Data assimilation into a numerical shallow water flow model: a stochastic optimal control approach

1995 ◽  
Vol 6 (1-2) ◽  
pp. 145-158 ◽  
Author(s):  
A.W. Heemink ◽  
I.D.M. Metzelaar
Keyword(s):  
Optimal Control ◽  
Data Assimilation ◽  
Shallow Water ◽  
Water Flow ◽  
Stochastic Optimal Control ◽  
Flow Model ◽  
Shallow Water Flow ◽  
Control Approach ◽  
Optimal Control Approach

scholarly journals The Heisenberg Uncertainty Principle as an Endogenous Equilibrium Property of Stochastic Optimal Control Systems in Quantum Mechanics

Symmetry ◽  
2020 ◽  
Vol 12 (9) ◽  
pp. 1533 ◽  
Author(s):  
Jussi Lindgren ◽  
Jukka Liukkonen
Keyword(s):  
Optimal Control ◽  
Quantum Mechanics ◽  
Uncertainty Principle ◽  
Stochastic Optimal Control ◽  
Stochastic Approach ◽  
Heisenberg Uncertainty Principle ◽  
Control Approach ◽  
Heisenberg Uncertainty ◽  
Original Interpretation ◽  
Optimal Control Approach

We provide a natural derivation and interpretation for the uncertainty principle in quantum mechanics from the stochastic optimal control approach. We show that, in particular, the stochastic approach to quantum mechanics allows one to understand the uncertainty principle through the “thermodynamic equilibrium”. A stochastic process with a gradient structure is key in terms of understanding the uncertainty principle and such a framework comes naturally from the stochastic optimal control approach to quantum mechanics. The symmetry of the system is manifested in certain non-vanishing and invariant covariances between the four-position and the four-momentum. In terms of interpretation, the results allow one to understand the uncertainty principle through the lens of scientific realism, in accordance with empirical evidence, contesting the original interpretation given by Heisenberg.

An Implicit 2-D Shallow Water Flow Model on Unstructured Quadtree Rectangular Mesh

2011 ◽  
Vol 59 ◽  
pp. 15-26 ◽  
Author(s):  
Weiming Wu ◽  
Alejandro Sánchez ◽  
Mingliang Zhang
Keyword(s):  
Shallow Water ◽  
Water Flow ◽  
Flow Model ◽  
Shallow Water Flow ◽  
Rectangular Mesh
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