5 papers
Boltzmann's Billiard Systems: Computation of the Billiard Mapping and Some Numerical Results
Michael Plum, Airi Takeuchi, Lei Zhao
L. Boltzmann proposed a billiard model with a planar central force problem reflected against a line not passing through the center. He asserted that such a system is ergodic, which…
Kustaanheimo-Stiefel Transformation, Birkhoff-Waldvogel Transformation and Integrable Mechanical Billiards
Airi Takeuchi, Lei Zhao
The three-dimensional Kepler problem is related to the four-dimensional isotropic harmonic oscillators by the Kustaanheimo-Stiefel Transformations. In the first part of this paper,…
An Augmented Lagrangian Approach to Conically Constrained Non-monotone Variational Inequality Problems
Lei Zhao, Daoli Zhu, Shuzhong Zhang
In this paper we consider a non-monotone (mixed) variational inequality model with (nonlinear) convex conic constraints. Through developing an equivalent Lagrangian function-like p…
Real-time Manipulation of Liquid Droplets using Photo-responsive Surfactant
Xichen Liang, Kseniia M. Karnaukh, Lei Zhao +12
Fast and programmable transport of liquid droplets on a solid substrate is desirable in microfluidic, thermal, biomedical, and energy devices. Past research has focused on designin…
Integrable Mechanical Billiards in Higher Dimensional Space Forms
Airi Takeuchi, Lei Zhao
In this article, we consider mechanical billiard systems defined with Lagrange's integrable extension of Euler's two-center problems in the Euclidean space, on the sphere, and in t…