Nejib Smaoui

• PhD
• Professor (Full) at Kuwait University

In this article, we consider a one-dimensional dispersive equation known in literature as Kuramoto-Sivashinsky (KS) equation. It models numerous physical phenomenon such as turbulent states in a distributed chemical reaction, flame propagation and waves in a viscous fluid. Motivated by practical reasons, a constant time-delay is assumed to occur in...

The main concern of this paper is to study the boundary stabilization problem of the disk-beam system. To do so, we assume that the boundary control is either of a force type control or a moment type control and is subject to the presence of a constant time-delay. First, we show that in both cases, the system is well-posed in an appropriate functio...

The dynamics and control of the Korteweg‐de Vries‐Kuramoto‐Sivashinsky (KdVKS) equation subject to periodic boundary conditions are considered. First, the dynamics of the KdVKS equation is analyzed using the Fourier Galerkin reduced‐order method. This reduced‐order method is used to generate a finite‐dimensional approximation of the KdVKS equation....

The paper is devoted to the input-feedback control design for a class of reaction-diffusion systems governed by the generalized Kuramoto–Sivashinsky (GKS) equation (a nonlinear partial differential equation that is first order in time, fourth order in space, and with a high-order nonlinearity subject to periodic boundary conditions). First, we show...

This paper treats the stabilization of a vibrating string by means of a switching time-delay boundary control. We show that the problem possesses a unique solution by means of semigroups theory of linear operators. Then, we provide a theoretical and numerical study of the exponential stability of the system under an appropriate delay coefficient.

The generalized Korteweg–de Vries–Burgers–Kuramoto–Sivashinsky equation (GKdVBKS) is a nonlinear partial differential equation that models propagation of waves in a thick elastic tube filled with a viscous fluid. First, the dynamics of the GKdVBKS equation that depend on the physical parameters ν$$ \nu $$ and γ2$$ {\gamma}_2 $$, where γ2$$ {\gamma}...

In this paper, we consider two internal stabilization problems for the multi-dimensional wave equation with a boundary time-delay. We prove that the first problem is well-posed in an appropriate functional space. Subsequently, we numerically study the exponential stability in a two-dimensional case under Geometric Control Condition (GCC) derived by...

The primary concern of this article is to establish the well‐posedness as well as the exponential stability of the zero solution to a nonlinear time‐delayed dispersive equation of order four in a bounded interval. The main ingredient of the proof is the exploitation of Schauder Fixed Point Theorem. This outcome considerably improves an earlier resu...

The primary concern of this article is to establish the well-posedness as well as the exponential stability of the zero solution to a nonlinear time-delayed dispersive equation of order four in a bounded interval. The main ingredient of the proof is the exploitation of Schauder Fixed Point Theorem. This outcome considerably improves an earlier resu...

This paper is devoted to the control problem of a nonlinear dynamical system obtained by a truncation of the two-dimensional (2D) Navier–Stokes (N-S) equations with periodic boundary conditions and with a sinusoidal external force along the x-direction. This special case of the 2D N-S equations is known as the 2D Kolmogorov flow. Firstly, the dynam...

The paper deals with the dynamics and control of the modified generalized Korteweg–de Vries–Burgers equation (MGKdVB) with periodic boundary conditions. First, the dynamics of the MGKdVB equation is studied using the Fourier Galerkin and the Karhunen–Loève (K–L) Galerkin methods. The Fourier Galerkin approach is used to generate a system of nine or...

This paper deals with the stability analysis of a nonlinear time-delayed dispersive equation of order four. First, we prove the well-posedness of the system and give some regularity results. Then, we show that the zero solution of the system exponentially converges to zero when the time tends to infinity provided that the time-delay is small and th...

This paper deals with the boundary stabilization problem of a one-dimensional wave equation with a switching time-delay in the boundary. We show that the problem is well-posed in the sense of semigroups theory of linear operators. Then, we provide a theoretical and numerical study of the exponential stability of the system under an appropriate dela...

This paper deals with the stability analysis of a nonlinear time-delayed dispersive equation of order four. First, we prove the well-posedness of the system and give some regularity results. Then, we show that the zero solution of the system exponentially converges to zero when the time tends to infinity provided that the time-delay is small and th...

This paper is concerned with the feedback flow control of an open-channel hydraulic system modeled by a diffusive wave equation with delay. Firstly, we put forward a feedback flow control subject to the action of a constant time delay. Thereafter, we invoke semigroup theory to substantiate that the closed-loop system has a unique solution in an ene...

