Uniform dilatation

The requirement I > 2 can be understood from the symmetry considerations. The case of no restoring force, 1=1, corresponds to a domain translation. Within our picture, this mode corresponds to the tunneling transition itself. The translation of the defects center of mass violates momentum conservation and thus must be accompanied by absorbing a phonon. Such resonant processes couple linearly to the lattice strain and contribute the most to the phonon absorption at the low temperatures, dominated by one-phonon processes. On the other hand, I = 0 corresponds to a uniform dilation of the shell. This mode is formally related to the domain growth at T>Tg and is described by the theory in Xia and Wolynes [ 1 ]. It is thus possible, in principle, to interpret our formalism as a multipole expansion of the interaction of the domain with the rest of the sample. Harmonics with I > 2 correspond to pure shape modulations of the membrane. 

Figure 3.38. Three ways of extending an interface (a) the usual way in a Langmuir trough (b) ideally uniform dilation (c) experimental approach to case (b).

Here 4 are the shear stresses in the phases a and b, respectively, with the interface of tension y. By introducing the shear stress s through the Newton s equation of liquid motion and by considering a uniform dilatation = y = 0, the surface stress tensor becomes scalar and Eq. (3.39) can be rewritten as... 

Disorders of the intestinal tract in the neonatal period usually present with abdominal distension and dilatation of the bowel. However, not all intestinal dilatations represent obstruction. Infants with medical disorders such as sepsis, electrolyte imbalance or necrotizing enterocolitis may present ileus characterized by uniform dilatation of the bowel to the level of the rectum. Also, infants on continuous positive airways pressure may swallow an excessive amount of air and exhibit important intestinal dilatation. This dilatation must be distinguished from mechanical obstruction, because the treatment is completely different. The differentiation between these two categories can usually be made on the basis of clinical history, laboratory tests, and appropriate radiographs (Hernanz-SCHULMAN 1999). 

The differentiation of F in (4.88)-(4.91) is geometrically equivalent to a small uniform dilation of a cube of homogeneous fluid. There is more than one way of deforming an inhomogeneous fluid, eadi of which leads to a different expression for the tensor p(r) indeed, as we shall see, there appears to be no unique definition of this quantity. Its gradient is well defined since in a fluid at equilibrium, d. (2.82),... 

The deformation potential constant is defined as follows. A uniform dilatation 0 changes the energy of the free positron ground state Cc by... 

In the cuspation—dilation thermoforming process developed in AustraHa, sheet formation is promoted by expanding blades extending into aU areas and distributing the material uniformly throughout the mold. This process is claimed to deHver uniform distribution of high barrier components of sheet coextmsions and laminations. The process also permits almost vertical side waUs to cups (2). 

At 1-atm pressure in the surroundings, polysaccharide deformation and flow are normally initiated either by gravity or an applied shear rate (y) solvent (water) only flows under temperature (T) and concentration (c,) gradients. When T)i is constant or independent of the rate of shear (y in s 1) or stress (t), the flow is Newtonian. Very dilute polysaccharide dispersions are characterized mostly by Newtonian flow. At moderate concentrations, ti, may decrease (shear-thinning synonymous with pseudoplastic) or increase (shear-thickening synonymous with dilatant) nonlinearly with y for these dispersions, is replaced with (the apparent viscosity). Low DP and uniform distribution of substituents are conducive to tH high DP and nonuniform distribution are conducive to. A high T a is believed to elicit the human oral sensation of thickness. ... 

The dilation of the whole volume, 8 v/v, will not in general be equal to 8 vc/vc, even if the solid is reasonably isotropic elastically, unless 8 pvc is a change in uniform hydrostatic pressure, which it is very unlikely to be if the adsorption is appreciable. Hence we write more or less empirically... 

