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PubMed2005

Resonant diffusion on modulated surfaces.

Some theoretical methods for description of the diffusion on modulated surfaces are reviewed. A general formula for calculation of the diffusion coefficient of a particle moving in the field of a periodic potential is developed, which takes into account both the potential barrier effect and the dependence of the friction coefficient on the potential. The application of the theory to the diffusion of dimers on solid surfaces reveals a non-monotonous dependence of the diffusion coefficient on the ratio between the dimer and solid spatial parameters. This resonant dependence sometimes can be suppressed by the rotations and vibrations on the dimer. In the present theory the latter are described via an adiabatic approach.

Biophysics↗

PubMed1988

The state of the art versus the state of the science. The diffusion of new medical technologies into practice.

This paper offers a theory to explain the diffusion of new medical technologies into local practice. Based on several hundred interviews with community hospital physicians, it anchors technology decisions in the norms and relationships of local practice. Physician descriptions of their use of different types of assessment information provide insight into the way in which local consenses on appropriate practice are formed, guide behavior, and change. To understand new technology adoption, it is necessary to (a) differentiate "formed" (complete) and "dynamic" (still developing) technologies, and (b) appreciate the extent to which medical practice is locally organized. Concepts from organizational literature, then, become useful in explaining the penetration of these medical communities and the circumstances under which a new modality takes hold in them. Within the framework presented, previously puzzling findings regarding variations in local practice and the poor relationship between practice behavior and the published literature become understandable.

Attitude of Health Personnel↗

PubMed2003

Diffusive-ballistic crossover in 1D quantum walks.

We show that particle transport, as characterized by the equilibrium mean square displacement, in a uniform, quantum multibaker map, is generically ballistic in the long time limit, for any fixed value of Planck's constant. However, for fixed times, the semiclassical limit leads to diffusion. Random matrix theory provides explicit analytical predictions for the mean square displacement of a particle in the system. These results exhibit a crossover from diffusive to ballistic motion, with crossover time on the order of the inverse of Planck's constant. We expect that, for a large class of 1D quantum random walks similar to the quantum multibaker, a sufficient condition for diffusion in the semiclassical limit is classically chaotic dynamics in each cell. The systems described generalize known quantum random walks and may have applications for quantum computation.

Journal Article↗

PubMedDate not supplied

Volume transmission and wiring transmission from cellular to molecular networks: history and perspectives.

The present paper deals with a fundamental issue in neuroscience: the inter-neuronal communication. The paper gives a brief account of our previous and more recent theoretical contributions to the subject and also reports new recent data that support some aspects of our proposal on two major modes of communication in the central nervous system: the wiring and the volume transmission. There exist two competing theories on inter-neuronal communication: the neuron doctrine and the theory of the diffuse nerve network, supported by Cajal and Golgi, respectively (see their respective Nobel Lectures). The present paper gives a brief account of a view on inter-neuronal communication in the brain, the volume and wiring transmission concept that to a great extent reconcile these two theories. Thus, the theory of volume and wiring transmission are summarized and its recent developments that allow to extend these two modes of communication from the cellular network to the molecular network level is also briefly illustrated. The explanatory value of this broadened view is further enhanced by our recent proposal on the existence of a Global Molecular Network enmeshing the entire central nervous system. It may be interesting to note that also the Global Molecular Network theory is reminiscent of the old reticular theory of Apathy. Finally, the so-called 'tide hypothesis' for diffusion of signals in the brain is briefly discussed and its possible extension to the molecular level is for the first time introduced. Early indirect evidence supporting volume transmission in the brain was the discovery of transmitter-receptor mismatches. Thus, as an experimental part of the present paper a new approach to evaluate transmitter-receptor mismatches is given and evidence for inter-relationships between temperature micro-gradients and mismatches is provided.

Cell Communication↗

PubMed2003

Fast crack propagation by surface diffusion.

We present a continuum theory which describes the fast growth of a crack by surface diffusion. This mechanism overcomes the usual cusp singularity by a self-consistent selection of the crack tip radius. It predicts the saturation of the steady state crack velocity appreciably below the Rayleigh speed and tip blunting. Furthermore, it includes the possibility of a tip splitting instability for high applied tensions.

Journal Article↗

PubMed2002

Diffusion on random-site percolation clusters: theory and NMR microscopy experiments with model objects.

