Mean life time

As we can see, from the results in Fig. 2, a metastable hadronic star can have a mean-life time many orders of magnitude larger than the age of the universe Tuniv = (13.7 0.2) x 109 yr = (4.32 0.06) x 1017 s (Spergel et al. 2003). As the star accretes a small amount of mass (of the order of a few per cent of the mass of the sun), the consequential increase of the central pressure lead to a huge reduction of the nucleation time and, as a result, to a dramatic reduction of the HS mean-life time. 

To summarize, in the present scenario pure hadronic stars having a central pressure larger than the static transition pressure for the formation of the Q -phase are metastable to the decay (conversion) to a more compact stellar configuration in which deconfined quark matter is present (i. e., HyS or SS). These metastable HS have a mean-life time which is related to the nucleation time to form the first critical-size drop of deconfined matter in their interior (the actual mean-life time of the HS will depend on the mass accretion or on the spin-down rate which modifies the nucleation time via an explicit time dependence of the stellar central pressure). We define as critical mass Mcr of the metastable HS, the value of the gravitational mass for which the nucleation time is equal to one year Mcr = Miis t = lyr). Pure hadronic stars with Mh > Mcr are very unlikely to be observed. Mcr plays the role of an effective maximum mass for the hadronic branch of compact stars. While the Oppenheimer-Volkov maximum mass Mhs,max (Oppenheimer Volkov 1939) is determined by the overall stiffness of the EOS for hadronic matter, the value of Mcr will depend in addition on the bulk properties of the EOS for quark matter and on the properties at the interface between the confined and deconfined phases of matter (e.g., the surface tension a). 

The possibility to have metastable hadronic stars, together with the feasible existence of two distinct families of compact stars, demands an extension of the concept of maximum mass of a neutron star with respect to the classical one introduced by Oppenheimer Volkoff (1939). Since metastable HS with a short mean-life time are very unlikely to be observed, the extended concept of maximum mass must be introduced in view of the comparison with the values of the mass of compact stars deduced from direct astrophysical observation. Having in mind this operational definition, we call limiting mass of a compact star, and denote it as Mum, the physical quantity defined in the following way ... 

There are various specific features and predictions of the present model, which we briefly mention in the following. The second explosion (QDN) take place in a baryon-clean environment due to the previous SN explosion. Is is possible to have different time delays between the two events since the mean-life time of the metastable hadronic star depends on the value of the stellar central pressure. Thus the model of Berezhiani et al. (2003) is able to interpret a time delay of a few years (as observed in GRB990705 (Amati et al. 2000 Lazzati et al. 2001)), of a few months (as in the case of GRB020813 (Butler et al. 2003)), of a few days (as deduced for GRB011211 (Reeves et al. 2002)), or the nearly simultaneity of the two events (as in the case of SN2003dh and GRB030329 (Hjorth et al. 2003). 

The broadening of each line is due to the shortening of the mean life time of two molecules. 

The main difference between a glass and its liquid is not structural but kinetic and depends on a microscopic quantity called the structural relaxation time t. This time is the mean life time for the movement of a structural unit over a distance equivalent to its size. Such a structural unit may consist of several SiO units in the case of a silicate glass. The... 

Fig. 1. Rate constants, for the exchange of water molecules from the first coordination sphere of a given metal ion and the corresponding mean life times, tm = l//zex, of a particular water molecule measured by " 0 NMR. The gray bars indicate values determined by NMR isotope exchange technique (except Cr + ).

Mean life-times and electron spin relaxation times of R(fod)3 pinacolone adducts obtained from line-broadening data at 90 MHz. 

Mean life-times of 1 2 R(fod)3-hexamethyl phosphoramide adducts at 273.2 K. 

Mutual transition of a dormant form into a living form and vice versa must be spontaneous, without external intervention. The concentrations of living and dormant forms are usually connected by an equilibrium. During macromolecule propagation, the centre can oscillate between the active and inactive states generally, the two forms have different mean life times. 

