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We use the conjugate angle of radial action (θ_R), the best representation of the orbital phase, to explore the “midplane,” “north branch,” “south branch,” and “Monoceros area” disk structures that were previously revealed in the LAMOST K giants. The former three substructures, identified by their 3D kinematical distributions, have been shown to be projections of the phase space spiral (resulting from nonequilibrium phase mixing). In this work, we find that all of these substructures associated with the phase spiral show high aggregation in conjugate angle phase space, indicating that the clumping in conjugate angle space is a feature of ongoing, incomplete phase mixing. We do not find theZ–V_Zphase spiral located in the “Monoceros area,” but we do find a very highly concentrated substructure in the quadrant of conjugate angle space with the orbital phase from the apocenter to the guiding radius. The existence of the clump in conjugate angle space provides a complementary way to connect the “Monoceros area” with the direct response to a perturbation from a significant gravitationally interactive event. Using test particle simulations, we show that these features are analogous to disturbances caused by the impact of the last passage of the Sagittarius dwarf spheroidal galaxy.

 

In this paper, we discuss the concept and properties of variance-based global sensitivity analysis, as an expansion of local sensitivity metrics (such as the degree of rate control), for modeling and design of catalytic reaction systems. Using an illustrative example and supporting theory, we show that: (i) for small variations in the parameters, global sensitivities are similar to local derivatives; (ii) for larger variations in the parameters (i.e., a larger parameter space), the global sensitivities provide a ranking of importance of parameters and impose a rigorous bound on the errors that arise from fixing one or more parameters to nominal values; and (iii) in general, the global sensitivities can be related to the extrema of local derivatives. We argue that the square root of the total global sensitivity of a parameter, computed by summing the global sensitivity of that parameter acting independently and in combination with others, is a “global” degree of rate control for catalytic systems.