25,305 research outputs found
Algebra diagrams: a HANDi introduction
A diagrammatic notation for algebra is presented – Hierarchical Al- gebra Network Diagrams, HANDi. The notation uses a 2D network notation with systematically designed icons to explicitly and coherently encode the fun- damental concepts of algebra. The structure of the diagrams is described and the rules for making derivations are presented. The key design features of HANDi are discussed and compared with the conventional formula notation in order demonstrate that the new notation is a more logical codification of intro- ductory algebra
Borcherds-Kac-Moody Symmetry of N=4 Dyons
We consider compactifications of heterotic string theory to four dimensions
on CHL orbifolds of the type T^6 /Z_N with 16 supersymmetries. The exact
partition functions of the quarter-BPS dyons in these models are given in terms
of genus-two Siegel modular forms. Only the N=1,2,3 models satisfy a certain
finiteness condition, and in these cases one can identify a Borcherds-Kac-Moody
superalgebra underlying the symmetry structure of the dyon spectrum. We
identify the real roots, and find that the corresponding Cartan matrices
exhaust a known classification. We show that the Siegel modular form satisfies
the Weyl denominator identity of the algebra, which enables the determination
of all root multiplicities. Furthermore, the Weyl group determines the
structure of wall-crossings and the attractor flows of the theory. For N> 4, no
such interpretation appears to be possible.Comment: 44 pages, 1 figur
Interpretation of Photoemission Spectra of (TaSe4)2I as Evidence of Charge Density Wave Fluctuations
The competition between different and unusual effects in
quasi-one-dimensional conductors makes the direct interpretation of
experimental measurements of these materials both difficult and interesting. We
consider evidence for the existence of large charge-density-wave fluctuations
in the conducting phase of the Peierls insulator (TaSe4)2I, by comparing the
predictions of a simple Lee, Rice and Anderson theory for such a system with
recent angle-resolved photoemission spectra. The agreement obtained suggests
that many of the unusual features of these spectra may be explained in this
way. This view of the system is contrasted with the behaviour expected of a
Luttinger liquid.Comment: Archive copy of published paper. 19 pages, 12 figures, uses IOP
macro
Positivity Problems for Low-Order Linear Recurrence Sequences
We consider two decision problems for linear recurrence sequences (LRS) over
the integers, namely the Positivity Problem (are all terms of a given LRS
positive?) and the Ultimate Positivity Problem} (are all but finitely many
terms of a given LRS positive?). We show decidability of both problems for LRS
of order 5 or less, with complexity in the Counting Hierarchy for Positivity,
and in polynomial time for Ultimate Positivity. Moreover, we show by way of
hardness that extending the decidability of either problem to LRS of order 6
would entail major breakthroughs in analytic number theory, more precisely in
the field of Diophantine approximation of transcendental numbers
The effectiveness of vane-aileron excitation in the experimental determination of flutter speed by parameter identification
The effectiveness of aerodynamic excitation is evaluated analytically in conjunction with the experimental determination of flutter dynamic pressure by parameter identification. Existing control surfaces were used, with an additional vane located at the wingtip. The equations leading to the identification of the equations of motion were reformulated to accommodate excitation forces of aerodynamic origin. The aerodynamic coefficients of the excitation forces do not need to be known since they are determined by the identification procedure. The 12 degree-of-freedom numerical example treated in this work revealed the best wingtip vane locations, and demonstrated the effectiveness of the aileron-vane excitation system. Results from simulated data gathered at much lower dynamic pressures (approximately half the value of flutter dynamic pressure) predicted flutter dynamic pressures with 2-percent errors
Photonic band-gap engineering for volume plasmon polaritons in multiscale multilayer hyperbolic metamaterials
We theoretically study the propagation of large-wavevector waves (volume
plasmon polaritons) in multilayer hyperbolic metamaterials with two levels of
structuring. We show that when the parameters of a subwavelength
metal-dielectric multilayer ("substructure") are modulated ("superstructured")
on a larger, wavelength scale, the propagation of volume plasmon polaritons in
the resulting multiscale hyperbolic metamaterials is subject to photonic band
gap phenomena. A great degree of control over such plasmons can be exerted by
varying the superstructure geometry. When this geometry is periodic, stop bands
due to Bragg reflection form within the volume plasmonic band. When a cavity
layer is introduced in an otherwise periodic superstructure, resonance peaks of
the Fabry-Perot nature are present within the stop bands. More complicated
superstructure geometries are also considered. For example, fractal Cantor-like
multiscale metamaterials are found to exhibit characteristic self-similar
