We present a cohomological method for obtaining the non-Abelian Seiberg-Witten map for any gauge group and to any order in θ. By introducing a ghost field, we are able to express the equations defining the Seiberg-Witten map through a coboundary operator, so that they can be solved by constructing a corresponding homotopy operator. * email address: dmbrace@lbl.gov † email address: BLCerchiai@lbl.gov ‡

Protein complexes called rosettasomes self-assemble in solution to form large-scale filamentous and planar structures. The relative abundance of these aggregates varies abruptly with environmental conditions and sample composition. Our simulations of a model of patchy nanoparticles can reproduce this sharp crossover, but only if particles are allowed to switch between two internal states favoring different geometries of local binding. These results demonstrate how local conformational adaptivity can fundamentally influence the cooperativity of pattern-forming dynamics.Group II chaperonin complexes from the hyperthermophilic archaeon Sulfolobus, called rosettasomes, spontaneously assemble in vitro into micron-scale structures [1,2]. Two remarkably different architectures can result from this process: bundles of filamentous chains of roughly spherical rosettasome units bound pole-to-pole, and stacks of hexagonally-packed sheets of units bound equator-to-equator. Such materials separately display great promise for nanotechnology. Sheets and strings of mutant chaperonins have been used to build ordered 2d arrays of quantum dots [2] and metallized conducting nanowires [3]. Filaments may also fulfill a biological role as components of the archaeal cytoskeleton [4]. The dual nature of rosettasome assembly offers further promise for materials science: the prospect of switching between the assembly of different structures by controlling only environmental conditions is very attractive. Conceptually, dual assembly poses new questions regarding the statistical dynamics of organized growth: How do multiple modes of assembly cooperate or interfere? Are hybrid structures an unavoidable endpoint when forces favoring different structural motifs combine?Emulating the complex self-assembly properties of rosettasomes with synthetic particles requires interactions of a 'patchy' nature. It may seem sufficient to situate a strongly sticky region at each particle's equator, and a distinct kind of stickiness at its poles. Several computer simulation studies [5][6][7][8][9][10][11][12][13][14][15] and a few ambitious experiments have adopted an analogous perspective, attempting to design specific aggregate geometries through anisotropy of microscopic forces. However, component design based solely on structural considerations rarely results in successful assembly. The picture emerging from these studies is one of intense †Author to whom correspondence should be addressed. E-mail: E-mail: geissler@berkeley.edu. * Current address: Molecular Foundry, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA NIH Public Access competition between thermodynamics and kinetics: even for simple patchy nanoparticles, stochastic growth dynamics and the difficulties of defect annealing condition successful assembly on the fine-tuning of nanoparticle attraction strengths and binding geometry specificities.In this paper we use theoretical models based on these physical perspectives to explain the dual nature of rosettasome assembly. We dr...

The Seiberg-Witten map for noncommutative Yang-Mills theories is studied and methods for its explicit construction are discussed which are valid for any gauge group. In particular the use of the evolution equation is described in some detail and its relation to the cohomological approach is elucidated. Cohomological methods which are applicable to gauge theories requiring the Batalin-Vilkoviskii antifield formalism are briefly mentioned. Also, the analogy of the Weyl-Moyal star product with the star product of open bosonic string field theory and possible ramifications of this analogy are briefly mentioned. * email address: BLCerchiai@lbl.gov †

A covariant quantization method is developed for the off-shell superparticle in 10 dimensions. On shell it is consistent with light cone quantization, while off shell it gives a noncommutative superspace that realizes nonlinearly a hidden 11-dimensional super Poincaré symmetry. The nonlinear commutation rules are then used to construct the supersymmetric generalization of the covariant Moyal star product in noncommutative superspace. As one of the possible applications, we propose this new product as the star product in supersymmetric string field theory. Furthermore, the formalism introduces new techniques and concepts in noncommutative ͑super͒geometry.