Asymptotic branch

As it has been noted above, the synthesis temperature increase within the range of T = 333-348 K results to final characteristics enhancement of this process for PHE - conversion degree Q and reduced viscosity tired, in the first approximation characterizing polymer molecular weight MM. In Fig. 12 the dependences of on synthesis duration t are adduced for PHE at four different T. As it follows from these plots, at first tired sharp increase at t growth is observed and then values ti achieve asymptotic branch. Thus, one can suppose, that at some t values ti (or MM) magnitudes achieve their hmit, depending on T. 

The set of the quaternary critical points comprises two asymptotic branches which meet at the cusp point - it defines the pentary critical point. These asymptotic branches are boundaries between systems with simple three-phase separation and systems with a more complex behaviour (two different three-phase regions, one of which may be unstable, and four-phase separation). 

The stochastic mean-field [20] (SMF) method simultaneously resolves the following two major issues with NA MD. First, decoherence effects within the quantum subsystem that take place due to its interaction with an environment are included. Second, decoherence naturally leads to the asymptotic branching of NA trajectories. That is, the implementation of the decoherence effect in the SMF approach automatically resolves the branching problem. By extending the ordinary quantum-classical MF approximation, the SMF approach accounts for the quantum features of the environment in the Lindblad formulation. The Lindblad formulation is exact for a bath of harmonic oscillators and is an approximation for other types of solvents. While the quantum nature of the environment is treated by SMF within an approximation, its classical properties are included exactly by classical MD with a true Hamiltonian. 

Let us note in conclusion the strong dependence of on the structure of the microgels, characterised by the fractal dimension D (Figure 3.48). As follows from Figure 3.48, a sharp decay in is observed for D growth at D < 2 and the values on the asymptotic branch are attained at D > 2. As it is known [92], within the frameworks of irreversible aggregation models the following relationship is true ... 

The height of the peak and area of the peak ai e traditionally used for calibration techniques in analytical chemistry. Peak maximum can also be evaluated by the height of a triangle formed by the tangents at the inflection points and the asymptotes to the peak branches. We propose to apply the tangent method for the maximum estimation of the overlapped peaks. 

Sstig, a. branched, branchy knotted, gnarled. Astronom, m. astronomer. astroDomisch, a. astronomical, astrophysikalisch, a. astrophysical. asymmetrisch, a. asymmetric, asymmetrical, asymptotisch, a. asymptotic, asynchron, a. asynchronous, aszendent, a. (Mtn.) primary. 

Lup059 Lupanov, O. B. Asymptotic estimates of the number of graphs having n branches. Dokl. Akad. Nauk. SSSR 126 (1959) 498-500. 

Fig. 2.4. The asymptotic behaviour of the IR spectrum beyond the edge of the absorption branch for CO2 dissolved in different gases (o) xenon (O) argon ( ) nitrogen ( ) neon (V) helium. The points are experimental data, the curves were calculated in [105] according to the quantum J-diffusion model and two vertical broken lines determine the region in which Eq. (2.58) is valid.

Fig. 6.3. Quasi-static behaviour of relaxation times tgj (upper curves) and r ,i in the case of strong (1,2) and weak (3,4) collisions. The straight lines are the asymptotics of the curves after Q-branch collapse.

The dependences ML(xf) for various Pe are plotted in Fig. 10.4b. The shape of these curves significantly depends on the value of the Peclet number. When Pe < 4 the raising and the falling branches of (((Xf) contain points (Xf)c and (xf)L on the abscissa axis and form canopy-shaped curves with characteristic maximum depending on Pe. Contrary to that, if Pe > 4, the curves ML(Xf) are not continuous. When Xf is large, the upper and lower branches have one (Pe = 4) or two (Pe > 4) asymptotes. 

The hrst step in theoretical predictions of pathway branching are electronic structure ab initio) calculations to define at least the lowest Born-Oppenheimer electronic potential energy surface for a system. For a system of N atoms, the PES has (iN — 6) dimensions, and is denoted V Ri,R2, - , RiN-6)- At a minimum, the energy, geometry, and vibrational frequencies of stationary points (i.e., asymptotes, wells, and saddle points where dV/dRi = 0) of the potential surface must be calculated. For the statistical methods described in Section IV.B, information on other areas of the potential are generally not needed. However, it must be stressed that failure to locate relevant stationary points may lead to omission of valid pathways. For this reason, as wide a search as practicable must be made through configuration space to ensure that the PES is sufficiently complete. Furthermore, a search only of stationary points will not treat pathways that avoid transition states. 

