Search results for: Finite Alphabet Case

Authors: Yanan Yang, Zhigang Wang, Xiang Chen

Abstract:

This paper presents the use of Legendre pseudospectral method for the optimization of finite-thrust orbital transfer for spacecrafts. In order to get an accurate solution, the System-s dynamics equations were normalized through a dimensionless method. The Legendre pseudospectral method is based on interpolating functions on Legendre-Gauss-Lobatto (LGL) quadrature nodes. This is used to transform the optimal control problem into a constrained parameter optimization problem. The developed novel optimization algorithm can be used to solve similar optimization problems of spacecraft finite-thrust orbital transfer. The results of a numerical simulation verified the validity of the proposed optimization method. The simulation results reveal that pseudospectral optimization method is a promising method for real-time trajectory optimization and provides good accuracy and fast convergence.

Keywords: Finite-thrust, Orbital transfer, Legendre pseudospectral method

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Authors: Ionel D. Craiu, Mihai Nedelcu

Abstract:

Thin-walled cylinders are often used by the offshore industry as columns of floating installations. Based on observed strains, the inverse Finite Element Method (iFEM) may rebuild the deformation of structures. Structural Health Monitoring uses this approach extensively. However, the number of in-situ strain gauges is what determines how accurate it is, and for shell structures with complicated deformation, this number can easily become too high for practical use. Any thin-walled beam member's complicated deformation can be modeled by the Generalized Beam Theory (GBT) as a linear combination of pre-specified cross-section deformation modes. GBT uses bar finite elements as opposed to shell finite elements. This paper proposes an iFEM/GBT formulation for the shape sensing of thin-walled cylinders based on these benefits. This method significantly reduces the number of strain gauges compared to using the traditional inverse-shell finite elements. Using numerical simulations, dent damage detection is achieved by comparing the strain distributions of the undamaged and damaged members. The effect of noise on strain measurements is also investigated.

Keywords: Damage detection, generalized beam theory, inverse finite element method, shape sensing.

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Authors: G. Partheepan, D.K. Sehgal, R.K. Pandey

Abstract:

This paper presents a method for determining the uniaxial tensile properties such as Young-s modulus, yield strength and the flow behaviour of a material in a virtually non-destructive manner. To achieve this, a new dumb-bell shaped miniature specimen has been designed. This helps in avoiding the removal of large size material samples from the in-service component for the evaluation of current material properties. The proposed miniature specimen has an advantage in finite element modelling with respect to computational time and memory space. Test fixtures have been developed to enable the tension tests on the miniature specimen in a testing machine. The studies have been conducted in a chromium (H11) steel and an aluminum alloy (AR66). The output from the miniature test viz. load-elongation diagram is obtained and the finite element simulation of the test is carried out using a 2D plane stress analysis. The results are compared with the experimental results. It is observed that the results from the finite element simulation corroborate well with the miniature test results. The approach seems to have potential to predict the mechanical properties of the materials, which could be used in remaining life estimation of the various in-service structures.

Keywords: ABAQUS, finite element, miniature test, tensileproperties

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Authors: Khaled Moaddy

Abstract:

In this paper, we present a fast and accurate numerical scheme for the solution of a Laplace equation with Dirichlet boundary conditions. The non-standard finite difference scheme (NSFD) is applied to construct the numerical solutions of a Laplace equation with two different Dirichlet boundary conditions. The solutions obtained using NSFD are compared with the solutions obtained using the standard finite difference scheme (SFD). The NSFD scheme is demonstrated to be reliable and efficient.

Keywords: Standard finite difference schemes, non–standard schemes, Laplace equation, Dirichlet boundary conditions.

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Authors: Swarniv Chandra, Basudev Ghosh

Abstract:

Using the quantum hydrodynamic (QHD) model for quantum plasma at finite temperature the modulational instability of electron plasma waves is investigated by deriving a nonlinear Schrodinger equation. It was found that the electron degeneracy parameter significantly affects the linear and nonlinear properties of electron plasma waves in quantum plasma.

Keywords: Amplitude Modulation, Electron Plasma Waves, Finite Temperature Model, Modulational Instability, Quantum Plasma.

