46,602 research outputs found
Adaptive multiscale model reduction with Generalized Multiscale Finite Element Methods
In this paper, we discuss a general multiscale model reduction framework
based on multiscale finite element methods. We give a brief overview of related
multiscale methods. Due to page limitations, the overview focuses on a few
related methods and is not intended to be comprehensive. We present a general
adaptive multiscale model reduction framework, the Generalized Multiscale
Finite Element Method. Besides the method's basic outline, we discuss some
important ingredients needed for the method's success. We also discuss several
applications. The proposed method allows performing local model reduction in
the presence of high contrast and no scale separation
Generalized Toda Theory from Six Dimensions and the Conifold
Recently, a physical derivation of the Alday-Gaiotto-Tachikawa correspondence
has been put forward. A crucial role is played by the complex Chern-Simons
theory arising in the 3d-3d correspondence, whose boundary modes lead to Toda
theory on a Riemann surface. We explore several features of this derivation and
subsequently argue that it can be extended to a generalization of the AGT
correspondence. The latter involves codimension two defects in six dimensions
that wrap the Riemann surface. We use a purely geometrical description of these
defects and find that the generalized AGT setup can be modeled in a pole region
using generalized conifolds. Furthermore, we argue that the ordinary conifold
clarifies several features of the derivation of the original AGT
correspondence.Comment: 27+2 pages, 3 figure
Defects in Jackiw-Teitelboim Quantum Gravity
We classify and study defects in 2d Jackiw-Teitelboim gravity. We show these
are holographically described by a deformation of the Schwarzian theory where
the reparametrization mode is integrated over different coadjoint orbits of the
Virasoro group. We show that the quantization of each coadjoint orbit is
connected to 2d Liouville CFT between branes with insertions of Verlinde loop
operators. We also propose an interpretation for the exceptional orbits. We use
this perspective to solve these deformations of the Schwarzian theory,
computing their partition function and correlators. In the process, we define
two geometric observables: the horizon area operator and the geodesic
length operator . We show this procedure is structurally related to
the deformation of the particle-on-a-group quantum mechanics by the addition of
a chemical potential. As an example, we solve the low-energy theory of complex
SYK with a U(1) symmetry and generalize to the non-abelian case.Comment: 66 pages, v4: clarifications added, typos corrected, matches
published versio
Renormalization of 3d quantum gravity from matrix models
Lorentzian simplicial quantum gravity is a non-perturbatively defined theory
of quantum gravity which predicts a positive cosmological constant. Since the
approach is based on a sum over space-time histories, it is perturbatively
non-renormalizable even in three dimensions. By mapping the three-dimensional
theory to a two-matrix model with ABAB interaction we show that both the
cosmological and the (perturbatively) non-renormalizable gravitational coupling
constant undergo additive renormalizations consistent with canonical
quantization.Comment: 14 pages, 3 figure
Analytical prediction of the interior noise for cylindrical models of aircraft fuselages for prescribed exterior noise fields. Phase 2: Models for sidewall trim, stiffened structures and cabin acoustics with floor partition
An airplane interior noise prediction model is developed to determine the important parameters associated with sound transmission into the interiors of airplanes, and to identify apropriate noise control methods. Models for stiffened structures, and cabin acoustics with floor partition are developed. Validation studies are undertaken using three test articles: a ring stringer stiffened cylinder, an unstiffened cylinder with floor partition, and ring stringer stiffened cylinder with floor partition and sidewall trim. The noise reductions of the three test articles are computed using the heoretical models and compared to measured values. A statistical analysis of the comparison data indicates that there is no bias in the predictions although a substantial random error exists so that a discrepancy of more than five or six dB can be expected for about one out of three predictions
Derivative F-Terms from Heterotic M-Theory Five-brane Instantons
We study non-perturbative effects due to a heterotic M-theory five-brane
wrapped on Calabi-Yau threefold. We show that such instantons contribute to
derivative F-terms described recently by Beasley and Witten rather than to the
superpotential.Comment: 10 pages, Latex, minor correction
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