In this paper, we study the nonlinear adaptive boundary control problem of the modified generalized Korteweg–de Vries–Burgers equation (MGKdVB) when the spatial domain is 0,1 . Four different nonlinear adaptive control laws are designed for the MGKdVB equation without assuming the nullity of the physical parameters ν , μ , γ1 , and γ2 and depending...

The synchronous reluctance motor (SynRM) drive system is known to exhibit chaotic behavior under specified conditions. In this paper, the discrete-time sliding mode control (DSMC) technique is used to synchronize two SynRMs starting from different sets of initial conditions. The mixed variable speed reaching law is adopted in the design of the cont...

Abstract The linear stabilization problem of the modified generalized Korteweg–de Vries–Burgers equation (MGKdVB) is considered when the spatial variable lies in [0,1] $[0,1]$. First, the existence and uniqueness of global solutions are proved. Next, the exponential stability of the equation is established in L2(0,1) $L^{2} (0,1)$. Then, a linear a...

Abstract In this paper, we study the modelling and nonlinear boundary stabilization problem of the modified generalized Korteweg–de Vries–Burgers equation (MGKdVB) when the spatial domain is [0,1] $[0,1]$. First, the MGKdVB equation is derived using the long-wave approximation and perturbation method. Then, two nonlinear boundary controllers are pr...

This paper is consecrated to the feedback stabilization of the rotating disk-beam system. The beam is assumed to be non-uniform and clamped at its left-end to the center of the disk where a torque control takes place, while a memory boundary control is acting at the right-end of the beam. First, the usual torque control is proposed, whereas the bou...

This paper deals with the projective synchronization (PS) of two identical discrete-time generalized four-dimensional (4D) hyperchaotic Henon maps using a master-slave configuration. A discrete sliding mode controller (DSMC) scheme is proposed to synchronize the master and the slave systems. The performance of the controlled systems is simulated; t...

A unique secure communication scheme that can be used for the transmission of gray-scale and color videos is presented in this paper. The proposed scheme is developed by using the Karhunen-Loéve (K-L) decomposition and the synchronization of the unified chaotic system with the hyperchaotic Chen system. First, the gray-scale or color video is repres...

Under certain conditions, power systems may exhibit chaotic behaviors which are harmful and undesirable. In this paper, the discrete time sliding mode control technique is used to control a chaotic power system. The objective of the control is to eliminate the chaotic oscillations and to bring order to the power system. Two discrete time sliding mo...

The symmetries, dynamics, and control problem of the two-dimensional (2D) Kolmogorov flow are addressed. The 2D Kolmogorov flow is known as the 2D Navier-Stokes (N-S) equations with periodic boundary conditions and with a sinusoidal external force along the x -direction. First, using the Fourier Galerkin method on the original 2D Navier-Stokes equa...

This paper is dedicated to the qualitative analysis as well as numerical simulations of a one dimensional open channel hydraulics system which is commonly used in hydraulic engineering to model the unsteady flow dynamics in a river. First, an output feedback control is proposed. Next, the closed-loop system is proved to possess a unique solution in...

This paper proposes a novel secure communication scheme based on the Karhunen–Loéve decomposition and the synchronization of a master and a slave hyperchaotic Lü systems. First, the Karhunen–Loéve decomposition is used as a data reduction tool to generate data coefficients and eigenfunctions that capture the essence of grayscale and color images in...

The control problem of the chaotic attractors of the two dimensional (2-d) Navier-Stokes (N-S) equations is addressed in this paper. First, the Fourier Galerkin method based on a reduced-order modelling approach developed by Chen and Price is applied to the 2-d N-S equations to construct a fifth-order system of nonlinear ordinary differential equat...

This paper deals with the dynamics and control of the two-dimensional (2-d) Navier–Stokes (N–S) equations with a spatially periodic and temporally steady forcing term. First, we construct a dynamical system of nine nonlinear differential equations by Fourier expansion and truncation of the 2-d N–S equations. Then, we study the dynamics of the obtai...

An approach for the determination of principal components using nonlinear principal component analysis (NLPCA) is proposed in the context of turbulent combustion. NLPCA addresses complex data sets where the contours of the inherent principal directions are curved in the original manifold. Thermo-chemical scalars' statistics are reconstructed from t...

This paper deals with the design of nonlinear controllers for the synchronization of two hyperchaotic systems. The feedback linearization control (FLC) technique as well as the sliding mode control (SMC) technique are used to synchronize two identical hyperchaotic Lu systems. We prove that the errors between the states of the master system and the...

