The Strong Magnetic Field Decay and Evolution of Radio Pulsars on the P--P Diagram
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In this work we have analysed various data on radio pulsars and we have shown that magnetic field decay of a factor about 10-20 is necessary to explain their evolution, in particular to remove the discrepancy between the characteristic and the real ages. The character of the field decay is exponential with a characteristic time of about 3$\times10^6$ yr. Observational data on single X-ray pulsars which radiate due to cooling also support this result.Keywords:
Exponential decay
Exponential decay
Intensity
Optically stimulated luminescence
Radioactive decay
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We analyse the decay of a single exponential function and develop an algorithm to determine the exponent and the constant, C, (C exp(-kt)) associated with this function . In essence this approach involves `transforming' exponential functions into harmonic functions. This manoeuvre allows techniques that are used to analyse harmonic functions to be used to characterise decaying exponential functions.
Exponential decay
Harmonic
Exponent
Constant (computer programming)
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An isolated bound state coupled to a continuum shows an exponential decay of its survival probability. Rates of the exponential decay occurring due to the bound-continuum coupling can be recovered from discretized continuum (L2) calculations using a computational technique known as Stieltjes-Chebyshev moment theory or Stieltjes imaging. At the same time, some genuinely discrete level systems, e.g., Bixon-Jortner model, also show an exponential (or approximately exponential) decay of the initially populated level before the onset of quantum revivals. Here, we demonstrate numerically that Stieltjes imaging can be used for calculation of the rates of the exponential decay in such discrete level systems. We apply the Stieltjes imaging technique to the approximately exponential decay of inner-valence vacancies in trans-butadiene in order to show that the breakdown of the molecular orbital picture of ionization in the inner valence region can be physically interpreted as an energy-forbidden Coster-Kronig transition.
Exponential decay
Riemann–Stieltjes integral
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The possible occurrence in bulk relaxation of pure-exponential, near-exponential, and non-exponential decay of the total energy is examined in terms of the normal-mode and information-theoretic approaches. Experimental tests are suggested for the identification of pure-exponential decay caused by adherence to the 'sum rule', and of near-exponential decay. In the case of near-exponential decay (as opposed to pure-exponential decay), it is not possible to derive reliable state-to-state rate constants by invoking approximate adherence to the sum rule.
Exponential decay
Exponential sum
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Dynamical billiards
Exponential decay
Exponent
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Hyperbola
Dimensionless quantity
Exponential decay
Stretched exponential function
Constant (computer programming)
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Using a method developed by Foias and Temam [J. Funct. Anal. 87, 359 (1989)], exponential decay of the spatial Fourier power spectrum for solutions of the incompressible Navier–Stokes equations is established and explicit rigorous lower bounds on a small length scale defined by the exponential decay rate are obtained.
Exponential decay
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The present paper is mainly concerned with the blow-up phenomena and exponential decay of solution for a three-component Camassa-Holm equation. Comparing with the result of Hu, ect. in the paper[1], a new wave-breaking solution is obtained. The results of exponential decay of solution in our paper cover and extent the corresponding results in [12, 19, 22].
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Component (thermodynamics)
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Abstract The effect of non‐exponential and multi‐exponential decay or relaxation behavior on the performance of the direct exponential curve resolution algorithm (DECRA) is investigated through a series of numerical simulations. Three different combinations of decay or relaxation behavior were investigated through DECRA analysis of simulated pulse gradient spin echo (PGSE) NMR diffusion spectra that contained the combination of two individual components. The diffusion decay behavior of one component was described by a single‐exponential decay, while the second component was described by either (1) a multi‐exponential decay, (2) a decay behavior described by the empirical Kohlrausch–Williams–Watts (KWW) relation or (3) a multi‐exponential decay behavior correlated with variations in the NMR spectral line shape. The magnitudes and types of errors produced during the DECRA analysis of spectral data with deviations from a pure single‐exponential decay behavior are presented. It is demonstrated that the deviation from single‐exponential decay impacts the resulting calculated line shapes, the calculated relative concentrations and the quantitative estimation of the decay or relaxation time constants of both components present in the NMR spectra. Copyright © 2004 John Wiley & Sons, Ltd.
Exponential decay
Line (geometry)
Exponential sum
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Exponential decay, bi-exponential decay, and related decay processes are common in the physical world. Stretched exponential time dependence of the form e−(kt)c has been observed in connection with the discharge of electrophotographic photoconductors, luminescence in porous silicon, dielectric relaxation in glassy and polymeric materials, as well as in other systems. Exponential decay, the stretched exponential, the Kohlrausch-Williams-Watts function KWW, and the Buettner function satisfy a differential equation that depends on the exponent c and the entropy of the system. The form of the decay function determined by the exponent c can be shown to be consistent with cooperative events occurring during relaxation and can be related to the chemical potential of the system. This indicates that probabilistic, cooperative events may play a role in the dynamics of stretched exponential decay processes in addition to distributions of relaxation times and relaxation paths.
Exponential decay
Stretched exponential function
Exponent
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