Fluctuation wave

We may contest such claims, especially if vacuum is a fluctuating wave medium. In that case, ordinary plane waves that are solutions of wave equations do not vanish at inhnity and therefore can be associated with the so-called zero-point energy. We can also assume that helicoidal helds are associated with zero-point energy. This question is not trivial since many authors consider that the inertia of bodies might be a consequence of the existence of the zero-point... 

Contemporary understanding of liquid film rupture is based on the Linear Stability Theory and the concept of existence of fluctuational waves on liquid surfaces [81]. According to this model the film is ruptured by unstable waves, i.e. waves the amplitudes of which increase with time. The rupture occurs at the moment when the amplitude Ah or the root mean... 

In thick films (h >0.1 xm) only capillary forces act against surface deformations (8pc <5I1) and fluctuation waves are practically stable for the whole wavelength spectrum (Eq. (3.66). Moreover, the steady state amplitudes of the capillary waves determined from the... 

All fluid interfaces, including lipid membranes and surfactant lamellas, are involved in a thermal fluctuation wave motion. The configurational confinement of such thermally exited modes within the narrow space between two approaching interfaces gives rise to short-range repulsive surface forces, which are considered below. 

Figure 10 Mechanisms of breakage of liquid films, (a) Fluctuation-wave-mechanism the film rupture results from growth of capillaty waves enhanced by attractive surface forces (92). (h) Pore-nudeation mechanism it is expected to be operative in very thin films, virtually representing two attached monolayers of amphiphilic molecules (99). (c) Solute-transport mechanism if a solute is transferred across the two surfaces of the liquid film due to gradients in the solute chemical potential, then Marangoni instability could appear and break the film...

Different from the secondary flows and flow channel spacer techniques, the pulsed flow method is to generate a pressure fluctuation wave in either the feed or permeate flow channel using certain oscillators. The fluctuating pressure wave can enhance the membrane filtration through reducing the boundary layer or induced instant local backflushing flow as discussed in Section 10.4.1. 

Pulsatile flow can be defined as flow with a periodic pressure fluctuation wave travelling along the flow path. As in a... 

First detailed dynamic light scattering (DLS) experiments using bulk liquid crystal samples have confirmed the theoretically predicted existence of two dissipative fluctuation eigenmodes in the nematic liquid crystalline phase the first mode being a combination of splay and bend distortion and the second one a combination of twist and bend fluctuations [55,56]. Both modes are overdamped and the relaxation rate 1/r of each mode depends on the fluctuation wave vector q and viscoelastic properties of the sample [57] ... 

Here, a = 1,2 denotes the splay-bend and twist-bend mode, respectively, i i,2,3 are the Prank elastic constants, 771 2 are the rotational viscosities, is the component of the fluctuation wave vector parallel to the director and q the component perpendicular to it. 

In confined geometries, however, this is not the case. In a planar sample, for example, the magnitude of the wave vector component parallel to the boundaries is arbitrary, whereas the fluctuation wave vector component perpendicular to the boundaries can only have certain values. In this case, the allowed wave vector components are determined by the sample thickness, viscoelastic properties of the liquid crystal, and also by the interaction of a liquid crystal with the aligning surface. If the director is strongly bound to the aligning substrate, it cannot deviate from the induced direction (easy axis) and the fluctuation amphtude at the boundary is zero. On the other hand, if the surface only weakly anchors the director orientation, the director can fluctuate to a certain degree around the easy axis. 

The important feature of the weak-coupling picture as described above is that F, which is related to the characteristic energy of the Fermi liquid phase still plays the role of the scaling energy. This fact is not surprising since only parts of the Fermi surface contribute to the anomalous properties. One should note however that this theory is not fully self-consistent because the AF fluctuation wave vector is not connected with any FS feature since the latter is assumed as spherical. 

Figure 2..30. Schematic of light scattering on Debye s thermoelastic waves or on fluctuation waves of concentration...

Fluctuation dynamics is characterized by the fall rate of the fluctuation wave amplitude. If a fluctuation perturbation is modelled by the sum of the Fourier transforms, then the relaxation rate of the component Sifg with the wave vector q is defined by 1/r,. 

If anchoring at the boundaries is strong but finite, the extrapolation length is small compared to the inverse fluctuation wave vector component and thus to d. The secular equation can be expanded in terms of small deviations in the wave vector from the value for infinite anchoring and for the fundamental mode N = 1) yields [8]... 

The functions of A((p) on inhomogeneity scale (fluctuation wave number), degree of polymerization, concentration etc. [7-9, 39] are known. 

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