Arnold diffusion in the dynamics of a 4-machine power system undergoing a large fault

We focus on the seemingly complicated dynamics of a four-machine power system which is undergoing a sudden fault. Adopting a Hamiltonian (energy) formulation, we consider the system as an interconnection of (one degree of freedom) subsystems. Under certain configuration (a star network) and parameter values we establish the presence of Arnold diffusion which entails periodic, almost periodic, and complicated nonperiodic dyanmics all simultaneously present; and erratic transfer of energies between the subsystems. In section 1 we introduce the transient stability problem in a mathematical setting and explain what our results mean in the power systems context. Section 2 provides insights into Arnold diffusion and summarizes its mathematical formulation as in [8], [1]. Section 3 gives conditions for which Arnold diffusion arises on certain energy levels of the swing equations. These conditions are verified analytically in the case when all but one subsystem (machine) undergo relatively small oscillations

The spread of the gluon k_t-distribution and the determination of the saturation scale at hadron colliders in resummed NLL BFKL

The transverse momentum distribution of soft hadrons and jets that accompany central hard-scattering production at hadron colliders is of great importance, since it has a direct bearing on the ability to separate new physics signals from Standard Model backgrounds. We compare the predictions for the gluonic k_t-distribution using two different approaches: resummed NLL BFKL and DGLAP evolution. We find that as long as the initial and final virtualities (k_t) along the emission chain are not too close to each other, the NLL resummed BFKL results do not differ significantly from those obtained using standard DGLAP evolution. The saturation momentum Q_s(x), calculated within the resummed BFKL approach, grows with 1/x even slower than in the leading-order DGLAP case.Comment: 24 pages, 8 figures, An improved, slightly more precise NLL resummation is used and the figures are updated accordingly. The conclusions are unchange

Extending QCD perturbation theory to higher energies

On the basis of the results of a new renormalisation group improved small-x resummation scheme, we argue that the range of validity of perturbative calculations is considerably extended in rapidity with respect to leading log expectations. We thus provide predictions for the energy dependence of the gluon Green function in its perturbative domain and for the resummed splitting function. As in previous analyses, high-energy exponents are reduced to phenomenologically acceptable values. Additionally, interesting preasymptotic effects are observed. In particular, the splitting function shows a shallow dip in the moderate small-x region, followed by the expected power increase.Comment: 12 pages, 4 figures. Expanded some discussions, clarified a figure, added some references. Version to appear in Phys. Lett.

Inclusive jet spectrum for small-radius jets

Following on our earlier work on leading-logarithmic (LLR) resummations for the properties of jets with a small radius, R, we here examine the phenomenological considerations for the inclusive jet spectrum. We discuss how to match the NLO predictions with small-R resummation. As part of the study we propose a new, physically-inspired prescription for fixed-order predictions and their uncertainties. We investigate the R-dependent part of the next-to-next-to-leading order (NNLO) corrections, which is found to be substantial, and comment on the implications for scale choices in inclusive jet calculations. We also examine hadronisation corrections, identifying potential limitations of earlier analytical work with regards to their $p_t$-dependence. Finally we assemble these different elements in order to compare matched (N)NLO+LLR predictions to data from ALICE and ATLAS, finding improved consistency for the R-dependence of the results relative to NLO predictions.Comment: 42 pages, 24 figures, additional material at http://microjets.hepforge.org/, updated to match published versio

Quark mass hierarchy in 3-3-1 models

We study the mass spectrum of the quark sector in an special type I-like model with gauge symmetry $SU(3)_c \otimes SU(3)_L \otimes U(1)_X$. By considering couplings with scalar triplets at large ($\sim TeV$) and small ($\sim GeV$) scales, we obtain specific zero-texture mass matrices for the quarks which predict three massless quarks ($u,d,s$) and three massive quarks ($c,b,t$) at the electroweak scale ($\sim$ GeV). Taking into account mixing couplings with three heavy quarks at large scales predicted by the model, the three massless quarks obtain masses at small order that depends on the inverse of the large scale. Thus, masses of the form $m_u \lesssim m_d < m_s \sim MeV$ and $m_{c,b,t} \sim GeV$ can be obtained naturally from the gauge structure of the model

Spectrum of D=6, N=4b Supergravity on AdS_3 x S^3

The complete spectrum of D=6, N=4b supergravity with n tensor multiplets compactified on AdS_3 x S^3 is determined. The D=6 theory obtained from the K_3 compactification of Type IIB string requires that n=21, but we let n be arbitrary. The superalgebra that underlies the symmetry of the resulting supergravity theory in AdS_3 coupled to matter is SU(1,1|2)_L x SU(1,1|2)_R. The theory also has an unbroken global SO(4)_R x SO(n) symmetry inherited from D=6. The spectrum of states arranges itself into a tower of spin-2 supermultiplets, a tower of spin-1, SO(n) singlet supermultiplets, a tower of spin-1 supermultiplets in the vector representation of SO(n) and a special spin-1/2 supermultiplet also in the vector representation of SO(n). The SU(2)_L x SU(2)_R Yang-Mills states reside in the second level of the spin-2 tower and the lowest level of the spin-1, SO(n) singlet tower and the associated field theory exhibits interesting properties.Comment: 37 pages, latex, 5 tables and 3 figures, typos corrected, a reference adde

Resummation

We review the work discussed and developed under the topic ``Resummation'' at Working Group 2 ``Multijet final states and energy flow'', of the HERA-LHC Workshop. We emphasise the role played by HERA observables in the development of resummation tools via, for instance, the discovery and resummation of non-global logarithms. We describe the event-shapes subsequently developed for hadron colliders and present resummed predictions for the same using the automated resummation program CAESAR. We also point to ongoing studies at HERA which can be of benefit for future measurements at hadron colliders such as the LHC, specifically dijet $E_t$ and angular spectra and the transverse momentum of the Breit current hemisphere.Comment: 15 pages, 6 figures. Submitted to the HERA-LHC workshop proceeding

Cascading and Local-Field Effects in Non-Linear Optics Revisited; A Quantum-Field Picture Based on Exchange of Photons

The semi-classical theory of radiation-matter coupling misses local-field effects that may alter the pulse time-ordering and cascading that leads to the generation of new signals. These are then introduced macroscopically by solving Maxwell's equations. This procedure is convenient and intuitive but ad hoc. We show that both effects emerge naturally by including coupling to quantum modes of the radiation field in the vacuum state to second order. This approach is systematic and suggests a more general class of corrections that only arise in a QED framework. In the semi-classical theory, which only includes classical field modes, the susceptibility of a collection of $N$ non-interacting molecules is additive and scales as $N$. Second-order coupling to a vacuum mode generates an effective retarded interaction that leads to cascading and local field effects both of which scale as $N^2$