4,300 research outputs found
Lattice walk area combinatorics, some remarkable trigonometric sums and Ap\'ery-like numbers
No full textExplicit algebraic area enumeration formulae are derived for various lattice
walks generalizing the canonical square lattice walk, and in particular for the
triangular lattice chiral walk recently introduced by the authors. A key
element in the enumeration is the derivation of some remarkable identities
involving trigonometric sums --which are also important building blocks of non
trivial quantum models such as the Hofstadter model-- and their explicit
rewriting in terms of multiple binomial sums. An intriguing connection is also
made with number theory and some classes of Ap\'ery-like numbers, the cousins
of the Ap\'ery numbers which play a central role in irrationality
considerations for {\zeta}(2) and {\zeta}(3).Comment: 31 pages, 4 figure
The Treatment of Ties in AP Correlation
No full textThe Kendall tau and AP correlation coefficients are very commonly use to compare two rankings over the same set of items. Even though Kendall tau was originally defined assuming that there are no ties in the rankings, two alternative versions were soon developed to account for ties in two different scenarios: measure the accuracy of an observer with respect to a true and objective ranking, and measure the agreement between two observers in the absence of a true ranking. These two variants prove useful in cases where ties are possible in either ranking, and may indeed result in very different scores. AP correlation was devised to incorporate a top-heaviness component into Kendall tau, penalizing more heavily if differences occur between items at the top of the rankings, making it a very compelling coefficient in Information Retrieval settings. However, the treatment of ties in AP correlation remains an open problem. In this paper we fill this gap, providing closed analytical formulations of AP correlation under the two scenarios of ties contemplated in Kendall tau. In addition,we developed an R package that implements these coefficients.Best Short Paper Accepted author manuscriptMultimedia ComputingWeb Information System
Probabilities and path-integral realization of exclusion statistics
No full textA microscopic formulation of Haldane's exclusions statistics is given in terms of a priori occupation probabilities of states. It is shown that negative probabilities are always necessary to reproduce fractional statistics. Based on this formulation, a pa</p
Solitons and fractional statistics
No full textSolitons in the continuum limit of the Calogero model are derived and shown to correspond to one-particle excitations. The statistical mechanics of exclusion statistics particles is then formulated in terms of a priori probabilities and a path integral is</p
Quasihole wave functions for the Calogero model
No full textThe one-quasihole wave functions and their norms are derived for the system of particles on the line with inverse-square interactions and harmonic confining potential.</p
Multidimensional Calogero systems from matrix models
No full textWe show that a particular many-matrix model gives rise, upon hamiltonian reduction, to a multidimensional version of the Calogero-Sutherland model and its spin generalizations. Some simple solutions of these models are demonstrated by solving the correspo</p
Unitary matrix model for toroidal compactifications of M theory
No full textA unitary matrix model is proposed as the large-N matrix formulation of M theory on flat space with toroidal topology. The model reproduces the motion of elementary D-particles on the compact space, and admits membrane states with nonzero wrapping around</p
Delamination Analysis of A Class of AP-PLY Composite Laminates
No full textA recently developed fiber placement architecture, AP-PLY, has been shown to give significantly improved damage tolerance characteristics of composite structures. The behavior of delaminations resulting from low speed impact damage is of particular concern. Major attention has been paid to expand current knowledge on the delamination response of simple AP-PLY composite structure and move towards in-depth understanding of the failure mechanisms behind the damage tolerance. This thesis presents the approaches to predict delamination onset and analyze delamination growth, in support of the search of the optimum woven pattern for AP-PLY composite laminates. The recovered interlaminar stress between layers combined with the maximum stress criterion determined the delamination onset of simple AP-PLY composite laminate under out-of-plane loads. 2D finite element models with cohesive elements inserted in the interfaces of woven layers have been built to evaluate the delamination initiation and propagation in the different woven patterns of simple AP-PLY composite beams. The parameters of the woven pattern, such as the woven angle, the number of woven plies, the number of straight filled plies, and the location of the woven patterns in through the thickness direction, were investigated and shown to have a significant effect on delamination creation and growth. An energy method based on beam theory was proposed to analyze the strain energy release rate (SERR) of an existing crack in an AP-PLY beam structure. The developed analytical method was implemented in isotropic materials and the obtained SERR of a crack was validated by reference results and finite element solutions. The general behavior of crack growth on the left or right crack tip was evaluated and basic trends leading to crack propagation on one side of the crack were established. A correction factor was introduced to improve the accuracy of the SERR of a small crack through the numerical calculation. The singularity of crack tip caused by dissimilar materials was investigated and was found that the inclusion of the singularity effect could increase the accuracy for small cracks. It has been shown that the neutral axis needs to be relocated to decouple the bending and membrane behavior of unsymmetrical composite laminates, thus to meet the requirement of minimizing the strain energy of the delaminated beam to calculate the SERR of a delaminated composite beam. The calculated SERR of a crack in a composite beam has been verified by comparing with a finite element model. The woven plies in AP-PLY composite laminate altered the layup and two conventional laminates with different stacking sequences were identified in an AP-PLY composite laminate based on the assumption that the resin areas were ignored. A step by step approach was developed to obtain the SERR of a crack that goes across different materials. The analytical SERR determined when two materials are used in sequence, sets the stage for optimization of AP-PLY composite laminates without taking account of the effect of the resin area. The procedure of optimization of simple AP-PLY pattern was proposed and industry may benefit for many applications. An equivalent stiffness approach was used to model regions containing resin pockets and straight or inclined composite layers. A series of three point bending tests was carried out where the failure process and loading capacity were evaluated. The methodology, procedure of optimization, philosophy outlined in this thesis might also be applied to the more complicated fully woven AP-PLY composite laminates. The work in this thesis contributes to the understanding of the behavior of AP-PLY composite laminates with delaminations
Structure function analysis of blazars AP Librae and 3c279
No full textHighest Honors in AstronomyBlazars AP Librae and 3c279 are analyzed for microvariability using a technique known as structure function analysis. AP Librae was observed in April
of 2005 and 3c279 was observed in April of 2007. The data for AP Librae was
previously reduced by Andrew Collazzi and the author reduced the data for
3c279. Both sets of data were reduced using Robert Knop's data reduction
program.
The author ran structure function analysis on both sets of data. Structure function analysis is a statistical analysis run on data that is suppose to
nd timescales of variability, periodicity, and the noise type of data. Previous analysis of AP Librae confirmed mircrovariability, which also shows up in
the structure function of AP Librae. Blazar 3c279 was much quieter than AP
Librae and showed no microvariability durning any of the nights.College of Arts and ScienceDepartment of Physics and Astronom
AP-based wireless intrusion detection systems
No full textThis thesis was scanned from the print manuscript for digital preservation and is copyright the author.
Researchers can access this thesis by asking their local university, institution or public library to
make a request on their behalf. Monash staff and postgraduate students can use the link in the References field
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