Fourier Eigenfunctions, Uncertainty Gabor Principle and Isoresolution Wavelets

Shape-invariant signals under Fourier transform are investigated leading to a class of eigenfunctions for the Fourier operator. The classical uncertainty Gabor-Heisenberg principle is revisited and the concept of isoresolution in joint time-frequency analysis is introduced. It is shown that any Fourier eigenfunction achieve isoresolution. It is shown that an isoresolution wavelet can be derived from each known wavelet family by a suitable scaling.Comment: 6 pages, XX Simp\'osio Bras. de Telecomunica\c{c}\~oes, Rio de Janeiro, Brazil, 2003. Fixed typo

AN EXPLICIT CONSTITUTIVE EQUATION FOR PLANE AND AXISYMMETRIC STEADY FLOWS WITH VISCOELASTIC EFFECTS

Non-Newtonian materials respond differently when submitted to shear or extension. A constitutive equation in which the stress is a function of both the rate of deformation and on the type of the flow is proposed and analyzed theoretically. It combines information obtained in shear, extension and rigid body motion in all regions of complex flow. The analysis has shown how to insert some elastic effects in a constitutive equation that depends only on the present time and position. One advantage of the model is that all the steady rheological functions in simple shear flow and in extensional flow are predicted exactly. Another important property that is included is the split of the extensional viscosity in two parts: one dissipative part that is related to the shear viscosity and an elastic part that is related to the first and second normal stress coefficients in shear. A discussion involving the dimensionless numbers that relate elastic and viscosity effects is also given

Cosmological scenarios from multiquintessence

In this work we derive and analyse cosmological scenarios coming from multi-component scalar field models. We consider a direct sum of a sine-Gordon with a Z2 model, and also a combination of those with a BNRT model. Moreover, we work with a modified version of the BNRT model, which breaks the Z2 x Z2 symmetry of the original BNRT potential, coupled with the sine-Gordon and with the standard Z2 models. We show that our approach can be straightforwardly elevated to $N$ fields. All the computations are made analytically and some parameters restriction is put forward in order to get in touch with complete and realistic cosmological scenarios

de Broglie-Proca and Bopp-Podolsky massive photon gases in cosmology

We investigate the influence of massive photons on the evolution of the expanding universe. Two particular models for generalized electrodynamics are considered, namely de Broglie-Proca and Bopp-Podolsky electrodynamics. We obtain the equation of state (EOS) $P=P(\varepsilon)$ for each case using dispersion relations derived from both theories. The EOS are inputted into the Friedmann equations of a homogeneous and isotropic space-time to determine the cosmic scale factor $a(t)$. It is shown that the photon non-null mass does not significantly alter the result $a\propto t^{1/2}$ valid for a massless photon gas; this is true either in de Broglie-Proca's case (where the photon mass $m$ is extremely small) or in Bopp-Podolsky theory (for which $m$ is extremely large).Comment: 8 pages, 2 figures; v2 matches the published versio