ABSTRACT
This paper considers laser-driven optimal control of an ensemble of non-interacting molecules whose dynamics lie in classical phase space. The molecules evolve independently under control to distinct final states. We consider a control landscape defined in terms of multi-target (MT) molecular states and analyze the landscape as a functional of the control field. The topology of the MT control landscape is assessed through its gradient and Hessian with respect to the control. Under particular assumptions, the MT control landscape is found to be free of traps that could hinder reaching the objective. The Hessian associated with an optimal control field is shown to have finite rank, indicating an inherent degree of robustness to control noise. Both the absence of traps and rank of the Hessian are shown to be analogous to the situation of specifying multiple targets for an ensemble of quantum states. Numerical simulations are presented to illustrate the classical landscape principles and further characterize the system behavior as the control field is optimized.
ABSTRACT
Optimal control of molecular dynamics is commonly expressed from a quantum mechanical perspective. However, in most contexts the preponderance of molecular dynamics studies utilize classical mechanical models. This paper treats laser-driven optimal control of molecular dynamics in a classical framework. We consider the objective of steering a molecular system from an initial point in phase space to a target point, subject to the dynamic constraint of Hamilton's equations. The classical control landscape corresponding to this objective is a functional of the control field, and the topology of the landscape is analyzed through its gradient and Hessian with respect to the control. Under specific assumptions on the regularity of the control fields, the classical control landscape is found to be free of traps that could hinder reaching the objective. The Hessian associated with an optimal control field is shown to have finite rank, indicating the presence of an inherent degree of robustness to control noise. Extensive numerical simulations are performed to illustrate the theoretical principles on (a) a model diatomic molecule, (b) two coupled Morse oscillators, and (c) a chaotic system with a coupled quartic oscillator, confirming the absence of traps in the classical control landscape. We compare the classical formulation with the mathematically analogous quantum state-to-state transition probability control landscape.
ABSTRACT
To analyze somatosensory neuron diversity in larval zebrafish, we identified several enhancers from the zebrafish and pufferfish genomes and used them to create five new reporter transgenes. Sequential deletions of three of these enhancers identified small sequence elements sufficient to drive expression in zebrafish trigeminal and Rohon-Beard (RB) neurons. One of these reporters, using the Fru.p2x3-2 enhancer, highlighted a somatosensory neuron subtype that expressed both the p2rx3a and pkcα genes. Comparison with a previously described trpA1b reporter revealed that it highlighted the same neurons as the Fru.p2x3-2 reporter. To determine whether neurons of this subtype possess characteristic peripheral branching morphologies or central axon projection patterns, we analyzed the morphology of single neurons. Surprisingly, although these analyses revealed diversity in peripheral axon branching and central axon projection, PKCα/p2rx3a/trpA1b-expressing RB cells did not possess obvious characteristic morphological features, suggesting that even within this molecularly defined subtype, individual neurons may possess distinct properties. The new transgenes created in this study will be powerful tools for further characterizing the molecular, morphological, and developmental diversity of larval somatosensory neurons.
