Albert C.J. Luo

Albert Chao Jun Luo (; born 1964) is a Chinese-American mechanical engineer. He is a Distinguished Research Professor at Southern Illinois University Edwardsville, where he has been a faculty member since 1998.

He authored books and articles in the fields of applied mathematics, nonlinear dynamics, and mechanics. His principal research interests lie in the field of Hamiltonian chaos, nonlinear mechanics, and discontinuous dynamical systems.

Early life and education Luo was born in 1964 in China.

Luo received a Bachelor of Science degree in mechanical engineering from the Sichuan University of Science and Engineering in China in 1984, a Master of Science degree in engineering mechanics from the Dalian University of Technology in China in 1990, and a Doctor of Philosophy degree in applied mechanics from the University of Manitoba in Canada in 1996. His doctoral supervisor was Ray Peng Siew Han . His doctoral dissertation was titled Analytical modeling of bifurcations, chaos and multifractals in nonlinear dynamics (1996).

Since 1998, Luo has been a faculty member at Southern Illinois University Edwardsville, where he has held the positions of assistant professor, associate professor, full professor, and distinguished research professor.

Luo received the 2014 Distinguished Research Professor Award from Southern Illinois University Edwardsville.

Research

Luo developed stability and bifurcation theory in nonlinear dynamical systems, and he also established the theoretical frames of discontinuous dynamical systems for many applications in science and engineering, and he developed analytical techniques that is very efficient to achieve periodic motions to chaos analytically. Since the 18th century, one has extensively used techniques such as perturbation methods to obtain approximate analytical solutions of periodic motions in nonlinear systems. Towards analytical chaos in nonlinear systems systematically presents an analytical approach to determine periodic flows to chaos or quasi-periodic flows in nonlinear dynamical systems with/without time-delay. The presented analytical techniques provide a better understanding of regularity and complexity of periodic motions to chaos in nonlinear dynamical systems. Luo developed a dynamical system synchronization theory based on the local singularity theory of discontinuous dynamical systems. Luo developed the implicit mapping dynamics for semi-analytical solutions of periodic motions to chaos in nonlinear systems, which are from symbolic dynamics to mapping dynamics in nonlinear dynamical systems. Further, one can measure chaos deterministically instead of stochastically. The quadratic dynamical systems presented by Luo provides a way to solve the Hilbert's 16th problems. Such a theory presents the bifurcations of the 1-dimensional flows in nonlinear dynamical systems. The infinite-equilibriums are the switching bifurcations of the two sets of equilibriums. Techniques can be implemented and applied to science and engineering.

His major contributions on nonlinear dynamical systems are:

A theory for stochastic and resonant layers in nonlinear Hamiltonian systems A local theory and singularity for discontinuous dynamical systems Flow barriers theory for discontinuous dynamical systems Synchronization of continuous dynamical systems under specific constraints Synchronization and companion of discrete dynamical systems Analytical solutions of periodic motions to chaos in nonlinear systems Discretization and implicit mapping dynamics in nonlinear dynamical systems Analytical periodic flows to chaos in time-delay systems Semi-analytical solutions of periodic motions to chaos in nonlinear systems Infinite homoclinic orbits in 3-D nonlinear systems (e.g., Lorenz and Rösller systems) Memorized nonlinear dynamical systems and time-delay Two-dimensional quadratic dynamical systems Two-dimensional cubic dynamical Systems Two-dimensional polynomial dynamical Systems (e.g., Hilbert 16th problems) In addition, Luo developed accurate theories for nonlinear deformable-body dynamics, machine tool dynamics and others:

An approximate plate theory A theory for soft structures A nonlinear theory for beams and rods Fluid-induced nonlinear structural vibration A large damage theory for anisotropic materials A generalized fractal theory

He has published over 400 peer-reviewed journal and conference papers. Luo was an editor for the Journal Communications in Nonlinear Science and Numerical simulation, and Luo is editors for the book series on Nonlinear Systems and Complexity (Springer), and Nonlinear Physical Science (Higher Education Press).

Publications