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Almost all western theorists in the field of urban studies pointed to urban vitality in their books and articles. Also, vitality is a fashionable word in the lexicon of urbanism in Iran, but in fact, it received little support from urban planners, urban designers, and geographers. During the years of confrontation with western achievements and modernism in Iran, people experience the incorrect manner of using imported terms, theories and inventions. Urban vitality is another example of such experiences, and the exact meaning and position of vitality in Iranian urban contexts is still unclear. There are lots of articles and projects focusing on urban vitality without clarifying the situation on which people can pursue vitality for an urban context. In the present study, the meaning and position for urban vitality, and the misuses of this concept in Iranian urban contexts is discussed.
 

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New approaches to semiotics with a phenomenological landscape further studies signification creation processes in a form beyond causal systems and emphasizes the role of cognitive-emotional competence of body. In this study, we used a descriptive - analytical method and interdisciplinary research methodology by referring to the components of the "complexity theory". We have shown that how the creation patterns of signification through interaction and "Co-Presence" of body subjects in semiotic system, have similar behavior and interactions of complex development systems where they are a function of the characteristics of chaotic behavior based on the "chaos theory". The result of this research is not only a query for the existence of adjustment pattern between the two theoretical fields, but also it provides scientific mapping based on interdisciplinary approach for the existence of patterns in the creative process that some of its characteristics are already studied in the semiotic adjustment and also in language systems as theoretical or empirical forms. Generally, systems of signification including "language" are not independent of the human subject, in the sense that they are the product of biochemical and neurological interactions of organism (a complex system) called "humans". It is expected that the semiotic systems as well as complex system be based on behavior patterns of "Chaos Theory".
Also the other function of the compliance, apart from providing scientific backing for the theoretical or empirical observations, is that it can explain the concepts such as "insecurity", "risk", "emotional contagion" and "perceptual sensitivity" in the process of signification creation in the compliance system based on chaos theory, yet some of the key features of the meaning production are explained both in language and verbal adaptation of the systems.
 
 
 

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This paper introduces a technique for controlling a class of uncertain chaotic systems using an adaptive fuzzy Proportional-Integrator-Derivative (PID) controller with H∞ tracking performance. The purpose of this work is to achieve optimal tracking performance of the controller using Backtracking Search Algorithm (BSA). BSA, which is a novel heuristic algorithm, has an easy structure with single control parameter. In BSA, three basic genetic operators (selection, mutation and crossover) are utilized to generate trial individuals. To this reason, the control problem in hand is considered as an optimization problem by defining an appropriate objective function. Stability analysis of the control scheme is provided based on Lyapunov theory and modified Riccati-like equation, where the robustness of the closed-loop system is guaranteed by H∞ tracking performance for any predefined level. To evaluate the performance of the proposed control method, it is employed for tracking control of Duffing uncertain chaotic system. Simulation results show the capability of the proposed controller.  

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In this paper, it is tried to propose a robust model for predicting inflation in Iran among alternative models. For doing this, monthly data from April 1990 to the end of September 2009 is used. Firstly, it is tried to determine whether the CPI data is chaotic or stochastic. It is shown that it is chaotic rather than stochastic. Therefore, it is predictable. Then, a stochastic differential equation model is estimated (specifically a geometric Brownian motion) for CPI in Iran. In order to compare the prediction power of the model other alternative models of prediction like ARMA, non-linear GARCH, EGARCH, TGARCH are also used to extrapolate inflation during a six month prediction period. Based on RMSE, MAE, U-Tail, it is revealed that stochastic differential equation model is much more robust than the alternative models mentioned above.

