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Curved Space-Time at the Planck Scale

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Journal of High Energy Physics, Gravitation and Cosmology 2024年第1期10卷 167-179页

作者： lewis nash Marietta GA USA

This paper presents a physically plausible and somewhat illuminating first step in extending the fundamental principles of mechanical stress and strain to space-time. Here the geometry of space-time, encoded in the metric tensor, is considered to be made up of a dynamic lattice of extremely small, localized fields that form a perfectly elastic Lorentz symmetric space-time at the global (macroscopic) scale. This theoretical model of space-time at the Planck scale leads to a somewhat surprising result in which matter waves in curved space-time radiate thermal gravitational energy, as well as an equally intriguing relationship for the anomalous dispersion of light in a gravitational field.

关键词： Schwarzschild Space-Time Continuum Mechanics Planck Lattice Gravitational Radiation

Gravitational Black-Body Radiation

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Journal of High Energy Physics, Gravitation and Cosmology 2022年第3期8卷 527-535页

作者： lewis nash Marietta USA

Analogous to a black body, the empty space surrounding a massive body is theoretically envisioned to radiate thermal gravitational energy in accordance with Planck’s radiation law. Gravitational black-body radiation offers a remarkably compelling solution to the deep, long-standing questions concerning galaxy rotation curves and strong gravitational lensing by large astrophysical systems, without the need to impose a dark matter or massive graviton hypothesis. As with the quantized orbits of the electron in the atom and the classical physics of Maxwell’s theory of electromagnetism, gravitational black-body radiation represents a truly profound break from the classical physics of Einstein’s general theory of relativity and the emergence of the fundamental quantum nature of gravity.

关键词： Black Body Graviton Milky Way Rotation Curve

Entangled Photon Pairs and Young’s Experiment

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Journal of Quantum Information Science 2021年第4期11卷 135-142页

作者： lewis nash Marietta GA USA

Bohm’s variation of the Einstein-Podolsky-Rosen thought experiment may be used to reveal the path a photon travels in Young’s experiment without destroying the observed interference pattern. Photons emitted by a light-source with zero spin are incident on a screen with two narrow slits separated by a small distance, with antiparallel polarized photonic spin filters placed in front of both slits. It follows that the slit through which an incident photon passed to form an interference pattern can be determined by performing an intermediate delayed choice measurement. This experimental probe is ideal for penetrating the shroud of mystery surrounding the wave-particle duality exhibited by quantum phenomena.

关键词： Double-Slit Entangled Wave-Particle Photon Pair Interference

Entangled Photon Pairs and Young’s Experiment

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Adaptive dynamic programming for online solution of a zero-sum differential game

Journal of Quantum Information Science（量子信息科学期刊） 2021年第4期

作者： lewis nash

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控制理论与应用（英文版） 2011年第3期9卷 353-360页

作者： Draguna VRABIE Frank lewis United Technologies Research Center East Hartford Automation and Robotics Research Institute University of Texas at Arlington

This paper will present an approximate/adaptive dynamic programming(ADP) algorithm,that uses the idea of integral reinforcement learning(IRL),to determine online the nash equilibrium solution for the two-player zerosum differential game with linear dynamics and infinite horizon quadratic *** algorithm is built around an iterative method that has been developed in the control engineering community for solving the continuous-time game algebraic Riccati equation(CT-GARE),which underlies the game *** here show how the ADP techniques will enhance the capabilities of the offline method allowing an online solution without the requirement of complete knowledge of the system *** feasibility of the ADP scheme is demonstrated in simulation for a power system control *** adaptation goal is the best control policy that will face in an optimal manner the highest load disturbance.

