Stability parameter maximum value

The surface viscosity or resistance to shear stress of the surface film is an index of its mechanical strength and is an important parameter related to the stability of films and foams ( ), Surface yield stress of BSA films were determined using the above parameters ( ). Maximum values were obtained in the pH range of 5-6, near the isoelectric point of BSA, and decreased rapidly above pH 6,0 [Table 1]. These observations again reflect the enhanced intermolecular interactions between protein components in the film as the isoelectric point is reached and the enhanced electrostatic repulsion between neighboring molecules as the pH is raised above the isoelectric point, i.e. net charge on the protein surface was increased. 

To analyze the stability of the ordered microphases, the simplest incompressible random-phase approximation [132] can be employed. Using this approach, the critical value of the Flory-Huggins parameter, x > and the corresponding spinodal temperature, T = l/x > can be determined by the condition that the scattering intensity S(q) reaches its maximum value at a nonzero wave vector q. Within the RPA the scattering intensity is given by [132,142]... 

Let us now see how the nullcline deformation due to recycling gives rise to birhythmicity. Shown in fig. 3.6 are the bifurcation diagrams obtained as a function of parameter v for eight increasing values of the maximum rate of recycling, a , for a fixed value of constant K. In each part, the steady-state value of the substrate ao is indicated, as well as the maximum value qim reached by the substrate during oscillations. Solid lines denote stable steady-state or periodic solutions both types of solution are indicated by dashed lines when unstable. The stability properties of the steady state were determined by linear stability analysis of eqns... 

The transition line which marks the appearance of the FISDW is not monotonic the mean positive slope indicates that the critical temperature for the transition from the metal to the SDW increases as the field increases, which shows that the SDW is stabilized by the magnetic field. Nevertheless, at the limit between two subphases, a negative slope is associated with a partial reentrance of the metallic phase into subphases (arrows on Fig. 1). In between a given quantized SDW phase, for a particular field B ax e transition temperature has a maximum value Tc(Bj 3x)- But when the field is increased,or decreased,from Bj x toward a phase boundary, T reaches a minimum at the multicritical point, i.e, at the metallic reentrance. This reentrance illustrates the competition between order parameters of adjacent SDW subphases. 

The first involves a study by Malysa et al. [5] of the surface elasticity and dynamic stability of wet foams for a homologous series n-alcohols (C4-Cxo). On ascending the series, the authors found that foam stability passed through a maximum with the Cg-Cg alcohols. This effect was found to be unrelated to the Marangoni dilational modulus. However, the authors also determined a parameter they called the effective elasticity which depended on the kinetics of adsorption. They foimd that at short time scales (0.05-0.10 s), the effective elasticity correlated well with foam stability, reaching a maximum value with the C7 alcohol. 

The full curves in the /c-/r parameter plane, expressed by (4.46) and (4.47), are shown in Fig. 4.3. There are two closed loops emerging from the origin. The outer loop, given by the upper root in (4.46) and the lower root with 0 < 6SS < 1, also touches the k axis at (fi = 0, k = 1). Outside this locus the stationary state is a stable node inside this loop it is a focus (we will discuss stability within this region in the next subsection). The maximum in this curve occurs for k = (3 + y/S) exp[ — (3 — /5)] 1.787. For larger values of the dimensionless reaction rate constant, e.g. for high ambient temperatures, no damped oscillatory states will be found. 

In the vicinity of /j. = -0.5, the numerical calculations show that an increase in the value of a leads to a jump of the ground state total spin from the maximum to the minimum value [41]. Therefore Eq. (35) is not valid for the estimation of the stability of the ferromagnetic state of the strip in this region of the values of parameter fi. 

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