Search results for: integral bridge
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 649

Search results for: integral bridge

619 Performance of Bridge Approach Slabs in Bridge Construction: A Case Study

Authors: Aurora Cerri, Niko Pullojani

Abstract:

Long-term differential settlement between the bridge structure and the bridge embankment typically results in an abrupt grade change, causing driver discomfort, impairing driver safety, and exerting a potentially excessive impact traffic loading on the abutment. This paper has analysed a case of study showing the effect of an approaching slab realized in a bridge constructed at Tirane-Elbasan Motorway. The layer thickness under the slab is modeled as homogenous, the slab is a reinforced concrete structure and over that the asphaltic layers take place. Analysis indicates that reinforced concrete approaching slab distributes the stresses quite uniformly into the road fill layers and settlements varies in a range less than 2.50 cm in the total slab length of 6.00 m with a maximum slope of 1/240. Results taken from analytical analysis are compared with topographic measurements done on field and they carry great similarities.

Keywords: Approach slab, bridge, road pavement, differential settlement.

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618 An Asymptotic Solution for the Free Boundary Parabolic Equations

Authors: Hsuan-Ku Liu, Ming Long Liu

Abstract:

In this paper, we investigate the solution of a two dimensional parabolic free boundary problem. The free boundary of this problem is modelled as a nonlinear integral equation (IE). For this integral equation, we propose an asymptotic solution as time is near to maturity and develop an integral iterative method. The computational results reveal that our asymptotic solution is very close to the numerical solution as time is near to maturity.

Keywords: Integral equation, asymptotic solution, free boundary problem, American exchange option.

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617 Approximate Solution of Nonlinear Fredholm Integral Equations of the First Kind via Converting to Optimization Problems

Authors: Akbar H. Borzabadi, Omid S. Fard

Abstract:

In this paper we introduce an approach via optimization methods to find approximate solutions for nonlinear Fredholm integral equations of the first kind. To this purpose, we consider two stages of approximation. First we convert the integral equation to a moment problem and then we modify the new problem to two classes of optimization problems, non-constraint optimization problems and optimal control problems. Finally numerical examples is proposed.

Keywords: Fredholm integral equation, Optimization method, Optimal control, Nonlinear and linear programming

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616 Advanced Gronwall-Bellman-Type Integral Inequalities and Their Applications

Authors: Zixin Liu, Shu Lü, Shouming Zhong, Mao Ye

Abstract:

In this paper, some new nonlinear generalized Gronwall-Bellman-Type integral inequalities with mixed time delays are established. These inequalities can be used as handy tools to research stability problems of delayed differential and integral dynamic systems. As applications, based on these new established inequalities, some p-stable results of a integro-differential equation are also given. Two numerical examples are presented to illustrate the validity of the main results.

Keywords: Gronwall-Bellman-Type integral inequalities, integrodifferential equation, p-exponentially stable, mixed delays.

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615 High Accuracy Eigensolutions in Elasticity for Boundary Integral Equations by Nyström Method

Authors: Pan Cheng, Jin Huang, Guang Zeng

Abstract:

Elastic boundary eigensolution problems are converted into boundary integral equations by potential theory. The kernels of the boundary integral equations have both the logarithmic and Hilbert singularity simultaneously. We present the mechanical quadrature methods for solving eigensolutions of the boundary integral equations by dealing with two kinds of singularities at the same time. The methods possess high accuracy O(h3) and low computing complexity. The convergence and stability are proved based on Anselone-s collective compact theory. Bases on the asymptotic error expansion with odd powers, we can greatly improve the accuracy of the approximation, and also derive a posteriori error estimate which can be used for constructing self-adaptive algorithms. The efficiency of the algorithms are illustrated by numerical examples.

Keywords: boundary integral equation, extrapolation algorithm, aposteriori error estimate, elasticity.

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614 Thermal Fracture Analysis of Fibrous Composites with Variable Fiber Spacing Using Jk-Integral

Authors: Farid Saeidi, Serkan Dag

Abstract:

In this study, fracture analysis of a fibrous composite laminate with variable fiber spacing is carried out using Jk-integral method. The laminate is assumed to be under thermal loading. Jk-integral is formulated by using the constitutive relations of plane orthotropic thermoelasticity. Developed domain independent form of the Jk-integral is then integrated into the general purpose finite element analysis software ANSYS. Numerical results are generated so as to assess the influence of variable fiber spacing on mode I and II stress intensity factors, energy release rate, and T-stress. For verification, some of the results are compared to those obtained using displacement correlation technique (DCT).

