Lagrangian optimization, quantum mechanics and quantum control

The goal of this paper is to address the critical needs for synergistic science and engineering research and developments in nanoscale to devise the fundamental understanding and apply resulting technological advances arising from the developed theoretical and applied results. Novel phenomena and processes have been observed at the nanoscale, e.g., the Brownian motor direction of displacement does not comply with the applied force, quantum effects in nanoelectronics and nanocomposites, etc. Significant challenges remain in the areas of fundamental understanding, modeling, analysis, and simulation of the Brownian motor as well as other organic and inorganic nanoscale systems and structures dynamics. These problems directly related to functionality, actuation, sensing, information processing, computing, adaptation, optimization and other mechanisms. Research in these areas supports the development of a fundamental understanding of nanostructures and processes, nanobiotechnology, and techniques for a broad range of applications in biomaterials, biosystem-based electronics, agriculture, energy, medicine, and health. The goal is to study biological and biologically inspired systems in which nanoscale phenomena and effects play important roles. This includes developing an understanding of the relationships among biochemical, electromagnetic, mechanical and chemical processes. This fundamental research will allow one to synthesize, design, manufacture novel high-performance nanostructures, nanodevices (nanoscale actuators and sensors, nanoelectronics, nanoICs), and nanoelectromechanical systems. For example, biomolecular motors (kinesin-protein process and bacterial flagellar motor) transport substance at the nanoscale level within biological cells, and the motor-cargo connected tether is elastic allowing the motor to defuse rapidly. The energy is stored by the high-energy chemical bonds (proton gradient across the cell´s inner membrane). In this paper we examine the coherence between Lagrangian and quantum mechanics as well as quantum optimization and control.