This paper deals with the adaptive synchronization of two identical hyperchaotic master and slave Chen systems. First, the slave system is assumed to have four inputs. Using Lyapunov theory, it is shown that the errors between the states of the master and the slave systems asymptotically converge to zero. Simulation results are pre¬sented to illust...

The paper considers 3 non-adaptive boundary controls of the forced GKdVB equation over the interval [0, 1]

In this paper, we consider the boundary control problem of the generalized Korteweg-de Vries-Burgers (GKdVB) equation when the spatial domain is [0, 1]. Two control laws are designed for the forced GKdVB equation when the parameter α is a positive integer. It is shown, using the Lyapunov theory, that the solutions of the controlled forced GKdVB equ...

This paper deals with the synchronization of two identical hyperchaotic master and slave systems. The slave system is assumed to have two inputs. A sliding mode controller is proposed to synchronize the two systems. Using Lyapunov theory, it is shown that the errors between the states of the master and slave systems asymptotically converge to zero...

This paper deals with the adaptive synchronization of two identical hyperchaotic master and slave systems. The master system and the slave system each consists of two subsystems: a hyperchaotic Chen subsystem and a unified chaotic subsystem. The asymptotic convergence of the errors between the states of the master system and the states of the slave...

This paper considers the adaptive control problem of the forced generalized Korteweg-de Vries-Burgers (GKdVB) equation when the spatial domain is [0,1]. Three different adaptive control laws are designed for the forced GKdVB equation when either the kinematic viscosity ν or the dynamic viscosity μ is unknown, or when both viscosities ν and μ are un...

The adaptive boundary control problem of the generalized Korteweg-de Vries-Burgers (GKdVB) equation when the spatial domain is [0,1] is considered. Three adaptive control laws are designed for the GKdVB equation when either the kinematic viscosity ν or the dynamic viscosity μ is unknown, or when both viscosities ν and μ are unknowns. Using the Lyap...

In this paper, we consider the boundary control problem of the unforced generalized Korteweg–de Vries–Burgers (GKdVB) equation when the spatial domain is [0,1]. Three control laws are derived for this equation and the L 2-global exponential stability of the solution is proved analytically. Numerical results using the finite element method (FEM) are...

The unified chaotic system incorporates the behaviors of the Lorenz, the Chen and the Lü chaotic systems. This paper deals with the synchronization of two identical unified chaotic systems where the slave system is assumed to have a single input. A sliding mode controller is proposed to synchronize the two systems. The asymptotic convergence to zer...

In this paper, we present a novel approach to encrypt a message (a text composed by some alphabets) using chaos and shadowing. First, we generate a numerical chaotic orbit based on the logistic map, and use the shadowing algorithm of Smaoui and Kostelich [Smaoui N, Kostelich E. Using chaos to shadow the quadratic map for all time. Int J Comput Math...

The Permanent Magnet Synchronous Motor (PMSM) is known to exhibit chaotic behavior under certain conditions. This paper proposes to use an instantaneous Lyapunov exponent control algorithm to control the PMSM. One of the objectives of the control approach is to bring order to the PMSM and to drive it to any user-defined desired state. Simulation re...

Two pseudorandom binary sequence generators, based on logistic chaotic maps intended for stream cipher applications, are proposed. The first is based on a single one-dimensional logistic map which exhibits random, noise-like properties at given certain parameter values, and the second is based on a combination of two logistic maps. The encryption s...

The paper deals with the finite dimensional control of the generalized Korteweg-de Vries Burgers (GKdVB) partial differential equation (PDE). A Karhunen-Loève Galerkin projection procedure is used to derive a system of ordinary differential equations (ODEs) that mimics the dynamics of the GKdVB equation. Using Lyapunov theory, it is shown that the...

This paper proposes a new technique for generating random-looking binary digits based on an irregularly decimated chaotic map. We present a class of irregularly decimated chaos-based keystream generators, related to the shrinking generator, for the generation of binary sequences. Each generator consists of two subsystems: a control subsystem and a...

This paper presents an approach to control the chaotic dynamics of discrete-time (or discretizable) systems. The objective of the paper is to focus on the suppression of the chaotic dynamics and the restoration of order with a state feedback controller. The proposed control method works by targeting instantaneous measures of the Lyapunov exponents...

