A way to improve the accuracy of the three-body problem model is taking into account the eccentricity of primary attractors. Elliptic Restricted Three-Body Problem (ER3BP) is a model for studying spacecraft trajectory within the three-body problem such that the orbital eccentricity of primaries is reflected in it. As the principal cause of perturbation in the employed dynamical model, the primaries eccentricity changes the structure of orbits compared to the ideal Circular Restricted Three-Body Problem (CR3BP). In this paper, the orbit dynamics of a spacecraft in the ER3BP are exploited to find periodic orbits as the spacecraft is considered to be in planar orbits around Lagrangian points. Periodic orbits are repetitious behaviors in which spacecraft orbital dynamics repeated periodically, these periodic behaviors are the main interest of this study because they are beneficial for future mission designs and allow delineation of the system's governing dynamics. Previous studies laid the foundation for finding periodic orbits or analyzing the stability of the obtained orbits in the ER3BP regime. While in this paper, at first, initial guesses for correction algorithms were derived through the well-known family of orbits in the CR3BP, then correction algorithms were used to refine the calculated orbit. Periodic orbits are portrayed and compared to previous studies and simpler models. Finally, the periodic orbits for the systems with different values of eccentricity and mass ratios are compared to determine their effect on the shape of the orbits in the ER3BP.

An important shortcoming about designing robust control for models generated from prediction error identification is that very few control design methods directly match the ellipsoidal parametric uncertainty regions that are generated by such identification methods. Models obtained from identification experiments in prediction error framework lie in an ellipsoid uncertainty region. In this contribution we present a joint robust control/input design procedure which guaranties stability and prescribed closed-loop performance using models identified from experimental data. Finite dimensional parameterization of the input spectrum is used to represent the input design problem as a convex optimization. A method for fixed-order H controller design for systems with ellipsoidal uncertainty is used and given H specifications on the closed-loop transfer function are translated into sufficient requirements on the input signal used to identify the system.

In post-core crown restorations, the use of prefabricated composite posts concentrate stress at the cervical region and the use of metal posts (prefabricated and customized posts) concentrates stress at the interfaces. Fiber reinforced composite posts (FRCs) with oval cross-section (oval posts) were proposed for post-core crown restorations to reduce the stress levels at the cervical region. The aim of the present study was to investigate the impact of oval cross-section composite posts on stress distribution of premolar with oval-shaped canal by using three-dimensional (3D) finite element analysis.
An extracted premolar tooth was mounted, sectioned, and photographed to create a 3D model. The surrounding tissues of the tooth, periodontal ligament, as well as cortical and trabecular bones were modeled. Seven taper posts with two different cross-section geometries (circular and oval shapes) were modeled, as well. Then, the effect of post geometry, post material (carbon fiber and fiberglass), and cement material were investigated by 3D finite element analysis and the stress distribution results were compared.
In all the models, the highest stress levels of the dentin were accumulated at the coronal third of the root, and the highest stress levels at the bonding layers were accumulated at the cervical margin. Narrow circular posts induced the highest stress levels, whereas the stress levels were reduced by using thick oval posts. Application of elastic cement reduces the stress at the bonding layers but increases stress at the dentin.
Finite element analysis showed that prefabricated oval posts are superior to traditional circular ones. The use of cement with low elastic modulus reduces the risk of debonding but raises the risk of root fracture.

In this study, the optimal performance of an irreversible regenerative Brayton cycle is sought through power maximization using the finite-time thermodynamic concept in finite-size components. Optimization is performed on the maximum power as the objective function using a genetic algorithm. In order to take into account the time and the size constraints in the current problem, the dimensionless mass-flow parameter is used. The behavior of the system parameters, such as maximum output power, exergy, exergy destruction, first and second law efficiencies, and effectiveness of the heat exchangers are investigated using the dimensionless mass-flow rate parameter. The influence of the unavoidable exergy destruction due to finite-time constraint is taken into account by developing the definition of thermal exergy. According to the results, the external exergy destruction increases and consequently the second law efficiency and heat exchangers effectiveness decrease with an increment of the dimensionless mass-flow rate parameter. However, as the dimensionless mass-flow rate parameter tends to zero, the efficiency and the power of the system approaches Carnot efficiency and zero value, respectively. Finally, the improved definitions are proposed for the heat exergy and the second law efficiency which will be compared with the conventional definitions and then their cumulative effects on cycle’s performance will be discussed.