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Chaotic dynamics of spin-orbit motion of a triaxial gyrostat satellite under the gravity gradient perturbations is considered. The Hamiltonian approach is used for modeling of the coupled spin-orbit equations of motion. The complex Hamiltonian of the system is reduced via the extended Deprit canonical transformation. This reduction yields to the derivation of the perturbation form of the Hamiltonian which can be used in the Ricci curvature criterion based on the Riemannian manifold geometry for the analysis of chaos. The results obtained from Ricci method as well as the values from the Lyapunov exponent demonstrate the presence of a strange attractor and chaos phenomenon in the perturbed system. The simulation results based on the numerical methods such as Poincare' section, trajectories of phase portrait, and time series responses confirm the heteroclinic bifurcation and chaos in the system.

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The accurate evaluation and experimental investigation of the gear dynamic response have indicated some interesting nonlinear phenomena such as bifurcation and chaotic behavior on some system parameters. The chaotic motion is an unusual and unpredictable behavior and has been considered as an undesirable phenomenon in the nonlinear gear vibration systems. Therefore, in order to design and develop an optimal gear transmission system, it is important to control and eliminate these nonlinear phenomena. This paper presents the design of a gear system in order to control and suppress the chaos. A generalized nonlinear dynamics model of a spur gear pair including the backlash and the static transmission error is formulated. The idea behind the design of this control system is applying an additional control excitation force to the driver gear. The parameter spaces of the control excitation force are obtained analytically by using the Melnikov approach. The numerical simulations including the bifurcation diagram, the phase portrait, and the time history are used to confirm the analytical predictions and show effectiveness of the proposed control system for chaos suppression in nonlinear gear systems.

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Generally, The dynamics which is observed in time series of a hydrologic system variable have been considered as complex and random behavior. During last decades, using various artificial intelligence approaches such as chaos theory to analyze and prediction of hydrologic systems have been increased. In chaos theory viewpoint, complexity and random-like behavior of a system can be resulted from a simple and hidden determinism. Therefore, systems such as dominant hydrologic system which controls flow in a river can have this kind of determinism. If such determinism is existed, can be observed through system phase space, which can be reconstructed using a time series by lags method. Based on such a pattern that formed in reconstructed phase space, various prediction models can be used to forecast system behavior in future. Hence, chaotic behavior of the Kashkan river daily discharge time series have been studied using False Nearest Neighbors and Lyapunov Exponent methods which evaluated fractal attractor and sensitivity to initial condition as two major characteristics of a chaotic system. Average Mutual Information method was used to determine optimal delay time in phase space reconstruction by delay method. In this paper, it has been suggested to use first global minimum of mutual information function as standard to select optimal delay time. According to the results which have been obtain by these methods, chaotic behavior in daily runoff time series of the Kashkan river have been observed. In False Nearest Neighbors method, the percent of false neighbors have been significantly decreased due to rising embedding dimension of phase space, which have been shown the existence of a fractal attractor in system phase space. In lyapunov exponent method, the sensitivity to initial condition has been evaluated through reconstructed phase space and positive lyapunov exponent has been obtained. Hence, chaos theory-based models can be used to forecast daily runoff in this system. Various local models were used to make prediction based on reconstructed phase space and the results have been compared. Local Average and Local Polynomial was among local models that employed in this study. In addition, as a new hybrid approach, Multi Layer Prespetron Artificial Neural Networks have been used to local modeling based on phase space. All prediction results show appropriate quality of local prediction models in base of attractor pattern in phase space of dominant system of the Kashkan river flow. The accuracy which have been resulted from local hybrid model with Artificial Neural Networks, have been not shown significant difference with other current local models such as Local Average and Local Polynomial prediction methods. However, the Local Polynomial model has been shown better forecasting accuracy in compare with other methods. Totally, Local chaotic methods are suggested to make daily prediction of runoff in the Kashkan river.

