Search results for "Matematica"
showing 10 items of 1637 documents
Some analytical considerations on two-scale relations
1994
Scaling functions that generate a multiresolution analysis (MRA) satisfy, among other conditions, the so-called «two-scale relation» (TSR). In this paper we discuss a number of properties that follow from the TSR alone, independently of any MRA: position of zeros (mainly for continuous scaling functions), existence theorems (using fixed point and eigenvalue arguments) and orthogonality relation between integer translates. © 1994 Società Italiana di Fisica.
Applications of wavelets to quantum mechanics: A pedagogical example
1995
We discuss in many details two quantum mechanical models of planar electrons which are very much related to the Fractional Quantum Hall Effect. In particular, we discuss the localization properties of the trial ground states of the models starting from considerations on the numerical results on the energy. We conclude that wavelet theory can be conveniently used in the description of the system. Finally we suggest applications of our results to the Fractional Quantum Hall Effect.
A mathematical description of glitches in neutron stars
2017
In a pulsar, there are gaps and difficulties in our knowledge of glitches, mainly because of the absence of information about the physics of the matter of the star. This has motivated several authors to suggest dynamical models that interpret most of the astronomical data. Many predictions are based on the assumption that the inner part is analogous to the structure of matter of superfluids. Here, we illustrate a new mathematical model, partially inspired by the dynamics of superfluid helium. We obtain two evolution equations for the angular velocities (of the crust and of superfluid), which are supported by another evolution equation for the average vortex line length per unit volume. This…
Vortex density waves and high-frequency second sound in superfluid turbulence hydrodynamics
2010
In this paper we show that a recent hydrodynamical model of superfluid turbulence describes vortex density waves and their effects on the speed of high-frequency second sound. In this frequency regime, the vortex dynamics is not purely diffusive, as for low frequencies, but exhibits ondulatory features, whose influence on the second sound is here explored.
Energy of string loops and thermodynamics of dark energy
2011
We discuss the thermodynamic aspects of a simple model of cosmic string loops, whose energy is nonlinearly related to their lengths. We obtain in a direct way an equation of state having the form p=-(1+{alpha}){rho}/3, with {rho} the energy density and 1+{alpha} the exponent which relates the energy u{sub l} of a loop with its length l as u{sub l}{approx}l{sup 1+{alpha}}. In the linear situation ({alpha}=0) one has p=-{rho}/3, in the quadratic one ({alpha}=1) p=-2{rho}/3, and in the cubic case ({alpha}=2) p=-{rho}. For all values of {alpha} the entropy goes as S{approx}(2-{alpha})L{sup 3/2} (L being the string length density). The expression of S is useful to explore the behavior of such st…
Duality-invariant Einstein-Planck relation and the speed of light at very short wavelengths
2011
We propose a generalized Einstein-Planck relation for photons which is invariant under the change $\ensuremath{\lambda}/a{l}_{P}$ to $a{l}_{P}/\ensuremath{\lambda}$, $\ensuremath{\lambda}$ being the photon wavelength, ${l}_{P}$ Planck's length, and $a$ a numerical constant. This yields a wavelength-dependent speed of light $v(\ensuremath{\lambda})=c/(1+{a}^{2}({l}_{P}/\ensuremath{\lambda}{)}^{2})$, with $c$ the usual speed of light in vacuo, indicating that the speed of light should decrease for sufficiently short wavelengths. We discuss the conceptual differences with the previous proposals related to a possible decrease of the speed of light for very short wavelengths based on quantum flu…
Relations between the Hepp-Lieb and the Alli-Sewell Laser Models
2009
In this paper we show that the dissipative version of the laser model proposed by Alli and Sewell can be obtained by considering the stochastic limit of the (open system) hamiltonian introduced by Hepp and Lieb in their seminal work. We also prove that the Dicke-Haken-Lax hamiltonian produces, after the stochastic limit is considered, the generator of a semigroup with equations of motion very similar to those of Alli-Sewell, and coinciding with these under suitable conditions.
Duality relation between radiation thermodynamics and cosmic string loop thermodynamics
2011
We discuss thermodynamics of electromagnetic radiation, with p=(1/3){rho} and S{proportional_to}T{sup 3}V, and of cosmic string loops, with p=-(1/3){rho} and S{proportional_to}T{sup -3}V, where p stands for pressure, T temperature, {rho} energy density, S entropy, and V volume. We write the thermodynamic formalisms under a common framework that illustrates their formal relationship and allows us to go from one to the other through a smooth transformation. From a microscopic perspective, these relations arise from the energy relations u({lambda})=hc/{lambda} for the photons of electromagnetic radiation, and u(l)=(c{sup 4}/a{sup 2}G)l for cosmic string loops, a being a numerical (dimensionles…
Detector blockbased on arrays of 144 SiPMs and monolithic scintillators: A performane study
2015
[EN] We have developed a detector block composed by a monolithic LYSO scintillator coupled to a custom made 12 12 SiPMs array. The design is mainly focused to applications such as Positron Emission Tomography. The readout electronics is based on 3 identical and scalable Application Specific Integrated Circuits (ASIC). We have determined the main performance of the detector block namely spatial, energy, and time resolution but also the system capability to determine the photon depth of interaction, for different crystal surface treatments. Intrinsic detector spatial resolution values as good as 1.7 mm FWHM and energies of 15% for black painted crystals were measured. & 2014 Elsevier B.V. All…
Turbulent Superfluid Profiles and Vortex Density Waves in a Counterflow Channel
2012
In this paper we study the two-dimensional profiles of the superfluid component velocity and the quantized vortex-points density in a counterflow channel where the influence of the walls cannot be neglected. The numerical results obtained show the presence of vortex density waves in the channel, as shown in a recent paper by means of the one-fluid model.