16,293 research outputs found
Discrete dynamics of complex bodies with substructural dissipation: variational integrators and convergence
For the linearized setting of the dynamics of complex bodies we construct
variational integrators and prove their convergence by making use of BV
estimates on the rate fields. We allow for peculiar substructural inertia and
internal dissipation, all accounted for by a d'Alembert-Lagrange-type
principle.Comment: 23 pages, in print on Discrete and Continuous Dynamical Systems
The Generalized Hypergeometric Structure of the Ward Identities of CFT's in Momentum Space in
We review the emergence of hypergeometric structures (of Appell
functions) from the conformal Ward identities (CWIs) in conformal field
theories (CFTs) in dimensions . We illustrate the case of scalar 3- and
4-point functions. 3-point functions are associated to hypergeometric systems
with 4 independent solutions. For symmetric correlators they can be expressed
in terms of a single 3K integral - functions of quadratic ratios of momenta -
which is a parametric integral of three modified Bessel functions. In the
case of scalar 4-point functions, by requiring the correlator to be conformal
invariant in coordinate space as well as in some dual variables (i.e. dual
conformal invariant), its explicit expression is also given by a 3K integral,
or as a linear combination of Appell functions which are now quartic ratios of
momenta. Similar expressions have been obtained in the past in the computation
of an infinite class of planar ladder (Feynman) diagrams in perturbation
theory, which, however, do not share the same (dual conformal/conformal)
symmetry of our solutions. We then discuss some hypergeometric functions of 3
variables, which define 8 particular solutions of the CWIs and correspond to
Lauricella functions. They can also be combined in terms of 4K integral and
appear in an asymptotic description of the scalar 4-point function, in special
kinematical limits.Comment: 31 pages, 1 figure. Invited contribution to appear in: Axioms (MDPI)
"Geometric Analysis and Mathematical Physics" Ed. Sorin Dragomir, revised
final version, typos correcte
Conformal Ward Identities and the Coupling of QED and QCD to Gravity
We present a general study of 3-point functions of conformal field theory
(CFT) in momentum space, following a reconstruction method for tensor
correlators, based on the solution of the conformal Ward identities (CWIs),
introduced in recent works. We investigate and detail the structure of the CWIs
and their non-perturbative solutions, and compare them to perturbation theory,
taking QED and QCD as examples. Exact solutions of CFT's in the flat background
limit in momentum space are matched by the perturbative realizations in free
field theories, showing that the origin the conformal anomaly is related to
efffective scalar interactions, generated by the renormalization of the
longitudinal components of the corresponding operators.Comment: 5 pages. Proceedings of the Workshop QCD@work 2018, 25-28 June 2018,
Matera, Ital
Exact Correlators from Conformal Ward Identities in Momentum Space and the Perturbative Vertex
We present a general study of 3-point functions of conformal field theory in
momentum space, following a reconstruction method for tensor correlators, based
on the solution of the conformal Ward identities (CWI' s), introduced in recent
works by Bzowski, McFadden and Skenderis (BMS). We investigate and detail the
structure of the CWI's, their non-perturbative solutions and the transition to
momentum space, comparing them to perturbation theory by taking QED as an
example. We then proceed with an analysis of the correlator, presenting
independent and detailed re-derivations of the conformal equations in the
reconstruction method of BMS, originally formulated using a minimal tensor
basis in the transverse traceless sector. A careful comparison with a second
basis introduced in previous studies shows that this correlator is affected by
one anomaly pole in the graviton (T) line, induced by renormalization. The
result shows that the origin of the anomaly, in this correlator, should be
necessarily attributed to the exchange of a massless effective degree of
freedom. Our results are then exemplified in massless QED at one-loop in
-dimensions, expressed in terms of perturbative master integrals. An
independent analysis of the Fuchsian character of the solutions, which bypasses
the 3K integrals, is also presented. We show that the combination of field
theories at one-loop - with a specific field content of degenerate massless
scalar and fermions - is sufficient to generate the complete non-perturbative
solution, in agreement with a previous study in coordinate space. The result
shows that free conformal field theories, in specific dimensions, arrested at
one-loop, reproduce the general result for the . Analytical checks of this
correspondence are presented in and spacetime dimensions[..].Comment: 79 pages, 3 Figures. Final version, with changes in section 8.
Accepted for publication in Nuclear Physics
Motion by Curvature of Planar Networks
We consider the motion by curvature of a network of smooth curves with
multiple junctions in the plane, that is, the geometric gradient flow
associated to the length functional. Such a flow represents the evolution of a
two--dimensional multiphase system where the energy is simply the sum of the
lengths of the interfaces, in particular it is a possible model for the growth
of grain boundaries. Moreover, the motion of these networks of curves is the
simplest example of curvature flow for sets which are ``essentially'' non
regular. As a first step, in this paper we study in detail the case of three
curves in the plane concurring at a single triple junction and with the other
ends fixed. We show some results about the existence, uniqueness and, in
particular, the global regularity of the flow, following the line of analysis
carried on in the last years for the evolution by mean curvature of smooth
curves and hypersurfaces
On the properties of the Lambda value at risk: robustness, elicitability and consistency
Recently, financial industry and regulators have enhanced the debate on the
good properties of a risk measure. A fundamental issue is the evaluation of the
quality of a risk estimation. On the one hand, a backtesting procedure is
desirable for assessing the accuracy of such an estimation and this can be
naturally achieved by elicitable risk measures. For the same objective, an
alternative approach has been introduced by Davis (2016) through the so-called
consistency property. On the other hand, a risk estimation should be less
sensitive with respect to small changes in the available data set and exhibit
qualitative robustness. A new risk measure, the Lambda value at risk (Lambda
VaR), has been recently proposed by Frittelli et al. (2014), as a
generalization of VaR with the ability to discriminate the risk among P&L
distributions with different tail behaviour. In this article, we show that
Lambda VaR also satisfies the properties of robustness, elicitability and
consistency under some conditions
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