Condition number estimates for combined potential integral operators in acoustics and their boundary element discretisation

We consider the classical coupled, combined-field integral equation formulations for time-harmonic acoustic scattering by a sound soft bounded obstacle. In recent work, we have proved lower and upper bounds on the $L^2$ condition numbers for these formulations, and also on the norms of the classical acoustic single- and double-layer potential operators. These bounds to some extent make explicit the dependence of condition numbers on the wave number $k$, the geometry of the scatterer, and the coupling parameter. For example, with the usual choice of coupling parameter they show that, while the condition number grows like $k^{1/3}$ as $k\to\infty$, when the scatterer is a circle or sphere, it can grow as fast as $k^{7/5}$ for a class of `trapping' obstacles. In this paper we prove further bounds, sharpening and extending our previous results. In particular we show that there exist trapping obstacles for which the condition numbers grow as fast as $\exp(\gamma k)$, for some $\gamma>0$, as $k\to\infty$ through some sequence. This result depends on exponential localisation bounds on Laplace eigenfunctions in an ellipse that we prove in the appendix. We also clarify the correct choice of coupling parameter in 2D for low $k$. In the second part of the paper we focus on the boundary element discretisation of these operators. We discuss the extent to which the bounds on the continuous operators are also satisfied by their discrete counterparts and, via numerical experiments, we provide supporting evidence for some of the theoretical results, both quantitative and asymptotic, indicating further which of the upper and lower bounds may be sharper.

Structure and magnetic properties of mono- and bi-dispersed ferrofluids as revealed by simulations

Using a Langevin molecular dynamics simulation, we show that the magnetic properties of a mono- and bi-dispersed ferrofluid system depend on the volume fraction and the dipolar coupling parameter. For the bi-dispersed system, most of the chains are formed by the large particles, but the aggregation behavior of the large particles is hindered by the presence of the small particles, which are predominantly attached to the end of the particle chain. To further elucidate the microscopic fluid structure, anisotropic structure factors are calculated.

Stability of breathers in simple mechanical models for DNA

This work studies through the Floquet theory the stability of breathers generated by the anti-continuous limit. We used the Peyrard-Bishop model for DNA and two kinds of nonlinear potential: the Morse potential and a potential with a hump. The comparison of their stability was done in function of the coupling parameter. We also investigate the dynamic behaviour of the system in stable and unstable regions. Qualitatively, the dynamic of mobile breathers resembles DNA.

Search for resonant second generation slepton production at the Fermilab Tevatron

We present a search for supersymmetry in the R-parity violating resonant production and decay of smuons and muon sneutrinos in the channels mu ->chi(0)(1)mu, mu ->chi(0)(2,3,4)mu, and nu(mu)->chi(+/-)(1,2)mu. We analyzed 0.38 fb(-1) of integrated luminosity collected between April 2002 and August 2004 with the D0 detector at the Fermilab Tevatron Collider. The observed number of events is in agreement with the standard model expectation, and we calculate 95% C.L. limits on the slepton production cross section times branching fraction to gaugino plus muon, as a function of slepton and gaugino masses. In the framework of minimal supergravity, we set limits on the coupling parameter lambda(')(211), extending significantly previous results obtained in Run I of the Tevatron and at the CERN LEP collider.

A path integral approach to the full Dicke model with dipole-dipole interaction

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Search for narrow resonances in dilepton mass spectra in pp collisions at root s=7 TeV CMS Collaboration

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Analytical calculation of the transition to complete phase synchronization in coupled oscillators

Here we present a system of coupled phase oscillators with nearest neighbors coupling, which we study for different boundary conditions. We concentrate at the transition to the total synchronization. We are able to develop exact solutions for the value of the coupling parameter when the system becomes completely synchronized, for the case of periodic boundary conditions as well as for a chain with fixed ends. We compare the results with those calculated numerically.

Search for Signatures of Extra Dimensions in the Diphoton Mass Spectrum at the Large Hadron Collider

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Search for resonances in the dilepton mass distribution in pp collisions at root s=7 TeV

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

VARIATIONAL SPIKED OSCILLATOR

A variational analysis of the spiked harmonic oscillator Hamiltonian -d2/dr2 + r2 + lambda/r5/2, lambda > 0, is reported. A trial function automatically satisfying both the Dirichlet boundary condition at the origin and the boundary condition at infinity is introduced. The results are excellent for a very large range of values of the coupling parameter lambda, suggesting that the present variational function is appropriate for the treatment of the spiked oscillator in all its regimes (strong, moderate, and weak interactions).