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Authors: Xi Yang, Bulent Chavdar, Alan Vonseggern, Taylan Altan

Abstract:

Fracture in hot precision forging of engine valves was investigated in this paper. The entire valve forging procedure was described and the possible cause of the fracture was proposed. Finite Element simulation was conducted for the forging process, with commercial Finite Element code DEFORMTM. The effects of material properties, the effect of strain rate and temperature were considered in the FE simulation. Two fracture criteria were discussed and compared, based on the accuracy and reliability of the FE simulation results. The selected criterion predicted the fracture location and shows the trend of damage increasing with good accuracy, which matches the experimental observation. Additional modification of the punch shapes was proposed to further reduce the tendency of fracture in forging. Finite Element comparison shows a great potential of such application in the mass production.

Keywords: Hot forging, engine valve, fracture, tooling.

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Authors: Komeil Valipourian

Abstract:

Urban advances and the growing need for developing infrastructures has increased the importance of deep excavations. In this study, after the introducing probability analysis as an important issue, an attempt has been made to apply it for the deep excavation project of Bangkok’s Metro as a case study. For this, the numerical probability model has been developed based on the Finite Difference Method and Monte Carlo sampling approach. The results indicate that disregarding the issue of probability in this project will result in an inappropriate design of the retaining structure. Therefore, probabilistic redesign of the support is proposed and carried out as one of the applications of probability analysis. A 50% reduction in the flexural strength of the structure increases the failure probability just by 8% in the allowable range and helps improve economic conditions, while maintaining mechanical efficiency. With regard to the lack of efficient design in most deep excavations, by considering geometrical and geotechnical variability, an attempt was made to develop an optimum practical design standard for deep excavations based on failure probability. On this basis, a practical relationship is presented for estimating the maximum allowable horizontal displacement, which can help improve design conditions without developing the probability analysis.

Keywords: Numerical probability modeling, deep excavation, allowable maximum displacement, finite difference method, FDM.

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Authors: Betül Gezer, Ahmet Tekcan, Osman Bizim

Abstract:

In elliptic curve theory, number of rational points on elliptic curves and determination of these points is a fairly important problem. Let p be a prime and Fp be a finite field and k ∈ Fp. It is well known that which points the curve y2 = x3 + kx has and the number of rational points of on Fp. Consider the circle family x2 + y2 = r2. It can be interesting to determine common points of these two curve families and to find the number of these common points. In this work we study this problem.

Keywords: Elliptic curves over finite fields, rational points on elliptic curves and circles.

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Authors: Tariq T. Darabseh

Abstract:

The transient thermoelastic response of thick hollow cylinder made of functionally graded material under thermal loading is studied. The generalized coupled thermoelasticity based on the Green-Lindsay model is used. The thermal and mechanical properties of the functionally graded material are assumed to be varied in the radial direction according to a power law variation as a function of the volume fractions of the constituents. The thermal and elastic governing equations are solved by using Galerkin finite element method. All the finite element calculations were done by using commercial finite element program FlexPDE. The transient temperature, radial displacement, and thermal stresses distribution through the radial direction of the cylinder are plotted.

Keywords: Finite element method, thermal stresses, Green-Lindsay theory, functionally graded material.

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Authors: Mattheos K. Protopapas, Elias B. Kosmatopoulos

Abstract:

An iterative algorithm is proposed and tested in Cournot Game models, which is based on the convergence of sequential best responses and the utilization of a genetic algorithm for determining each player-s best response to a given strategy profile of its opponents. An extra outer loop is used, to address the problem of finite accuracy, which is inherent in genetic algorithms, since the set of feasible values in such an algorithm is finite. The algorithm is tested in five Cournot models, three of which have convergent best replies sequence, one with divergent sequential best replies and one with “local NE traps"[14], where classical local search algorithms fail to identify the Nash Equilibrium. After a series of simulations, we conclude that the algorithm proposed converges to the Nash Equilibrium, with any level of accuracy needed, in all but the case where the sequential best replies process diverges.

Keywords: Best response, Cournot oligopoly, genetic algorithms, Nash equilibrium.

