arXiv subjects

R. Brown

Publications and source records attributed to R. Brown.

27 records · Page 2Linked to original sources

arXiv2004

A homotopy double groupoid of a Hausdorff space II: a van Kampen theorem

This paper is the second in a series exploring the properties of a functor which assigns a homotopy double groupoid with connections to a Hausdorff space. We show that this functor satisfies a version of the van Kampen theorem, and so is a suitable tool for nonabelian, 2-dimensional, local-to-global problems. The methods are analogous to those developed by Brown and Higgins for similar theorems for other higher homotopy groupoids. An integral part of the proof is a detailed discussion of commutative cubes in a double category with connections, and a proof of the key result that any composition of commutative cubes is commutative. These results have recently been generalised to all dimensions by Philip Higgins.

math.AT↗

arXiv2003

The STAR Time Projection Chamber: A Unique Tool for Studying High Multiplicity Events at RHIC

The STAR Time Projection Chamber (TPC) is used to record collisions at the Relativistic Heavy Ion Collider (RHIC). The TPC is the central element in a suite of detectors that surrounds the interaction vertex. The TPC provides complete coverage around the beam-line, and provides complete tracking for charged particles within +- 1.8 units of pseudo-rapidity of the center-of-mass frame. Charged particles with momenta greater than 100 MeV/c are recorded. Multiplicities in excess of 3,000 tracks per event are routinely reconstructed in the software. The TPC measures 4 m in diameter by 4.2 m long, making it the largest TPC in the world.

nucl-ex↗

arXiv2002

Cubical abelian groups with connections are equivalent to chain complexes

The theorem of the title is deduced from the equivalence between crossed complexes and cubical $ω$-groupoids with connections proved by the authors in 1981. In fact we prove the equivalence of five categories defined internally to an additive category with kernels.

math.AT↗

arXiv2002

Advanced Camera for Surveys Observations of Young Star Clusters in the Interacting Galaxy UGC 10214

We present the first Advanced Camera for Surveys (ACS) observations of young star clusters in the colliding/merging galaxy UGC 10214. The observations were made as part of the Early Release Observation (ERO) program for the newly installed ACS during service mission SM3B for the Hubble Space Telescope (HST). Many young star clusters can be identified in the tails of UGC 10214, with ages ranging from ~3 Myr to 10 Myr. The extreme blue V-I (F606W-F814W) colors of the star clusters found in the tail of UGC 10214 can only be explained if strong emission lines are included with a young stellar population. This has been confirmed by our Keck spectroscopy of some of these bright blue stellar knots. The most luminous and largest of these blue knots has an absolute magnitude of M_V = -14.45, with a half-light radius of 161 pc, and if it is a single star cluster, would qualify as a super star cluster (SSC). Alternatively, it could be a superposition of multiple scaled OB associations or clusters. With an estimated age of ~ 4-5 Myr, its derived mass is < 1.3 x 10^6 solar masses. Thus the young stellar knot is unbound and will not evolve into a normal globular cluster. The bright blue clusters and associations are much younger than the dynamical age of the tail, providing strong evidence that star formation occurs in the tail long after it was ejected. UGC 10214 provides a nearby example of processes that contributed to the formation of halos and intra-cluster media in the distant and younger Universe.

astro-ph↗

arXiv2002

Galois theory and a new homotopy double groupoid of a map of spaces

The authors have used generalised Galois Theory to construct a homotopy double groupoid of a surjective fibration of Kan simplicial sets. Here we apply this to construct a new homotopy double groupoid of a map of spaces, which includes constructions by others of a 2-groupoid, cat^1-group or crossed module. An advantage of our construction is that the double groupoid can give an algebraic model of a foliated bundle.

math.AT↗

arXiv2001

Homotopies and automorphisms of crossed modules of groupoids

We give a detailed description of the structure of the actor 2-crossed module related to the automorphisms of a crossed module of groupoids. This generalises work of Brown and Gilbert for the case of crossed modules of groups, and part of this is needed for work on 2-dimensional holonomy to be developed elsewhere (see math.DG/0009082).

math.CT↗

arXiv2000

Local subgroupoids II: Examples and properties

The notion of local subgroupoid as a generalisation of a local equivalence relation was defined in a previous paper by the first two authors. Here we use the notion of star path connectivity for a Lie groupoid to give an important new class of examples, generalising the local equivalence relation of a foliation, and develop in this new context basic properties of coherence, due earlier to Rosenthal in the special case. These results are required for further applications to holonomy and monodromy.

math.DG↗

arXiv1999

Zero Zeros After All These (20) Years

We celebrate two birthdays connected with the radiation zero phenomenon. First, a striking dip in the theoretical angular distributions of radiative weak-boson production was discovered twenty years ago. The key experimental interest is that this will not occur in any deviation from the standard model. Second, the classical training of Stanley Brodsky began sixty years ago, which was instrumental in understanding why theoretical spin-independent radiation zeros appear in almost all Born amplitudes for the radiation of photons and gluons and other massless gauge bosons (but rarely in physical kinematic regions). And there are approximate zeros for massive bosons and ``Type II'' zeros that can also be studied. We discuss how the difficulties in observing the original Mikaelian-Samuel-Sahdev zero finally may be surmounted next year.

hep-ph↗

arXiv1998

Constructing transportable behavioural models for nonlinear electronic devices

We use radial basis functions to model the input--output response of an electronic device. A new methodology for producing models that accuratly describe the response of the device over a wide range of operating points is introduced. A key to the success of the method is the ability to find a polynomial relationship between the model parameters and the operating points of the device.

chao-dyn↗