40,286 research outputs found
Theoretical status of epsilon'/epsilon
The Standard Model prediction for epsilon'/epsilon is updated, taking into
account the most recent theoretical developments. The final numerical value,
epsilon'/\epsilon = (17\pm 6) x 10^{-4}, is in good agreement with present
measurements.Comment: 6 pages. Invited talk at the 4th Int. Conference on Hyperons, Charm
and Beauty Hadrons (Valencia, June 2000
Numerical methods for multiscale inverse problems
We consider the inverse problem of determining the highly oscillatory
coefficient in partial differential equations of the form
from given
measurements of the solutions. Here, indicates the smallest
characteristic wavelength in the problem (). In addition to the
general difficulty of finding an inverse, the oscillatory nature of the forward
problem creates an additional challenge of multiscale modeling, which is hard
even for forward computations. The inverse problem in its full generality is
typically ill-posed and one common approach is to replace the original problem
with an effective parameter estimation problem. We will here include microscale
features directly in the inverse problem and avoid ill-posedness by assuming
that the microscale can be accurately represented by a low-dimensional
parametrization. The basis for our inversion will be a coupling of the
parametrization to analytic homogenization or a coupling to efficient
multiscale numerical methods when analytic homogenization is not available. We
will analyze the reduced problem, , by proving uniqueness of the inverse
in certain problem classes and by numerical examples and also include numerical
model examples for medical imaging, , and exploration seismology,
Bootstrapping the Minimal 3D SCFT
We study the conformal bootstrap constraints for 3D conformal field theories
with a or parity symmetry, assuming a single relevant scalar
operator that is invariant under the symmetry. When there is
additionally a single relevant odd scalar , we map out the allowed
space of dimensions and three-point couplings of such "Ising-like" CFTs. If we
allow a second relevant odd scalar , we identify a feature in the
allowed space compatible with 3D superconformal symmetry and
conjecture that it corresponds to the minimal supersymmetric
extension of the Ising CFT. This model has appeared in previous numerical
bootstrap studies, as well as in proposals for emergent supersymmetry on the
boundaries of topological phases of matter. Adding further constraints from 3D
superconformal symmetry, we isolate this theory and use the
numerical bootstrap to compute the leading scaling dimensions and three-point couplings
and
. We additionally place bounds on
the central charge and use the extremal functional method to estimate the
dimensions of the next several operators in the spectrum. Based on our results
we observe the possible exact relation
.Comment: 16 pages, 6 figures; V2: references adde
Test of renormalization predictions for universal finite-size scaling functions
We calculate universal finite-size scaling functions for systems with an
n-component order parameter and algebraically decaying interactions. Just as
previously has been found for short-range interactions, this leads to a
singular epsilon-expansion, where epsilon is the distance to the upper critical
dimension. Subsequently, we check the results by numerical simulations of spin
models in the same universality class. Our systems offer the essential
advantage that epsilon can be varied continuously, allowing an accurate
examination of the region where epsilon is small. The numerical calculations
turn out to be in striking disagreement with the predicted singularity.Comment: 6 pages, including 3 EPS figures. To appear in Phys. Rev. E. Also
available as PDF file at
http://www.cond-mat.physik.uni-mainz.de/~luijten/erikpubs.htm
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