Experimental exploration over a quantum control landscape through nuclear magnetic resonance

The growing successes in performing quantum control experiments motivated the development of control landscape analysis as a basis to explain these findings.When a quantum system is controlled by an electromagnetic field, the observable as a functional of the control field forms a landscape. Theoretical analyses have revealed many properties of control landscapes, especially regarding their slopes, curvatures, and topologies. A full experimental assessment of the landscape predictions is important for future consideration of controlling quantum phenomena. Nuclear magnetic resonance (NMR) is exploited here as an ideal laboratory setting for quantitative testing of the landscape principles. The experiments are performed on a simple two-level proton system in a H$_2$O-D$_2$O sample. We report a variety of NMR experiments roving over the control landscape based on estimation of the gradient and Hessian, including ascent or descent of the landscape, level set exploration, and an assessment of the theoretical predictions on the structure of the Hessian. The experimental results are fully consistent with the theoretical predictions. The procedures employed in this study provide the basis for future multispin control landscape exploration where additional features are predicted to exist

Market structure and environmental amenities in hedonic pricing of rural cottages

Site-specific characteristics are attributes of tourism services for consumers and a factor influencing their costs and quality for producers. These services are a fine illustration of territorial rents. Using estimates from hedonic price equations, we test the role of environmental/territorial variables as services differentiation tools in the context of a non-competitive market, and recover the value of territorial rent generated by tourism managers' strategies. Two territories of reference are chosen, one currently benefiting from the renewed interest of the public, and a usual tourist destination. The results of a comparative analysis suggest that tourists' preferences for new destinations, combined with firms' strategies generate some catching up effect by emerging territories.ENVIRONMENTAL VALUATION; HEDONIC METHOD; SERVICE DIFFERENTIATION; TOURISM

Minimal Curvature Trajectories: Riemannian Geometry Concepts for Model Reduction in Chemical Kinetics

In dissipative ordinary differential equation systems different time scales cause anisotropic phase volume contraction along solution trajectories. Model reduction methods exploit this for simplifying chemical kinetics via a time scale separation into fast and slow modes. The aim is to approximate the system dynamics with a dimension-reduced model after eliminating the fast modes by enslaving them to the slow ones via computation of a slow attracting manifold. We present a novel method for computing approximations of such manifolds using trajectory-based optimization. We discuss Riemannian geometry concepts as a basis for suitable optimization criteria characterizing trajectories near slow attracting manifolds and thus provide insight into fundamental geometric properties of multiple time scale chemical kinetics. The optimization criteria correspond to a suitable mathematical formulation of "minimal relaxation" of chemical forces along reaction trajectories under given constraints. We present various geometrically motivated criteria and the results of their application to three test case reaction mechanisms serving as examples. We demonstrate that accurate numerical approximations of slow invariant manifolds can be obtained.Comment: 22 pages, 18 figure

Urban detection, delimitation and morphology: comparative analysis of selective "megacities"

Postprint (published version