Sharif Digital Repository

Tipping points occur in diverse systems in various disciplines such as ecology, climate science, economy, sociology, and engineering. Critical thresholds in system parameters or state variables at which a tiny perturbation can lead to a qualitative change in the system exist in many subsystems in complex systems. These thresholds are called tipping points, and these subsystems are called tipping elements. Additionally, many systems with tipping points can be modeled as networks of coupled multistable subsystems. Domino-like tippings are called tipping cascades. Considering that these tipping cascades are primarily unprecedented, it is essential to study the dynamics and control of these... 

In this thesis, we review recent advances on controlling of complex systems. We provide in details, the concepts of synchronizability and synchronization controllability.Then we will investigate synchronization controllability under different pinning schemes, and propose a new pinning strategy to increase controllability and consequently decrease the number of required pinned nodes (known as driver nodes) to assure a stable synchronized state. We also study the network characteristics of resulted sequence of driver nodes. Finally, we will employ our proposed schemes to study the controllability of complex networks of chaotic Rossler oscillators  

In this thesis we would like to investigate structural disorder of Graphene and its effect on electronic properties. Graphene is a one-layer crystal of Carbon atoms which was the first two dimensional crystal observed experimentally. Low energy current carriers on Graphene behave like mass-less Dirac fermions and this interesting electronic property attracts much attention on studying Graphene. Structural disorder of Graphene highly affects its electronic properties. We study thermal fluctuations of Graphene sheet, disorder super lattice, and static ripples, as structural disorders of Graphene. Disorders due to thermal fluctuations of graphene induce a disordered gauge field on the graphene... 

In recent decades the Due to development of coating techniques and the diversity of high organic matter, Discussion of organic coating materials being raised. Moreover, because of many applications of organic thin film in electronic and optical systems for example OTFTs and OLEDs Organic thin film growth topic is very interesting for scientists. Among these, some scientists study the theory and another bunch of scientists pay to practical aspects of this topic. In this thesis I pay to the theoretical level of Organic thin film growth and I simulate the system includes a collection of molecules, Went on to study some statistical properties of the system will be discussed and the dynamic... 

In this thesis we study the dispersion of one-dimensional scalar waves in a random media. We used the finite difference method to obtain the numerical solution of wave equation in this media. Then we were able to find wave signals for different disorder intensities and at different distances from the source. Using the Wavelet Transform, intresting features such as phase and group velocity can be studied. The Morlet function is used as the mother wavelet for decomposing the signals at different places. Cross-correlation functions of Wavlet transforms of the signals at different positions are used to obtain phase velocity and its dependence on frequency. We show how the phase velocity at the... 

The synchronization phenomena are abundant is science, nature, engineering, and social life. Systems as diverse as clocks, singing crickets, cardiac pacemakers, firing neurons, and applauding audiences exhibit a tendency to operate in synchrony. These phenomena are universal and can be understood within a common framework based on modern nonlinear dynamics. First chapter of this thesis describes the basic ideas of the synchronization in an intuitive way. The main physical concepts are presented with experimental examples.
One of the main effects of synchronization is the ability to infer the directionality of coupling for two time series. Uncovering the directionality of coupling is a... 

In this thesis the resilience of a neural network is examined under structural perturbation.The network consists of Spiking neurons with specific dynamics or they are binary neurons and the network is non-spiking. Neural network is a multi-dimensional and multi-stable system therefore we can map their dynamical equations to effective one-dimensional equation with one parameter which shows the environmental conditions.The resilience of the system is evaluated with respect to changes in weights and edges of the network and the the resilience pattern of the system is obtained.Finally, the recovery and control methods are briefly discussed  

In this thesis, we first briefly review the basic concepts of stochastic processes. After reviewing and studying the dynamic equation that can explain a stochastic process, we show how one can find on a data-driven basis, the first-, second- and higher-order interactions between different subunits of a complex system by disentangling the dynamics of multivariate time series into stochastic and deterministic parts. Our data-driven approach is to detect different degrees of interactions obtained using conditional moments of Kramers-Moyal coefficients from unconditioned correlation functions and statistical moments of multivariate N-dimensional multivariate time series. Finally, we study the... 

In this thesis, we first provide a brief overview of the basic concepts of stochastic processes and the mathematical tools required to study these processes. Then, we demonstrate that by using a data-driven approach, one can obtain the corresponding coefficients for deterministic, diffusion, and jump components of the stochastic process. In this method, the conditional moments of Kramers–Moyal coefficients are calculated using statistical moments of N-dimensional time series. These coefficients enable us to determine different orders of interactions, diffusion and jump properties, and %relationships coupling coefficients between time series. Furthermore, to evaluate the accuracy of the... 

In this thesis, we study the resilience of complex systems under structural perturbations. After a brief review of the resilience and its importance, we show that how one can map a system of N-coupled dynamical equations onto an effective one-dimensional dynamics. This procedure is based on a nearest neighbor averaging. The obtained map, helps us study the response of the system to the effective one-dimensional control parameter, instead of all parameters that are affecting the structure of the network. Next, we use this procedure and unveil the resilience pattern of second-order Kuramoto oscillators on complex networks. Moreover, we propose a control strategy for complex systems which is... 

