15,939 research outputs found
Expert systems and finite element structural analysis - a review
Finite element analysis of many engineering systems is practised more as an art than as a science . It involves high level expertise (analytical as well as heuristic) regarding problem modelling (e .g. problem specification,13; choosing the appropriate type of elements etc .), optical mesh design for achieving the specified accuracy (e .g . initial mesh selection, adaptive mesh refinement), selection of the appropriate type of analysis and solution13; routines and, finally, diagnosis of the finite element solutions . Very often such expertise is highly dispersed and is not available at a single place with a single expert. The design of an expert system, such that the necessary expertise is available to a novice to perform the same job even in the absence of trained experts, becomes an attractive proposition. 13; In this paper, the areas of finite element structural analysis which require experience and decision-making capabilities are explored . A simple expert system, with a feasible knowledge base for problem modelling, optimal mesh design, type of analysis and solution routines, and diagnosis, is outlined. Several efforts in these directions, reported in the open literature, are also reviewed in this paper
Instantons, supersymmetric vacua, and emergent geometries
We study instanton solutions and superpotentials for the large number of
vacua of the plane-wave matrix model and a 2+1 dimensional Super Yang-Mills
theory on with sixteen supercharges. We get the superpotential in
the weak coupling limit from the gauge theory description. We study the gravity
description of these instantons. Perturbatively with respect to a background,
they are Euclidean branes wrapping cycles in the dual gravity background.
Moreover, the superpotential can be given by the energy of the electric charge
system characterizing each vacuum. These charges are interpreted as the
eigenvalues of matrices from a reduction for the 1/8 BPS sector of the gauge
theories. We also discuss qualitatively the emergence of the extra spatial
dimensions appeared on the gravity side.Comment: 29 pages, 3 figures, latex. v2: references added, comments added. v3:
accepted version in PR
A Multitrace Matrix Model from Fuzzy Scalar Field Theory
We present the analytical approach to scalar field theory on the fuzzy sphere
which has been developed in arXiv:0706.2493 [hep-th]. This approach is based on
considering a perturbative expansion of the kinetic term in the partition
function. After truncating this expansion at second order, one arrives at a
multitrace matrix model, which allows for an application of the saddle-point
method. The results are in agreement with the numerical findings in the
literature.Comment: 8 pages, talk given by CS at the International Workshop
"Supersymmetries and Quantum Symmetries" (SQS'07), Dubna, July 30 - August 4
2007; to appear in the proceeding
The beat of a fuzzy drum: fuzzy Bessel functions for the disc
The fuzzy disc is a matrix approximation of the functions on a disc which
preserves rotational symmetry. In this paper we introduce a basis for the
algebra of functions on the fuzzy disc in terms of the eigenfunctions of a
properly defined fuzzy Laplacian. In the commutative limit they tend to the
eigenfunctions of the ordinary Laplacian on the disc, i.e. Bessel functions of
the first kind, thus deserving the name of fuzzy Bessel functions.Comment: 30 pages, 8 figure
The Fuzzy Disc
We introduce a finite dimensional matrix model approximation to the algebra
of functions on a disc based on noncommutative geometry. The algebra is a
subalgebra of the one characterizing the noncommutative plane with a * product
and depends on two parameters N and theta. It is composed of functions which
decay exponentially outside a disc. In the limit in which the size of the
matrices goes to infinity and the noncommutativity parameter goes to zero the
disc becomes sharper. We introduce a Laplacian defined on the whole algebra and
calculate its eigenvalues. We also calculate the two--points correlation
function for a free massless theory (Green's function). In both cases the
agreement with the exact result on the disc is very good already for relatively
small matrices. This opens up the possibility for the study of field theories
on the disc with nonperturbative methods. The model contains edge states, a
fact studied in a similar matrix model independently introduced by
Balachandran, Gupta and Kurkcuoglu.Comment: 17 pages, 8 figures, references added and correcte
Comments on the Entanglement Entropy on Fuzzy Spaces
We locate the relevant degrees of freedom for the entanglement entropy on
some 2+1 fuzzy models. It is found that the entropy is stored in the near
boundary degrees of freedom. We give a simple analytical derivation for the
area law using like expansion when only the near boundary degrees of
freedom are incorporated. Numerical and qualitative evidences for the validity
of near boundary approximation are finally given .Comment: 14 pages, 2 figure
Mutual information on the fuzzy sphere
We numerically calculate entanglement entropy and mutual information for a
massive free scalar field on commutative (ordinary) and noncommutative (fuzzy)
spheres. We regularize the theory on the commutative geometry by discretizing
the polar coordinate, whereas the theory on the noncommutative geometry
naturally posseses a finite and adjustable number of degrees of freedom. Our
results show that the UV-divergent part of the entanglement entropy on a fuzzy
sphere does not follow an area law, while the entanglement entropy on a
commutative sphere does. Nonetheless, we find that mutual information (which is
UV-finite) is the same in both theories. This suggests that nonlocality at
short distances does not affect quantum correlations over large distances in a
free field theory.Comment: 16 pages, 10 figures. Fixed minor typos, references updated,
discussion slightly expande
Fuzzy Scalar Field Theory as a Multitrace Matrix Model
We develop an analytical approach to scalar field theory on the fuzzy sphere
based on considering a perturbative expansion of the kinetic term. This
expansion allows us to integrate out the angular degrees of freedom in the
hermitian matrices encoding the scalar field. The remaining model depends only
on the eigenvalues of the matrices and corresponds to a multitrace hermitian
matrix model. Such a model can be solved by standard techniques as e.g. the
saddle-point approximation. We evaluate the perturbative expansion up to second
order and present the one-cut solution of the saddle-point approximation in the
large N limit. We apply our approach to a model which has been proposed as an
appropriate regularization of scalar field theory on the plane within the
framework of fuzzy geometry.Comment: 1+25 pages, replaced with published version, minor improvement
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