designed to answer specific questions about the real world An imitation, analogue, or representation of a real world process or structure; or A conceptual, mathematical, or physical tool to assist a decision maker. Together, these definitions are broad enough to encompass physical engineering models used in the verification of a system design, as well as schematic models like a functional flow block diagram and mathematical (i.e., quantitative) models used in the trade study process. This section focuses on the last. The main reason for using mathematical models and diagrams in trade studies is to provide estimates of system effectiveness, performance or technical attributes, and cost from a set of known or estimable quantities. Typically, a collection of separate models is needed to provide all of these outcome variables. The heart of any mathematical model is a set of meaningful quantitative relationships among its inputs and outputs. These relationships can be as simple as adding up constituent quantities to obtain a total, or as complex as a set of differential equations describing the trajectory of a spacecraft in a gravitational field. Ideally, the relationships express causality, not just correlation. Furthermore, key to successful systems engineering activities are also the methods with which these models are efficiently and effectively managed and used to simulate the systems. However, diverse domains often present recurring problems of modeling and simulation for systems engineering, and new advancements are aiming to cross-fertilize methods among distinct scientific and engineering communities, under the title of 'Modeling & Simulation-based Systems Engineering'. Modeling formalisms and graphical representations Initially, when the primary purpose of a systems engineer is to comprehend a complex problem, graphic representations of a system are used to communicate a system's functional and data requirements. Common graphical representations include: Functional flow block diagram (FFBD) Model-based design Data flow diagram (DFD) N2 chart IDEF0 diagram Use case diagram Sequence diagram Block diagram Signal-flow graph USL function maps and type maps Enterprise architecture frameworks A graphical representation relates the various subsystems or parts of a system through functions, data, or interfaces. Any or each of the above methods are used in an industry based on its requirements. For instance, the N2 chart may be used where interfaces between systems is important. Part of the design phase is to create structural and behavioral models of the system. Once the requirements are understood, it is now the responsibility of a systems engineer to