Keywords: Jk-integral, variable fiber spacing, thermoelasticity, t-stress, finite element method, fibrous composite.

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613 Structural Performance of a Timber-Concrete Bridge Prototype

Authors: Pedro Gutemberg de Alcântara Segundinho, José Antonio Matthiesen, Marcelo Rodrigo Carreira

Abstract:

Timber-concrete structures were recently introduced in Brazil as a viable option for bridge construction on side roads. Binding between timber and concrete is fundamentally important to assure the rigidity and performance of this structural system. The objective of this study was to assess the structural performance of a timber-concrete bridge prototype with width of 170cm and span of 400cm, whose binding among timber beams and concrete slabs was made with metal pins, obtained from CA 50 construction steel bars of 12.5mm diameter. It was possible to conclude, from the results obtained experimentally in laboratory, that the timber-concrete bridge prototype showed a good structural performance. This structural system provides an economical, rapid implementation solution, which may be used on side roads, favoring regional integration and agricultural production flow.

Keywords: Binding, bridge prototype, timber and concrete

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612 Site Inspection and Evaluation Behavior of Qing Shang Concrete Bridge

Authors: Haleem K. Hussain, Liu Gui Wei, Zhang Lian Zhen, Yongxue Li

Abstract:

It is necessary to evaluate the bridges conditions and strengthen bridges or parts of them. The reinforcement necessary due to some reasons can be summarized as: First, a changing in use of bridge could produce internal forces in a part of structural which exceed the existing cross-sectional capacity. Second, bridges may also need reinforcement because damage due to external factors which reduced the cross-sectional resistance to external loads. One of other factors could listed here its misdesign in some details, like safety of bridge or part of its.This article identify the design demands of Qing Shan bridge located in is in Heilongjiang Province He gang - Nen Jiang Road 303 provincial highway, Wudalianchi area, China, is an important bridge in the urban areas. The investigation program was include the observation and evaluate the damage in T- section concrete beams , prestressed concrete box girder bridges section in additional evaluate the whole state of bridge includes the pier , abutments , bridge decks, wings , bearing and capping beam, joints, ........etc. The test results show that the bridges in general structural condition are good. T beam span No 10 were observed, crack extended upward along the ribbed T beam, and continue to the T beam flange. Crack width varying between 0.1mm to 0.4mm, the maximum about 0.4mm. The bridge needs to be improved flexural bending strength especially at for T beam section.

Keywords: Field investigation, prestressed concrete box girder, maintenance, Qing Shan Bridge

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611 Topology Optimization of Cable Truss Web for Prestressed Suspension Bridge

Authors: Vadims Goremikins, Karlis Rocens, Dmitrijs Serdjuks

Abstract:

A suspension bridge is the most suitable type of structure for a long-span bridge due to rational use of structural materials. Increased deformability, which is conditioned by appearance of the elastic and kinematic displacements, is the major disadvantage of suspension bridges. The problem of increased kinematic displacements under the action of non-symmetrical load can be solved by prestressing. The prestressed suspension bridge with the span of 200 m was considered as an object of investigations. The cable truss with the cross web was considered as the main load carrying structure of the prestressed suspension bridge. The considered cable truss was optimized by 47 variable factors using Genetic algorithm and FEM program ANSYS. It was stated, that the maximum total displacements are reduced up to 29.9% by using of the cable truss with the rational characteristics instead of the single cable in the case of the worst situated load.

Keywords: Decreasing displacements, Genetic algorithm.

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610 Experimental Study of Local Scour Depth around Cylindrical Bridge Pier

Authors: Mohammed T. Shukri

Abstract:

The failure of bridges due to excessive local scour during floods poses a challenging problem to hydraulic engineers. The failure of bridges piers is due to many reasons such as localized scour combined with general riverbed degradation. In this paper, we try to estimate the temporal variation of scour depth at nonuniform cylindrical bridge pier, by experimental work conducted in hydraulic laboratories of Gaziantep University Civil Engineering Department on a flume having dimensions of 8.3 m length, 0.8 m width and 0.9 m depth. The experiments will be carried on 20 cm depth of sediment layer having d50=0.4 mm. Three bridge pier shapes having different scaled models will be constructed in a 1.5m of test section in the channel.