关键词： Approximate/Adaptive dynamic programming Game algebraic Riccati equation Zero-sum differential game nash equilibrium

Heterogeneous multi-player imitation learning

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Control Theory and Technology 2023年第3期21卷 281-291页

作者： Bosen Lian Wenqian Xue Frank L.lewis Department of Electrical and Computer Engineering Auburn UniversityAuburnAL 36849USA State Key Laboratory of Synthetical Automation for Process Industries and International Joint Research Laboratory of Integrated Automation Northeastern UniversityShenyang 110819LiaoningChina UTA Research Institute University of Texas at Arlington(UTA)Fort WorthTX 76118USA

This paper studies imitation learning in nonlinear multi-player game systems with heterogeneous control input *** propose a model-free data-driven inverse reinforcement learning(RL)algorithm for a leaner to find the cost functions of a N-player nash expert system given the expert's states and control *** allows us to address the imitation learning problem without prior knowledge of the expert's system *** achieve this,we provide a basic model-based algorithm that is built upon RL and inverse optimal *** serves as the foundation for our final model-free inverse RL algorithm which is implemented via neural network-based value function *** analysis and simulation examples verify the methods.

关键词： Imitation learning Inverse reinforcement learning Heterogeneous multi-player games Data-driven model-free control

Discrete-time dynamic graphical games:model-free reinforcement learning solution

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Control Theory and Technology 2015年第1期13卷 55-69页

作者： Mohammed I.ABOUHEAF Frank L.lewis Magdi S.MAHMOUD Dariusz G.MIKULSKI Systems Engineering Department King Fahd University of Petroleum & Mineral UTA Research Institute University of Texas at ArlingtonFort Worth Texas U.S.A. State Key Laboratory of Synthetical Automation for Process Industries Northeastern University Ground Vehicle Robotics (GVR) U.S. Army TARDEC Warren MI U.S.A.

This paper introduces a model-free reinforcement learning technique that is used to solve a class of dynamic games known as dynamic graphical games. The graphical game results from to make all the agents synchronize to the state of a command multi-agent dynamical systems, where pinning control is used generator or a leader agent. Novel coupled Bellman equations and Hamiltonian functions are developed for the dynamic graphical games. The Hamiltonian mechanics are used to derive the necessary conditions for optimality. The solution for the dynamic graphical game is given in terms of the solution to a set of coupled Hamilton-Jacobi-Bellman equations developed herein. nash equilibrium solution for the graphical game is given in terms of the solution to the underlying coupled Hamilton-Jacobi-Bellman equations. An online model-free policy iteration algorithm is developed to learn the nash solution for the dynamic graphical game. This algorithm does not require any knowledge of the agents＇ dynamics. A proof of convergence for this multi-agent learning algorithm is given under mild assumption about the inter-connectivity properties of the graph. A gradient descent technique with critic network structures is used to implement the policy iteration algorithm to solve the graphical game online in real-time.

关键词： Dynamic graphical games nash equilibrium discrete mechanics optimal control model-free reinforcementlearning policy iteration

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地球两极

人与自然 2023年第2期 73-80页

作者：乔纳森·贝利教授林肯(译) lewis Blackwell Jacob Churchill John nash 蒂姆·弗拉克(摄影) 不详

当太阳辐射进入地球磁场并与大气层发生碰撞时,会发出一种奇妙的光,通常只出现在南极圈和北极圈内。太阳的辐射在大约11年的周期内变化:太阳活动高峰期会产生大量黑子,地球上的光照不仅更频繁,而且会出现在低纬度地区。最近一次太阳活... 详细信息

当太阳辐射进入地球磁场并与大气层发生碰撞时,会发出一种奇妙的光,通常只出现在南极圈和北极圈内。太阳的辐射在大约11年的周期内变化:太阳活动高峰期会产生大量黑子,地球上的光照不仅更频繁,而且会出现在低纬度地区。最近一次太阳活动高峰期是在2001~2013年,下一次预测会在2022~2024年,但也并不总是很有规律。1645~1715年,太阳黑子显然很少。

关键词：太阳黑子地球磁场太阳辐射低纬度地区北极圈

Multi-agent Differential Graphical Games

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Multi-agent Differential Graphical Games