Isotropic cell

These equations assume isotropic cell fluctuations, whereas Eqs. [84] allow anisotropy in cell dynamics. Note that different thermostats are coupled to the system and barostat variables in Eq. [178]. The total Liouvillian governing the evolution of the phase space variables, [q, p, r, Vy, V, v, q, is given by... 

Isotropic cell structures, and therefore same mechanical strengths in directions both parallel and perpendicular to foam rise... 

Figure 3. Lateral root tip from a pea plant. The plant was grown in an aqueous saturated solution of trifluralin for 48 h. Note the isotropic cells in the zone of elongation (arrow). Magnification =...

Figure 5, Apex of Chara plant treated with an aqueous saturated solution of trifiuralin for 9 days. Isotropic cell enlargement has occurred in the internode cell and in lateral cells arising from the node of the main axis. Magnification = 12X.

Neal and Nader [260] considered diffusion in homogeneous isotropic medium composed of randomly placed impermeable spherical particles. They solved steady-state diffusion problems in a unit cell consisting of a spherical particle placed in a concentric shell and the exterior of the unit cell modeled as a homogeneous media characterized by one parameter, the porosity. By equating the fluxes in the unit cell and at the exterior and applying the definition of porosity, they obtained... 

The geometry and structure of a bone consist of a mineralised tissue populated with cells. This bone tissue has two distinct structural forms dense cortical and lattice-like cancellous bone, see Figure 7.2(a). Cortical bone is a nearly transversely isotropic material, made up of osteons, longitudinal cylinders of bone centred around blood vessels. Cancellous bone is an orthotropic material, with a porous architecture formed by individual struts or trabeculae. This high surface area structure represents only 20 per cent of the skeletal mass but has 50 per cent of the metabolic activity. The density of cancellous bone varies significantly, and its mechanical behaviour is influenced by density and architecture. The elastic modulus and strength of both tissue structures are functions of the apparent density. 

Other defects should be considered, such as uniform strain, which causes isotropic contraction/expan-sion of the cell giving rise to diffraction line shifts (but not broadening), chemical and/or phase segregation and... 

The symbols used are Vc, unit cell volume Bj, isotropic thermal factor of the yth atom. 

MHz, from 20% w/w CTAB-D20 (41 °C) at observed, consistent with an ordered phase, different positions across the annular gap of a while near the outer wall the single peak of an cylindrical Couette cell and at an apparent isotropic phase is seen. In between, a mixed shear rate of 20 s 1. Near the inner wall, where phase region exists (adapted from Ref. [38]). 

Asymmetrical Peaks are rarely found in WAXS from polymers, but they are ubiquitous in the MAXS of liquid crystalline polymers. For asymmetrical peaks in isotropic patterns it is best to determine the peak position from the maximum of the peak, if peak asymmetry is a result of linear or planar disorder. Linear disorder means that the crystals are more or less one-dimensional (a tower of unit cells). Planar disorder means that the crystallites are made from only very few layers of unit cells (cf. Guinier [6] Chap. 7). 

The estimated distribution of A1 atoms is shown in Figure 2. Both the siting as well as therelative concentration of A1 in the individual T sites significantly vary. Our QM-Pot calculations of ZSM-5 structures (PI symmetry) containing one A1 atom per unit cell resulted in the 24 structures corresponding to A1 substitution into the 24 distinguishable T sites of the monoclinic ZSM-5 and yielded 24 values of shieldings which were converted into 24 values of isotropic chemical shift. 

Figure 14. The phase diagram of the gradient copolymer melt with the distribution functions g(x) = l — tanh(ciit(x —fo)) shown in the insert of this figure for ci = 3,/o = 0.5 (solid line), and/o — 0.3 (dashed line), x gives the position of ith monomer from the end of the chain in the units of the linear chain length. % is the Flory-Huggins interaction parameter, N is a polymerization index, and/ is the composition (/ = J0 g(x) dx). The Euler characteristic of the isotropic phase (I) is zero, and that of the hexagonal phase (H) is zero. For the bcc phase (B), XEuier = 4 per unit cell for the double gyroid phase (G), XEuier = -16 per unit cell and for the lamellar phases (LAM), XEuier = 0.

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