Keywords: Scour, local scour, bridge piers, scour depth.

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609 Multimodal Biometric Authentication Using Choquet Integral and Genetic Algorithm

Authors: Anouar Ben Khalifa, Sami Gazzah, Najoua Essoukri BenAmara

Abstract:

The Choquet integral is a tool for the information fusion that is very effective in the case where fuzzy measures associated with it are well chosen. In this paper, we propose a new approach for calculating fuzzy measures associated with the Choquet integral in a context of data fusion in multimodal biometrics. The proposed approach is based on genetic algorithms. It has been validated in two databases: the first base is relative to synthetic scores and the second one is biometrically relating to the face, fingerprint and palmprint. The results achieved attest the robustness of the proposed approach.

Keywords: Multimodal biometrics, data fusion, Choquet integral, fuzzy measures, genetic algorithm.

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608 Loss Analysis of Half Bridge DC-DC Converters in High-Current and Low-Voltage Applications

Authors: A. Faruk Bakan, İsmail Aksoy, Nihan Altintaş

Abstract:

In this paper, half bridge DC-DC converters with transformer isolation presented in the literature are analyzed for highcurrent and low-voltage applications under the same operation conditions, and compared in terms of losses and efficiency. The conventional and improved half-bridge DC-DC converters are simulated, and current and voltage waveforms are obtained for input voltage Vdc=500V, output current IO=450A, output voltage VO=38V and switching frequency fS=20kHz. IGBTs are used as power semiconductor switches. The power losses of the semiconductor devices are calculated from current and voltage waveforms. From simulation results, it is seen that the capacitor switched half bridge converter has the best efficiency value, and can be preferred at high power and high frequency applications.

Keywords: Isolated half bridge DC-DC converter, high-current low-voltage applications, soft switching, high efficiency.

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607 A Note on the Numerical Solution of Singular Integral Equations of Cauchy Type

Authors: M. Abdulkawi, Z. K. Eshkuvatov, N. M. A. Nik Long

Abstract:

This manuscript presents a method for the numerical solution of the Cauchy type singular integral equations of the first kind, over a finite segment which is bounded at the end points of the finite segment. The Chebyshev polynomials of the second kind with the corresponding weight function have been used to approximate the density function. The force function is approximated by using the Chebyshev polynomials of the first kind. It is shown that the numerical solution of characteristic singular integral equation is identical with the exact solution, when the force function is a cubic function. Moreover, it also shown that this numerical method gives exact solution for other singular integral equations with degenerate kernels.

Keywords: Singular integral equations, Cauchy kernel, Chebyshev polynomials, interpolation.

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606 Solution of First kind Fredholm Integral Equation by Sinc Function

Authors: Khosrow Maleknejad, Reza Mollapourasl, Parvin Torabi, Mahdiyeh Alizadeh,

Abstract:

Sinc-collocation scheme is one of the new techniques used in solving numerical problems involving integral equations. This method has been shown to be a powerful numerical tool for finding fast and accurate solutions. So, in this paper, some properties of the Sinc-collocation method required for our subsequent development are given and are utilized to reduce integral equation of the first kind to some algebraic equations. Then convergence with exponential rate is proved by a theorem to guarantee applicability of numerical technique. Finally, numerical examples are included to demonstrate the validity and applicability of the technique.

Keywords: Integral equation, Fredholm type, Collocation method, Sinc approximation.

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605 Performance of Bridge Girder with Perforations under Tsunami Wave Loading

Authors: Sadia Rahman, Shatirah Akib, M. T. R. Khan, R. Triatmadja

Abstract:

Tsunami disaster poses a great threat to coastal infrastructures. Bridges without adequate provisions for earthquake and tsunami loading is generally vulnerable to tsunami attack. During the last two disastrous tsunami event (i.e. Indian Ocean and Japan Tsunami) a number of bridges were observed subsequent damages by tsunami waves. In this study, laboratory experiments were conducted to study the effects of perforations in bridge girder in force reduction. Results showed that significant amount of forces were reduced using perforations in girder. Approximately 10% to 18% force reductions were achieved by using about 16% perforations in bridge girder. Subsequent amount of force reductions revealed that perforations in girder are effective in reducing tsunami forces as perforations in girder let water to be passed through. Thus, less bridge damages are expected with the presence of perforations in girder during tsunami period.

Keywords: Bridge, force, girder, perforation, tsunami, wave.