Plotting the overpotential against the decadic logarithm of the absolute value of the current density yields the Tafel plot (see Fig. 5.3). Both branches of the resultant curve approach the asymptotes for r RT/F. When this condition is fulfilled, either the first or second exponential term on the right-hand side of Eq. (5.2.28) can be neglected. The electrode reaction then becomes irreversible (cf. page 257) and the polarization curve is given by the Tafel equation... 

Theoretical models for nucleosynthesis in asymptotic giant branch stars predict a large contribution to the cosmic nitrogen abundance from intermediate-mass stars [1], In particular, hot-bottom-burning in stars above a certain mass produces [C/N] —1 [2]. However, observations of C and N abundances in C-rich, metal-poor stars, usually using the CH and CN bands, show [C/N] values that vary between —0.5 and 1.5. (Fig. 1). If any of these stars have been polluted by intermediate mass AGB stars, then they should have lower [C/N] ratios. However, most of the CH stars with detailed abundances have [C/Fe] > 1.0, and it is more likely than stars mildly enhanced in C have been polluted by N-rich stars. 

Fig. la shows the abundance ratio [Ba/Fe] for this sample as a function of [C/Fe]. Thirty stars (77% of the sample) have [Ba/Fe] > +0.7, while the others have [Ba/Fe] < 0.0. There is a clear gap in the Ba abundances between the two groups, suggesting at least two different origins of the carbon excesses. Ba-enhanced stars The Ba-enhanced stars exhibit a correlation between the Ba and C abundance ratios (Fig. la). This fact suggests that carbon was enriched in the same site as Ba. The Ba excesses in these objects presumably originated from the s-process, rather than the r-process, because (1) nine stars in this group for which detailed abundance analysis is available clearly show abundance patterns associated with the s-process [2], and (2) there is no evidence of an r-process excess in the other 21 objects. Hence, the carbon enrichment in these objects most likely arises from Asymptotic Giant Branch (AGB) stars, which are also the source of the s-process elements. 

The most metal-rich stars in dwarf spheroidals (dSph) have been shown to have significantly lower even-Z abundance ratios than stars of similar metallicity in the Milky Way (MW). In addition, the most metal-rich dSph stars are dominated by an s-process abundance pattern in comparison to stars of similar metallicity in the MW. This has been interpreted as excessive contamination by Type la super-novae (SN) and asymptotic giant branch (AGB) stars ( Bonifacio et al. 2000, Shetrone et al. 2001, Smecker-Hane McWilliam 2002). By comparing these results to MW chemical evolution, Lanfranchi Matteucci (2003) conclude that the dSph galaxies have had a slower star formation rate than the MW (Lanfranchi Matteucci 2003). This slow star formation, when combined with an efficient galactic wind, allows the contribution of Type la SN and AGB stars to be incorporated into the ISM before the Type II SN can bring the metallicity up to MW thick disk metallicities. 

Abstract. We have performed the chemical analysis of extragalactic carbon stars from VLT/UVES spectra. The derived individual abundances of metals and s-elements as well as the well known distance of the selected stars in the Small Magellanic Cloud and the Sagittarius dwarf galaxies permit us to test current models of stellar evolution and nucleosynthesis during the Asymptotic Giant Branch phase in low metallicity environments. 

Abstract. We present the results of a spectroscopic analysis of bright stars in the Carina dSph galaxy. We collected low-resolution FORS2 VLT spectra of ss 200 stars. Our spectroscopic targets have been selected among the evolved Carina stars, in particular we selected low-mass, old Red Giant, Asymptotic, and Horizontal Branch stars, as well as intermediate-age stars of the Red Clump. We present preliminary estimates concerning the radial velocities of old and intermediate-age populations. 

Fig. 4.8. Colour-magnitude (HR) diagram of the globular cluster Messier 68 with [Fe/H] —2. In order of successive evolutionary stages, MS (sd) indicates the main sequence occupied by cool subdwarfs, with the position of the Sun shown for comparison, SGB indicates the subgiant branch, RGB the red giant branch, HB the horizontal branch including a gap in the region occupied by RR Lyrae pulsating variables and AGB the asymptotic giant branch. Adapted from McClure etal. (1987).

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