Force fluctuation wave

M. G. Rozman, M. Urbakh, J. Klafter. Stick-slip motion and force fluctuations in a driven two-wave potential. Phys Rev Lett 77 683-686, 1996. 

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...

As discussed earlier, the particle/droplet dynamics can be significantly modified by timing the fuel injection to be in- or out-of-phase with the large-scale vortex structures. To explore if timed fuel injection could alter the stability characteristics, the flow was forced at the quarter-wave mode of the inlet and droplet injection was timed to be in- or out-of-phase with the forcing. Results from these simulations show that the pressure fluctuations at the quarter-wave mode of the inlet can indeed be amplified or attenuated depending on the phasing of the droplet injection. 

These methods have been applied to calculate the polarizabilities of atoms,31 and the long-ranged forces between atoms,33 with a typical calculated accuracy of 10 % or less. Thus, we have been able to estimate successfully the significant features of zero-point fluctuations of atomic dipole moments, without actually solving the quantum equations of motion to obtain all the excited state energies and wave functions. 

The expectation value of the property A at the space-time point (r, t) depends in general on the perturbing force F at all earlier times t — t and at all other points r in the system. This dependence springs from the fact that it takes the system a certain time to respond to the perturbation that is, there can be a time lag between the imposition of the perturbation and the response of the system. The spatial dependence arises from the fact that if a force is applied at one point of the system it will induce certain properties at this point which will perturb other parts of the system. For example, when a molecule is excited by a weak field its dipole moment may change, thereby changing the electrical polarization at other points in the system. Another simple example of these nonlocal changes is that of a neutron which when introduced into a system produces a density fluctuation. This density fluctuation propagates to other points in the medium in the form of sound waves. 

Why Because the frequencies at which charges spontaneously fluctuate are the same as those at which they naturally move, or resonate, to absorb external electromagnetic waves. This is the essence of the "fluctuation-dissipation theorem." It states that the spectrum (frequency distribution) over which charges in a material spontaneously fluctuate directly connects with the spectrum of their ability to dissipate (absorb) electromagnetic waves imposed on them. Computation of charge-fluctuation forces is essentially a conversion of observed absorption spectra. By its very nature, the measured absorption spectrum of a liquid or solid automatically includes all the interactions and couplings among constituent atoms or molecules. 

The wave equation is built from V E cx pext/ - Because electrostatic double-layer equations are easier to think about in terms of potentials rather than electric fields E = -V0, we set up the problem of ionic-charge-fluctuation forces in terms of potentials. Charges pext come from the potential 0 through the Boltzmann relation... 

For ionic-fluctuation forces, the e s are now the dielectric constants in the limit of zero frequency (f = 0). The integration over wave vectors u, v can be converted to a p, ir integration ... 

The frequency correlation time xm corresponds to the time it takes for a single vibrator to sample all different cavity sizes. The fluctuation-dissipation theorem (144) shows that this time can be found by calculating the time for a vertically excited v = 0 vibrator to reach the minimum in v = 1. This calculation is carried out by assuming that the solvent responds as a viscoelastic continuum to the outward push of the vibrator. At early times, the solvent behaves elastically with a modulus Goo. The push of the vibrator launches sound waves (acoustic phonons) into the solvent, allowing partial expansion of the cavity. This process corresponds to a rapid, inertial solvent motion. At later times, viscous flow of the solvent allows the remaining expansion to occur. The time for this diffusive motion is related to the viscosity rj by Geo and the net force constant at the cavity... 

After more than one 100 years of unquestionable successes [128], there is a general agreement that quantum mechanics affords a reliable description of the physical world. The phenomenon of quantum jumps, which can be experimentally detected, should force the physicists to extend this theory so as to turn the wave-function collapse assumption, made by the founding fathers of quantum mechanics, into a dynamical process, probably corresponding to an extremely weak random fluctuation. This dynamical process can be neglected in the absence of the enhancement effects, triggered either by the deliberate measurement act or by the fluctuation-dissipation phenomena such as Brownian motion. This enhancement process must remain within the limits of ordinary statistical physics. In this limiting case, the new theory must become identical to quantum mechanics. 

It is often said that wave mechanics produces effects that are too small to be noticed on anything larger than atoms and molecules. The wave character of an electron can be easily detected but not the wave character of a baseball. But London forces are the result of random fluctuations in the electron density of atoms and molecules that are predicted by the wave equation. The gecko relies on those flickering shifts in electron density to astound scientists by running across a ceiling. 

The front is inherently unstable, however, and this is often studied by a linear stability analysis. Infinitesimal perturbations are applied to all of the variables to simulate reservoir heterogeneities, density fluctuations, and other effects. Just as in the Buckley-Leverett solution, the perturbed variables are governed by force and mass balance equations, and they can be solved for a perturbation of any given wave number. These solutions show whether the perturbation dies out or if it grows with time. Any parameter for which the perturbation grows indicates an instability. For water flooding, the rate of growth, B, obeys the proportionality... 

The magnitude of the fluctuations in volume (dilatation) and density (condensation) associated with US wave is controlled by the properties of the medium and the applied forces. The velocity of sound in mixtures and suspensions will therefore be controlled by the mean density and mean compressibility as expressed by the Urick equation (see Eq.9.7-9.10). The equation can be formulated in terms of partial molar volumes by forming an identity between the volume fraction of the solute, its partial volume Vm2), the mean molar volume of the solution Vm) and the mole fraction Cm) as follows ... 

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