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604 Analytical Study on the Shape of T-type Girder Modular Bridge Connection by Using Parameter

Authors: Jongho Park, Jinwoong Choi, Sungnam Hong, Seung-Kyung Kye, Sun-Kyu Park

Abstract:

Recently, to cope with the rapidly changing construction trend with aging infrastructures, modular bridge technology has been studied actively. Modular bridge is easily constructed by assembling standardized precast structure members in the field. It will be possible to construct rapidly and reduce construction cost efficiently. However, the shape of the transverse connection of T-type girder newly developed between the segmented modules is not verified. Therefore, the verification of the connection shape is needed. In this study, shape of the modular T-girder bridge transverse connection was analyzed by finite element model that was verified in study which was verified model of transverse connection using Abaqus. Connection angle was chosen as the parameter. The result of analyses showed that optimal value of angle is 130 degree.

Keywords: Modular bridge, optimal transverse shape, parameter, FEM.

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603 Hybrid Function Method for Solving Nonlinear Fredholm Integral Equations of the Second Kind

Authors: jianhua Hou, Changqing Yang, and Beibo Qin

Abstract:

A numerical method for solving nonlinear Fredholm integral equations of second kind is proposed. The Fredholm type equations which have many applications in mathematical physics are then considered. The method is based on hybrid function  approximations. The properties of hybrid of block-pulse functions and Chebyshev polynomials are presented and are utilized to reduce the computation of nonlinear Fredholm integral equations to a system of nonlinear. Some numerical examples are selected to illustrate the effectiveness and simplicity of the method.

Keywords: Hybrid functions, Fredholm integral equation, Blockpulse, Chebyshev polynomials, product operational matrix.

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602 Improved Robust Stability Criteria of a Class of Neutral Lur’e Systems with Interval Time-Varying Delays

Authors: Longqiao Zhou, Zixin Liu, Shu Lü

Abstract:

This paper addresses the robust stability problem of a class of delayed neutral Lur’e systems. Combined with the property of convex function and double integral Jensen inequality, a new tripe integral Lyapunov functional is constructed to derive some new stability criteria. Compared with some related results, the new criteria established in this paper are less conservative. Finally, two numerical examples are presented to illustrate the validity of the main results.

Keywords: Lur’e system, Convex function, Jensen integral inequality, Triple-integral method, Exponential stability.

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601 Efficient Numerical Model for Studying Bridge Pier Collapse in Floods

Authors: Thanut Kallaka, Ching-Jong Wang

Abstract:

High level and high velocity flood flows are potentially harmful to bridge piers as evidenced in many toppled piers, and among them the single-column piers were considered as the most vulnerable. The flood flow characteristic parameters including drag coefficient, scouring and vortex shedding are built into a pier-flood interaction model to investigate structural safety against flood hazards considering the effects of local scouring, hydrodynamic forces, and vortex induced resonance vibrations. By extracting the pier-flood simulation results embedded in a neural networks code, two cases of pier toppling occurred in typhoon days were reexamined: (1) a bridge overcome by flash flood near a mountain side; (2) a bridge washed off in flood across a wide channel near the estuary. The modeling procedures and simulations are capable of identifying the probable causes for the tumbled bridge piers during heavy floods, which include the excessive pier bending moments and resonance in structural vibrations.

Keywords: Bridge piers, Neural networks, Scour depth, Structural safety, Vortex shedding

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600 Developing Damage Assessment Model for Bridge Surroundings: A Study of Disaster by Typhoon Morakot in Taiwan

Authors: Jieh-Haur Chen, Pei-Fen Huang

Abstract:

This paper presents an integrated model that automatically measures the change of rivers, damage area of bridge surroundings, and change of vegetation. The proposed model is on the basis of a neurofuzzy mechanism enhanced by SOM optimization algorithm, and also includes three functions to deal with river imagery. High resolution imagery from FORMOSAT-2 satellite taken before and after the invasion period is adopted. By randomly selecting a bridge out of 129 destroyed bridges, the recognition results show that the average width has increased 66%. The ruined segment of the bridge is located exactly at the most scour region. The vegetation coverage has also reduced to nearly 90% of the original. The results yielded from the proposed model demonstrate a pinpoint accuracy rate at 99.94%. This study brings up a successful tool not only for large-scale damage assessment but for precise measurement to disasters.

