Angular reduction in multiparticle matrix elements

A general method for the reduction of coupled spherical harmonic products is presented. When the total angular coupling is zero, the reduction leads to an explicitly real expression in the scalar products within the unit vector arguments of the spherical harmonics. For non-scalar couplings, the reduction gives Cartesian tensor forms for the spherical harmonic products, with tensors built from the physical vectors in the original expression. The reduction for arbitrary couplings is given in closed form, making it amenable to symbolic manipulation on a computer. The final expressions do not depend on a special choice of coordinate axes, nor do they contain azimuthal quantum number summations, nor do they have complex tensor terms for couplings to a scalar. Consequently, they are easily interpretable from the properties of the physical vectors they contain.Comment: This version contains added comments and typographical corrections to the original article. Now 27 pages, 0 figure

Experiments, Simulations, and Epistemic Privilege

Experiments are commonly thought to have epistemic privilege over simulations. Two ideas underpin this belief: First, experiments generate greater inferential power than simulations, and second, simulations cannot surprise us the way experiments can. In this paper I argue that neither of these claims is true of experiments versus simulations in general. We should give up the common practice of resting in-principle judgments about the epistemic value of cases of scientific inquiry on whether we classify those cases as experiments or simulations, per se. To the extent that either methodology puts researchers in a privileged epistemic position, this is context-sensitive

Microbes, mathematics, and models

Microbial model systems have a long history of fruitful use in fields that include evolution and ecology. In order to develop further insight into modelling practice, we examine how the competitive exclusion and coexistence of competing species have been modelled mathematically and materially over the course of a long research history. In particular, we investigate how microbial models of these dynamics interact with mathematical or computational models of the same phenomena. Our cases illuminate the ways in which microbial systems and equations work as models, and what happens when they generate inconsistent findings about shared targets. We reveal an iterative strategy of comparative modelling in different media, and suggest reasons why microbial models have a special degree of epistemic tractability in multimodel inquiry

Microbes, mathematics, and models

Microbial model systems have a long history of fruitful use in fields that include evolution and ecology. In order to develop further insight into modelling practice, we examine how the competitive exclusion and coexistence of competing species have been modelled mathematically and materially over the course of a long research history. In particular, we investigate how microbial models of these dynamics interact with mathematical or computational models of the same phenomena. Our cases illuminate the ways in which microbial systems and equations work as models, and what happens when they generate inconsistent findings about shared targets. We reveal an iterative strategy of comparative modelling in different media, and suggest reasons why microbial models have a special degree of epistemic tractability in multimodel inquiry