The paper deals with the distributed control of the generalized Kortweg-de Vries-Burgers equation (GKdVB) subject to periodic boundary conditions via the Karhunen-Loève (K-L) Galerkin method. The decomposition procedure of the K-L method is presented to illustrate the use of this method in analyzing the numerical simulations data which represent th...

A predator-prey interaction is considered, where the prey has a stage structure — i.e., two life stages, immature and mature. The predator consumes both the immature and mature prey, and the prey is more prone to the predator at higher prey population densities. Both local and global stability of the system equilibria are discussed. With harvesting...

This paper considers the boundary control problem of the generalized Korteweg–de Vries–Burgers (GKdVB) equation on the interval [0, 1]. We derive a control law of the form \(u(0,t)$ $=$ $u_{x}(1,t)$ $=$ $u_{xx}(1,t)$ $+$ $\frac{1}{\mu(\alpha+2)}u^{\alpha+1}$ $(1,t) = 0$, where $\mu > 0\) and α is a positive integer, and prove that it guarantees L 2...

This paper considers the nonlinear boundary control problem of the generalized Korteweg-de Vries-Burgers (GKdVB) equation: u t =νu xx -μu xxx -u α u x , x∈[0,1], t>0. Different control laws are derived for different values of α (i.e., when α is an even positive integer, and when α is an odd positive integer) to show that the dynamics of the GKdVB e...

The nonlinear boundary control problem of the Generalized Korteweg-de Vrie-Burgers (GKdVB) equation: ut = vuxx -- μuxxx -- uαux, x ∈ [0, 1], t > 0 is considered. Different control laws were derived for different values of α (i.e., when α is an even positive integer, and when α is an odd positive integer) to show that the dynamics of the GKdVB equat...

This paper considers the distributed control of the generalized Korteweg–de-Vries–Burgers equation (GKdVB) with discontinuous initial condition via the Karhunen–Loève (K-L) Galerkin method. First, the K-L method is presented to extract coherent structures or eigenfunctions that span the data set in an optimal way. Then the K-L Galerkin projection m...

This paper deals with the sliding mode control (SMC) of the forced generalized Burgers equation via the Karhunen-Loéve (K-L) Galerkin method. The decomposition procedure of the K-L method is presented to illustrate the use of this method in analysing the numerical simulations data which represent the solutions of the forced generalized Burgers equa...

In this paper, the dynamics of the forced Burgers equation: ut=νuxx-uux+f(x), subject to both Neumann boundary conditions and periodic boundary conditions using boundary and distributed control is analyzed. For the boundary control problem, we show that the controlled unforced Burgers equation (i.e., the closed loop system) is exponentially stable...

A hybrid approach consisting of two neural networks is used to model the oscillatory dynamical behavior of the Kuramoto-Sivashinsky (K-S) equation at a bifurcation parameter α = 84.25. This oscillatory behavior results from a fixed point that occurs at α = 72 having a shape of twohumped curve that becomes unstable and undergoes a Hopf bifurcation a...

We investigate analytically as well as numerically Burgers equation with a high-order nonlinearity (i.e., ut=νuxx−unux+mu+h(x)). We show existence of an absorbing ball in L2[0,1] and uniqueness of steady state solutions for all integer n≥1. Then, we use an adaptive nonlinear boundary controller to show that it guarantees global asymptotic stability...

A hybrid approach consisting of two neural networks is used to model the oscillatory dynamical behavior of the Kuramoto-Sivashinsky (KS) equation at a bifurcation parameter α = 84.25 . This oscillatory behavior results from a fixed point that occurs at α = 72 having a shape of two-humped curve that becomes unstable and undergoes a Hopf bifurcation...

The dynamics of two nonlinear partial differential equations (PDEs) known as the Kuramoto–Sivashinsky (K–S) equation and the two-dimensional Navier–Stokes (N–S) equations are analyzed using Karhunen–Loéve (K–L) decomposition and artificial neural networks (ANN). For the K–S equation, numerical simulations using a pseudospectral Galerkin method is p...

In this paper, the adaptive and non-adaptive stabilization of the generalized Burgers equation by nonlinear boundary control are analyzed. For the non-adaptive case, we show that the controlled system is exponentially stable in L2. As for the adaptive case, we present a novel and elegant approach to show the L2 regulation of the solution of the gen...

We consider the generalized Burgers equation with and without a time delay when the boundary conditions are periodic with period 2π. For the generalized Burgers equation without a time delay, that is, ut=vuxx−uux+u+h(x), 0<x<2π, t>0, u(0,t)=u(2π,t), u(x,0)=u0(x), a Lyapunov function method is used to show boundedness and uniqueness of a steady stat...

