Search results for "derivati"
showing 10 items of 1360 documents
QUANTIZATION CONDITION FOR HIGHLY EXCITED STATES
1999
We develop a quantization condition for the excited states of simple quantum-mechanical models. The approach combines perturbation theory for the oscillatory part of the eigenfunction with a rational approximation to the logarithmic derivative of the nodeless part of it. We choose one-dimensional anharmonic oscillators as illustrative examples.
Zu notwendigen Resonanzkriterien im station�ren Einkanal-Fall
1975
First will be exhibited, for the stationary case, a connection between the probability, to find a particle in the region of interaction, and the derivative of the scattering phase shift for the momentum. From the idea, that in stationary scattering a resonance is linked with an appreciable increase of this probability, one obtains new and quantitative criteria for the behavior ofδl(k). For instance, the nonresonant behavior can be characterised by the condition 2kdδl(k)/dk<1. The maximum of probability for the particle to be in the region of interaction, is considered in accordance with the criterium of maximal change of the phase shift, as a function ofk. This characterises the location of…
Fractional-order theory of heat transport in rigid bodies
2014
Abstract The non-local model of heat transfer, used to describe the deviations of the temperature field from the well-known prediction of Fourier/Cattaneo models experienced in complex media, is framed in the context of fractional-order calculus. It has been assumed (Borino et al., 2011 [53] , Mongiovi and Zingales, 2013 [54] ) that thermal energy transport is due to two phenomena: ( i ) A short-range heat flux ruled by a local transport equation; ( ii ) A long-range thermal energy transfer proportional to a distance-decaying function, to the relative temperature and to the product of the interacting masses. The distance-decaying function is assumed in the functional class of the power-law …
Timing of the 2008 outburst of SAX J1808.4–3658 with XMM-Newton: a stable orbital-period derivative over ten years
2009
We report on a timing analysis performed on a 62-ks long XMM-Newton observation of the accreting millisecond pulsar SAX J1808.4-3658 during the latest X-ray outburst that started on September 21, 2008. By connecting the time of arrivals of the pulses observed during the XMM observation, we derived the best-fit orbital solution and a best-fit value of the spin period for the 2008 outburst. Comparing this new set of orbital parameters and, in particular, the value of the time of ascending-node passage with the orbital parameters derived for the previous four X-ray outbursts of SAX J1808.4-3658 observed by the PCA on board RXTE, we find an updated value of the orbital period derivative, which …
Revised orbital parameters of the accreting millisecond pulsar SAX J1808.4-3658
2005
We present temporal analysis of the three outbursts of the X-ray millisecond pulsar SAX J1808.4-3658 that occurred in 1998, 2000 and 2002. With a technique that uses the chi^2 obtained with an epoch folding search to discriminate between different possible orbital solutions, we find an unique solution valid over the whole five years period for which high temporal resolution data are available. We revise the estimate of the orbital period, P_orb =7249.1569(1) s and reduce the corresponding error by one order of magnitude with respect to that previously reported. Moreover we report the first constraint on the orbital period derivative, -6.6 x 10^-12 < Pdot < +0.8 x 10^-12 s/s. These val…
On the convexity of Relativistic Hydrodynamics
2013
The relativistic hydrodynamic system of equations for a perfect fluid obeying a causal equation of state is hyperbolic (Anile 1989 {\it Relativistic Fluids and Magneto-Fluids} (Cambridge: Cambridge University Press)). In this report, we derive the conditions for this system to be convex in terms of the fundamental derivative of the equation of state (Menikoff and Plohr 1989 {\it Rev. Mod. Phys.} {\bf 61} 75). The classical limit is recovered.
L-Rigidity in Newtonian approximation
2008
Newtonian limit of L-Rigidity is obtained. In this formalism, L-Rigidity is reduced to steady Newtonian rigid motions in a Newtonian frame of reference in which the observer is at rest.
Non-isospectral Hamiltonians, intertwining operators and hidden hermiticity
2011
We have recently proposed a strategy to produce, starting from a given hamiltonian $h_1$ and a certain operator $x$ for which $[h_1,xx^\dagger]=0$ and $x^\dagger x$ is invertible, a second hamiltonian $h_2$ with the same eigenvalues as $h_1$ and whose eigenvectors are related to those of $h_1$ by $x^\dagger$. Here we extend this procedure to build up a second hamiltonian, whose eigenvalues are different from those of $h_1$, and whose eigenvectors are still related as before. This new procedure is also extended to crypto-hermitian hamiltonians.
Innovative modeling of Tuned Liquid Column Damper motion
2015
Abstract In this paper a new model for the liquid motion within a Tuned Liquid Column Damper (TLCD) device is developed, based on the mathematical tool of fractional calculus. Although the increasing use of these devices for structural vibration control, it is shown that existing model does not always lead to accurate prediction of the liquid motion. A better model is then needed for accurate simulation of the behavior of TLCD systems. As regards, it has been demonstrated how correctly including the first linear liquid sloshing mode, through the equivalent mechanical analogy well established in literature, produces numerical results that highly match the corresponding experimental ones. Sin…
Fractional-Order Theory of Thermoelasticity. II: Quasi-Static Behavior of Bars
2018
This work aims to shed light on the thermally-anomalous coupled behavior of slightly deformable bodies, in which the strain is additively decomposed in an elastic contribution and in a thermal part. The macroscopic heat flux turns out to depend upon the time history of the corresponding temperature gradient, and this is the result of a multiscale rheological model developed in Part I of the present study, thereby resembling a long-tail memory behavior governed by a Caputo's fractional operator. The macroscopic constitutive equation between the heat flux and the time history of the temperature gradient does involve a power law kernel, resulting in the anomaly mentioned previously. The interp…