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Abstract We develop and study a generalization of commutative rings calledbands, along with the corresponding geometric theory ofband schemes. Bands generalize both hyperrings, in the sense of Krasner, and partial fields in the sense of Semple and Whittle. They form a ring‐like counterpart to the field‐like category ofidyllsintroduced by the first and third authors in the previous work. The first part of the paper is dedicated to establishing fundamental properties of bands analogous to basic facts in commutative algebra. In particular, we introduce various kinds of ideals in a band and explore their properties, and we study localization, quotients, limits, and colimits. The second part of the paper studies band schemes. After giving the definition, we present some examples of band schemes, along with basic properties of band schemes and morphisms thereof, and we describe functors into some other scheme theories. In the third part, we discuss some “visualizations” of band schemes, which are different topological spaces that one can functorially associate to a band scheme . 

Scientific simulation workflows executing on very large scale computing systems are essential modalities for scientific investigation. The increasing scales and resolution of these simulations provide new opportunities for accurately modeling complex natural and engineered phenomena. However, the increasing complexity necessitates managing, transporting, and processing unprecedented amounts of data, and as a result, researchers are increasingly exploring data-staging and in-situ workflows to reduce data movement and data-related overheads. However, as these workflows become more dynamic in their structures and behaviors, data staging and in-situ solutions must evolve to support new requirements. In this paper, we explore how the service-oriented concept can be applied to extreme-scale in-situ workflows. Specifically, we explore persistent data staging as a service and present the design and implementation of DataSpaces as a Service, a service-oriented data staging framework. We use a dynamically coupled fusion simulation workflow to illustrate the capabilities of this framework and evaluate its performance and scalability.