Models in Scientific Practice

This dissertation presents an account of the practice of modeling in science in which scientists' perceptual and bodily interactions with external representations take center stage. I argue that modeling is primarily a practice of constructing, manipulating, and analyzing external representations in service of cognitive and epistemic aims of research, and show that this account better captures important aspects of the practice of modeling than accounts currently popular in philosophy of science. Philosophical accounts of the practice of modeling classify models according to the categories of abstract and concrete entities developed in metaphysics. I argue that this type of account obscures the practice of modeling. In particular, using the analysis of the Lotka-Volterra model as an example, I argue that understanding mathematical models as abstract entities---non-spatiotemporally located, imperceptible entities---obscures the fact that the analysis of the Lotka-Volterra model relies primarily on visual perception of external representations, especially hand- or computer-generated graphs. Instead, I suggest that we apply the concepts of internal and external representations, developed in cognitive science, to models, including mathematical models. I then present two case studies that illustrate different aspects of modeling, understood as a practice of constructing, manipulating, and analyzing external representations. First, using Sewall Wright's long-term research on isolation by distance, I articulate the relationship between the uses of a model, the particular aims of research, and the criteria of success relevant to a given use of the model. I argue that uses of the same model can shift over the course of scientists' research in response to shifts in aim and that criteria of success for one use of a model can be different from those for another use of the same model. Second, I argue that in successful scientific research, a scientist uses a model according to the methodological principles of realism and instrumentalism despite the tension that they create among the scientist's uses of the model over time. This thesis is supported by a detailed analysis of successful scientific research done by Seymour Benzer in the 1950s and 60s

Stripe antiferromagnetic correlations in LaFeAsO1-xFx probed by 75As NMR

The anisotropy of the nuclear spin-lattice relaxation rate $1/T_{1}$ of $^{75}$As was investigated in the iron-based superconductor LaFeAs(O$_{1-x}$F$_{x}$) ($x = 0.07, 0.11$ and 0.14) as well as LaFeAsO. While the temperature dependence of the normal-state $1/T_1T$ in the superconducting (SC) $x = 0.07$ is different from that in the SC $x = 0.11$, their anisotropy of $1/T_1$, $R \equiv (1/T_{1})_{H \parallel ab}/(1/T_{1})_{H \parallel c}$ in the normal state is almost the same ($\simeq$ 1.5). The observed anisotropy is ascribable to the presence of the local stripe correlations with $Q = (\pi, 0)$ or $(0, \pi)$. In contrast, $1/T_1$ is isotropic and $R$ is approximately 1 in the overdoped $x = 0.14$ sample, where superconductivity is almost suppressed. These results suggest that the presence of the local stripe correlations originating from the nesting between hole and electron Fermi surfaces is linked to high-$T_c$ superconductivity in iron pnictides.Comment: 4 pages, 3 figures, Accepted for publication in Phys. Rev.

ALMA Observations of the Gravitational Lens SDP.9

We present long-baseline ALMA observations of the strong gravitational lens H-ATLAS J090740.0-004200 (SDP.9), which consists of an elliptical galaxy at $z_{\mathrm{L}}=0.6129$ lensing a background submillimeter galaxy into two extended arcs. The data include Band 6 continuum observations, as well as CO $J$=6$-$5 molecular line observations, from which we measure an updated source redshift of $z_{\mathrm{S}}=1.5747$. The image morphology in the ALMA data is different from that of the HST data, indicating a spatial offset between the stellar, gas, and dust component of the source galaxy. We model the lens as an elliptical power law density profile with external shear using a combination of archival HST data and conjugate points identified in the ALMA data. Our best model has an Einstein radius of $\theta_{\mathrm{E}}=0.66\pm0.01$ and a slightly steeper than isothermal mass profile slope. We search for the central image of the lens, which can be used constrain the inner mass distribution of the lens galaxy including the central supermassive black hole, but do not detect it in the integrated CO image at a 3$\sigma$ rms level of 0.0471 Jy km s$^{-1}$.Comment: Accepted for publication in ApJL; 6 pages, 2 figures, 3 table

Spin Dynamics in Iron-based Layered Superconductor (La_{0.87}Ca_{0.13})FePO Revealed by ^{31}P and ^{139}La NMR Studies

We report ^{31}P and ^{139}La NMR studies of (La_{0.87}Ca_{0.13})FePO, which is a family member of the recently discovered superconductor LaFeAs(O_{1-x}F_x). In the normal state, Knight shift and $1/T_1T$ show that a Fermi-liquid state with moderate ferromagnetic fluctuations emerges below 30K. From 1/T_1T of ^{31}P and ^{139}La, quasi-two dimensional electronic structure is suggested, in which the FeP layer is more conductive than the LaO layer. In the superconducting (SC) state, although a clear Meissner signal was observed, 1/T_1T increases below T_c, in contrast to a decrease of 1/T_1T due to the opening of a SC gap, suggesting that novel low-energy spin dynamics develop in the SC state.Comment: Phys. Rev. Lett. 101, 077006 (2008