spectral signatures in the volume plasmonic band. Multiscale hyperbolic
metamaterials are shown to be a promising platform for large-wavevector bulk
plasmonic waves, whether they are considered for use as a new kind of
information carrier or for far-field subwavelength imaging.Comment: 12 pages, 10 figures, now includes Appendix
Loop algorithms for quantum simulations of fermion models on lattices
Two cluster algorithms, based on constructing and flipping loops, are
presented for worldline quantum Monte Carlo simulations of fermions and are
tested on the one-dimensional repulsive Hubbard model. We call these algorithms
the loop-flip and loop-exchange algorithms. For these two algorithms and the
standard worldline algorithm, we calculated the autocorrelation times for
various physical quantities and found that the ordinary worldline algorithm,
which uses only local moves, suffers from very long correlation times that
makes not only the estimate of the error difficult but also the estimate of the
average values themselves difficult. These difficulties are especially severe
in the low-temperature, large- regime. In contrast, we find that new
algorithms, when used alone or in combinations with themselves and the standard
algorithm, can have significantly smaller autocorrelation times, in some cases
being smaller by three orders of magnitude. The new algorithms, which use
non-local moves, are discussed from the point of view of a general prescription
for developing cluster algorithms. The loop-flip algorithm is also shown to be
ergodic and to belong to the grand canonical ensemble. Extensions to other
models and higher dimensions is briefly discussed.Comment: 36 pages, RevTex ver.
Exploring Periodic Orbit Expansions and Renormalisation with the Quantum Triangular Billiard
A study of the quantum triangular billiard requires consideration of a
boundary value problem for the Green's function of the Laplacian on a trianglar
domain. Our main result is a reformulation of this problem in terms of coupled
non--singular integral equations. A non--singular formulation, via Fredholm's
theory, guarantees uniqueness and provides a mathematically firm foundation for
both numerical and analytic studies. We compare and contrast our reformulation,
based on the exact solution for the wedge, with the standard singular integral
equations using numerical discretisation techniques. We consider in detail the
(integrable) equilateral triangle and the Pythagorean 3-4-5 triangle. Our
non--singular formulation produces results which are well behaved
mathematically. In contrast, while resolving the eigenvalues very well, the
standard approach displays various behaviours demonstrating the need for some
sort of ``renormalisation''. The non-singular formulation provides a
mathematically firm basis for the generation and analysis of periodic orbit
expansions. We discuss their convergence paying particular emphasis to the
computational effort required in comparision with Einstein--Brillouin--Keller
quantisation and the standard discretisation, which is analogous to the method
of Bogomolny. We also discuss the generalisation of our technique to smooth,
chaotic billiards.Comment: 50 pages LaTeX2e. Uses graphicx, amsmath, amsfonts, psfrag and
subfigure. 17 figures. To appear Annals of Physics, southern sprin
Dyson Equation Approach to Many-Body Greens Functions and Self-Consistent RPA, First Application to the Hubbard Model
An approach for particle-hole correlation functions, based on the so-called
SCRPA, is developed. This leads to a fully self-consistent RPA-like theory
which satisfies the -sum rule and several other theorems. As a first step, a
simpler self-consistent approach, the renormalized RPA, is solved numerically
in the one-dimensional Hubbard model. The charge and the longitudinal spin
susceptibility, the momentum distribution and several ground state properties
are calculated and compared with the exact results. Especially at half filling,
our approach provides quite promising results and matches the exact behaviour
apart from a general prefactor. The strong coupling limit of our approach can
be described analytically.Comment: 35 pages, 18 Figures, Feynman diagrams as 10 additional eps-files,
revised and enhanced version, accepted in Phys. Rev.
Resonant state expansion applied to planar open optical systems
The resonant state expansion (RSE), a novel perturbation theory of
Brillouin-Wigner type developed in electrodynamics [Muljarov, Langbein, and
Zimmermann, Europhys. Lett., 92, 50010(2010)], is applied to planar,
effectively one-dimensional optical systems, such as layered dielectric slabs
and Bragg reflector microcavities. It is demonstrated that the RSE converges
with a power law in the basis size. Algorithms for error estimation and their
reduction by extrapolation are presented and evaluated. Complex
eigenfrequencies, electro-magnetic fields, and the Green's function of a
selection of optical systems are calculated, as well as the observable
transmission spectra. In particular we find that for a Bragg-mirror
microcavity, which has sharp resonances in the spectrum, the transmission
calculated using the resonant state expansion reproduces the result of the
transfer/scattering matrix method
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