Expansivity fluctuations

Easier V, Schweiss P, Meingast C, Obst B, Wuhl H, Rykov A I and Tajima S 1998 3D-XY critical fluctuations of the thermal expansivity in detwinned YBa2Cu30y g single crystals near optimal doping Phys. Rev. Lett. 81 1094-7... 

Undoubtedly the most successful model of the nematic-smectic A phase transition is the Landau-de Gennes model [201. It is applied in the case of a second-order phase transition by combining a Landau expansion for the free energy in tenns of an order parameter for smectic layering with the elastic energy of the nematic phase [20]. It is first convenient to introduce an order parameter for the smectic stmcture, which allows both for the layer periodicity (at the first hannonic level, cf equation (C2.2A)) and the fluctuations of layer position ur [20] ... 

Noise Control Sound is a fluctuation of air pressure that can be detected by the human ear. Sound travels through any fluid (e.g., the air) as a compression/expansion wave. This wave travels radially outward in all directions from the sound source. The pressure wave induces an oscillating motion in the transmitting medium that is superimposed on any other net motion it may have. These waves are reflec ted, refracted, scattered, and absorbed as they encounter solid objects. Sound is transmitted through sohds in a complex array of types of elastic waves. Sound is charac terized by its amplitude, frequency, phase, and direction of propagation. 

Liquids can also exert pressure due to thermal expansion. Table 4.15 provides an indication of pressure increases due to temperature increases for selected common liquids in full containers or pipes. Serious accidents can arise unless the design of rigid plant items such as pipework takes into account the changes in volume of liquids with temperature fluctuation by the following or combinations thereof ... 

Often the most important effective cluster interaction of the concentration fluctuation expansion of the configurational free energy is the EPI which is defined as... 

Other benefits of light-colored roofs include a potential increase in their useful life. The daily temperature fluctuation and concomitant expansion/coii-traction of a light-colored roof is less than that of a dark one. Also, materials degradation because of absorption of ultra-violet light is temperature-dependent. Thus, cooler roofs may last longer than... 

Corrosion fatigue due to inadequate allowance for expansion and contraction with consequent buckling as the temperature fluctuates. 

Incompressible Limit In order to obtain the more familiar form of the Navier-Stokes equations (9.16), we take the low-velocity (i,e. low Mach number M = u I /cs) limit of equation 9,104, We also take a cue from the continuous case, where, if the incompressible Navier-Stokes equations are derived via a Mach-number expansion of the full compressible equations, density variations become negligible everywhere except in the pressure term [frisch87]. Thus setting p = peq + p and allowing density fluctuations only in the pressure term, the low-velocity limit of equation 9,104 becomes... 

The model of non-correlated potential fluctuations is of special interest. First, it can be solved analytically, second, the assumption that subsequent values of orienting field are non-correlated is less constrained from the physical point of view. The theory allows for consideration of a rather general orienting field. When the spherical shape of the cell is distorted and its symmetry becomes axial, the anisotropic potential is characterized by the only given axis e. However, all the spherical harmonics built on this vector contribute to its expansion, not only the term of lowest order... 

Rough correlations have been made of minimum fluidization velocity, minimum bubbling velocity, bed expansion, bed level fluctuation, and disengaging height. Experts recommend, however, that any real design be based on pilot plant work. 

The increased fluctuations of protein structures at elevated temperatures is reflected in the thermal expansion of proteins [433], that may contribute to the marked temperature dependence of the rate of Ca transport. 

Third, a further simplification of the Boltzmann equation is the use of the two-term spherical harmonic expansion [231 ] for the EEDF (also known as the Lorentz approximation), both in the calculations and in the analysis in the literature of experimental data. This two-term approximation has also been used by Kurachi and Nakamura [212] to determine the cross section for vibrational excitation of SiHj (see Table II). Due to the magnitude of the vibrational cross section at certain electron energies relative to the elastic cross sections and the steep dependence of the vibrational cross section, the use of this two-term approximation is of variable accuracy [240]. A Monte Carlo calculation is in principle more accurate, because in such a model the spatial and temporal behavior of the EEDF can be included. However, a Monte Carlo calculation has its own problems, such as the large computational effort needed to reduce statistical fluctuations. 

This result holds in so far as fluctuations about the most probable trajectory are relatively negligible. Writing twice the left-hand side as the expansion about the first argument plus the expansion about the second argument, it follows that... 

The morphological stability of initially smooth electrodeposits has been analyzed by several authors [48-56]. In a linear stability analysis, the current distribution on a low-amplitude sinusoidal surface is found as an expansion around the distribution on the flat surface. The first order current distribution is used to calculate the rate of amplification of the surface corrugation. A plot of amplification rate versus mode number or wavelength separates the regimes of stable and unstable fluctuation and... 

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