A complex system consists of a large number of subsystems that interact with each other and with the environment. These systems have collective behaviors that may are desired and undesired. Learning, intelligence and epilepsy are examples of desirable and undesirable collective behaviors. Control of these systems arises when they are out of the desired state or one wants to avoid approaching the system to its undesired state. For control of complex systems, we need external functions that apply to specific subsystems. These functions can be obtained from the numerical solution of Hamilton-Jacobi-Bellman equation. The Hamilton-Jacobi-Bellman equation is nonlinear and must be solved at very... 

Control of complex networks is the main topic in this study. In this thesis, we consider the methods to steer the dynamics of a network from an initial state to the desired final state. To achieve this goal, one needs to inject appropriate control signals from some of the network nodes, known as driver nodes. We consider the quadratic sum of control signals as a cost function, to control the dynamics of the network. By minimising the cost function, we obtain the control signals as well as driver nodes for a linear time-invariant system. As an example, we provide the results of an energy minimization strategy to control the second order Kuramoto and Rössler dynamics in Erdos-Renyi and... 

In this thesis, some aspects of the Burges and Kardar-Parisi-Zhang (KPZ) equations will be studied. At first we introduce Turbulence and describe historical view of Burgers and KPZ equations. Then in second section we study analytically the time issue of Burgers equation in 1+1-dimenssion. Then by using recently developed precise numerical methods by J. Bec and U. Frisch, we check result of previous section numerically. Our numerical simulation of the Burgers equation stirred by a kicking force support our analytical results. In small time scale our result show dynamical exponent of structure function z is one. This is the essence of the assumption first made by Sir G. I. Taylor in his 1938... 

The electrons scatter by the impurities during propagation through the media and become localized by increasing the impurities. So the metal insulator transition occurs. This phenomenon was first proposed by W. Anderson and is known as Anderson Localization. In this thesis the Anderson localization of electromagnetic waves is investigated. The disordered media with random dielectric constant is studied by considering Maxwell’s equations. There are different numerical methods to study this phenomenon such as transfer matrix method and level statistics we have used in this thesis. In three dimension, different scaling behavior shows the phase transition from localized states to extended states... 

In a one-dimensional disordered system, Anderson localization is known to occur at any energy in the thermodynamic limit when the disorder is uncorrelated and white noise structure.
A great interest for 1D disordered models with correlated disorder has been growing since 2002, as it has become progressively clear that the correlation of the random potentials can deeply affect the electronic localization properties. Spatial correlation of disorder can unexpectedly create extended states at some particular energies.
In this thesis, we study the metal-insulator transition in one dimensional Anderson binary alloy with long range disordered hopping integral and on-site energy, using the... 

One of the most important studies in cosmology is the study of Large Scale Structure of cosmos, where one of the useful and valuable tools is Excursion Set Theory(EST). EST or Extended Press-Schechter is a theory based on stochastic processes which gives us the distribution function(mass function) of dark matter halos. In order to having smoothed density feld Excursion Set Theory uses a specifc window function(flter) called sharp k-space, which is a top-hat in Fourier space. If one use this specifc window function the process of density feld with respect to variance will be a Markov process, with any other window function the process won’t be a Markov process. Excursion Set Theory using the... 

The purpose of the thesis is to investigate the phonon localization in disordered media and in the presence of nonlinear effect. As a simple model, we consider a system of spring-coupled masses, where the value of mass in each site fluctuates around a positive mean. Using transfer matrix method, we calculate the frequency dependence of the localization length (in the absence of the nonlinear effect) for diffrent strength of disorder in one dimention. For given localized mode, by turning on the nonliner term, we study whether nonlinearity will enhance localization or extend the localized mode? To study the nonlinear effect, since the transfer matrix method is only applicable for the linear... 

In this thesis, we investigate the imprint of gravitational microlensing effects on the light curves of Gamma-ray burst (GRBs) to estimate compact object mass in the form of black holes in the Universe. We assume a point mass model of the gravitational lens and a geometry in which the source−lens are at the same direction that manifests in the GRB light curve as superimposed peaks by the time delay between the two images and searches the Fermi/GBM catalog. According to the sensitivity of our detection method, we consider microlensing events with a time delay on the order of 10 s due to point-mass lenses in the range of 〖10〗^5- 〖10〗^7 M_(⊙ ). We found one microlensed GRB candidate out of... 

Complex systems are composed of a large number of subsystems behaving in a collective manner. In such systems, which are usually far from equilibrium, collective behavior arises due to self-organization and results in the formation of temporal, spatial, spatio-temporal and functional structures. The dynamics of order parameters in complex systems are generally non-stationary and can interact with each other in nonlinear manner. As a result, the analysis of the behavior of complex systems must be based on the assessment of the nonlinear interactions, as well as the determination of the characteristics and the strength of the fluctuating forces. This leads to the problem of retrieving a...