Nonlinear transport phenomena

Of course the results concerning nonlinear transport phenomena must be transformed correspondingly. 

Rohrlich, B. Parisi, J. Peinke, J. Rossler, O. E. 1986. A Simple Morphogenetic Reaction-Diffusion Model Describing Nonlinear Transport Phenomena in Semiconductors, Z. Phys. B Cond. Matter 65, 259-266. 

First, and most important, nonlinear dynamics provides an intellectual framework to pursue the consequences of nonlinear behavior of transport systems, which is simply not possible in an intellectual environment that is based upon a linear mentality, characterized by well-behaved, regular solutions of idealized problems. One example that illustrates the point is the phenomenon of hydrodynamic dispersion in creeping flows of nondilute suspensions. It is well known that Stokes flows are exactly reversible in the sense that the particle trajectories are precisely retraced when the direction of the mean flow is reversed. Nevertheless, the lack of reversibility that characterizes hydrodynamic dispersion in such suspensions has been recently measured experimentally [17] and simulated numerically [18], Although this was initially attributed to the influence of nonhydrodynamic interactions among the particles [17], the numerical simulation [18] specifically excludes such effects. A more general view is that the dispersion observed is a consequence of (1) deterministic chaos that causes infinitesimal uncertainties in particle position (due to arbitrarily weak disturbances of any kind—... 

For transporters, relatively low protein expression level and limited transport capacity makes for nonlinear, enzyme-like transport kinetics that is, the transport rate saturates with increasing substrate concentration. This phenomenon is the basis for the competitive interactions generally found for chemicals that are handled by one or more common transporters this is usually manifest as inhibition of the transport of one chemical by a structural analog. The extent to which these competitive interactions are important depends on the concentrations of the chemicals involved, their relative affinities for the common transporter, and their phar-macological/toxicological profiles (effects, effective concentrations, therapeutic index). Competition for transport is discussed below in the context of drug-drug interactions. 

For centuries, metal nanoparticles have never ceased to attract scientists and artists from many diverse cultures. In this section we briefly introduce a phenomenon of metal nanoparticles that still inspires scientists localized surface plasmon resonance (LSPR) (Hutter and Fendler, 2004). Metal nanoparticles show nonlinear electronic transport (single-electron transport of Coulomb blockade) and nonlinear/ultrafast optical response due to the SPR. Conduction electrons (—) and ionic cores (-F) in a metal form a plasma state. When external electric fields (i.e., electromagnetic waves, electron beams etc.) are applied to a metal, electrons move so as to screen perturbed charge distribution, move beyond the neutral states, return to the neutral states, and so on. This collective motion of electrons is called a plasma oscillation. SPR is a collective excitation mode of the plasma localized near the surface. Electrons confined in a nanoparticle conform the LSPR mode. The resonance frequency of the surface plasmon is different... 

The phenomenological description of the excitability phenomenon given in Section 1.3 cannot claim to contain a final solution to the problem of the nature of transport systems of biological membranes responsible for nervous impuse generation. Where we stand, we can only conclude that the membrane as a whole is a nonlinear ion conductor whose properties are largely dependent upon the electrice field. For all that, the fact that the use of certain specific blocking compounds—tetrodotoxin and tetraethylammonium—allows the sodium and potassium ionic currents to be separated is alone sufficient to support the conception of selective transport systems located in the lipid matrix... 

TWO DIMENSIONAL SIMULATION MODELS WITH A NON-LINEAR DIFFUSION TERM. The accumulation of the experimental data suggests that the investigated phenomenon may indeed be an authentic non-linear reaction/diffusion coupling process. Furthermore, the low sensitivity to the type of chemical reaction suggests that non-linearities in the transport processes are the dominant factors. Therefore, many of our simulation efforts have been directed towards this type of nonlinearity. We exemplify the approach with one model others will appear elsewhere., ... 

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