(62c) Sustainability Identification for Infinite-Dimensional Systems

Masih Jorat

Dept. of Chemical and Biomolecular Engineering, UCLA, Los Angeles, CA, 90095

Vasilios I. Manousiouthakis

Dept. of Chemical and Biomolecular Engineering, UCLA, Los Angeles, CA, 90095

The need for a multifaceted assessment of human impact on the environment has led to the emergence of comprehensive concepts like sustainability and sustainable development. Setting the priorities for sustainable initiatives requires that a value system first be established. This can only be accomplished within the context of a clearly stated definition of sustainability. In other words, the development of sustainability strategies cannot be pursued in an efficient manner, without a comprehensive, rigorous, and unbiased definition of sustainability. The prevalent common factor among sustainability definitions is the endurance of the system’s dynamic behavior over time. Through utilizing the concept of positive invariant sets, the novel concept of Sustainability Over Sets (SOS) [1] provides a conceptual framework within which the time evolution of a system can be analyzed. SOS formalizes the incorporation of human input into the sustainability assessment process, first by defining a set in state-space which exactly quantifies human input regarding what is sustainable, and by then modifying the question “is a system sustainable?” to “is a system sustainable over a predefined set?” which is amenable to definitive (yes or no) answers. A system is sustainable over a set (SOS) in the system’s state-space, if the system’s state trajectories initiated within the set, remain for all time within the set, in other words the system’s vector field is directing inwards at the set's boundaries. The previously presented studies of the (SOS) concept were limited to sustainability assessments of the systems, whose behavior is modeled through a set of ODEs. In this work a developed version of the SOS concept will be presented which has the ability to assess the sustainability of infinite dimensional systems which their dynamic behavior has been captured by a system of Partial Differential Equations (PDE’s). In this regard we present necessary and sufficient conditions for sustainability of systems, whose behavior is captured by parabolic and hyperbolic PDE systems, commonly arising in chemical engineering applications, such as diffusion and convection-reaction systems over desired sets. furthermore, the practical applicability of the introduced conditions will be demonstrated through multiple case studies.

[1] Manousiouthakis VI, Jorat M. Sustainability over sets. Environmental Progress & Sustainable Energy. 2017 Oct.