48 research outputs found
Locally Self-Adjusting Skip Graphs
We present a distributed self-adjusting algorithm for skip graphs that
minimizes the average routing costs between arbitrary communication pairs by
performing topological adaptation to the communication pattern. Our algorithm
is fully decentralized, conforms to the model (i.e. uses
bit messages), and requires bits of memory for each
node, where is the total number of nodes. Upon each communication request,
our algorithm first establishes communication by using the standard skip graph
routing, and then locally and partially reconstructs the skip graph topology to
perform topological adaptation. We propose a computational model for such
algorithms, as well as a yardstick (working set property) to evaluate them. Our
working set property can also be used to evaluate self-adjusting algorithms for
other graph classes where multiple tree-like subgraphs overlap (e.g. hypercube
networks). We derive a lower bound of the amortized routing cost for any
algorithm that follows our model and serves an unknown sequence of
communication requests. We show that the routing cost of our algorithm is at
most a constant factor more than the amortized routing cost of any algorithm
conforming to our computational model. We also show that the expected
transformation cost for our algorithm is at most a logarithmic factor more than
the amortized routing cost of any algorithm conforming to our computational
model
Four-dimensional pure compact U(1) gauge theory on a spherical lattice
We investigate the confinement-Coulomb phase transition in the
four-dimensional (4D) pure compact U(1) gauge theory on spherical lattices. The
action contains the Wilson coupling beta and the double charge coupling gamma.
The lattice is obtained from the 4D surface of the 5D cubic lattice by its
radial projection onto a 4D sphere, and made homogeneous by means of
appropriate weight factors for individual plaquette contributions to the
action. On such lattices the two-state signal, impeding the studies of this
theory on toroidal lattices, is absent for gamma le 0. Furthermore, here a
consistent finite-size scaling behavior of several bulk observables is found,
with the correlation length exponent nu in the range nu = 0.35 - 40. These
observables include Fisher zeros, specific-heat and cumulant extrema as well as
pseudocritical values of beta at fixed gamma. The most reliable determination
of nu by means of the Fisher zeros gives nu = 0.365(8). The phase transition at
gamma le 0 is thus very probably of 2nd order and belongs to the universality
class of a non-Gaussian fixed point.Comment: 40 pages, LaTeX, 12 figure
Vortex-line percolation in the three-dimensional complex |psi|^4 model
In discussing the phase transition of the three-dimensional complex |psi|^4
theory, we study the geometrically defined vortex-loop network as well as the
magnetic properties of the system in the vicinity of the critical point. Using
high-precision Monte Carlo techniques we investigate if both of them exhibit
the same critical behavior leading to the same critical exponents and hence to
a consistent description of the phase transition. Different percolation
observables are taken into account and compared with each other. We find that
different connectivity definitions for constructing the vortex-loop network
lead to different results in the thermodynamic limit, and the percolation
thresholds do not coincide with the thermodynamic phase transition point.Comment: 11 pages, 9 figure
Aerodynamic Shape Optimization of Axial Turbines in Three Dimensional Flow
Aerodynamic shape optimization of axial gas turbines in three dimensional flow is addressed. An effective and practical shape parameterization strategy for turbine stages is introduced to minimize the adverse effects of three-dimensional flow features on the turbine performance. The optimization method combines a genetic algorithm (GA), with a Response Surface Approximation (RSA) of the Artifcial Neural Network (ANN) type. During the optimization process, the individual objectives and constraints are approximated using ANN that is trained and tested using a few three-dimensional CFD ow simulations; the latter are obtained using the commercial CFD package Ansys-Fluent. To minimize three-dimensional effects, the stator and rotor stacking curves are taken as the design variable. They are parametrically represented using a quadratic rational Bezier curve (QRBC) whose parameters are directly and explicitly related to the blade lean, sweep and bow, which are used as the design variables. In addition, a noble representation of the stagger angle in the spanwise direction is introduced. The described strategy was applied to optimize the performance of the E/TU-3 axial turbine stage which is designed and tested in Germany. The optimization objectives introduced the isentropic efficiency and the streamwise vorticity, subject to some constraints. This optimization strategy proved to be successful, fexible and practical, and resulted in remarkable improvements in stage performance
Scaling Limits of Lattice Quantum Fields by Wavelets
We present a rigorous renormalization group scheme for lattice quantum field theories in terms of operator algebras. The renormalization group is considered as an inductive system of scaling maps between lattice field algebras. We construct scaling maps for scalar lattice fields using Daubechies’ wavelets, and show that the inductive limit of free lattice ground states exists and the limit state extends to the familiar massive continuum free field, with the continuum action of spacetime translations. In particular, lattice fields are identified with the continuum field smeared with Daubechies’ scaling functions. We compare our scaling maps with other renormalization schemes and their features, such as the momentum shell method or block-spin transformations