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Authors: M. Sasajima, M. Watanabe, T. Yamaguchi, Y. Kurosawa, Y. Koike

Abstract:

Sound pathways in the enclosures of small earphones are very narrow. In such narrow pathways, the speed of sound propagation and the phase of sound waves change because of the air viscosity. We have developed a new finite element method that includes the effects of damping due to air viscosity for modeling the sound pathway. This method is developed as an extension of the existing finite element method for porous sound-absorbing materials. The numerical calculation results using the proposed finite element method are validated against the existing calculation methods.

Keywords: Simulation, FEM, air viscosity, damping.

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Authors: M. Ikhwan Z. Ridzwan, Bidyut Pal, Ulrich N. Hansen

Abstract:

Finite element method was applied to model damage development in the femoral neck during a sideways fall. The femoral failure was simulated using the maximum principal strain criterion. The evolution of damage was consistent with previous studies. It was initiated by compressive failure at the junction of the superior aspect of the femoral neck and the greater trochanter. It was followed by tensile failure that occurred at the inferior aspect of the femoral neck before a complete transcervical fracture was observed. The estimated failure line was less than 50° from the horizontal plane (Pauwels type II).

Keywords: Femoral Strength, Finite Element Models, Hip Fracture, Progressive Failure, Sideways Fall.

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Authors: Jamal Laaouine, Mohammed Elhassani Charkani

Abstract:

Let p be a prime and let b be an integer. MDS b-symbol codes are a direct generalization of MDS codes. The γ-constacyclic codes of length pˢ over the finite commutative chain ring Fₚm [u]/ < u² > had been classified into four distinct types, where is a nonzero element of the field Fₚm. Let C₃ be a code of Type 3. In this paper, we obtain the b-symbol distance db(C₃) of the code C₃. Using this result, necessary and sufficient conditions under which C₃ is an MDS b-symbol code are given.

Keywords: constacyclic code, repeated-root code, maximum distance separable, MDS codes, b-symbol distance, finite chain rings

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Authors: K. Kamalanand, S. Srinivasan

Abstract:

Analysis of blood vessel mechanics in normal and diseased conditions is essential for disease research, medical device design and treatment planning. In this work, 3D finite element models of normal vessel and atherosclerotic vessel with 50% plaque deposition were developed. The developed models were meshed using finite number of tetrahedral elements. The developed models were simulated using actual blood pressure signals. Based on the transient analysis performed on the developed models, the parameters such as total displacement, strain energy density and entropy per unit volume were obtained. Further, the obtained parameters were used to develop artificial neural network models for analyzing normal and atherosclerotic blood vessels. In this paper, the objectives of the study, methodology and significant observations are presented.

Keywords: Blood vessel, atherosclerosis, finite element model, artificial neural networks

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Authors: Mojtaba Aghamiri Esfahani, Mohammad Karkon, Seyed Majid Hosseini Nezhad, Reza Hosseini-Ara

Abstract:

In this study, the effect of uncertainty in elastic modulus of a plate on free vibration response is investigated. For this purpose, the elastic modulus of the plate is modeled as stochastic variable with normal distribution. Moreover, the distance autocorrelation function is used for stochastic field. Then, by applying the finite element method and Monte Carlo simulation, stochastic finite element relations are extracted. Finally, with a numerical test, the effect of uncertainty in the elastic modulus on free vibration response of a plate is studied. The results show that the effect of uncertainty in elastic modulus of the plate cannot play an important role on the free vibration response.

Keywords: Stochastic finite elements, plate bending, free vibration, Monte Carlo, Neumann expansion method.

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Authors: S. Sfarni, E. Bellenger, J. Fortin, M. Guessasma

Abstract:

The use of the mechanical simulation (in particular the finite element analysis) requires the management of assumptions in order to analyse a real complex system. In finite element analysis (FEA), two modeling steps require assumptions to be able to carry out the computations and to obtain some results: the building of the physical model and the building of the simulation model. The simplification assumptions made on the analysed system in these two steps can generate two kinds of errors: the physical modeling errors (mathematical model, domain simplifications, materials properties, boundary conditions and loads) and the mesh discretization errors. This paper proposes a mesh adaptive method based on the use of an h-adaptive scheme in combination with an error estimator in order to choose the mesh of the simulation model. This method allows us to choose the mesh of the simulation model in order to control the cost and the quality of the finite element analysis.