GROUND-STATE-ENERGY OF SINGULAR POTENTIALS

It is shown that for singular potentials of the form lambda/r(alpha),the asymptotic form of the wave function both at r --> infinity and r --> 0 plays an important role. Using a wave function having the correct asymptotic behavior for the potential lambda/r(4), it is, shown that it gives the exact ground-state energy for this potential when lambda --> 0, as given earlier by Harrell [Ann. Phys. (NY) 105, 379 (1977)]. For other values of the coupling parameter X, a trial basis;set of wave functions which also satisfy the correct boundary conditions at r --> infinity and r --> 0 are used to find the ground-state energy of the singular potential lambda/r(4) It is shown that the obtained eigenvalues are in excellent agreement with their exact ones for a very large range of lambda values.

Nonmodal energetics of resistive drift waves

The modal and nonmodal linear properties of the Hasegawa-Wakatani system are examined. This linear model for plasma drift waves is nonnormal in the sense of not having a complete set of orthogonal eigenvectors. A consequence of nonnormality is that finite-time nonmodal growth rates can be larger than modal growth rates. In this system, the nonmodal time-dependent behavior depends strongly on the adiabatic parameter and the time scale of interest. For small values of the adiabatic parameter and short time scales, the nonmodal growth rates, wave number, and phase shifts (between the density and potential fluctuations) are time dependent and differ from those obtained by normal mode analysis. On a given time scale, when the adiabatic parameter is less than a critical value, the drift waves are dominated by nonmodal effects while for values of the adiabatic parameter greater than the critical value, the behavior is that given by normal mode analysis. The critical adiabatic parameter decreases with time and modal behavior eventually dominates. The nonmodal linear properties of the Hasegawa-Wakatani system may help to explain features of the full system previously attributed to nonlinearity.

Search for exotic resonances decaying into WZ/ZZ in pp collisions at √s=7 TeV

A search for new exotic particles decaying to the VZ final state is performed, where V is either a W or a Z boson decaying into two overlapping jets and the Z decays into a pair of electrons, muons or neutrinos. The analysis uses a data sample of pp collisions corresponding to an integrated luminosity of 5 fb-1 collected by the CMS experiment at the LHC at √s=7 TeV in 2011. No significant excess is observed in the mass distribution of the VZ candidates compared with the background expectation from standard model processes. Model-dependent upper limits at the 95% confidence level are set on the product of the cross section times the branching fraction of hypothetical particles decaying to the VZ final state as a function of mass. Sequential standard model W′ bosons with masses between 700 and 940 GeV are excluded. In the Randall-Sundrum model for graviton resonances with a coupling parameter of 0.05, masses between 750 and 880 GeV are also excluded. © 2013 CERN for the benefit of the CMS collaboration.

Search for exotic resonances in diboson final states with the CMS detector at the LHC

The results of searches for new resonances decaying to a pair of massive vector bosons (WW, WZ, ZZ) are presented. All searches are performed using 5.0 fb-1 of proton-proton collisions, at TeV of center of mass energy, collected by the Compact Muon Solenoid detector at the Large Hadron Collider. No significant excess compared to the standard model background expectation is observed, and upper limits at 95% confidence level are set on the production cross section times the branching fraction of hypothetical particles decaying to a pair of vector bosons. The results are interpreted in the context of several benchmark models, such as the Randall-Sundrum gravitons, the Sequential Standard Model W′, and Technicolor. Graviton resonances in the Randall-Sundrum model with masses smaller than 940 GeV/c2, for coupling parameter k/MPl = 0.05 are excluded. Bulk (ADPS) Randall-Sundrum gravitons with masses smaller than 610 GeV/c2 are excluded, for k/MPl = 0.05. Sequential Standard Model W′ with masses smaller than 1143 GeV/c2 are excluded, as well as ρTC in the 167-687 GeV/c2 mass range, in Low Scale Technicolor models with M(πTC) = 3/4 M(ρTC) - 25 GeV/c2. © 2013 IOP Publishing Ltd.

Conseqüências fenomenológicas de um propagador de gluons com massa dinâmica

Pós-graduação em Física - IFT