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pro vyhledávání: '"Parkinson, Christian"'
In this paper, we consider an optimal distributed control problem for a reaction-diffusion-based SIR epidemic model with human behavioral effects. We develop a model wherein non-pharmaceutical intervention methods are implemented, but a portion of th
Externí odkaz:
http://arxiv.org/abs/2407.17298
We develop a discrete differential geometry for surfaces of non-constant negative curvature, which can be used to model various phenomena from the growth of flower petals to marine invertebrate swimming. Specifically, we derive and numerically integr
Externí odkaz:
http://arxiv.org/abs/2309.08117
Autor:
Parkinson, Christian, Polage, Kyle
We present a semi-real-time algorithm for minimal-time optimal path planning based on optimal control theory, dynamic programming, and Hamilton-Jacobi (HJ) equations. Partial differential equation (PDE) based optimal path planning methods are well-es
Externí odkaz:
http://arxiv.org/abs/2309.02357
Autor:
Parkinson, Christian, Boyle, Isabelle
We present a partial-differential-equation-based optimal path-planning framework for curvature constrained motion, with application to vehicles in 2- and 3-spatial-dimensions. This formulation relies on optimal control theory, dynamic programming, an
Externí odkaz:
http://arxiv.org/abs/2304.12377
Autor:
Parkinson, Christian, Wang, Weinan
Recent work from public health experts suggests that incorporating human behavior is crucial in faithfully modeling an epidemic. We present a reaction-diffusion partial differential equation SIR-type population model for an epidemic including behavio
Externí odkaz:
http://arxiv.org/abs/2303.01489
Autor:
Parkinson, Christian, Ceccia, Madeline
We consider the problem of time-optimal path planning for simple nonholonomic vehicles. In previous similar work, the vehicle has been simplified to a point mass and the obstacles have been stationary. Our formulation accounts for a rectangular vehic
Externí odkaz:
http://arxiv.org/abs/2111.09951
Autor:
Parkinson, Christian, Boyle, Isabelle
Publikováno v:
In Journal of Computational Physics 15 July 2024 509
Autor:
Peng, Kaiyan, Lu, Zheng, Lin, Vanessa, Lindstrom, Michael R., Parkinson, Christian, Wang, Chuntian, Bertozzi, Andrea L., Porter, Mason A.
During the COVID-19 pandemic, conflicting opinions on physical distancing swept across social media, affecting both human behavior and the spread of COVID-19. Inspired by such phenomena, we construct a two-layer multiplex network for the coupled spre
Externí odkaz:
http://arxiv.org/abs/2107.01713
We address the problem of optimal path planning for a simple nonholonomic vehicle in the presence of obstacles. Most current approaches are either split hierarchically into global path planning and local collision avoidance, or neglect some of the am
Externí odkaz:
http://arxiv.org/abs/2005.03623
We present a method for optimal path planning of human walking paths in mountainous terrain, using a control theoretic formulation and a Hamilton-Jacobi-Bellman equation. Previous models for human navigation were entirely deterministic, assuming perf
Externí odkaz:
http://arxiv.org/abs/2005.03615