Quasi-two-dimensional random-site percolation model objects were fabricated based on computer-generated templates. Samples consisting of two compartments, a reservoir of H2O gel attached to a percolation model object, which was initially filled with D2O, were examined with nuclear magnetic resonance microscopy for rendering proton spin density maps. The propagating proton/deuteron interdiffusion profiles were recorded and evaluated with respect to anomalous diffusion parameters. The deviation of the concentration profiles from those expected for unobstructed diffusion directly reflects the anomaly of the propagator for diffusion on a percolation cluster. The fractal dimension of the random walk d(w) evaluated from the diffusion measurements on the one hand and the fractal dimension d(f) deduced from the spin density map of the percolation object on the other permits one to experimentally compare dynamical and static exponents. Approximate calculations of the propagator are given on the basis of the fractional diffusion equation. Furthermore, the ordinary diffusion equation was solved numerically for the corresponding initial and boundary conditions for comparison. The anomalous diffusion constant was evaluated and is compared to the Brownian case. Some ad hoc correction of the propagator is shown to pay tribute to the finiteness of the system. In this way, anomalous solutions of the fractional diffusion equation could experimentally be verified.

Journal Article↗

PubMed1987

Solvent flow in osmosis and hydraulics: network thermodynamics and representation by bond graphs.

A tutorial introduction to network thermodynamics and bond graphs as a modeling technique for any physiochemical system is presented with a particular emphasis on reaction diffusion systems. It combines the generality of nonequilibrium thermodynamics with the advantages of a graph theory. It is applied to the representation of osmotic and hydraulic flows across a semipermeable membrane on the basis of the solvent diffusion theory of osmosis. This theory allows for an easy derivation of the van't Hoff law of osmotic pressure from the Fick law of diffusion. Molar flows and volume flows are transformed into one another by transducers, the modulus of which is the partial molar volume of water, in such a way that power is conserved by a reciprocal transformation between the chemical potential and the pressure. Osmotic and hydraulic resistances are calculated, and their dependence on pore size is estimated.

Diffusion↗

PubMed1986

Reduction of anoxia through myoglobin-facilitated diffusion of oxygen.

At relatively low perfusion rates, anoxic regions may occur in tissue even though oxygen remains in the blood as it leaves the capillary at the venous end. In this paper a mathematical theory of facilitated diffusion is developed and used to determine the extent to which myoglobin increases the removal of oxygen from blood and aids in the reduction or elimination of regions of anoxia.

Anaerobiosis↗

PubMed2005

Sorption kinetics of strontium in porous hydrous ferric oxide aggregates I. The Donnan diffusion model.

Sorption of ions by hydrous ferric oxide (HFO) often shows a fast initial sorption reaction followed by a much slower sorption process. The second step is diffusion-controlled and can continue for days or months before equilibrium is reached. In this paper, we demonstrate that the diffusion rate may be explained by electrostatic interactions. The internal and external surfaces of HFO are generally positively charged and therefore repel cations. This can result in extremely low cation concentrations in pores, and therefore a significant reduction in pore diffusion rate. The theory is demonstrated here for sorption of Sr(2+) in HFO aggregates. The ion concentrations in the pore space are calculated using a Donnan model and diffusion is calculated from the Donnan concentration and potential gradients. This diffusion model is compared with nonelectrostatic pore diffusion, which does not take electrostatic interactions into account. The Donnan model predicts very low concentrations of Sr(2+) in the pores and diffusion rates that are up to 8000 times lower than predicted with a nonelectrostatic model.

Journal Article↗

PubMed2002

Systematic derivation of reaction-diffusion equations with distributed delays and relations to fractional reaction-diffusion equations and hyperbolic transport equations: application to the theory of Neolithic transition.

We introduce a general method for the systematic derivation of nonlinear reaction-diffusion equations with distributed delays. We study the interactions among different types of moving individuals (atoms, molecules, quasiparticles, biological organisms, etc). The motion of each species is described by the continuous time random walk theory, analyzed in the literature for transport problems, whereas the interactions among the species are described by a set of transformation rates, which are nonlinear functions of the local concentrations of the different types of individuals. We use the time interval between two jumps (the transition time) as an additional state variable and obtain a set of evolution equations, which are local in time. In order to make a connection with the transport models used in the literature, we make transformations which eliminate the transition time and derive a set of nonlocal equations which are nonlinear generalizations of the so-called generalized master equations. The method leads under different specified conditions to various types of nonlocal transport equations including a nonlinear generalization of fractional diffusion equations, hyperbolic reaction-diffusion equations, and delay-differential reaction-diffusion equations. Thus in the analysis of a given problem we can fit to the data the type of reaction-diffusion equation and the corresponding physical and kinetic parameters. The method is illustrated, as a test case, by the study of the neolithic transition. We introduce a set of assumptions which makes it possible to describe the transition from hunting and gathering to agriculture economics by a differential delay reaction-diffusion equation for the population density. We derive a delay evolution equation for the rate of advance of agriculture, which illustrates an application of our analysis.

Biophysical Phenomena↗

PubMed2000

Enzymatic degradation of guar and substituted guar galactomannans.