Keywords: remote sensing image, damage assessment, typhoon disaster, bridge, ANN, fuzzy, SOM, optimization.

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599 Dynamic Response Analyses for Human-Induced Lateral Vibration on Congested Pedestrian Bridges

Authors: M. Yoneda

Abstract:

In this paper, a lateral walking design force per person is proposed and compared with Imperial College test results. Numerical simulations considering the proposed walking design force which is incorporated into the neural-oscillator model are carried out placing much emphasis on the synchronization (the lock-in phenomenon) for a pedestrian bridge model with the span length of 50 m. Numerical analyses are also conducted for an existing pedestrian suspension bridge. As compared with full scale measurements for this suspension bridge, it is confirmed that the analytical method based on the neural-oscillator model might be one of the useful ways to explain the synchronization (the lock-in phenomenon) of pedestrians being on the bridge.

Keywords: Pedestrian bridge, human-induced lateral vibration, neural-oscillator, full scale measurement, dynamic response analysis.

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598 A Wind Farm Reduced Order Model Using Integral Manifold Theory

Authors: M. Sedighizadeh, A. Rezazadeh

Abstract:

Due to the increasing penetration of wind energy, it is necessary to possess design tools that are able to simulate the impact of these installations in utility grids. In order to provide a net contribution to this issue a detailed wind park model has been developed and is briefly presented. However, the computational costs associated with the performance of such a detailed model in describing the behavior of a wind park composed by a considerable number of units may render its practical application very difficult. To overcome this problem integral manifolds theory has been applied to reduce the order of the detailed wind park model, and therefore create the conditions for the development of a dynamic equivalent which is able to retain the relevant dynamics with respect to the existing a.c. system. In this paper integral manifold method has been introduced for order reduction. Simulation results of the proposed method represents that integral manifold method results fit the detailed model results with a higher precision than singular perturbation method.

Keywords: Wind, Reduced Order, Integral Manifold.

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597 Hermite–Hadamard Type Integral Inequalities Involving k–Riemann–Liouville Fractional Integrals and Their Applications

Authors: Artion Kashuri, Rozana Liko

Abstract:

In this paper, some generalization integral inequalities of Hermite–Hadamard type for functions whose derivatives are s–convex in modulus are given by using k–fractional integrals. Some applications to special means are obtained as well. Some known versions are recovered as special cases from our results. We note that our inequalities can be viewed as new refinements of the previous results. Finally, our results have a deep connection with various fractional integral operators and interested readers can find new interesting results using our idea and technique as well.

Keywords: Hermite–Hadamard’s inequalities, k–Riemann–Liouville fractional integral, H¨older’s inequality, Special means.

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596 MP-SMC-I Method for Slip Suppression of Electric Vehicles under Braking

Authors: Tohru Kawabe

Abstract:

In this paper, a new SMC (Sliding Mode Control) method with MP (Model Predictive Control) integral action for the slip suppression of EV (Electric Vehicle) under braking is proposed. The proposed method introduce the integral term with standard SMC gain , where the integral gain is optimized for each control period by the MPC algorithms. The aim of this method is to improve the safety and the stability of EVs under braking by controlling the wheel slip ratio. There also include numerical simulation results to demonstrate the effectiveness of the method.

Keywords: Sliding Mode Control, Model Predictive Control, Integral Action, Electric Vehicle, Slip suppression.

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595 A Numerical Study on Semi-Active Control of a Bridge Deck under Seismic Excitation

Authors: A. Yanik, U. Aldemir

Abstract:

This study investigates the benefits of implementing the semi-active devices in relation to passive viscous damping in the context of seismically isolated bridge structures. Since the intrinsically nonlinear nature of semi-active devices prevents the direct evaluation of Laplace transforms, frequency response functions are compiled from the computed time history response to sinusoidal and pulse-like seismic excitation. A simple semi-active control policy is used in regard to passive linear viscous damping and an optimal non-causal semi-active control strategy. The control strategy requires optimization. Euler-Lagrange equations are solved numerically during this procedure. The optimal closed-loop performance is evaluated for an idealized controllable dash-pot. A simplified single-degree-of-freedom model of an isolated bridge is used as numerical example. Two bridge cases are investigated. These cases are; bridge deck without the isolation bearing and bridge deck with the isolation bearing. To compare the performances of the passive and semi-active control cases, frequency dependent acceleration, velocity and displacement response transmissibility ratios Ta(w), Tv(w), and Td(w) are defined. To fully investigate the behavior of the structure subjected to the sinusoidal and pulse type excitations, different damping levels are considered. Numerical results showed that, under the effect of external excitation, bridge deck with semi-active control showed better structural performance than the passive bridge deck case.

