Developing estimation algorithms for state bounds of nonlinear systems has been of high importance in robustness analysis for various systems including engineering systems and biological systems. For many cases, Monte-Carlo simulation might be the only tool to estimate these bounds for a general type of nonlinear systems. In order to obtain tight bounds the number of required simulations would ...

We discuss the integrability properties of the Boussinesq equations in the language of geometrical quantities defined on an appropriately chosen coset manifold connected with the W 3 algebra of Zamolodchikov. We provide a geometrical interpretation to the commuting conserved quantities, Lax-pair formulation, zero-curvature representation, Miura maps, etc. in the framework of nonlinear realizati...

We discuss the integrability properties of the Boussinesq equations in the language of geometrical quantities defined on an appropriately chosen coset manifold connected with the W 3 algebra of Zamolodchikov. We provide a geometrical interpretation to the commuting conserved quantities, Lax-pair formulation, zero-curvature representation, Miura maps, etc. in the framework of nonlinear realizati...

We discuss the integrability properties of the Boussinesq equations in the language of geometrical quantities defined on an appropriately chosen coset manifold connected with the W 3 algebra of Zamolodchikov. We provide a geometrical interpretation to the commuting conserved quantities, Lax-pair formulation, zero-curvature representation, Miura maps, etc. in the framework of nonlinear realizati...

BACKGROUND Long-range oscillations of the mammalian cell proliferation rate are commonly observed both in vivo and in vitro. Such complicated dynamics are generally the result of a combination of stochastic events and deterministic regulation. Assessing the role, if any, of chaotic regulation is difficult. However, unmasking chaotic dynamics is essential for analysis of cellular processes relat...

Explosion and fire on an offshore rig can lead to its minor or complete damage and sinking which means the loss of life or environmental pollution. Hence the use of techniques such as blast wall is crucial to reduce the detrimental effects. These blast walls are designed for explosion wave of length between 0.1 to 1 of load mainly to protect the personnel and critical sections. In this research...

In this paper, based on the nonlocal Timoshenko beam theory, a nonlinear model is presented for the vibrational behavior of carbon nanotubes (CNTs) embedded in elastic medium in thermal environment. Using the Timoshenko beam theory and nonlocal elasticity of Eringen, the influences of rotary inertia, transverse shear deformation and small scale effect are taken into account. To model the intera...

A new method, the biepipole constraint algorithm, is developed to estimate the fundamental matrix (F-matrix) based on an 8-parameter model and the geometrical analysis. First, through the analysis of the new constraints, the four parameters of the F-matrix can be estimated by solving a nonlinear unconstraint optimization problem. The objective function of the optimization problem is an equation...

It is empirically established that, due to a number of factors involved, a classical (linear) analysis of buckling pressure is impossible. Nonlinear theories of buckling are, therefore, required that involve effective factors such as imperfections and welding effects. In this study, models are developed which are as close to allowable standard deviations as possible. In the next stage, their bu...