Keywords: Finite element, discretization errors, adaptivity.

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Authors: T.C. Manjunath, B. Bandyopadhyay

Abstract:

This paper features the modeling and design of a Robust Decentralized Fast Output Sampling (RDFOS) Feedback control technique for the active vibration control of a smart flexible multimodel Euler-Bernoulli cantilever beams for a multivariable (MIMO) case by retaining the first 6 vibratory modes. The beam structure is modeled in state space form using the concept of piezoelectric theory, the Euler-Bernoulli beam theory and the Finite Element Method (FEM) technique by dividing the beam into 4 finite elements and placing the piezoelectric sensor / actuator at two finite element locations (positions 2 and 4) as collocated pairs, i.e., as surface mounted sensor / actuator, thus giving rise to a multivariable model of the smart structure plant with two inputs and two outputs. Five such multivariable models are obtained by varying the dimensions (aspect ratios) of the aluminium beam. Using model order reduction technique, the reduced order model of the higher order system is obtained based on dominant Eigen value retention and the Davison technique. RDFOS feedback controllers are designed for the above 5 multivariable-multimodel plant. The closed loop responses with the RDFOS feedback gain and the magnitudes of the control input are obtained and the performance of the proposed multimodel smart structure system is evaluated for vibration control.

Keywords: Smart structure, Euler-Bernoulli beam theory, Fastoutput sampling feedback control, Finite Element Method, Statespace model, Vibration control, LMI, Model order Reduction.

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Authors: Faheem Ahmed, Fareed Ahmed, Yongheng Guo, Yong Yang

Abstract:

This paper deals with a high-order accurate Runge Kutta Discontinuous Galerkin (RKDG) method for the numerical solution of the wave equation, which is one of the simple case of a linear hyperbolic partial differential equation. Nodal DG method is used for a finite element space discretization in 'x' by discontinuous approximations. This method combines mainly two key ideas which are based on the finite volume and finite element methods. The physics of wave propagation being accounted for by means of Riemann problems and accuracy is obtained by means of high-order polynomial approximations within the elements. High order accurate Low Storage Explicit Runge Kutta (LSERK) method is used for temporal discretization in 't' that allows the method to be nonlinearly stable regardless of its accuracy. The resulting RKDG methods are stable and high-order accurate. The L1 ,L2 and L∞ error norm analysis shows that the scheme is highly accurate and effective. Hence, the method is well suited to achieve high order accurate solution for the scalar wave equation and other hyperbolic equations.

Keywords: Nodal Discontinuous Galerkin Method, RKDG, Scalar Wave Equation, LSERK

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Authors: Akram G., Jasmy Y.

Abstract:

The finite-difference time-domain (FDTD) method is one of the most widely used computational methods in electromagnetic. This paper describes the design of two-dimensional (2D) FDTD simulation software for transverse magnetic (TM) polarization using Berenger's split-field perfectly matched layer (PML) formulation. The software is developed using Matlab programming language. Numerical examples validate the software.

Keywords: Finite difference time domain (FDTD) method, perfectly matched layer (PML), split-filed formulation, transverse magnetic (TM) polarization.

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Authors: Nopparat Pochai

Abstract:

Smoke discharging is a main reason of air pollution problem from industrial plants. The obstacle of a building has an affect with the air pollutant discharge. In this research, a mathematical model of the smoke dispersion from two sources and one source with a structural obstacle is considered. The governing equation of the model is an isothermal mass transfer model in a viscous fluid. The finite element method is used to approximate the solutions of the model. The triangular linear elements have been used for discretising the domain, and time integration has been carried out by semi-implicit finite difference method. The simulations of smoke dispersion in cases of one chimney and two chimneys are presented. The maximum calculated smoke concentration of both cases are compared. It is then used to make the decision for smoke discharging and air pollutant control problems on industrial area.