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In the present paper, nondeterministic CFD has been performed using polynomial chaos expansion and Gram-Schmidt orthogonalization method. The Gram-Schmidt method has been used in the literature for constructing orthogonal basis of polynomial chaos expansion in the projection method. In the present study, for the first time the Gram-Schmidt method is used in regression method. For the purpose of code verification, the output numerical basis of code for uniform and Gaussian probability distribution functions is compared to their corresponding analytical basis. The numerical method is further validated using a classical challenging function. Comparison of numerical and analytical statistics shows that developed numerical method is able to return reliable results for statistical quantities of interest. Subsequently, the problem of stochastic heat transfer in a grooved channel was investigated. The inlet velocity, hot wall temperature and fluid conductivity were considered uncertain with arbitrary probability distribution functions. The UQ analysis was performed by coupling the UQ code with a CFD code. The validity of numerical results was evaluated using a Monte-Carlo simulation with 2000 LHS samples. Comparison of polynomial chaos expansion and Monte-Carlo simulation results reveals an acceptable agreement. In addition a sensitivity analysis was carried out using Sobol indices and sensitivity of results on each input uncertain parameter was studied.

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The chaotic behavior of a flexible rotor supported by active magnetic bearings is numerically investigated in this work. A statically unbalanced disk is mounted on the the shaft. The rotor is modeled by three lumped mass and 8 D.O.F. The rotor-AMB systems include many non-linear factors, such as nonlinear function of the coil current and the air gap between the rotor and the stator, nonlinearity due to geometric coupling of magnetic actuator, eddy current effect and hysteresis losses of the magnetic core material. In this work, the influence of weight parameter on nonlinear response of the system is investigated. Numerical results showed considering of weight parameter have important effect on the response of the rotor and exhibit a rich variety of nonlinear dynamical behavior including synchronous, sub-synchronous, quasi-periodic and chaotic vibrations. Bifurcation diagrams, phase planes, power spectra ,Poincar’e map and maximum lyapanov exponents are used to analyze the response of the system under different operational conditions. Chaotic vibrations should be avoided as they induce fluctuating stresses that may lead to premature failure of the machinery’s main component. It will be beneficial to the design of AMB system.

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Uncertainty inherently exists in quantity of a system’s parameters (e.g., loading or elastic modulus of a structure), and thus its effects have always been considered as an important issue for engineers. Meanwhile, numerical methods play significant role in stochastic computational mechanics, particularly for the problems without analytical solutions. In this article, spectral finite element method is utilized for stochastic spectral finite element analysis of 2D continua considering material uncertainties. Here, Lobatto family of higher order spectral elements is extended, and then influence of mesh configuration and order of interpolation functions are evaluated. Furthermore, Fredholm integral equation due to Karhunen Loève expansion is numerically solved through spectral finite element method such that different meshes and interpolation functions’ orders are also chosen for comparison and assessment of numerical solutions solved for this equation. This method needs fewer elements compared to the classic finite element method, and it is specifically useful in dynamic analysis as supplies desirable accuracy with having diagonal mass matrix. Also, these spectral elements accelerate the computation process along with Karhunen Loève and polynomial chaos expansions involving numerical solution of Fredholm integral equation. This research examines elastostatic and elastodynamic benchmark problems to demonstrate the effects of the undertaken parameters on accuracy of the stochastic analysis. Moreover, results demonstrate the effects of higher-order spectral elements on speed, accuracy and efficiency of static and dynamic analysis of continua.

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In this paper, we investigate chaos in attitude dynamics of a rigid satellite in an elliptic orbit analytically and numerically. The goal in the analytical part is to prove the existence of chaos and then to find a relation for the width of chaotic layers based on the parameters of the system. The numerical part is aimed at validating the analytical method using the Poincare maps and the plots obtained on the sensitivity to initial conditions. For this end, first, the Hamiltonian for the unperturbed system is derived. This Hamiltonian has three degrees of freedom due to the three-axis free rotation of the satellite. However, the unperturbed attitude dynamics has two first-integrals of motion, namely, the energy and the angular momentum. Next, we use the Serret-Andoyer transformation and reduce the unperturbed system Hamiltonian to one-degree of freedom. Then, the gravity gradient perturbation due to moving in an elliptic orbit is approximated in Serret-Andoyer variables and time. Due to this approximation and simplification, the system Hamiltonian transforms to a one-degree-of-freedom non-autonomous one. After that, Melnikov’s method is used to prove the existence of chaos around the heteroclinic orbits of the system. Finally, a relation for calculating the width of chaotic layers around the heteroclinic orbits in the Poincare map of the Serret-Andoyer variables is analytically derived. Results show that the analytical method gives a good approximation of the width of chaotic layers. Moreover, the results show that the analytical method is accurate even for orbits with large eccentricities.

