Numerical analysis of the relation between interactions and structure in a molecular fluid

Coarse graining is a popular technique used in physics to speed up the computer simulation of molecular fluids. An essential part of this technique is a method that solves the inverse problem of determining the interaction potential or its parameters from the given structural data. Due to discrepancies between model and reality, the potential is not unique, such that stability of such method and its convergence to a meaningful solution are issues.rnrnIn this work, we investigate empirically whether coarse graining can be improved by applying the theory of inverse problems from applied mathematics. In particular, we use the singular value analysis to reveal the weak interaction parameters, that have a negligible influence on the structure of the fluid and which cause non-uniqueness of the solution. Further, we apply a regularizing Levenberg-Marquardt method, which is stable against the mentioned discrepancies. Then, we compare it to the existing physical methods - the Iterative Boltzmann Inversion and the Inverse Monte Carlo method, which are fast and well adapted to the problem, but sometimes have convergence problems.rnrnFrom analysis of the Iterative Boltzmann Inversion, we elaborate a meaningful approximation of the structure and use it to derive a modification of the Levenberg-Marquardt method. We engage the latter for reconstruction of the interaction parameters from experimental data for liquid argon and nitrogen. We show that the modified method is stable, convergent and fast. Further, the singular value analysis of the structure and its approximation allows to determine the crucial interaction parameters, that is, to simplify the modeling of interactions. Therefore, our results build a rigorous bridge between the inverse problem from physics and the powerful solution tools from mathematics. rn

The structuring body : a critical study in the description & explanation of perceptual experience

The aims of the dissertation are to find the right description of the structure of perceptual experience and to explore the ways in which the structure of the body might serve to explain it. In the first two parts, I articulate and defend the claim that perceptual experience seems direct and the claim that its objects seem real. I defend these claims as integral parts of a coherent metaphysically neutral conception of perceptual experience. Sense-datum theorists, certain influential perceptual psychologists, and early modern philosophers (most notably Berkeley) all disputed the claim that perceptual experience seems direct. In Part I, I argue that the grounds on which they did so were poor. The aim is then, in Part II, to give a proper appreciation of the distinctive intentionality of perceptual experience whilst remaining metaphysically neutral. I do so by drawing on the early work of Edmund Husserl, providing a characterisation of the perceptual experience of objects as real, qua mind-independent particulars. In Part III, I explore two possible explanations of the structure characterising the intentionality of perceptual experience, both of which accord a distinctive explanatory role to the body. On one account, perceptual experience is structured by an implicit pre-reflective consciousness of oneself as a body engaged in perceptual activity. An alternative account makes no appeal to the metaphysically laden concept of a bodily self. It seeks to explain the structure of perceptual experience by appeal to anticipation of the structural constraints of the body. I develop this alternative by highlighting the conceptual and empirical basis for the idea that a first-order structural affordance relation holds between a bodily agent and certain properties of its body. I then close with a discussion of the shared background assumptions that ought to inform disputes over whether the body itself (in addition to its representation) ought to serve as an explanans in such an account.