42,587 research outputs found
Monitoring a PGD solver for parametric power flow problems with goal-oriented error assessment
This is the peer reviewed version of the following article: [García-Blanco, R., Borzacchiello, D., Chinesta, F., and Diez, P. (2017) Monitoring a PGD solver for parametric power flow problems with goal-oriented error assessment. Int. J. Numer. Meth. Engng, 111: 529–552. doi: 10.1002/nme.5470], which has been published in final form at http://onlinelibrary.wiley.com/doi/10.1002/nme.5470/full. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.The parametric analysis of electric grids requires carrying out a large number of Power Flow computations. The different parameters describe loading conditions and grid properties. In this framework, the Proper Generalized Decomposition (PGD) provides a numerical solution explicitly accounting for the parametric dependence. Once the PGD solution is available, exploring the multidimensional parametric space is computationally inexpensive. The aim of this paper is to provide tools to monitor the error associated with this significant computational gain and to guarantee the quality of the PGD solution. In this case, the PGD algorithm consists in three nested loops that correspond to 1) iterating algebraic solver, 2) number of terms in the separable greedy expansion and 3) the alternated directions for each term. In the proposed approach, the three loops are controlled by stopping criteria based on residual goal-oriented error estimates. This allows one for using only the computational resources necessary to achieve the accuracy prescribed by the end- user. The paper discusses how to compute the goal-oriented error estimates. This requires linearizing the error equation and the Quantity of Interest to derive an efficient error representation based on an adjoint problem. The efficiency of the proposed approach is demonstrated on benchmark problems.Peer ReviewedPostprint (author's final draft
Higgs couplings beyond the Standard Model
We consider the Higgs boson decay processes and its production, and provide a
parameterisation tailored for testing models of new physics beyond the Standard
Model. We also compare our formalism to other existing parameterisations based
on scaling factors in front of the couplings and to effective Lagrangian
approaches. Different formalisms allow to best address different aspects of the
Higgs boson physics. The choice of a particular parameterisation depends on a
non-obvious balance of quantity and quality of the available experimental data,
envisaged purpose for the parameterisation and degree of model independence,
importance of the radiative corrections, scale at which new particles appear
explicitly in the physical spectrum. At present only simple parameterisations
with a limited number of fit parameters can be performed, but this situation
will improve with the forthcoming experimental LHC data. Detailed fits can only
be performed by the experimental collaborations at present, as the full
information on the different decay modes is not completely available in the
public domain. It is therefore important that different approaches are
considered and that the most detailed information is made available to allow
testing the different aspects of the Higgs boson physics and the possible hints
beyond the Standard Model.Comment: 22 pages, 5 figures, 5 tables. This version is an update including
the most recent Higgs data and new fits to two extra model
On structure constants with two spinning twist-two operators
I consider three-point functions of one protected and two unprotected
twist-two operators with spin in N=4 SYM at weak coupling. At one loop I
formulate an empiric conjecture for the dependence of the corresponding
structure constants on the spins of the operators. Using such an ansatz and
some input from explicit perturbative results, I fix completely various
infinite sets of one-loop structure constants of these three-point functions.
Finally, I determine the two-loop corrections to the structure constants for a
few fixed values of the spins of the operators.Comment: 21 page
Markov models for fMRI correlation structure: is brain functional connectivity small world, or decomposable into networks?
Correlations in the signal observed via functional Magnetic Resonance Imaging
(fMRI), are expected to reveal the interactions in the underlying neural
populations through hemodynamic response. In particular, they highlight
distributed set of mutually correlated regions that correspond to brain
networks related to different cognitive functions. Yet graph-theoretical
studies of neural connections give a different picture: that of a highly
integrated system with small-world properties: local clustering but with short
pathways across the complete structure. We examine the conditional independence
properties of the fMRI signal, i.e. its Markov structure, to find realistic
assumptions on the connectivity structure that are required to explain the
observed functional connectivity. In particular we seek a decomposition of the
Markov structure into segregated functional networks using decomposable graphs:
a set of strongly-connected and partially overlapping cliques. We introduce a
new method to efficiently extract such cliques on a large, strongly-connected
graph. We compare methods learning different graph structures from functional
connectivity by testing the goodness of fit of the model they learn on new
data. We find that summarizing the structure as strongly-connected networks can
give a good description only for very large and overlapping networks. These
results highlight that Markov models are good tools to identify the structure
of brain connectivity from fMRI signals, but for this purpose they must reflect
the small-world properties of the underlying neural systems
Electroweak Phase Transition and Baryogenesis in Composite Higgs Models
We present a comprehensive study of the electroweak phase transition in
composite Higgs models, where the Higgs arises from a new, strongly-coupled
sector which confines near the TeV scale. This work extends our study in Ref.
[1]. We describe the confinement phase transition in terms of the dilaton, the
pseudo-Nambu-Goldstone boson of broken conformal invariance of the composite
Higgs sector. From the analysis of the joint Higgs-dilaton potential we
conclude that in this scenario the electroweak phase transition can naturally
be first-order, allowing for electroweak baryogenesis. We then extensively
discuss possible options to generate a sufficient amount of CP violation -
another key ingredient of baryogenesis - from quark Yukawa couplings which vary
during the phase transition. For one such an option, with a varying charm quark
Yukawa coupling, we perform a full numerical analysis of tunnelling in the
Higgs-dilaton potential and determine regions of parameter space which allow
for successful baryogenesis. This scenario singles out the light dilaton region
while satisfying all experimental bounds. We discuss future tests. Our results
bring new opportunities and strong motivations for electroweak baryogenesis.Comment: 61 pages, 29 figures, 2 tables; v2: Analysis updated to account for
washout of the baryon asymmetry during reheating after the phase transition,
JHEP versio
Effective Field Theory for Few-Nucleon Systems
We review the effective field theories (EFTs) developed for few-nucleon
systems. These EFTs are controlled expansions in momenta, where certain
(leading-order) interactions are summed to all orders. At low energies, an EFT
with only contact interactions allows a detailed analysis of renormalization in
a non-perturbative context and uncovers novel asymptotic behavior. Manifestly
model-independent calculations can be carried out to high orders, leading to
high precision. At higher energies, an EFT that includes pion fields justifies
and extends the traditional framework of phenomenological potentials. The
correct treatment of QCD symmetries ensures a connection with lattice QCD.
Several tests and prospects of these EFTs are discussed.Comment: 55 pages, 18 figures, to appear in Ann. Rev. Nucl. Part. Sci. 52
(2002
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