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  Appropriate methods for prediction of future trends in capital markets lead to a better decision making for market participants. Classic methods don not perform well in prediction of financial markets due to the nonlinear and chaotic nature of these markets. Moreover, information extracted from data disappear quickly, so these method are not workable in the long run. The goal of this paper is using ant colony optimization algorithm for prediction of Tehran Stock Exchange's total return index (TEDPIX) data. First, we used the largest Lyapunov exponent to the consider chaotic nature of TEDPIX and then the ant colony optimization paradigm we employed to analyze topological structure of the attractor behind the given time series and to single out the typical sequences corresponding to the different parts of the attractor. The typical sequences were used to predict the time series values. Eventually with respect to MSE , RMSE and MAE, ACO has lower error than GARCH and EGARCH models; however, Diebold Marino test shows that there is no difference if we use ACO or GARCH models for prediction; this represents that differences of error for different models in this article are very little. This article with detachment of typical sequences allows a structural method for prediction of chaotic data. So in prediction of data with many fluctuations and in long term, it can result to a better predictions. The algorithm of this paper is able to provide robust prognosis to the periods comparable with the horizon of prediction.   Keywords

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In this paper, the nonlinear vibration of a Euler–Bernoulli nanobeam resting on a non-linear viscoelastic foundation is investigated. It is assumed that the nanobeam is subjected to a harmonic excitation that can be representative of an electrostatic field. The non-linear viscoelastic foundation is considered for both hardening and softening cases. By neglecting of the in-plane inertia, Eringen's nonlocal elasticity theory is used to model and derive the equation of motion of the nanobeam. Using the Galerkin method and the first mode shape, the obtained partial differential equation is reduced to the ordinary differential equation. Calculating the system's equilibrium points lead to heteroclinic bifurcation and the heteroclinic orbits are obtained. Then, using the Melnikov integral method, the chaotic motion of the system is studied analytically, and the safe region of the system is determined respect to the parametric space of the problem. When the viscoelastic foundation has a hardening characteristic, the chaotic behavior in the system does not occur. It has been observed that the use of nonlocal elasticity theory is necessary to investigate the chaotic behavior of nanobeam, and using the classical theory of elasticity may place the system in the chaotic region.

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In this paper, an atomic force microscope is modeled based on non-classical nonlocal theory and nonlinear vibration of the system is analyzed and controlled. In this modeling, the Hamilton principle is used to derive the governing equation of Euler-Bernoulli nanocantilever based on the Eringen nonlocal elasticity theory considering Von-Karman geometric non-linearity. In the next step, using the Galerkin method, the governing dynamics differential equation of the atomic force microscope is obtained in the presence of attractive and repulsive van der Waals forces. The governing nonlinear equation is solved by employing multiple time scales method, and primary and secondary resonance of the atomic force microscope is studied. In this regard, the frequency response and excitation amplitude curves of primary, superharmonic and subharmonic resonances are plotted for different values ​​of the nonlocal parameter. Accordingly, it is shown that primary, superharmonic and subharmonic resonances of atomic force microscope are significantly affected by the nonlocal parameter. The results show that the use of nonlocal theory is a fundamental necessity for analyzing nonlinear vibrations of the atomic force microscope. Then, in addition to dynamic analysis, the chaotic vibrations are completely controlled and removed in the nonlocal model of the atomic force microscope by designing and implementing the robust adaptive fuzzy controller. For this task, the robust adaptive fuzzy controller which is considered as a powerful method of chaos controlling is used in the nonlocal model of atomic force microscope. The obtained results are used in the design and control process of the atomic force microscope.