The Function of Boundary Conditions in the Physical Sciences

Abstract

Early philosophical accounts of explanation mistook the function of boundary conditions for that of contingent facts. I diagnose where this misunderstanding arose and establish that it persists. I disambiguate between uses of the term "boundary conditions" and argue that boundary conditions are explanatory via their roles as components of models. Using case studies from fluid mechanics and the physics of waves, I articulate four explanatory functions for boundary conditions in physics: specifying the scope of a model, enabling stable descriptions of phenomena in the model, generating descriptions of novel phenomena, and connecting models from differing theoretical backgrounds.

Carbon Nanotubes (CNTs) Nanofluids Flow and Heat Transfer under MHD Effect over a Moving Surface

“…This model is incorporated with the boundary conditions where these conditions are reasonably important for governing our model and completing our computational process wisely [46]. In addition, Bursten [47] believed that specifying boundary conditions can limit the scope of a model to a limited subclass of systems to which a set of governing equations applied. The complete boundary conditions can be written as follows…”

Comment on “Groundwater Affects the Geomorphic and Hydrologic Properties of Coevolved Landscapes” by Litwin et al.

“…(2020) there is a single typology of the NoHyd model which can be rescaled to obtain all results the model may produce.” These conclusions need to be revised because the role of the boundary conditions is not included in the dimensional analysis. While the dimensional analysis of the LEM is facilitated by the fact that some of the main variables and parameters are clearly listed in the governing equations, the obtained solutions depend on the initial and boundary conditions as much as they do on the equations (Bursten, 2021).…”

Econophysics: making sense of a chimera

“…Assuming that traders' market interactions are representable as a lattice framework, the 'Ising model' of phase transitions in paramagnetic-ferromagnetic phenomena is posited as a strongly analogical model. These phase transitions have been modelled successfully as early as the 1920s in the work of Whilhelm Lenz and Ernest Ising, and later culminated in 'renormalization group methods' in the work of Nobel laureate Kenneth Wilson,11 of which the JLS model builds upon (Wilson 1979). In physical systems, one defines the 'susceptibility' of the system to be a variable χ defined as:…”

“…20 Recent work in both the philosophy of physics and philosophy of economics have noted how important boundary conditions are in understanding both physical and economic mechanisms, especially with respect to those mechanisms' ability to provide explanations of phenomena. In physics, the boundaries are not only the mereological, topological, and geometric boundaries of a physical system but boundaries on its solution space (Bursten 2021); in economics, these considerations apply with additional concerns regarding the boundaries of what is considered to be a specifically from the 'critical realism' school of social science (Lawson 1997;Fleetwood 2004). 19 I thank an anonymous referee for drawing my attention to this work.…”