Choosing for rAB of small molecules the probable value of 5 x 10-1°m, Ksr becomes about 0.3 mol dm3. Small molecules thus generate a collision pair at a rate characterized by a rate constant often reaching the value 109 to 1010 mol-1 dm3 s". For /c(u this gives a value of 1010 s-1. Thus the mean life time of the pair is about 10 10 s. Ion association si affected by strong electrostatic interactions. These forces are considered in association constant calculations they are usually included in the Boltzmann factor. 

The product p[M] is equivalent to the number of monomer molecules added to the active centre per unit time (s) and n is the mean life time of the centres. In radical polymerization, which are the most frequent representatives of the systems discussed, the relation... 

Shchori et al. (62,63) obtained the following expression for the reciprocal mean life-time ... 

Only compound XII was observed, which illustrates once more the anti-Markovnikov regioselectivity of the addition reaction. However, the divergent fate of intermediate XI must be governed by the relative rates of the two competing processes A and B (Scheme 40.2), so the radical mechanism cannot be dismissed on the basis of this experiment alone [Eq. (2) of Scheme 40.2]. It has been estimated that the rate of step B is of the order of k = 3 X 10 s" and the activation energy is only 13 kcal/mol. This means that if the mean life time of XI—before it is trapped by I—is shorter than 300 thousandths of a second, pathway B will be blocked and only compound XII will be produced. 

According to Groh , the mean life-time of the state emitting fluorescence is less than 8 x 10 sec, while Okabe and Noyes reported a value of 2.5 x 10 sec. Fluorescence is not quenched by oxygen however, its efficiency decreases, to some extent, with increasing temperature. The fluorescence is much less dependent on temperature than the phosphorescence. 

Table. Values of individual components Xi and their relative amplitudes Ai as well as mean life times for the non-exponential decays of CdSe quantum dots for various molar ratios x=Couinonc/CQD.

Under the assumption that molecular propagation in single-file systems proceeds by activated jumps of step length I with a mean life time r between succeeding jump attempts, and that jump attempts are only successful if they are directed to a vacant site, the mobility factor may be shown to be given by the relation [10]... 

It has been demonstrated by numerical simulations [9] that, with this definition, eq. 2 provides a reasonable order-of-magnitude estimate of the effectiveness factor also in the case of single-file diffusion. While in the case of ordinary diffnsion the intracrystalline mean life time may be easily correlated with the crystal size and the internal mobility [11], similar analytical expressions for single-file diffusion have not been established. The rule-of-thumb given in Ref. [10] on the basis of a few first numerical simulations turned out to be of rather limited validity in recent more refined considerations [12]. 

For an estimate of the correlation between t he intracrystalline mean life time and the system properties, the exchange curve between the (labelled) molecules of a single-file system and the (unlabelled) surroundings ( tracer exchange curve ) may be assumed to be determined by a single dimensionless parameter... 

Unless otherwise indicated, the constants are presumed to be elementary reactions at T = 25 °C and zero ionic strength. Mean life times for the second-order reactions, r, are given for the case in which one of the reactants has an initial concentration (assumed to be 10 m) that is in great excess of the other. 

The synthesis of 26A1 in secondary components of close binaries was found to deserve special attention. The reason is that for 26 Al, as it is /J-unstable with a mean life time of 1.03 106yr (ti/2 = 7.2 105 yr), not only the amount which is synthesised matters, but also the time of the synthesis. The 7-ray line emission from the decay of 26Al in the Galaxy is observed. However, we can only see the decay of 26 Al nuclei in the interstellar medium the decay inside stars is unobservable. Therefore, the 26Al which is observed... 

Prom Fig. 3.17 it can be observed that with increasing local current density jloml, the nominal current density jn differs more and more from jtocal. This is particularly striking for jiocai larger than / p, where 0 > pc. The predication jn = 0 is due to the fact that the dynamics of the infinite cluster was neglected (the mean life time of the gas film is considered to be infinite). 

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