Transport structure, multidimensional

S. Honjo and K. Kaneko, Structure of Resonances and Transport in Multidimensional... 

STRUCTURE OF RESONANCES AND TRANSPORT IN MULTIDIMENSIONAL HAMILTONIAN DYNAMICAL SYSTEMS... 

In reply to Professor Ubbelohde, research on ionophores reported in Professor Simon s paper emerged from studies of the properties of natural compounds such as valinomycin and macrotetrolides. That confirms once more the importance of such studies as initial points for the investigations of the multidimensional world of biology. I would like to add also that the natural ionophores resemble in several respects the much larger enzymes (I) they are specific and stereospecific, (2) their active sites are located in cavities, (3) their stable secondary structure, which is essential for activity, is determined by the primary structure, and (4) they transport hydrophilic substrates through lipophilic membranes. 

This chapter concerns the structures and propagation velocities of the deflagration waves defined in Chapter 2. Deflagrations, or laminar flames, constitute the central problem of combustion theory in at least two respects. First, the earliest combustion problem to require the simultaneous consideration of transport phenomena and of chemical kinetics was the deflagration problem. Second, knowledge of the concepts developed and results obtained in laminar-flame theory is essential for many other studies in combustion. Attention here is restricted to the steadily propagating, planar laminar flame. Time-dependent and multidimensional effects are considered in Chapter 9. 

We introduce a simple model to investigate and calculate a diffusion coefficient as a basic quantity describing transport in Section II, and then we visualize resonances to detect the structure of the Arnold web and overlapped resonances in Section III. With the aid of this representation, to clarify the relevance of Arnold diffusion and diffusion induced by resonance overlap to global transport in the phase space, we compute transition diagrams in the frequency space in Section IV. In Section V, we extend the resonance overlap criterion to multidimensional systems to identify the pathway for fast transport, and in Section VI we revisit the diffusion coefficient to ensure fast transport affecting the global diffusion. A brief summary is given in Section VII. 

Consequently, the proposed model allows the necessary information regarding the electrolyte-metal electrode interface and about the character of the electronic conductivity in solid electrolytes to be obtained. To an extent, this is additionally reflected by the broad range of theoretical studies currently published in the scientific media and is inconsistent with some of the research outcomes relative to both physical chemistry of phenomena on the electrolyte-electrode interfaces and their structures. Partially, this is due to relative simplifications of the models, which do not take into account multidimensional effects, convective transport within interfaces, and thermal diffusion owing to the temperature gradients. An opportunity may exist in the further development of a number of the specific mathematical and numerical models of solid electrolyte gas sensors matched to their specific applications however, this must be balanced with the resistance of sensor manufacturers to carry out numerous numbers of tests for verification and validation of these models in addition to the technological improvements. 

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