Enzymatic degradation of guar galactomannan is studied using gel permeation chromatography (GPC) and steady shear viscometry. In very dilute polymer solutions, reaction rate increases with first-order kinetics with substrate concentration. In the intermediate concentration regime, the enzyme/polymer binding saturates, and the degradation kinetics is zero-order. The observations are in accord with a Michaelis-Menton kinetics model. The Michaelis-Menton parameter, Km and Vmax, were determined to be 0.6 mM and 7.8 x 10(-10) mol/(mL s) for guar at pH = 7, where the maximal velocity of the reaction, Vmax, was measured in terms of the molar concentration of glycosidic bonds broken per unit time. However, as the solution increases in concentration, the reaction rate decreases and the enzyme diffusion through the concentrated polymer gel becomes a limiting factor. A reaction-diffusion model is presented to express the competition between enzyme reaction and diffusion. The scaling theory and kinetic data are used to define the boundaries of the polymer concentration regimes between substrate (i.e., polymer strand) limited reactions, enzyme limited reactions, and hindered diffusion limited reactions. The influence of polymer derivatization on the degradation kinetics was also explored. The degradation rate was shown to be greatly affected by the type of substituent groups as well as the degree of substitution. The triggering mechanism and controlled degradation were found for the enzymatic hydrolysis of cationically derivatized guar solutions.

Algorithms↗

PubMed2005

Molecular simulation of loading-dependent diffusion in nanoporous materials using extended dynamically corrected transition state theory.

A dynamically corrected transition state theory method is presented that is capable of computing quantitatively the self-diffusivity of adsorbed molecules in confined systems at nonzero loading. This extension to traditional transition state theory is free of additional assumptions and yields a diffusivity identical to that obtained by conventional molecular-dynamics simulations. While molecular-dynamics calculations are limited to relatively fast diffusing molecules, our approach extends the range of accessible time scales significantly beyond currently available methods. We show results for methane, ethane, and propane in LTL- and LTA-type zeolites over a wide range of temperatures and loadings, and demonstrate the extensibility of the method to mixtures.

Journal Article↗

PubMed2001

Are mitochondria mesoscopic?

Systems whose length scales are small enough to be near the threshold where macroscopic thermodynamic descriptions fail are called mesoscopic. This is particularly appropriate for studies of mitochondrial function since basic and important ideas such as protomotive force, and models finding common applications, such as the Gouy-Chapman theory describing the diffuse ionic charge layer near the inner membrane, depend on the macroscopic thermodynamic notion of chemical potential. This paper shows that the length scales in Gouy-Chapman theory are not consistent with the premises upon which Gouy-Chapman theory was based, a failure typical of mesoscopic systems. Furthermore, while there are good reasons for a protomotive force to be a valid description for a collection of mitochondria, it is a marginal description even for an entire individual mitochondrion for similar reasons. Mitochondria are, therefore, physically mesoscopic systems.

Algorithms↗

PubMed2002

Regulation of lipid composition in Acholeplasma laidlawii and Escherichia coli membranes: NMR studies of lipid lateral diffusion at different growth temperatures.

Lipid lateral diffusion coefficients have been directly determined by pulsed field gradient NMR spectroscopy on macroscopically aligned, fully hydrated lamellar phases containing dimyristoylphosphatidylcholine and total lipid extracts from Acholeplasma laidlawii and Escherichia coli. The temperature dependence of the diffusion coefficient was of the Arrhenius type in the temperature interval studied. The sharp increase in the diffusion coefficient at the growth temperature of E. coli obtained by FRAP measurements, using a fluorescent probe molecule (Jin, A. J., Edidin, M., Nossal, R., and Gershfeld, N. L. (1999) Biochemistry 38, 13275-13278), was not observed. Thus, we conclude that the lipid structural properties (i.e., those affecting the lipid phase behavior), rather than the lipid dynamics, are involved in the adjustment of the membrane lipid composition. Further support for this conclusion is given by the finding that lipid extracts from A. laidlawii grown at different temperatures have about the same diffusion coefficients. Finally, the lipid lateral diffusion in bilayers of phospholipids was found to be much faster than that in bilayers of mainly glucolipids, which can be understood in terms of a free volume theory for the diffusion process.

Acholeplasma laidlawii↗

PubMed2005

Trans-interface diffusion-controlled coarsening.

Accurate theoretical predictions of the volume-fraction dependence during diffusion-controlled coarsening of a polydisperse assembly of particles have proved difficult. Here, a new model of coarsening is presented, involving diffusive transport through the coherent interface between ordered and disordered phases, which atomistic calculations show has a ragged structure. The interface is a diffusion bottleneck when the ordered phase is dispersed. It is predicted that the square of the average radius grows linearly with time, that the depletion of solute decreases as the inverse square-root of time, and that there is no effect of volume fraction on kinetics and the scaled particle-size distributions. These differ dramatically from predictions of modern theories of diffusion-controlled coarsening. Data on coarsening in Ni-Al alloys is examined. We show that no other theory is consistent with the experimentally observed absence of an effect of volume fraction on coarsening of ordered gamma' (Ni3Al) precipitates in a disordered Ni-Al (gamma) matrix, and the strong volume-fraction dependence of coarsening of gamma precipitates in an ordered gamma' matrix.

