722,958 research outputs found
Lectures on walking technicolor, holography and gauge/gravity dualities
Dynamical electro-weak symmetry breaking is an appealing, strongly-coupled
alternative to the weakly-coupled models based on an elementary scalar field
developing a vacuum expectation value. In the first two sections of this set of
lectures, I summarize the arguments, based on low-energy phenomenology,
supporting walking technicolor as a realistic realization of this idea. This
pedagogical introduction to walking technicolor, and more generally to the
physics of extensions of the standard model, makes extensive use of effective
field theory arguments, symmetries and counting rules. The strongly-coupled
nature of the underlying interactions, and the peculiar quasi-conformal
behavior of the theory, require to use non-perturbative methods in order to
address many fundamental questions within this framework. The recent
development of gauge/gravity dualities provides an ideal set of such
non-perturbative instruments. The remaining two sections illustrate the
potential of these techniques with two technical examples, one within the
bottom-up phenomenological approach to holography in five-dimensions, the other
within a more systematic top-down construction derived from ten-dimensional
type-IIB supergravity.Comment: 67 pages, 16 figures
POD model order reduction with space-adapted snapshots for incompressible flows
We consider model order reduction based on proper orthogonal decomposition
(POD) for unsteady incompressible Navier-Stokes problems, assuming that the
snapshots are given by spatially adapted finite element solutions. We propose
two approaches of deriving stable POD-Galerkin reduced-order models for this
context. In the first approach, the pressure term and the continuity equation
are eliminated by imposing a weak incompressibility constraint with respect to
a pressure reference space. In the second approach, we derive an inf-sup stable
velocity-pressure reduced-order model by enriching the velocity reduced space
with supremizers computed on a velocity reference space. For problems with
inhomogeneous Dirichlet conditions, we show how suitable lifting functions can
be obtained from standard adaptive finite element computations. We provide a
numerical comparison of the considered methods for a regularized lid-driven
cavity problem
Exponential formulas for models of complex reflection groups
In this paper we find some exponential formulas for the Betti numbers of the
De Concini-Procesi minimal wonderful models Y_{G(r,p,n)} associated to the
complex reflection groups G(r,p,n). Our formulas are different from the ones
already known in the literature: they are obtained by a new combinatorial
encoding of the elements of a basis of the cohomology by means of set
partitions with weights and exponents.
We also point out that a similar combinatorial encoding can be used to
describe the faces of the real spherical wonderful models of type
A_{n-1}=G(1,1,n), B_n=G(2,1,n) and D_n=G(2,2,n). This provides exponential
formulas for the f-vectors of the associated nestohedra: the Stasheff's
associahedra (in this case closed formulas are well known) and the graph
associahedra of type D_n.Comment: with respect to v.1: misprint corrected in Example 3.
Unitarity of the Leptonic Mixing Matrix
We determine the elements of the leptonic mixing matrix, without assuming
unitarity, combining data from neutrino oscillation experiments and weak
decays. To that end, we first develop a formalism for studying neutrino
oscillations in vacuum and matter when the leptonic mixing matrix is not
unitary. To be conservative, only three light neutrino species are considered,
whose propagation is generically affected by non-unitary effects. Precision
improvements within future facilities are discussed as well.Comment: Standard Model radiative corrections to the invisible Z width
included. Some numerical results modified at the percent level. Updated with
latest bounds on the rare tau decay. Physical conculsions unchange
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