38,957 research outputs found
hp-version time domain boundary elements for the wave equation on quasi-uniform meshes
Solutions to the wave equation in the exterior of a polyhedral domain or a
screen in exhibit singular behavior from the edges and corners.
We present quasi-optimal -explicit estimates for the approximation of the
Dirichlet and Neumann traces of these solutions for uniform time steps and
(globally) quasi-uniform meshes on the boundary. The results are applied to an
-version of the time domain boundary element method. Numerical examples
confirm the theoretical results for the Dirichlet problem both for screens and
polyhedral domains.Comment: 41 pages, 11 figure
The K\"ahler-Ricci flow on surfaces of positive Kodaira dimension
The existence of K\"ahler-Einstein metrics on a compact K\"ahler manifold has
been the subject of intensive study over the last few decades, following Yau's
solution to Calabi's conjecture. The Ricci flow, introduced by Richard Hamilton
has become one of the most powerful tools in geometric analysis.
We study the K\"ahler-Ricci flow on minimal surfaces of Kodaira dimension one
and show that the flow collapses and converges to a unique canonical metric on
its canonical model. Such a canonical is a generalized K\"ahler-Einstein
metric. Combining the results of Cao, Tsuji, Tian and Zhang, we give a metric
classification for K\"aher surfaces with a numerical effective canonical line
bundle by the K\"ahler-Ricci flow. In general, we propose a program of finding
canonical metrics on canonical models of projective varieties of positive
Kodaira dimension
Fast Isogeometric Boundary Element Method based on Independent Field Approximation
An isogeometric boundary element method for problems in elasticity is
presented, which is based on an independent approximation for the geometry,
traction and displacement field. This enables a flexible choice of refinement
strategies, permits an efficient evaluation of geometry related information, a
mixed collocation scheme which deals with discontinuous tractions along
non-smooth boundaries and a significant reduction of the right hand side of the
system of equations for common boundary conditions. All these benefits are
achieved without any loss of accuracy compared to conventional isogeometric
formulations. The system matrices are approximated by means of hierarchical
matrices to reduce the computational complexity for large scale analysis. For
the required geometrical bisection of the domain, a strategy for the evaluation
of bounding boxes containing the supports of NURBS basis functions is
presented. The versatility and accuracy of the proposed methodology is
demonstrated by convergence studies showing optimal rates and real world
examples in two and three dimensions.Comment: 32 pages, 27 figure
D-wave correlated Critical Bose Liquids in two dimensions
We develop a description of a new quantum liquid phase of interacting bosons
in 2d which possesses relative D-wave two-body correlations and which we call a
D-wave Bose Liquid (DBL). The DBL has no broken symmetries, supports gapless
boson excitations residing on "Bose surfaces" in momentum space, and exhibits
power law correlations with continuously variable exponents. While the DBL can
be constructed for bosons in the 2d continuum, the state only respects the
point group symmetries of the square lattice. On the lattice the DBL respects
all symmetries and does not require a particular filling. But lattice effects
allow a second distinct phase, a quasi-local variant which we call a D-wave
Local Bose Liquid (DLBL). Remarkably, the DLBL has short-range boson
correlations and hence no Bose surfaces, despite sharing gapless excitations
and other critical signatures with the DBL. Moreover, both phases are metals
with a resistance that vanishes as a power of the temperature. We establish
these results by constructing a class of many-particle wavefunctions for the
DBL, which are time reversal invariant analogs of Laughlin's quantum Hall
wavefunction for bosons at . A gauge theory formulation leads to a
simple mean field theory, and an N-flavor generalization enables incorporation
of gauge field fluctuations to deduce the properties of the DBL/DLBL; various
equal time correlation functions are in qualitative accord with the properties
inferred from the wavefunctions. We also identify a promising Hamiltonian which
might manifest the DBL or DLBL, and perform a variational study comparing to
other competing phases. We suggest how the DBL wavefunction can be generalized
to describe an itinerant non-Fermi liquid phase of electrons on the square
lattice with a no double occupancy constraint, a D-wave metal phase.Comment: 33 pages, 17 figure
Curvature effect on nuclear pasta: Is it helpful for gyroid appearance?
In supernova cores and neutron star crusts, nuclei are thought to deform to
rodlike and slablike shapes, which are often called nuclear pasta. We study the
equilibrium properties of the nuclear pasta by using a liquid drop model with
curvature corrections. It is confirmed that the curvature effect acts to lower
the transition densities between different shapes. We also examine the gyroid
structure, which was recently suggested as a different type of nuclear pasta by
analogy with the polymer systems. The gyroid structure investigated in this
paper is approximately formulated as an extension of the periodic minimal
surface whose mean curvature vanishes. In contrast to our expectations, we find
from the present approximate formulation that the curvature corrections act to
slightly disfavor the appearance of the gyroid structure. By comparing the
energy corrections in the gyroid phase and the hypothetical phases composed of
d-dimensional spheres, where d is a general dimensionality, we show that the
gyroid is unlikely to belong to a family of the generalized dimensional
spheres.Comment: 14 pages, 8 figure
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