. One proved that the rolling traction force is always smaller than the sliding friction force; i.e., the double-cone is rolling without slipping. Results obtained in this work can be used to achieve the proper design of such gravitational motor.

Keywords: Truncated double-cone, friction, rolling and sliding, dynamic model, gravitational motor.

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