• SPATIAL CONTROL OF LOCALIZED OSCILLATIONS IN ARRAYS OF COUPLED LASER DIMERS 

  Shena, Joniald; Kominis, Yannis; Bountis, Anastasios; Kovanis, Vassilios (PHYSICAL REVIEW E, 2020)

  Arrays of coupled semiconductor lasers are systems possessing radically complex dynamics that makes them useful for numerous applications in beam forming and beam shaping. In this work, we investigate the spatial ...
• Synchronization of Coupled Nonlinear Oscillators with Applications to Photonic Arrays 

  Zharas, Banu (Nazarbayev University School of Science and Technology, 2019-05-01)

  In recent years, the study of synchronization of coupled oscillators have been the subject of intense research interest, leading to many new and unexpected phenomena. Our research is first focused on the analysis of a ...
• The Dynamics of Hamiltonian Lattices With Application to Hollomon Oscillators 

  Zholmaganbetova, Aigerim (Nazarbayev University School of Science and Technology, 2019-05-29)

  Many problems in theoretical physics are expressed in the form of Hamiltonian systems. Among these the first to be extensively studied were low-dimensional, possessing as few as two (or three) degrees of freedom. In the ...
• Convergence Rate of Fourier Neural Networks 

  Zhumekenov, Abylay (Nazarbayev University School of Science and Technology, 2019-04-26)

  The paper investigates a convergence rate for 2-layer feedforward Fourier Neural Network (FNN). Such networks are motivated by the approximation properties of wellknown Fourier series. Several implementations of FNNs ...
• Explorations on chaotic behaviors of Recurrent Neural Networks 

  Myrzakhmetov, Bagdat (Nazarbayev University School of Science and Technology, 2019-04-29)

  In this thesis work we analyzed the dynamics of the Recurrent Neural Network architectures. We explored the chaotic nature of state-of-the-art Recurrent Neural Networks: Vanilla Recurrent Network, Recurrent Highway ...
• Numerical computations of complexification of Legendrian knots 

  Yerzhigit, Bauyrzhan (Nazarbayev University School of Science and Technology, 2019-04-29)

  With the recent interest in knots, it is interesting to study their complexification. We have chosen to study Legendrian knots as they have the property that we can reconstruct the original knot from its projection. This ...
• Multigrid method for Mild-Slope equation in Coastal Wave Modelling 

  Tabarek, Rysbergen (Nazarbayev University School of Science and Technology, 2019-04-19)

  In this thesis we propose and study an efficient iterative multigrid method for the time independent modified mild slope equation with and without energy dissipation term. The algorithm relies on a multigrid method ...
• Pulse vaccination of a time-delayed SIRS epidemic model with nonlinear incidence rate 

  Yeleussinova, Meruyert (Nazarbayev University School of Science and Technology, 2019-05-03)

  This work deals with an application of pulse vaccination for a varying size of the population of time-delayed 𝑆𝐼𝑅𝑆 epidemic model. The dynamics of the infectious disease depends on the threshold value, 𝑅0, known as ...
• Global stability analysis for a tick-borne model 

  Azamat, Daiana (Nazarbayev University School of Science and Technology, 2019-05-06)

  This thesis consider three type of epidemiological models: SIR, SIS and SIRS with nonlinear incidence rate and piecewise constant delay of generalized type. In this paper the total population size is varied with time elapse. ...
• The lumped model parameters approach for static and dynamic power-law beam problems 

  Begzhigitov, Madi (Nazarbayev University School of Science and Technology, 2019-04-29)

  It is important to estimate the natural frequencies of the structural elements in the design of mechanical or electromechanical structures. There is a wide use of single lumped-parameter spring-mass models in the industry ...
• Experimental study of Pac-Man conditions for learn-ability of discrete linear dynamical systems 

  Damiyev, Zhaksybek (Nazarbayev University School of Science and Technology, 2019-05-01)

  In this work, we are going to reconstruct parameters of a discrete dynamical system with a hidden layer, given by a quadruple of matrices (𝐴,𝐵,𝐶,𝐷), from system’s past behaviour. First, we reproduced experimentally ...
• Well-Posedness of the Nonlinear Schrödinger Equation 

  Orumbayeva, Sara (Nazarbayev University School of Science and Technology, 2019-08-07)

  The Nonlinear Schrödinger equation (NLSE) is a prototypical example of nonlinear partial differential equation. It is commonly used to describe propagation of light in nonlinear optical fibers and is of great importance ...
• Nonlinear Schrodinger Equation 

  Kazbek, Moldir (Nazarbayev University School of Science and Technology, 2019-08-08)

  Rogue waves are fascinating destructive phenomena in nature that have not been fully explained so far [1-3]. Oceanographers commonly agree that linear theories cannot provide explanations for their existence[6,7]. Only ...
• Analytic Solutions for a Nonlinear Transport Equation 

  Biyar, Magzhan (Nazarbayev University School of Science and Technology, 2019-08-07)

  We prove that the Cauchy problem for a transport equation with algebraic nonlinearity of degree p with initial data in Gevrey spaces is locally well-posed. In particular, we show that the analyticity of solutions persists ...
• Nonlinear Regression Analysis of the generalized Logistic Model as an Actuarial life contingency model 

  Kadenova, Aida (Nazarbayev University School of Science and Technology, 2019-08-08)

  The aim of this project is to analyze three different population models such as Gompertz, Logistic and Generalized Logistic based USA population data. Finding the appropriate model is essential in actuarial application. ...
• Copula functions in Credit Metrics’ VaR estimation 

  Magzanov, Shynggys (Nazarbayev University School of Science and Technology, 2019-08-08)

  Credit risk modelling of a portfolio of exposures is essential part of activity of every financial institution. However this procedure is complicated since the joint behavior of chosen exposures must be known. In this paper ...
• Frobenius Singularities of Algebraic Sets of Matrices 

  Yerlanov, Madi (Nazarbayev University School of Science and Technology, 2019-08-07)

  When one studies certain rings, it is natural to classify them according to certain properties. This project focuses on the study of properties of commutative rings associated with algebraic sets. In particular, we consider ...
• The Asymmetric Active Coupler: Stable Nonlinear Supermodes and Directed Transport 

  Kominis, Yannis; Bountis, Tassos; Flach, Sergej (Scientific Reports, 2016-09-19)

  We consider the asymmetric active coupler (AAC) consisting of two coupled dissimilar waveguides with gain and loss. We show that under generic conditions, not restricted by parity-time symmetry, there exist finite-power, ...
• The effect of long–range interactions on the dynamics and statistics of 1D Hamiltonian lattices with on–site potential 

  Christodoulidi, H.; Bountis, Tassos; Drossos, L. (arXiv, 2018-04)

  We examine the role of long–range interactions on the dynamical and statistical properties of two 1D lattices with on–site potentials that are known to support discrete breathers: the Klein–Gordon (KG) lattice which ...
• Stability through asymmetry: Modulationally stable nonlinear supermodes of asymmetric non-Hermitian optical couplers 

  Kominis, Yannis; Bountis, Tassos; Flach, Sergej (Physical Review A, 2017-06-21)

  We analyze the stability of a non-Hermitian coupler with respect to modulational inhomogeneous perturbations in the presence of unbalanced gain and loss. At the parity-time (PT ) symmetry point the coupler is unstable. Suitable ...

View more