Keywords: Bridge structures, passive control, seismic, semi-active control, viscous damping.

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594 Uniform Distribution of Ductility Demand in Irregular Bridges using Shape Memory Alloy

Authors: Seyed Mohyeddin Ghodratian, Mehdi Ghassemieh, Mohammad Khanmohammadi

Abstract:

Excessive ductility demand on shorter piers is a common problem for irregular bridges subjected to strong ground motion. Various techniques have been developed to reduce the likelihood of collapse of bridge due to failure of shorter piers. This paper presents the new approach to improve the seismic behavior of such bridges using Nitinol shape memory alloys (SMAs). Superelastic SMAs have the ability to remain elastic under very large deformation due to martensitic transformation. This unique property leads to enhanced performance of controlled bridge compared with the performance of the reference bridge. To evaluate the effectiveness of the devices, nonlinear time history analysis is performed on a RC single column bent highway bridge using a suite of representative ground motions. The results show that this method is very effective in limiting the ductility demand of shorter pier.

Keywords: bridge, ductility demand, irregularity, shape memory alloy

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593 Treatment of Spin-1/2 Particle in Interaction with a Time-Dependent Magnetic Field by the Fermionic Coherent-State Path-Integral Formalism

Authors: Aouachria Mekki

Abstract:

We consider a spin-1/2 particle interacting with a time-dependent magnetic field using path integral formalism. The propagator is first of all written in the standard form replacing the spin by two fermionic oscillators via the Schwinger model. The propagator is then exactly determined, thanks to a simple transformation, and the transition probability is deduced.

Keywords: Path integral, formalism, Propagator.

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592 Integral Domains and Their Algebras: Topological Aspects

Authors: Shai Sarussi

Abstract:

Let S be an integral domain with field of fractions F and let A be an F-algebra. An S-subalgebra R of A is called S-nice if R∩F = S and the localization of R with respect to S \{0} is A. Denoting by W the set of all S-nice subalgebras of A, and defining a notion of open sets on W, one can view W as a T0-Alexandroff space. Thus, the algebraic structure of W can be viewed from the point of view of topology. It is shown that every nonempty open subset of W has a maximal element in it, which is also a maximal element of W. Moreover, a supremum of an irreducible subset of W always exists. As a notable connection with valuation theory, one considers the case in which S is a valuation domain and A is an algebraic field extension of F; if S is indecomposed in A, then W is an irreducible topological space, and W contains a greatest element.

Keywords: Algebras over integral domains, Alexandroff topology, valuation domains, integral domains.

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591 Hybrid Stainless Steel Girder for Bridge Construction

Authors: Tetsuya Yabuki, Yasunori Arizumi, Tetsuhiro Shimozato, Samy Guezouli, Hiroaki Matsusita, Masayuki Tai

Abstract:

The main object of this paper is to present the research results of the development of a hybrid stainless steel girder system for bridge construction undertaken at University of Ryukyu. In order to prevent the corrosion damage and reduce the fabrication costs, a hybrid stainless steel girder in bridge construction is developed, the stainless steel girder of which is stiffened and braced by structural carbon steel materials. It is verified analytically and experimentally that the ultimate strength of the hybrid stainless steel girder is equal to or greater than that of conventional carbon steel girder. The benefit of the life-cycle cost of the hybrid stainless steel girder is also shown.

Keywords: Smart structure, hybrid stainless steel members, ultimate strength, steel bridge, corrosion prevention.

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590 Spline Collocation for Solving System of Fredholm and Volterra Integral Equations

Authors: N. Ebrahimi, J. Rashidinia

Abstract:

In this paper, numerical solution of system of Fredholm and Volterra integral equations by means of the Spline collocation method is considered. This approximation reduces the system of integral equations to an explicit system of algebraic equations. The solution is collocated by cubic B-spline and the integrand is approximated by the Newton-Cotes formula. The error analysis of proposed numerical method is studied theoretically. The results are compared with the results obtained by other methods to illustrate the accuracy and the implementation of our method.

Keywords: Convergence analysis, Cubic B-spline, Newton- Cotes formula, System of Fredholm and Volterra integral equations.

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