Spatial phase shaping

Action potentials, self-propagating. Action potentials of smooth muscle differ from the typical nerve action potential in at least three ways. First, the depolarization phases of nearly all smooth muscle action potentials are due to an increase in calcium rather than sodium conductance. Consequently, the rates of rise of smooth action potentials are slow, and the durations are long relative to most neural action potentials. Second, smooth muscle action potentials arise from membrane that is autonomously active and tonically modulated by autonomic neurotransmitters. Therefore, conduction velocities and action potential shapes are labile. Finally, smooth muscle action potentials spread along bundles of myocytes which are interconnected in three dimensions. Therefore the actual spatial patterns of spreading of the action potential vary. 

Two macromolecular computational problems are considered (i) the atomistic modeling of bulk condensed polymer phases and their inherent non-vectorizability, and (ii) the determination of the partition coefficient of polymer chains between bulk solution and cylindrical pores. In connection with the atomistic modeling problem, an algorithm is introduced and discussed (Modified Superbox Algorithm) for the efficient determination of significantly interacting atom pairs in systems with spatially periodic boundaries of the shape of a general parallelepiped (triclinic systems). 

To ensure that the detector electrode used in MEMED is a noninvasive probe of the concentration boundary layer that develops adjacent to the droplet, it is usually necessary to employ a small-sized UME (less than 2 /rm diameter). This is essential for amperometric detection protocols, although larger electrodes, up to 50/rm across, can be employed in potentiometric detection mode [73]. A key strength of the technique is that the electrode measures directly the concentration profile of a target species involved in the reaction at the interface, i.e., the spatial distribution of a product or reactant, on the receptor phase side. The shape of this concentration profile is sensitive to the mass transport characteristics for the growing drop, and to the interfacial reaction kinetics. A schematic of the apparatus for MEMED is shown in Fig. 14. 

The computation of the curvatures from the bulk field differential geometry has proven to be rather imprecise. The errors produced by the use of the approximate formulas (100)-(104) are especially big if the spatial derivatives of the field sharp peaks at the phase interface. This is a common situation in the late-stage kinetics of the phase separating/ordering process, when the order parameter is saturated and the domains are separated by thin walls. Here, to calculate the curvatures, we propose a much more accurate method. It is based on the observation that the local curvatures are quantities that can be inferred solely from the shape of the interface, without appealing to the properties of the bulk field [Pg.212]

The analysis of x-ray diffraction data is divided into three parts. The first of these is the geometrical analysis, where one measures the exact spatial distribution of x-ray reflections and uses these to compute the size and shape of a unit cell. The second phase entails a study of the intensities of the various reflections, using this information to determine the atomic distribution within the unit cell. Finally, one looks at the x-ray diagram to deduce qualitative information about the quality of the crystal or the degree of order within the solid. This latter analysis may permit the adoption of certain assumptions that may aid in the solving of the crystalline structure. 

This description is elaborated below with an idealized model shown in Figure 17. Imagine a molecule tightly enclosed within a cube (model 10). Under such conditions, its translational mobility is restricted in all three dimensions. The extent of restrictions experienced by the molecule will decrease as the walls of the enclosure are removed one at a time, eventually reaching a situation where there is no restriction to motion in any direction (i.e., the gas phase model 1). However, other cases can be conceived for a reaction cavity which do not enforce spatial restrictions upon the shape changes suffered by a guest molecule as it proceeds to products. These correspond to various situations in isotropic solutions with low viscosities. We term all models in Figure 17 except the first as reaction cavities even... 

---