In this paper, we study both the static and dynamic stabilities of submerged and inclined concentric pipes conveying uid. The governing equation for the inner tubular beam is derived under small deformation assumptions. We obtain the dis-cretized dynamical equations using spatial nite diierence schemes. In the case of steady ow, both buckling and utter instabilities are investigated. In the cas...

We develop a qualitative method for understanding and representing phase space structures of complex systems. To demonstrate this method, a program has been constructed that understands qualitatively different regions of the phase spaces and represents and extracts geometric shape information about these regions, using deep domain knowledge of dynamical system theory. Given a dynamical system s...

Sensitivity analysis, especially adjoint based sensitivity analysis, is a powerful tool for engineering design which allows for the efficient computation of sensitivities with respect to many parameters. However, these methods break down when used to compute sensitivities of long-time averaged quantities in chaotic dynamical systems. The following paper presents a new method for sensitivity ana...

Abstract Discovering governing equations of complex dynamical systems directly from data is a central problem in scientific machine learning. In recent years, the sparse identification nonlinear dynamics (SINDy) framework, powered by heuristic regression methods, has become dominant tool for learning parsimonious models. We propose an exact formulation SINDy using mixed-integer optimization (MI...

In this paper, the nonlinear dynamic system of equations, a type of nuclear ssion reactor is solved analytically and numerically. Considering that the direct solution of three-dimensional dynamical systems analysis and more in order to determine the stability and instability, in terms of algebraicsystems is dicult. Using certain situations in mathematics called Hurwitz criterion, Necessary and ...

The Kirchhoo-Love equations governing the spatial equilibria of long thin elastic rods subject to end tension and moment are reviewed and used to examine the existence of localized buckling solutions. The eeects of shear and axial extension are not considered , but the model does additionally allow for nonlinear constitutive laws. Under the assumption of innnite length, the dynamical phase spac...

In the present paper an embedded-boundary formulation that is applicable to fluid structure interaction problems is presented. The Navier-Stokes equations for incompressible flow are solved on a fixed grid which is not aligned with the body. A corotational formulation is used to describe the dynamics of a body that moves through the fixed grid undergoing large-angle/large-displacement rigid bod...

We show that the problem "real-time numerical differentiation" of a given noisy signal in time, by supplementing a compensated controller in the second-order robust exact differentiator, the tracking differentiator or the continuous hybrid differentiator, can be viewed as a set of differential algebraic equations (DAEs) to enhance a precise tracking of the given noisy signal. Thus, we are able ...

Optimization-oriented reduced-order models should target a particular output functional, span an applicable range of dynamic and parametric inputs, and respect the underlying governing equations of the system. To achieve this goal, we present an approach for determining a projection basis that uses a goal-oriented, modelconstrained optimization framework. The mathematical framework permits cons...

Presented is a data-driven machine learning framework for modeling traveling wave spatiotemporal dynamics. The presented based on the steadily propagating ansatz, u(x,t)=U(?=x?ct+a). For known evolution equations, this coordinate transformation reduces governing partial differential equations to set of coupled ordinary (ODEs) in ?. Although waves are readily observed many physical systems, unde...