Two techniques for dimensionality reduction of high-dimensional dynamical systems are presented. The first is based on Karhunen--Loeve (K-L) analysis and the second on autoassociative neural networks (ANNs). First, we analyze the dynamics of two partial differential equations, namely, the one-dimensional (1-d) Kuramoto--Sivashinsky (K-S) equation a...

A finite-dimensional feedback control scheme of the Kuramoto-Sivashinsky (K-S) partial differential equation (PDE) with periodic boundary conditions is presented. First, the dynamical behavior of the K-S equation at the bifurcation parameter α = 17.75 representing a homoclinic connection in phase space is investigated, where a pseudo-spectral Galer...

Two approaches, namely the Box–Jenkins (BJ) approach and the artificial neural networks (ANN) approach were combined to model time series data of water consumption in Kuwait. The BJ approach was used to predict unrecorded water consumption data from May 1990 to December 1991 due to the Iraqi invasion of Kuwait in August 1990. A supervised feedforwa...

Video data from experiments on the dynamics of two dimensional flames are analyzed. The tools used are Karhunen--Loève (K-L) decomposition and autoassociative neural networks (ANN). The K-L decomposition, known for its wide applications in scientific problems for data compression, noise filtering, and feature identification, is used to determine an...

A novel approach to categorize and identify human faces is presented. The approach is based on two techniques, namely Karhunen-Loe´ve decomposition (K-L) and radial basis function networks (RBF). K-L decomposition, known for its wide applications in scientific problems for data compression and feature identification, is used to extract coherent str...

The article describes the application of the Karhunen–Loéve (K–L) decomposition in characterizing miscible displacements in geostatistically generated permeable media. A large number of simulation runs were performed in several heterogeneous reservoirs, each with different dimensionless scaling groups, and the spatial fluid concentrations were mapp...

Finite-dimensional feedback control schemes of the Kuramoto-Sivashinsky (K-S) partial differential equation (PDE) with periodic boundary conditions are presented. First, the dynamical behavior of the K-S equation at the bifurcation parameter α = 17.75 representing a homoclinic connection in phase space is investigated, where a pseudo-spectral Galer...

Two approaches, namely Box-Jenkins approach and artificial neural networks approach (ANN) are combined to model time series data of water consumption in Kuwait. The Box-Jenkins approach was used to predict unrecorded water consumption data from May 1990 to December 1991 due to the Iraqi invasion of Kuwait in August 1990. A supervised feedforward ba...

The convective diffusion equation with drift b(x) and indefinite weight r(x), ∂ϕ∂t=∂∂x[a∂ϕ∂x−b(x)ϕ]+λr(x)ϕ, (1) is introduced as a model for population dispersal. Strong connections between Equation (1) and the forced Burgers equation with positive frequency (m≥0), ∂u∂t=∂2u∂x2−u∂u∂x+mu+k(x), (2) are established through the Hopf-Cole transformation....

Spiral state and ratcheting state regimes observed in two dimensional flames are analyzed. The tools used are Karhunen-Loéve (K-L) decomposition and autoassociative neural networks (ANN). K-L decomposition is used to extract coherent structures or eigenfunctions from those two regimes. For each of the spiral state and the ratcheting state regime, f...

The study describes the application of the Karhunen-Loeve (KL) Decomposition in characterizing miscible displacements in geostatistically generated permeable media. A large number of simulation runs were performed in these heterogeneous reservoirs, each with different dimensionless scaling groups. The spatial fluid concentrations were then mapped a...

Quasi-periodic and bursting behaviors of the two-dimensional (2D) Navier--Stokes flow are analyzed. The tools used are the proper orthogonal decomposition (POD) method and the artificial neural network (ANN) method. The POD is used to extract coherent structures and prominent features from PDE simulations of a quasi-periodic regime and a bursting r...

In this paper, we describe an approach to model fluid displacements in porous media that combines two powerful techniques, namely Karhunen–Loéve (KL) decomposition and artificial neural networks (ANNs). The KL decomposition, for data compression and feature identification, is used to extract coherent structures or eigenfunctions using fluid concent...

A method is presented to reduce noise in chaotic attractors without knowing the underlying maps. The method is based on using Artificial Neural Network (ANN) for moderate levels of additive noise. For high levels of additive noise, a combination of a refinement procedure with ANN is used. In this case, only one refinement is needed for the successf...

