An HDG Method for Dirichlet Boundary Control of Convection Dominated Diffusion PDE

We first propose a hybridizable discontinuous Galerkin (HDG) method to approximate the solution of a \emph{convection dominated} Dirichlet boundary control problem. Dirichlet boundary control problems and convection dominated problems are each very challenging numerically due to solutions with low regularity and sharp layers, respectively. Although there are some numerical analysis works in the literature on \emph{diffusion dominated} convection diffusion Dirichlet boundary control problems, we are not aware of any existing numerical analysis works for convection dominated boundary control problems. Moreover, the existing numerical analysis techniques for convection dominated PDEs are not directly applicable for the Dirichlet boundary control problem because of the low regularity solutions. In this work, we obtain an optimal a priori error estimate for the control under some conditions on the domain and the desired state. We also present some numerical experiments to illustrate the performance of the HDG method for convection dominated Dirichlet boundary control problems

Unworking Milton: Steps to a Georgics of the Mind

Traditionally read as a poem about laboring subjects who gain power through abstract and abstracting forms of bodily discipline, John Milton’s Paradise Lost (1667, 1674) more compellingly foregrounds the erotics of the Garden as a space where humans and nonhumans intra-act materially and sexually. Following Christopher Hill, who long ago pointed to not one but two revolutions in the history of seventeenth-century English radicalism—the first, ‘the one which succeeded[,] . . . the protestant ethic’; and the second, ‘the revolution which never happened,’ which sought ‘communal property, a far wider democracy[,] and rejected the protestant ethic’—I show how Milton’s Paradise Lost gives substance to ‘the revolution which never happened’ by imagining a commons, indeed a communism, in which human beings are not at the center of things, but rather constitute one part of the greater ecology of mind within Milton’s poem. In the space created by this ecological reimagining, plants assume a new agency. I call this reimagining ‘ecology to come.

Neptune to the Common-wealth of England (1652): the republican Britannia and the continuity of interests

In the seventeenth century, John Kerrigan reminds us, “models of empire did not always turn on monarchy”. In this essay, I trace a vision of “Neptune’s empire” shared by royalists and republicans, binding English national interest to British overseas expansion. I take as my text a poem entitled “Neptune to the Common-wealth of England”, prefixed to Marchamont Nedham’s 1652 English translation of Mare Clausum (1635), John Selden’s response to Mare Liberum (1609) by Hugo Grotius. This minor work is read alongside some equally obscure and more familiar texts in order to point up the ways in which it speaks to persistent cultural and political interests. I trace the afterlife of this verse, its critical reception and its unique status as a fragment that exemplifies the crossover between colonial republic and imperial monarchy at a crucial moment in British history, a moment that, with Brexit, remains resonant

The manuscript

Part of the introduction to a critical edition of Lucy Hutchinson's translation of Lucretius' De rerum natura. The edition takes its text from a manuscript written out by Hutchinson and a scribe (British Library Additional MS 19333). This section of the introduction describes and analyses the manuscript's physical features--watermarks, gatherings and hand-writing--in an attempt to reconstruct the stages through which Hutchinson and her scribe went in putting the manuscript together