Keywords: Air pollution, Smoke dispersion, Finite element method, Stream function, Vorticity equation, Convection-diffusion equation, Semi-implicit method

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Authors: Abdur Rosyid, Mohamed El-Madany, Mohanad Alata

Abstract:

Due to simplicity and low cost, rotordynamic system is often modeled by using lumped parameters. Recently, finite elements have been used to model rotordynamic system as it offers higher accuracy. However, it involves high degrees of freedom. In some applications such as control design, this requires higher cost. For this reason, various model reduction methods have been proposed. This work demonstrates the quality of model reduction of rotor-bearing-support system through substructuring. The quality of the model reduction is evaluated by comparing some first natural frequencies, modal damping ratio, critical speeds, and response of both the full system and the reduced system. The simulation shows that the substructuring is proven adequate to reduce finite element rotor model in the frequency range of interest as long as the number and the location of master nodes are determined appropriately. However, the reduction is less accurate in an unstable or nearly-unstable system.

Keywords: Finite element model, rotordynamic system, model reduction, substructuring.

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Authors: S. Tupsie, A. Isaramongkolrak, P. Pao-la-or

Abstract:

This paper presents the mathematical model of electric field and magnetic field in transmission system, which performs in second-order partial differential equation. This research has conducted analyzing the electromagnetic field radiating to atmosphere around the transmission line, when there is the transmission line transposition in case of long distance distribution. The six types of 500 kV transposed HV transmission line with double circuit will be considered. The computer simulation is applied finite element method that is developed by MATLAB program. The problem is considered to two dimensions, which is time harmonic system with the graphical performance of electric field and magnetic field. The impact from simulation of six types long distance distributing transposition will not effect changing of electric field and magnetic field which surround the transmission line.

Keywords: Transposition, Electromagnetic Field, Finite Element Method (FEM), Transmission Line, Computer Simulation

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Authors: T.C. Manjunath, B. Bandyopadhyay

Abstract:

Active Vibration Control (AVC) is an important problem in structures. One of the ways to tackle this problem is to make the structure smart, adaptive and self-controlling. The objective of active vibration control is to reduce the vibration of a system by automatic modification of the system-s structural response. This paper features the modeling and design of a Periodic Output Feedback (POF) control technique for the active vibration control of a flexible Timoshenko cantilever beam for a multivariable case with 2 inputs and 2 outputs by retaining the first 2 dominant vibratory modes using the smart structure concept. The entire structure is modeled in state space form using the concept of piezoelectric theory, Timoshenko beam theory, Finite Element Method (FEM) and the state space techniques. Simulations are performed in MATLAB. The effect of placing the sensor / actuator at 2 finite element locations along the length of the beam is observed. The open loop responses, closed loop responses and the tip displacements with and without the controller are obtained and the performance of the smart system is evaluated for active vibration control.

Keywords: Smart structure, Timoshenko theory, Euler-Bernoulli theory, Periodic output feedback control, Finite Element Method, State space model, Vibration control, Multivariable system, Linear Matrix Inequality

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Authors: M.Z. Islam, C.W. Lim

Abstract:

Based on the standard finite element method, a new finite element method which is known as nonlocal finite element method (NL-FEM) is numerically implemented in this article to study the nonlocal effects for solving 1D nonlocal elastic problem. An Eringen-type nonlocal elastic model is considered. In this model, the constitutive stress-strain law is expressed interms of integral equation which governs the nonlocal material behavior. The new NL-FEM is adopted in such a way that the postulated nonlocal elastic behavior of material is captured by a finite element endowed with a set of (cross-stiffness) element itself by the other elements in mesh. An example with their analytical solutions and the relevant numerical findings for various load and boundary conditions are presented and discussed in details. It is observed from the numerical solutions that the torsional deformation angle decreases with increasing nonlocal nanoscale parameter. It is also noted that the analytical solution fails to capture the nonlocal effect in some cases where numerical solutions handle those situation effectively which prove the reliability and effectiveness of numerical techniques.

Keywords: NL-FEM, nonlocal elasticity, nanoscale, torsion.