Side weirs are used to control the amount of discharge in main channels and rivers. One of the types of side weirs are labyrinth Semi-elliptical side weir and Due to the greater crest length in a certain range of transverse, have more the discharge capacity than rectangular weirs. For these reasons in this study, flow around a semi-elliptical and rectangular labyrinth side weir was simulated with three-dimensional modeling finite volumeand compared with laboratory measurment. The effects of increasing the flow in the main channel and the height and length semi-elliptical side weirs on flow pattern in subcritical flow conditions were studied and finally the experimental results were compared with the simulated results for rectangular side weir. Numerical results indicated that the model can predict the the flow pattern on the side weir with high accuracy .The results of the simulation showed that the effects of secondary flows in both weirs were reduced by increasing the height of the rectangular and semi-elliptical side weirs and then, the water surface profile would be more uniform and the error rate decreas. The maximum of velocity in semi-elliptical side weir is induced in the near of free surface at the end of the side weir and the discharge coefficient of semi-elliptical side weir is more than rectangular side weir.In this study an equation was offered in order to determine De-Marchi discharge coefficient for semi-elliptical side weir.This coefficient in subcritical flow conditions depends on the Froude number in the main channel, the ratio of upstream depth to the height of side weir, the ratio of upstream depth to the length of side weir and the ratio of small ellipse radius to large ellipse radius.

Height is amongst the most delicate subjects of geodesy. Thanks to the Global Navigation Satellite Systems (GNSS) like GPS or GLONASS, 3D point positioning of points, by geometrical positioning, since years ago has become a common practice. The height derived from these ways has a geometrical concept. In civil projects the physical concept of the height is more demanded. Orthometric height,, is one kind of the physical concepts of the height. The Orthometric height of point i,, can be calculated by where is the mean value of the gravity along the plumb line between the geoid and the surface point i and is the geo-potential number of point i, which is calculated using One of the problems in orthometric height calculation is computation of. The value of the gravity at the point with mean height is calculated by Where is gravity observation value at point i. The orthometric height computed by this mean value of the gravity is called Helmert orthometric height, according to Sanso and Sona (1993) the idea for earth gravity determination. In this paper a methodology to calculate value of the gravity at the point with mean height from the geoid has been supposed. Derived gravity from this method is composed from three parts, (1) global and regional gravity computed by ellipsoidal harmonic expansion to degree and order 360 plus the centrifugal acceleration (2) gravitational due to terrain masses within the radius of 55km around the computational point (3) incremental gravity intensity at the computational point. The first and second parts are computed by global geopotential models and digital terrain models. Computation of the third part is possible by solving a boundary value problem. In this paper for computing the incremental gravity intensity at the point with mean height, a method by solving a fixed-free two-boundary nonlinear value problem is addressed. This boundary value problem constructed for observables of the type (i) modulus of gravity (ii) gravity potential (iii) satellite altimetry data (iv) astronomical latitude (v) astronomical longitude. The first step towards the solution of the proposed fixed geodetic boundary value problem is the linearization of the problem. After linearization we obtained a linear boundary value problem that its solution gives us the incremental gravity potential at the surface of the reference ellipsoid. Out of the reference ellipsoid surface, this answer could be obtained by solving the following Dirichlet boundary value problem: In this paper harmonic splines supposed by Freeden (1987) are used to solve the Dirichlet problem. By applying the gradient operator on the incremental gravity potential, due to solving Dirichlet problem, incremental gravity at every point out of the reference ellipsoid can be calculated (Jekeli, 2005). Second section of this paper is an introduction on harmonic splines analysis. The construction of self productive Hilbert space and optimum interpolation answer is presented in the third section. In the final section the application of harmonic splines for solving the Dirichlet boundary value problem is discussed and by the proposed methodology the mean value of gravity in the first order leveling of Iran is calculated.