Lues of T0 , k and . The numerical final results are in fantasticLues of

Lues of T0 , k and . The numerical final results are in fantastic
Lues of T0 , k and . The numerical benefits are in fantastic agreement together with the analytical result obtained in Equation (171) at higher T0 and k. Modest discrepancies may be noticed within the vicinity with the boundary (for 1) and at T0 0.five -1 . The agreement involving the numerical benefits and also the analytical expression is maintained also at k = two. Panels (c) and (d) show – 2 and 2 ( – ;an ) as functions with the temperature, confirming the validity of each of the terms in Equation (171). We now discuss the properties of 1 , presented graphically in Figure eight. Panels (a ) show profiles of 1 inside the equatorial plane. In panel (a), where massless quanta k = 0 are considered, a peculiarity of 1 is revealed, namely that it can be coordinate-independent when = 0. That is as a result of the fact that the cos6 r term inside the denominator of the prefactor in Equation (168) is cancelled by the coordinate-dependent part of three = cos6 r/ sinh6 ( j 0 /2 ) j(the hypergeometric function reduces to unity when k = 0). At finite , we see that 1 becomes point-dependent, much more strikingly for smaller sized temperature (no point dependence could be distinguished around the scale from the plot when T0 = two). The worth of -1 in the originSymmetry 2021, 13,36 ofexhibits a monotonic increase with . Panel (b) presents benefits for = 0 and numerous values of k, displaying that -1 becomes point-dependent when k 0, decreasing in the vicinity from the boundary as k is increased. Panel (c) shows outcomes at higher temperature ( T0 = 2) for vanishing and big (k = 3) masses. Within the vanishing mass case (also for smaller masses), 1 is quite nicely approximated by its high temperature limit in Equation (171). Ultimately, panel (d) shows -1 computed at the Alpha-1 Antitrypsin 1-6 Proteins Biological Activity origin for different values of k and as a function on the temperature T0 . It could be seen that the significant temperature limit 2/27 two is SARS-CoV-2 S1 Protein NTD Proteins site accomplished in all situations as T0 is improved.1 T0 = 0.five, = 0 = 0.9 =1 T0 = two, = 0 = 0.9 =0.(b)0.(= /2) T0 = 2)0.(0.– two 0.0.0.(k (= 0) = /2) 0.two 0.4 0.six 0.(a)k = 0, = 0 = 0.9 =1 k = two, = 0 = 0.9 =1 0 0.two 0.4 0.six 0.80.001 02r/101 k=0 2/3 2/ 3 Ean0.2r/10– ;an )0.k=0 1/ 3 2/3 1 2/ 3 -;an-10-10–0.10-(c)(= /2)(two (10-( (d)= /2)(= 1)-0.004 0.10-6 0.= 1)0.TTFigure 7. (a,b) Profiles from the circular heat conductivity – in the equatorial plane ( = /2). (a) Massless (k = 0) quanta at low (T0 = 0.five -1 ) and high (T0 = 2 -1 ) temperatures, for many values of . (b) High-temperature benefits for k = 0 and k = two at several . (c) Log-log plot of – at crucial rotation ( = 1) within the equatorial plane ( = /2) as a function of T for several values of k. (d) Linear-log plot from the distinction – ;an between the numerical outcome and the high temperature analytical expression in Equation (171) at critical rotation = 1 and = /2. The black dotted lines represent the high-temperature outcome in Equation (171).Symmetry 2021, 13,37 of0.008 2/27 two 0.0.008 2/270.0.0.0.0.–0.(k0.(= 0, = /2)0.0.0.T0 = 0.5, = 0 = 0.5 = 0.99 =1 T0 = two, = 0 = 0.5 = 0.99 =1 0 0.2 0.four 0.six 0.0.= 0, = /2)0.0.(a)T0 = 0.four, k = 0 k = 0.2 k = 0.4 T0 = 2, k = 0 k=1 k=2 0 0.two 0.four 0.(b)0.0040 0.82r/0.008 2/270.008 k = 0, = 0 = 1/ 2 =1 k = two, = 0 = 1/ 2 =2r/0.2/270.0.0.-0.(-T0 = two, = /2) k = 0, = 0 = 1/3 = 2/3 k = 3, = 0 = 1/3 = 2/3 0 0.2 0.four 0.0.0.0.0.0.(r= 0)(c)(d)(= /2)0 0.80 0.0.2r/TFigure eight. (a ) Profiles with the coefficient 1 , taken with unfavorable sign, in the equatorial plane ( = /2). (a) Results for massless quanta (k = 0) at numerous values of and T0 ; (b) Static ( = 0) states at low (T0 = 0.5 -1 ) and high (T0 = two -1 ) te.