806 research outputs found
The path space of a higher-rank graph
We construct a locally compact Hausdorff topology on the path space of a
finitely aligned -graph . We identify the boundary-path space
as the spectrum of a commutative -subalgebra
of . Then, using a construction similar to that of Farthing, we
construct a finitely aligned -graph \wt\Lambda with no sources in which
is embedded, and show that is homeomorphic to a
subset of \partial\wt\Lambda . We show that when is row-finite, we
can identify with a full corner of C^*(\wt\Lambda), and deduce
that is isomorphic to a corner of D_{\wt\Lambda}. Lastly, we show
that this isomorphism implements the homeomorphism between the boundary-path
spaces.Comment: 30 pages, all figures drawn with TikZ/PGF. Updated numbering and
minor corrections to coincide with published version. Updated 29-Feb-2012 to
fix a compiling error which resulted in the arXiv PDF output containing two
copies of the articl
A direct approach to co-universal algebras associated to directed graphs
We prove directly that if E is a directed graph in which every cycle has an
entrance, then there exists a C*-algebra which is co-universal for
Toeplitz-Cuntz-Krieger E-families. In particular, our proof does not invoke
ideal-structure theory for graph algebras, nor does it involve use of the gauge
action or its fixed point algebra.Comment: 9 pages; V2: the definition of a Toeplitz-Cuntz-Krieger -family
has been correcte
A Numerical Study of the Conjugate Conduction-Convection Heat Transfer Problem
This study investigates some of the basic aspects of conjugate, or coupled, heat transfer problems. The ultimate interest is in the improvement of an existing computational fluid dynamics (CFD) code by the inclusion of such a coupling capability. Many CFD codes in the past have treated the thermal boundary conditions of a bounding solid as the simple cases of either a surface across which there is no heat flux, or as a surface along which the temperature is a constant with respect to both space and time. These conditions are acceptable for some applications, but many real-world problems require a more-realistic treatment of the thermal wall condition. A thermal coupling may be accomplished by maintaining a continuous heat flux and temperature across the fluid-solid boundary. A heat flux is calculated on the fluid-side of the interface, and this is used as a boundary condition for a heat-conduction solver to calculate the temperature field within the solid and return an interface temperature to the fluid. This process is executed for each time-step iteration of the code, and, therefore, the temperature field of the solid and the fluid-solid interface temperature are allowed to evolve with time and space. A new heat-conduction solver is developed and coupled with an existing flow solver. For this reason, some of the study is devoted to the testing of the accuracy of the new heat-conduction solver on simple problems for which there exist analytical solutions. Additional coverage is devoted to the possibility of thermal communication between solid grid blocks. This is due to the fact that multiple grid blocking of the solid may be required for more complex geometries. For such cases, a similar procedure as that described for the fluid-solid interface is used to accomplish the solid-solid block-to-block communication. Relatively simple test cases of fluid-solid and solid-solid coupling are conducted; these cases are limited to two-dimensional grids. Other limitations include: the assumption of constant thermophysical properties for the solid, no consideration for thermal expansion of the solid, and no consideration for the radiation mode of heat transfer. The results indicate that the heat-conduction/flow solver shows potential
The Path Space of a Directed Graph
We construct a locally compact Hausdorff topology on the path space of a
directed graph , and identify its boundary-path space as the
spectrum of a commutative -subalgebra of . We then show that
is homeomorphic to a subset of the infinite-path space of any
desingularisation of . Drinen and Tomforde showed that we can realise
as a full corner of , and we deduce that is isomorphic
to a corner of . Lastly, we show that this isomorphism implements the
homeomorphism between the boundary-path spaces.Comment: 12 pages, all figures drawn with TikZ/PG
High-Energy theory for close Randall Sundrum branes
We obtain an effective theory for the radion dynamics of the two-brane
Randall Sundrum model, correct to all orders in brane velocity in the limit of
close separation, which is of interest for studying brane collisions and early
Universe cosmology. Obtained via a recursive solution of the Bulk equation of
motions, the resulting theory represents a simple extension of the
corresponding low-energy effective theory to the high energy regime. The
four-dimensional low-energy theory is indeed not valid when corrections at
second order in velocity are considered. This extension has the remarkable
property of including only second derivatives and powers of first order
derivatives. This important feature makes the theory particularly easy to
solve. We then extend the theory by introducing a potential and detuning the
branes.Comment: Version published in the Physical Review
von Neuman algebras of strongly connected higher-rank graphs
We investigate the factor types of the extremal KMS states for the preferred
dynamics on the Toeplitz algebra and the Cuntz--Krieger algebra of a strongly
connected finite -graph. For inverse temperatures above 1, all of the
extremal KMS states are of type I. At inverse temperature 1, there is
a dichotomy: if the -graph is a simple -dimensional cycle, we obtain a
finite type I factor; otherwise we obtain a type III factor, whose Connes
invariant we compute in terms of the spectral radii of the coordinate matrices
and the degrees of cycles in the graph.Comment: 16 pages; 1 picture prepared using TikZ. Version 2: this version to
appear in Math. An
On some fundamental results about higher-rank graphs and their C*-algebras
Results of Fowler and Sims show that every k-graph is completely determined
by its k-coloured skeleton and collection of commuting squares. Here we give an
explicit description of the k-graph associated to a given skeleton and
collection of squares and show that two k-graphs are isomorphic if and only if
there is an isomorphism of their skeletons which preserves commuting squares.
We use this to prove directly that each k-graph {\Lambda} is isomorphic to the
quotient of the path category of its skeleton by the equivalence relation
determined by the commuting squares, and show that this extends to a
homeomorphism of infinite-path spaces when the k-graph is row finite with no
sources. We conclude with a short direct proof of the characterisation,
originally due to Robertson and Sims, of simplicity of the C*-algebra of a
row-finite k-graph with no sources.Comment: 21 pages, two pictures prepared using TiK
High-energy effective theory for matter on close Randall Sundrum branes
Extending the analysis of hep-th/0504128, we obtain a formal expression for
the coupling between brane matter and the radion in a Randall-Sundrum
braneworld. This effective theory is correct to all orders in derivatives of
the radion in the limit of small brane separation, and, in particular, contains
no higher than second derivatives. In the case of cosmological symmetry the
theory can be obtained in closed form and reproduces the five-dimensional
behaviour. Perturbations in the tensor and scalar sectors are then studied.
When the branes are moving, the effective Newtonian constant on the brane is
shown to depend both on the distance between the branes and on their velocity.
In the small distance limit, we compute the exact dependence between the
four-dimensional and the five-dimensional Newtonian constants.Comment: Updated version as published in PR
- …