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Authors: Lee Feng Koo, Tze Jin Wong, Pang Hung Yiu, Nik Mohd Asri Nik Long

Abstract:

Greater common divisor (GCD) attack is an attack that relies on the polynomial structure of the cryptosystem. This attack required two plaintexts differ from a fixed number and encrypted under same modulus. This paper reports a security reaction of Lucas Based El-Gamal Cryptosystem in the Elliptic Curve group over finite field under GCD attack. Lucas Based El-Gamal Cryptosystem in the Elliptic Curve group over finite field was exposed mathematically to the GCD attack using GCD and Dickson polynomial. The result shows that the cryptanalyst is able to get the plaintext without decryption by using GCD attack. Thus, the study concluded that it is highly perilous when two plaintexts have a slight difference from a fixed number in the same Elliptic curve group over finite field.

Keywords: Decryption, encryption, elliptic curve, greater common divisor.

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Authors: H.Seidi, M.Jalali Azizpour, S.A.Zahedi

Abstract:

Today, Hydroforming technology provides an attractive alternative to conventional matched die forming, especially for cost-sensitive, lower volume production, and for parts with irregular contours. In this study the critical fluid pressures which lead to rupture in the workpiece has been investigated by theoretical and finite element methods. The axisymmetric analysis was developed to investigate the tearing phenomenon in cylindrical Hydroforming Deep Drawing (HDD). By use of obtained equations the effect of anisotropy, drawing ratio, sheet thickness and strain hardening exponent on tearing diagram were investigated.

Keywords: Hydroforming deep drawing, Pressure path, Axisymmetric analysis, Finite element simulation.

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Authors: Camille A. Issa, Omar Masri

Abstract:

In this study, the commercial finite element software ABAQUS was used to develop a three-dimensional nonlinear finite element model capable of simulating the pull-out test of reinforcing bars from underwater concrete. The results of thirty-two pull-out tests that have different parameters were implemented in the software to study the effect of the concrete cover, the bar size, the use of stirrups, and the compressive strength of concrete. The interaction properties used in the model provided accurate results in comparison with the experimental bond-slip results, thus the model has successfully simulated the pull-out test. The results of the finite element model are used to better understand and visualize the distribution of stresses in each component of the model, and to study the effect of the various parameters used in this study including the role of the stirrups in preventing the stress from reaching to the sides of the specimens.

Keywords: Bond strength, nonlinear finite element analysis, pull-out test, underwater concrete.

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Authors: Muna Tabuni

Abstract:

The paper contains an investigation of winding numbers of paths of zeros of analytic theta functions. We have considered briefly an analytic representation of finite quantum systems ZN. The analytic functions on a torus have exactly N zeros. The brief introduction to the zeros of analytic functions and there time evolution is given. We have discussed the periodic finite quantum systems. We have introduced the winding numbers in general. We consider the winding numbers of the zeros of analytic theta functions.

Keywords: Winding numbers, period, paths of zeros.

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Authors: Md Rashadul Islam, Mesbah U. Ahmed, Rafiqul A. Tarefder

Abstract:

This study evaluates the back calculation of stiffness of a pavement section on Interstate 40 (I-40)in New Mexico through numerical analysis. Falling Weight Deflectometer (FWD) test has been conducted on a section on I-40. Layer stiffness of the pavement has been backcalculated by a backcalculation software, ELMOD, using the FWD test data. Commercial finite element software, ABAQUS, has been used to develop the Finite Element Model (FEM) of this pavement section. Geometry and layer thickness are collected from field coring. Input parameters i.e. stiffnesses of different layers of the pavement are used as the backcalculated ones. Resulting surface deflections at different radial distances from the FEM analysis are compared with field FWD deflection values. It shows close agreement between the FEM and FWD outputs. Therefore, the FWD test method can be considered to be a reliable test procedure for evaluating the in situ stiffness of pavement material.

Keywords: Falling weight deflectometer test, Finite element model, Flexible pavement, moduli, surface deflection.

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Authors: Ahmet Tekcan

Abstract:

Let p ≥ 5 be a prime number and let Fp be a finite field. In this work, we determine the number of rational points on singular curves Ea : y2 = x(x - a)2 over Fp for some specific values of a.

Keywords: Singular curve, elliptic curve, rational points.

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