Flight test techniques for wake-vortex minimization studies

Flight test techniques developed for use in a study of wake turbulence and used recently in flight studies of wake minimization methods are discussed. Flow visualization was developed as a technique for qualitatively assessing minimization methods and is required in flight test procedures for making quantitative measurements. The quantitative techniques are the measurement of the upset dynamics of an aircraft encountering the wake and the measurement of the wake velocity profiles. Descriptions of the instrumentation and the data reduction and correlation methods are given

Extended two-level quantum dissipative system from bosonization of the elliptic spin-1/2 Kondo model

We study the elliptic spin-1/2 Kondo model (spin-1/2 fermions in one dimension with fully anisotropic contact interactions with a magnetic impurity) in the light of mappings to bosonic systems using the fermion-boson correspondence and associated unitary transformations. We show that for fixed fermion number, the bosonic system describes a two-level quantum dissipative system with two noninteracting copies of infinitely-degenerate upper and lower levels. In addition to the standard tunnelling transitions, and the transitions driven by the dissipative coupling, there are also bath-mediated transitions between the upper and lower states which simultaneously effect shifts in the horizontal degeneracy label. We speculate that these systems could provide new examples of continuous time quantum random walks, which are exactly solvable.Comment: 7 pages, 1 figur

Low-loss photonic crystal fibers for transmission systems and their dispersion properties

We report on a single-mode photonic crystal fiber with attenuation and effective area at 1550 nm of 0.48 dB/km and 130 square-micron, respectively. This is, to our knowledge, the lowest loss reported for a PCF not made from VAD prepared silica and at the same time the largest effective area for a low-loss (< 1 dB/km) PCF. We briefly discuss the future applications of PCFs for data transmission and show for the first time, both numerically and experimentally, how the group velocity dispersion is related to the mode field diameterComment: 5 pages including 3 figures + 1 table. Accepted for Opt. Expres

The packing of two species of polygons on the square lattice

We decorate the square lattice with two species of polygons under the constraint that every lattice edge is covered by only one polygon and every vertex is visited by both types of polygons. We end up with a 24 vertex model which is known in the literature as the fully packed double loop model. In the particular case in which the fugacities of the polygons are the same, the model admits an exact solution. The solution is obtained using coordinate Bethe ansatz and provides a closed expression for the free energy. In particular we find the free energy of the four colorings model and the double Hamiltonian walk and recover the known entropy of the Ice model. When both fugacities are set equal to two the model undergoes an infinite order phase transition.Comment: 21 pages, 4 figure

Critical properties of joint spin and Fortuin-Kasteleyn observables in the two-dimensional Potts model

The two-dimensional Potts model can be studied either in terms of the original Q-component spins, or in the geometrical reformulation via Fortuin-Kasteleyn (FK) clusters. While the FK representation makes sense for arbitrary real values of Q by construction, it was only shown very recently that the spin representation can be promoted to the same level of generality. In this paper we show how to define the Potts model in terms of observables that simultaneously keep track of the spin and FK degrees of freedom. This is first done algebraically in terms of a transfer matrix that couples three different representations of a partition algebra. Using this, one can study correlation functions involving any given number of propagating spin clusters with prescribed colours, each of which contains any given number of distinct FK clusters. For 0 <= Q <= 4 the corresponding critical exponents are all of the Kac form h_{r,s}, with integer indices r,s that we determine exactly both in the bulk and in the boundary versions of the problem. In particular, we find that the set of points where an FK cluster touches the hull of its surrounding spin cluster has fractal dimension d_{2,1} = 2 - 2 h_{2,1}. If one constrains this set to points where the neighbouring spin cluster extends to infinity, we show that the dimension becomes d_{1,3} = 2 - 2 h_{1,3}. Our results are supported by extensive transfer matrix and Monte Carlo computations.Comment: 15 pages, 3 figures, 2 table

A tree-decomposed transfer matrix for computing exact Potts model partition functions for arbitrary graphs, with applications to planar graph colourings

Combining tree decomposition and transfer matrix techniques provides a very general algorithm for computing exact partition functions of statistical models defined on arbitrary graphs. The algorithm is particularly efficient in the case of planar graphs. We illustrate it by computing the Potts model partition functions and chromatic polynomials (the number of proper vertex colourings using Q colours) for large samples of random planar graphs with up to N=100 vertices. In the latter case, our algorithm yields a sub-exponential average running time of ~ exp(1.516 sqrt(N)), a substantial improvement over the exponential running time ~ exp(0.245 N) provided by the hitherto best known algorithm. We study the statistics of chromatic roots of random planar graphs in some detail, comparing the findings with results for finite pieces of a regular lattice.Comment: 5 pages, 3 figures. Version 2 has been substantially expanded. Version 3 shows that the worst-case running time is sub-exponential in the number of vertice

On the universality of compact polymers

Fully packed loop models on the square and the honeycomb lattice constitute new classes of critical behaviour, distinct from those of the low-temperature O(n) model. A simple symmetry argument suggests that such compact phases are only possible when the underlying lattice is bipartite. Motivated by the hope of identifying further compact universality classes we therefore study the fully packed loop model on the square-octagon lattice. Surprisingly, this model is only critical for loop weights n < 1.88, and its scaling limit coincides with the dense phase of the O(n) model. For n=2 it is exactly equivalent to the selfdual 9-state Potts model. These analytical predictions are confirmed by numerical transfer matrix results. Our conclusions extend to a large class of bipartite decorated lattices.Comment: 13 pages including 4 figure

Finite average lengths in critical loop models

A relation between the average length of loops and their free energy is obtained for a variety of O(n)-type models on two-dimensional lattices, by extending to finite temperatures a calculation due to Kast. We show that the (number) averaged loop length L stays finite for all non-zero fugacities n, and in particular it does not diverge upon entering the critical regime n -> 2+. Fully packed loop (FPL) models with n=2 seem to obey the simple relation L = 3 L_min, where L_min is the smallest loop length allowed by the underlying lattice. We demonstrate this analytically for the FPL model on the honeycomb lattice and for the 4-state Potts model on the square lattice, and based on numerical estimates obtained from a transfer matrix method we conjecture that this is also true for the two-flavour FPL model on the square lattice. We present in addition numerical results for the average loop length on the three critical branches (compact, dense and dilute) of the O(n) model on the honeycomb lattice, and discuss the limit n -> 0. Contact is made with the predictions for the distribution of loop lengths obtained by conformal invariance methods.Comment: 20 pages of LaTeX including 3 figure