Figure 10.29 Response of an aligned smectic to layer dilation, (a) Initial equilibrium sample, (b) For a very small dilation Sh < Ink, the layer spacing simply increases, (c) A uniform rotation of the layers decreases the spacing toward that of equilibrium, but doesn t satisfy the boundary conditions, (d) Hence, the sample undergoes an mdulational instability, which also narrows the layer spacing while satisfying homeotropic boundary conditions, (e) For a large enough dilation, the undulation instability leads to formation of parabolic focal conic defects. (From Rosenblatt et al. 1977, with permission from EDP Sciences.)...

Let us consider an isotropic material whose temperature uniformly rises owing to external causes, for example heating, or the dissipation of energy produced in the body by the deformation. The cubic dilatation taking place in the material because of the effect of the change in temperature is given by... 

It will be assumed that the temperature field is uniform, that is, the sample is homogeneously cooled or heated, and for this reason there is no spatial temperature dependence. Also a constant dilatation coefficient and a sudden jump in the temperature will be assumed. This thermal history, though not very realistic, refers to the most unfavorable situation. 

Physically, this equation tells us how unidirectional dilation, as in a Langmuir trough, induces shear in the bulk. When the dilation Is not uniform, the resulting bulk shear is also position-dependent. 

Particle shape can also affect blending processes. Spherical and cubic shaped particles typically exhibit good flow properties and therefore promote blending. However, readily flowing materials may also be more prone to segregation. Plates and needle shaped particles have poor flow properties, are harder to dilate/expand, and are more likely to agglomerate. As a result, it may be more difficult to achieve uniformity when blending plate and needle shaped particles. Conversely, a benefit to this decreased mobility is that once blended, these are more likely to stay blended. 

In this section, devoted to dynamic surface tension, we consider mostly nonionic surfactant solutions. In Section 5.2.2.4 we address the more complicated case of ionic surfactants. We will restrict our considerations to the simplest case of relaxation of an initial uniform interfacial dilatation. The more complex case of simultaneous adsorption and dilatation is considered elsewhere. ... 

Morphologically, emphysema is associated with a destruction of the alveolar septum, which results in a dilation and consequent enlargement of the alveolar spaces (Fig. 19). This is apparently caused by a breakdown of the interstitial connective tissue proteins (primarily elastin) that provide the major structural framework of the lung parenchyma. Two types of emphysema have been defined on the basis of the types of destruction of the alveolar septa observed and the type of dilation of the terminal respiratory unit (the acini) that is observed. A typical acinus branches from a terminal bronchiole and consists of the respiratory bronchioles that have alveolated walls and lead to the alveolar ducts and ultimately to the alveolar sacs (see Fig. 3). In centrilobular (or centriacinar) emphysema, the sites of degradation and dilation are limited to the region of the terminal and respiratory bronchioles. In panlobular (or panacinar) emphysema, the entire acinus (including the alveolar ducts and sacs) is more uniformly affected. 

Automated Droplet Tensiometer. Surface tension and surface dilational moduli were measured by an automated droplet tensiometer (ADT) (IT concept, France) as a function of ageing time of the droplet.22 Surface tension was determined by drop shape analysis of a gas bubble formed in a cuvette containing the protein solution. The bubble was illuminated by a uniform light source and its profile imaged and digitised by a CCD camera and a computer. The profile was used to calculate the surface tension using Laplace s equation. The... 

Hoffman [1972, 1974], Strivens [1976], van de Ven [1984, 1985], Tomita et al. [1982, 1984], and Otsubo [1994] reported pseudoplastic/dilatant flow of concentrated suspensions of uniform and polydispersed spheres. A dramatic change in light diffraction pattern was systematically observed at the shear rate corresponding to the onset of dilatancy. Van de Ven and his collaborators demonstrated that, depending on concentration and shear rate, the distance between the sliding layers of uniform spheres in a parallel plate rheometer can vary by as much as 10%. 

ONODA, G.Y. 6c LINIGER, E.G. 1990. Random loose packings of uniform spheres and the dilatancy onset. Phys. Rev. Lett. 64, 2727-2730. 

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