Parallel transport applications

For the Berry phase, we shall quote a definition given in [164] ""The phase that can be acquired by a state moving adiabatically (slowly) around a closed path in the parameter space of the system. There is a further, somewhat more general phase, that appears in any cyclic motion, not necessarily slow in the Hilbert space, which is the Aharonov-Anandan phase [10]. Other developments and applications are abundant. An interim summai was published in 1990 [78]. A further, more up-to-date summary, especially on progress in experimental developments, is much needed. (In Section IV we list some publications that report on the experimental determinations of the Berry phase.) Regarding theoretical advances, we note (in a somewhat subjective and selective mode) some clarifications regarding parallel transport, e.g., [165], This paper discusses the projective Hilbert space and its metric (the Fubini-Study metric). The projective Hilbert space arises from the Hilbert space of the electronic manifold by the removal of the overall phase and is therefore a central geometrical concept in any treatment of the component phases, such as this chapter. 

The parallel transport model considers the total flux as the contribution from the molecules travelling via surface diffusion and from the molecules travelling via Knudsen diffusion [27,36,49,50]. This model does not consider transition stages and is applicable to pores that remain roughly the same size throughout the entire membrane such as nanotube-based membranes. Gilron and Softer [27] presented the following expression. 

We begin by reviewing the principles of SECM methods, and present an overview of the instrumentation needed for experimental studies. A major factor in the success of SECM, in quantitative applications, has been the parallel development of theoretical models for mass transport. A detailed treatment of the theory for the most common SECM modes that have been used to study liquid interfaces is therefore given, along with key results from these models. A comprehensive assessment of the applications of SECM is provided and the prospects for the future developments of the methodology are highlighted. 

The second variant is designed for solid state reactants to the exclusion of liquid or gas. This powder variant of Thermostar is described by the Fig. 1.19 (right). The microwave applicator is the same as for the device for liquids heating but the reactant transport is ensured by a metallic screw set within the dielectric pipe. This specific traveling metallic screw crosses all the microwave applicators. The coexistence of this metallic screw with the electric field is ensured by the fact that the major electric field direction is parallel to the major direction and perpendicular to the local curving of the screw. A typical industrial unit for solid or liquid reactants is powered with microwave generators units of 2 or 6 kW for a total microwave power close to 20 or 60 kW. 

Current utilization In practical application electrodialysis is affected by incomplete current utilization. The reasons for the incomplete current utilization are poor membrane permselectivity, parallel current through the stack manifold, and water transport by convection and due to osmosis and electro-osmosis. In a well-designed stack with no pressure difference between diluate and the concentrate convective water transport is negligibly low and also the current through the manifold can be neglected. Under these conditions the overall current utilization is given by ... 

Taking into account typical numbers for a and D, this underlines that the channel width should be considerably smaller than 1 mm (1000 pm) in order to achieve short residence times. Actually, heat exchangers of such small dimensions are not completely new, because liquid cooled microchannel heat sinks for electronic applications allowing heat fluxes of 790 watts/cm2 were already known in 1981 [46]. About 9 years later a 1 cm3 cross flow heat exchanger with a high aspect ratio and channel widths between 80 and 100 pm was fabricated by KFK [10, 47]. The overall heat transport for this system was reported to be 20 kW. This concept of multiple, parallel channels of short length to obtain small pressure drops has also been realized by other workers, e.g. by PNNL and IMM. IMM has reported a counter-current flow heat exchanger with heat transfer coefficients of up to 2.4 kW/m2 K [45] (see Fig. 3). 

A second field of application may be in the on-site and on-demand production [3,8,25]. A number of chemicals, especially those which are explosive or toxic, can not be efficiently produced at present on a medium or small scale, although large-scale processes exist. A parallelization of several microreactor units could synthesize flexible amounts of chemicals and may even allow a transport of the reaction units if desired. 

The strong and specific biotin-streptavidin binding was used to assemble biomolecule-functionalized nanoparticles in multilayered structures.67 Application of an electrical field allowed the assembly of multilayer structures by using extremely low concentrations of nanoparticles with minimal nonspecific binding. A microelectrode array was used to facilitate the rapid parallel electrophoretic transport and binding of biotin- and streptavidin-functionalized fluorescent nanoparticles to specific sites. By controlling the current, voltage, and activation time at each nanoparticle adsorption step, the directed assembly of more than 50 layers of nanoparticles was accomplished within an hour. 

---