1,839,089 research outputs found
Singular vector expansion functions for finite methods
This paper describes the fundamental properties of new singular vector bases that incorporate the edge conditions in curved triangular elements. The bases are fully compatible with the interpolatory or hierarchical high-order regular vector bases used in adjacent elements. Several numerical results confirm the faster convergence of these bases on wedge problems and the capability to model regular fields when the singularity is not excite
A study of query expansion methods for patent retrieval
Patent retrieval is a recall-oriented search task where the objective is to find all possible relevant documents. Queries in patent retrieval are typically very long since they take the form of a patent claim or even a full patent application in the case of priorart patent search. Nevertheless, there is generally a significant mismatch between the query and the relevant documents, often leading to low retrieval effectiveness. Some previous work has
tried to address this mismatch through the application of query expansion (QE) techniques which have generally showed
effectiveness for many other retrieval tasks. However, results of QE on patent search have been found to be very disappointing. We present a review of previous investigations of QE in patent retrieval, and explore some of these techniques on a prior-art patent search task. In addition, a novel method for QE using automatically generated synonyms set is presented. While previous QE techniques fail to improve over baseline retrieval, our new approach show statistically better retrieval precision over
the baseline, although not for recall. In addition, it proves to be significantly more efficient than existing techniques. An extensive analysis to the results is presented which seeks to better understand situations where these QE techniques succeed or fail
Character Expansion Methods for Matrix Models of Dually Weighted Graphs
We consider generalized one-matrix models in which external fields allow
control over the coordination numbers on both the original and dual lattices.
We rederive in a simple fashion a character expansion formula for these models
originally due to Itzykson and Di Francesco, and then demonstrate how to take
the large N limit of this expansion. The relationship to the usual matrix model
resolvent is elucidated. Our methods give as a by-product an extremely simple
derivation of the Migdal integral equation describing the large limit of
the Itzykson-Zuber formula. We illustrate and check our methods by analyzing a
number of models solvable by traditional means. We then proceed to solve a new
model: a sum over planar graphs possessing even coordination numbers on both
the original and the dual lattice. We conclude by formulating equations for the
case of arbitrary sets of even, self-dual coupling constants. This opens the
way for studying the deep problem of phase transitions from random to flat
lattices.Comment: 22 pages, harvmac.tex, pictex.tex. All diagrams written directly into
the text in Pictex commands. (Two minor math typos corrected.
Acknowledgements added.
Boson Expansion Methods in (1+1)-dimensional Light-Front QCD
We derive a bosonic Hamiltonian from two dimensional QCD on the light-front.
To obtain the bosonic theory we find that it is useful to apply the boson
expansion method which is the standard technique in quantum many-body physics.
We introduce bilocal boson operators to represent the gauge-invariant quark
bilinears and then local boson operators as the collective states of the
bilocal bosons. If we adopt the Holstein-Primakoff type among various
representations, we obtain a theory of infinitely many interacting bosons,
whose masses are the eigenvalues of the 't Hooft equation. In the large
limit, since the interaction disappears and the bosons are identified with
mesons, we obtain a free Hamiltonian with infinite kinds of mesons.Comment: 20 pages, latex, no figures, journal version (no significant
changes), to appear in Phys. Rev.
A Thermal Gradient Approach for the Quasi-Harmonic Approximation and its Application to Improved Treatment of Anisotropic Expansion
We present a novel approach to efficiently implement thermal expansion in the
quasi-harmonic approximation (QHA) for both isotropic and more importantly,
anisotropic expansion. In this approach, we rapidly determine a crystal's
equilibrium volume and shape at a given temperature by integrating along the
gradient of expansion from zero Kelvin up to the desired temperature. We
compare our approach to previous isotropic methods that rely on a brute-force
grid search to determine the free energy minimum, which is infeasible to carry
out for anisotropic expansion, as well as quasi-anisotropic approaches that
take into account the contributions to anisotropic expansion from the lattice
energy. We compare these methods for experimentally known polymorphs of
piracetam and resorcinol and show that both isotropic methods agree to within
error up to 300 K. Using the Gr\"{u}neisen parameter causes up to 0.04 kcal/mol
deviation in the Gibbs free energy, but for polymorph free energy differences
there is a cancellation in error with all isotropic methods within 0.025
kcal/mol at 300 K.
Anisotropic expansion allows the crystals to relax into lattice geometries
0.01-0.23 kcal/mol lower in energy at 300 K relative to isotropic expansion.
For polymorph free energy differences all QHA methods produced results within
0.02 kcal/mol of each other for resorcinol and 0.12 kcal/mol for piracetam, the
two molecules tested here, demonstrating a cancellation of error for isotropic
methods.
We also find that when expanding in more than a single volume variable, there
is a non-negligible rate of failure of the basic approximations of QHA.
Specifically, while expanding into new harmonic modes as the box vectors are
increased, the system often falls into alternate, structurally distinct
harmonic modes unrelated by continuous deformation from the original harmonic
mode.Comment: 38 pages, including 9 pages supporting informatio
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