Complex dilations

Such nonequilihrium surface tension effects ate best described ia terms of dilatational moduh thanks to developments ia the theory and measurement of surface dilatational behavior. The complex dilatational modulus of a single surface is defined ia the same way as the Gibbs elasticity as ia equation 2 (the factor 2 is halved as only one surface is considered). 

P. Krylstedt, N. Elander, E. Brandas, A Complex Dilated Study of Shape Resonances and Negative Ions in Electron-Atom Scattering, within an Asymptotic Complete Form of Continuum Exchange, J. Phys. B At. Mol. Opt. Phys. 22 (1989) 1623. 

C.A. Chatzidimitriou-Dreismann, E.J. Brandas, E. Karlsson, Quantum Correlation Effects in the Spin Dynamics of Gd at High Temperatures in the Light of Complex Dilation Theory, Phys. Rev. Rapid. Commun. B 42 (1990) 2704. 

The development of a full angular momentum, three dimensional, smooth exterior complex dilated, finite element method for computing bound and resonant states in a wide class of quantum systems is described. Applications to the antiprotonic helium system, doubly excited states in the helium atom and to a model of a molecular van der Waals complex are discussed. 2001 by Academic Press. 

The eigenenergies and eigenfunctions of resonant eigenstates may be obtained by the complex dilation method[21, 22] which is illustrated in fig. 4. The... 

Figure 5 Real (open symbols) and imaginary (filled symbols) parts of the complex dilational modulus of an adsorbed layer at equilibrium. The circles, diamonds and triangles correspond to the MeC concentration of 3 x 10 4, 0.1 and 16 gfl, respectively...

In the section on the evolution of network, we described the visual development of strain patterns in the flow of interacting PEO solutions (Figure 10) leading to frilly developed flow instability (flare). Similar effects can be found in wejl-characterized monodisperse a-PS, as shown in Figure 30, for a 7.7 X 10 a-PS dissolved in decahydronaphthalene (0.35%) and its corresponding AP vs. e trace (Figure 27). Complex dilatant effects can be observed (curve b) when compared with pure solvent (curve a) and with dilute solutions (Figure 5). 

In the complex coordinate method the real configuration space coordinates are transformed by a complex dilatation. The Hamiltonian of the system is thus continued into the complex plane. This has the effect that, according to the boundaries of the representation, complex resonances are uncovered with square-integrable wavefunc-tions and hence the space boundary conditions remain simple. This square integrability is achieved through an additional exponentially decreasing term... 

P. Froelich, O. Goscinski and N. Moiseyev Resonances from the Complex Dilated Hamiltonians in Dilation-Adapted Basis Set vith a New Stabilization Parameter J. Chem. Phys. 84, 3931 (1985). 

The main factors, which determine the foam formation ability and physical stability of the foams in mixed Lys-MR solutions, are surface activity and complex dilatation modulus. With increase of MR concentration in certain range a surface activity and complex dilatation modulus of interfacial layers increased and phase angle decreased. It means that viscoelasticity of interfacial layers became higher. In these conditions the foam volume and mutiplicity as well as stability of foams were growing. This effect may be used for creation of mixed protein-MR system foam type for pharmaceutical applications with improved physical stability and wide range of antibacterial actions. 

Many technologies and natural phenomena involve processes of fast expansion or compression of fluid interfaces covered with surfactant adsorption layers. The dynamic system properties depend on the mechanisms and rate of equilibrium restoration after a deformation. At small magnitudes of deformation the mechanical relaxation of an interface can be described by the complex dilational viscoelastic modulus [1,2]. For sinusoidal deformations it is deflned as the ratio of complex amplitudes of interfacial tension variation and the relative surface area variation f (I ty) = dy /din A being a function of frequency. This modulus may include... 

The goal of many experimental studies is to obtain the complex dilational viscoelasticity as a function of frequency (ico) from the measured interfacial tension response because this... 

The applied signal can be either the pressure change at the opposite end of the capillary (Fig. 2) [16, 17] as in the previous case, or the volume variation in the cell produced by a pulsating rod or a piezodriver at constant pressure near the opposite capillary end (Fig. 3) [4, 14, 18-20]. In all cases from the comparison of the applied and the measured signals the complex dilational viscoelasticity c(i(o) can be obtained as a function of frequency after elimination of all contributions caused by the bulk phase behaviour. It is possible also to measure both the pressure in the cell and the meniscus volume and to compare them [21-23]. 

The surface tension variation in Eq. (12) can be expressed with the help of the complex dilatational modulus e(icb) [9-11]... 

The regimes of transient and established oscillations are observed for pure liquids as well as for surfactant solutions. For surfactant solutions the characteristic frequencies and the attenuation in the system depend on the relaxation processes in the adsorption layer and the system behaviour becomes more complicated. Many surfactants are characterised by a diffusion mechanism of the surface relaxation, and the complex dilatational modulus is given by [11]... 

Most adsorbed surfactant and polymer coils at the oil-water (0/W) interface show non-Newtonian rheological behavior. The surface shear viscosity Pg depends on the applied shear rate, showing shear thinning at high shear rates. Some films also show Bingham plastic behavior with a measurable yield stress. Many adsorbed polymers and proteins show viscoelastic behavior and one can measure viscous and elastic components using sinusoidally oscillating surface dilation. For example the complex dilational modulus c obtained can be split into an in-phase (the elastic component e ) and an out-of-phase (the viscous component e") components. Creep and stress relaxation methods can be applied to study viscoelasticity. 

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