We study numerically the long-time dynamics of a system of reaction-diffusion equations that arise from the viscous forced Burgers equation (ut+uux−vuxx=F). A nonlinear transformation introduced by Kwak is used to embed the scalar Burgers equation into a system of reaction diffusion equations. The Kwak transformation is used to determine the exis...

A quasiperiodic and a bursting behavior of the 2-D Navier-Stokes flow are analyzed using the Proper Orthogonal Decomposition method (POD) and the Artificial Neural Network (ANN) method. The POD method is used to extract coherent structures and prominent features from PDE simulations of a quasiperiodic regime and a bursting regime. Calculations of t...

The Karhunen-Loéve decomposition, known for its wide applications in scientific problems for data compression, noise filtering and feature identification, is used to predict the fluid distributions of miscible displacements inside a porous medium. Various first-contact miscible displacement experiments were conducted, and the fluid distributions in...

The paper describes a novel approach to model unstable fluid displacements in porous media. The approach is based on the Karhunen-Loeve (K-L) decomposition which is able to predict the fluid distributions of miscible displacements inside a porous medium. Several first-contact miscible displacement experiments, each with different fluid properties,...

A back-propagation neural network model has been used to estimate tight gas sand permeability from porosity, mean pore size, and mineralogical data . The optimal network topology consists of an eight-neuron input layer, two five-neuron hidden layers that use nonlinear sigmoid transfer functions, and a linear single-neuron output layer. The network...

We present a new way of proving that a computer-generated orbit for the chaotic attractor outside the periodic windows of the quadratic map fa = ax (1 - x) can be shadowed for all time (i-e., there exist true orbits {xy}kj-1i=0 which stay near a numerical orbit {pi}Ni=0 for all time). This is done by computing a numerical orbit for a particular val...

In general obtaining a mathematical model from experimental data of a system with spatio-temporal variation is a challenging task. In this article Karhunen-Loéve (KL) decomposition and artificial neural networks (ANN) are used to extract a simple and accurate dynamic model from video data from experiments of two-dimensional flames of a radial extin...

In general, obtaining a mathematical model from experimental data of a system with spatio-temporal variation is a challeging task. We use Karhunen-Loéve (KL) decomposition and Artificial Neural Network (ANN) to extract a simple and accurate dynamical model from video data from experiments of two dimensional flames of a radial extinction mode regime...

. The Karhunen--Loeve (K--L) analysis is widely used to generate low-dimensional dynamical systems, which have the same low-dimensional attractors as some large-scale simulations of PDEs. If the PDE is symmetric with respect to a symmetry group G, the dynamical system has to be equivariant under G to capture the full phase space. It is shown that s...

The Karhunen-Loéve (KL) decomposition, known for its wide applications in scientific problems for data compression, noise filtering, and feature identification, is used to determine an intrinsic coordinate system, or eigenfunctions, that best represents a data set. Projections of the data set onto these eigenfunctions reduces the data set to a set...

This paper describes a novel approach to model unstable fluid displacements in porous media. The approach is based on the Karhunen-Loève (K-L) decomposition, which is able to predict the fluid distributions of miscible displacements inside a porous medium. Several first-contact miscible displacement experiments, each with different fluid properties...

Simulations of forced 2-D Navier-Stokes equations are analyzed. The forcing is spatially periodic and temporally steady. A Karhunen-Loève analysis is used to identify the structures in phase space that generate the PDE behavior. Their relationship to the invariant subspaces generated by the symmetry group is discussed. It is shown that certain mode...

Simulations of forced 2-D Navier-Stokes equations are analyzed. The forcing is spatially periodic and temporally steady. Two regimes are analyzed: a bursting regime and a regime that exhibits discrete traveling waves. A Karhunen Loeve analysis is used to identify the structures in phase space that generate the PDE behavior. Their relationship to th...

This paper considers the boundary control problem of the Generalized Korteweg-de Vries-Burgers (GKdVB) equation on the interval (0,1). We derive a control law that guarantees the global exponential stabil- ity of the GKdVB equation in . Numerical results supporting the analytical ones for both the controlled and uncontrolled equations are presented...

The Karhunen-Loéve (KL) decomposition known for its wide applications in scientific problems for data compression, noise filtering and feature identification is used to determine an intrinsic coordinate system or eigenfunctions that best represent a dataset. Projection of the dataset onto these eigenfunctions reduces the dataset to a set of data co...

Thesis (M.S.)--Arizona State University, 1990. Vita. Includes bibliographical references (leaves [76]-77).