A general formula for decay rates of nonlinear dissipative systems

2004 ◽  
Vol 338 (1) ◽  
pp. 35-40 ◽  
Author(s):  
Fatiha Alabau-Boussouira
1985 ◽  
Vol 32 (5) ◽  
pp. 3348-3350 ◽  
Author(s):  
Hermann Grabert ◽  
Peter Olschowski ◽  
Ulrich Weiss

1987 ◽  
Vol 36 (4) ◽  
pp. 1931-1951 ◽  
Author(s):  
Hermann Grabert ◽  
Peter Olschowski ◽  
Ulrich Weiss

2019 ◽  
Vol 25 (1) ◽  
pp. 97-110
Author(s):  
Muhammad I. Mustafa ◽  
Mohammad Kafini

Abstract In this paper, we consider a nonlinear quasilinear system of two coupled viscoelastic equations and investigate the asymptotic behavior of this system. We establish an explicit and general formula for the energy decay rates. Our result allows a wider class of relaxation functions, which improves earlier results existing in the literature.


1999 ◽  
Vol 4 ◽  
pp. 31-86 ◽  
Author(s):  
R. Katilius ◽  
A. Matulionis ◽  
R. Raguotis ◽  
I. Matulionienė

The goal of the paper is to overview contemporary theoretical and experimental research of the microwave electric noise and fluctuations of hot carriers in semiconductors, revealing sensitivity of the noise spectra to non-linearity in the applied electric field strength and, especially, in the carrier density. During the last years, investigation of electronic noise and electron diffusion phenomena in doped semiconductors was in a rapid progress. By combining analytic and Monte Carlo methods as well as the available experimental results on noise, it became possible to obtain the electron diffusion coefficients in the range of electric fields where inter-electron collisions are important and Price’s relation is not necessarily valid. Correspondingly, a special attention to the role of inter-electron collisions and of the non-linearity in the carrier density while shaping electric noise and diffusion phenomena in the non-equilibrium states will be paid. The basic and up-to-date information will be presented on methods and advances in this contemporary field - the field in which methods of non-linear analytic and computational analysis are indispensable while seeking coherent understanding and interpretation of experimental results.


2013 ◽  
Vol 12 (10) ◽  
pp. 719-726
Author(s):  
R. Ayadi ◽  
Mohamed Boujelbene ◽  
T. Mhiri

The present paper is interested in the study of compounds from the apatite family with the general formula Ca10 (PO4)6A2. It particularly brings to light the exploitation of the distinctive stereochemistries of two Ca positions in apatite. In fact, Gd-Bearing oxyapatiteCa8 Gd2 (PO4)6O2 has been synthesized by solid state reaction and characterized by X-ray powder diffraction. The site occupancies of substituents is0.3333 in Gd and 0.3333 for Ca in the Ca(1) position and 0. 5 for Gd in the Ca (2) position.  Besides, the observed frequencies in the Raman and infrared spectra were explained and discussed on the basis of unit-cell group analyses.


2002 ◽  
Vol 2 (3) ◽  
pp. 131-138 ◽  
Author(s):  
D.L. Craig ◽  
H.J. Fallowfield ◽  
N.J. Cromar

A laboratory based microcosm study utilising intact non-sterile sediment cores was undertaken to determine the survival of the faecal indicator organisms Escherichia coli, Enterococcus faecium and somatic coliphage in both recreational coastal water and sediment. Overlying water was inoculated with the test organisms and incubated at 10°C, 20°C or 30°C. E. coli, enterococcus and coliphage were enumerated from the water column and sediment by the membrane filtration method, Enterolert (IDEXX Laboratories) and the double-agar overlay methods respectively on days 0, 1, 2, 7, 14 and 28 following inoculation. It was demonstrated that for all organisms, greater decay (k; d-1) occurred in the water column compared to sediment. Sediment characteristics were found to influence decay, with lowest decay rates observed in sediment consisting of high organic carbon content and small particle size. Decay of E. coli was significantly greater in both the water column and sediment compared with enterococcus and coliphage under all conditions. Decay of enterococcus was found to closely resemble that of coliphage decay. Survival of all organisms was inversely related to temperature, with greatest decay at 30°C. However, increased temperature had a less significant impact on survival of enterococcus and coliphage compared with E. coli. The importance of this study for estimating risk from recreational exposure is great if some pathogenic microorganisms behave similarly to the organisms tested in this study. In particular if survival rates of pathogens are similar to enterococcus and coliphage, then their ability to accumulate in coastal sediment may lead to an increased risk of exposure if these organisms are resuspended into the water column due to natural turbulence or human recreational activity.


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