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- Bogdan I. Epureanu, Henry S. Greenside
- SIAM Review
- 1998

An intriguing and unexpected result for students learning numerical analysis is that Newton’s method, applied to the simple polynomial z − 1 = 0 in the complex plane, leads to intricately interwoven basins of attraction of the roots. As an example of an interesting open question that may help to stimulate student interest in numerical analysis, we… (More)

A = aerodynamic stiffness matrix C = speed of sound E = complex Fourier matrix f , F = physical and modal forces h = height of stream tube j = imaginary unit K, M = stiffness and mass matrices NB = number of blades P, Q = modal transformation matrices p = flow pressure Q = flow mass flux at the boundary q = generalized (modal) coordinate s = distance along… (More)

- Joosup Lim, Bogdan I. Epureanu
- Physical review. E, Statistical, nonlinear, and…
- 2011

Forecasting bifurcations before they occur is a significant challenge and an important need in several fields. Existing approaches detect bifurcations before they occur by exploiting the critical slowing down phenomenon. However, the perturbations used in those approaches are limited to being very small and this represents a significant drawback. Large… (More)

- Woochul Nam, Bogdan I. Epureanu
- PLoS Computational Biology
- 2015

Kinesins are nano-sized biological motors which walk by repeating a mechanochemical cycle. A single kinesin molecule is able to transport its cargo about 1 μm in the absence of external loads. However, kinesins perform much longer range transport in cells by working collectively. This long range of transport by a team of kinesins is surprising because the… (More)

- Adam G. Hendricks, Bogdan I. Epureanu, Edgar Meyhöfer
- Physical review. E, Statistical, nonlinear, and…
- 2009

Motor proteins are biological enzymes that convert chemical energy to mechanical work in cells. Kinesin-1 is a motor protein that transports vesicles along microtubules and is widely believed to be responsible for anterograde transport of synaptic vesicles in neurons. Advances in single-molecule techniques have shown that single kinesin motors are capable… (More)

- Bogdan I. Epureanu, Liaosha S. Tang, Michael P. Paı̈doussis
- 2004

A panel forced by buffeting aerodynamic loads and undergoing limit-cycle oscillations and chaos is investigated. The interaction of dynamic and static instabilities is shown to lead to very complex dynamics, which includes static deformations, limit-cycle oscillations, and chaos. The sensitivity of the chaotic behavior to parametric changes is shown to be… (More)

One of the most important aspects of detecting damage in the framework of structural health monitoring is increasing the sensitivity of the monitored feature to the presence, location, and extent of damage. Distinct from previous techniques of obtaining information about the monitored structure—such as measuring frequency response functions—the approach… (More)

Currently, most sensor placement methodologies are focused on maximizing the controllability and observability of the monitored structure. Recently, there have been several sensor placement techniques proposed for damage detection. Thework herein provides an integrated sensor placement and reduced-order health assessment approach that can be applied to both… (More)

A damage detection method is developed for nonlinear systems using model updating. The method uses a nonlinear discrete model of the system and the form of the nonlinearities to create an augmented linear model of the system. A modal analysis technique that uses forcing that is known but not prescribed is then used to solve for the modal properties of the… (More)

- Shih-Hsun Yin, Bogdan I. Epureanu
- Philosophical transactions. Series A…
- 2006

The dynamic responses of a thermo-shielding panel forced by unsteady aerodynamic loads and a classical Duffing oscillator are investigated to detect structural damage. A nonlinear aeroelastic model is obtained for the panel by using third-order piston theory to model the unsteady supersonic flow, which interacts with the panel. To identify damage, we… (More)