The recent solar minimum, marking the end of solar cycle 23, has been unique in a number of ways. In particular, the polar photospheric flux was substantially weaker, coronal holes were notably smaller, and unipolar streamers were considerably more prevalent than previous minima. To understand the origins of some of these phenomena, we have computed global solutions using a three-dimensional, time-dependent MHD model of the solar corona and heliosphere. In this report, we present a brief overview of a selection of model results, illustrating: (1) how observations are being used to better constrain model properties; and (2) how the model results can be applied to understanding complex coronal and interplanetary phenomena, and, specifically, unipolar streamers.

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