Alloys↗

PubMed2004

Pursuing the course from research to practice.

Diffusion of Innovation Theory describes the typical course by which innovations become standard practice. Research-based prevention programs are one such innovation. These programs have passed through the early phases of diffusion-innovation development and adoption by progressive schools that seek out innovations. With one quarter of the nation's schools having adopted a research-based program, the field is currently in the early majority phase of diffusion. If the patterns of normal diffusion hold true, this phase is likely to be characterized by emerging tensions between program developers and adopting schools. There are several concerns that require attention from researchers and practitioners. Practitioners need to develop their capacity to implement programs with fidelity and to adapt programs appropriately to meet their circumstance. Program developers need to simplify and redesign programs to make them appealing and useful to teachers. Operational capacity to fulfill orders and provide training needs to be developed.

Diffusion of Innovation↗

PubMed2002

Frequency-domain theory of laser infrared photothermal radiometric detection of thermal waves generated by diffuse-photon-density wave fields in turbid media.

A three-dimensional theory of the frequency-domain thermal-wave field generated inside a turbid medium with optical and thermal properties of human tissue is presented. The optical source is treated as a three-dimensional harmonically modulated diffuse-photon-density wave (DPDW) field in the diffusion approximation of the radiative transfer theory. Unlike earlier Green-function-based theoretical models, exact boundary conditions are used based on the requirement that there should be no diffuse photon intensity entering the turbid medium from the outside. Explicit analytical expressions for the DPDW field and for the dependent thermal-wave field are obtained in the spatial Hankel-transform domain. The formalism is further extended to the calculation of the infrared photothermal radiometric signal arising from the nonradiatively generated thermal-wave distribution in turbid media with instantaneous nonradiative deexcitation as well as in media with nonzero fluorescence relaxation lifetimes. Numerical inversions have been performed and presented as examples of selected special cases of the theory. It is found that the present theory with exact DPDW-field boundary conditions is valid throughout the entire domain of the turbid medium, with the exception of the very near-surface ballistic photon "skin layer" (7-50 microm). Photothermal radiometric signals were found to be more reliably predicted than DPDW signals within this layer, due to the depth-integration nature of this detection methodology.

Biophysical Phenomena↗

PubMed1988

Melting of a self-complementary DNA minicircle. Comparison of optical melting theory with exchange broadening of the nuclear magnetic resonance spectrum.

Melting curves are calculated for the 16-base-pair duplex DNA sequence 5' GTATCCGTACGGATAC 3' linked on the ends by TTTT single-strand loops. The equilibrium statistical thermodynamic theory of DNA melting is modified to include effects of end-loops on the melting transition. An excellent fit of the experimental melting curve in 0.2 M-NaCl is obtained using two adjustable parameters, one for end-loop formation and the other for formation of the complete 40-base single-strand loop. The best-fit calculated melting curve permits evaluation of these parameters. The free energy to close a TTTT end-loop is 2.12 kcal/mol (1 cal = 4.184 J). A TTTT end-loop or hairpin loop is significantly more stable than an internal loop of comparable size sandwiched between two helical regions, even after allowing for the different stacking contributions. Reasons for this increased stability are presented. The loop free energy of the 40-base single-strand open minicircle is evaluated to be +1.27 kcal/mol, thus favoring the melting of two end-loops into the large open minicircle. The present results are compared with those of others for d(T-A) oligomers. The sequence TTTT forms a more stable end-loop, or hairpin, than TATA by about 2.0 kcal/mol. Theoretical rate constants for the proton-transfer step in the standard hydrogen-exchange model are calculated by extending the theory of diffusion-controlled reactions to take account of the electrostatic potential of the DNA. The predicted ratios of rate constants for different pairs of catalysts exchanging an A.T proton agree satisfactorily with the available experimental data for a 14-base-pair linear duplex, which confirms the diffusion-control of the proton-transfer step. Data presented here for the 16 base-pair duplex of the minicircle are consistent with catalysis-limited exchange in which the proton-transfer step is likewise diffusion-controlled. Under catalysis-limited conditions, the imino proton exchange rates are predicted from the catalytic rate constants, prevailing buffer catalyst concentrations, and the equilibrium constants to form the unstacked open state of optical melting theory. The observed exchange rates of the A.T base-pairs show no sign of the strong predicted end-melting trend, and exceed the predicted values by factors of 10 to 400. Moreover, the succession of "melting" in the nuclear magnetic resonance line-broadening deviates from that predicted by optical melting theory.(ABSTRACT TRUNCATED AT 400 WORDS)

Base Sequence↗