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We investigate the diffusion of particles on heterogeneous lattices with two kinds of nonequivalent sites. General analytical expressions for the chemical and jump diffusion coefficients have been derived in the case of strong inhomogeneity. We have calculated coverage dependencies of the diffusion coefficients and other necessary thermodynamic quantities for some representative values of the lateral pairwise interaction between the particles. The analytical data have been compared with the numerical data obtained by the kinetic Monte Carlo simulations. Almost perfect agreement between the respective results has been found.

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Restricted diffusion of gas in the lung is in many ways similar to restricted diffusion in other porous media: atomic collisions with boundaries restrict the measured value, and there is a critical dependence on the time and distance scales of the measurement. The large free diffusivity of gases allows large pores (300 microns or larger) to be studied. The high signals of hyperpolarization permit rapid diffusion imaging of the gas itself, though fluorinated hydrocarbons are simple by comparison and are a potential alternative. The complicated nature of bifurcating human lung structure provides challenges in interpretation of results of restricted diffusion. At times sufficiently short, the short-time slope of D(t)/D0 can be related to the surface-to-volume ratio - an important measure of lung structure and early emphysema. During times of a few milliseconds, diffusion anisotropy is observed, and the principal components of diffusion are related to geometric parameters of individual airways within the pulmonary acinus. This permits regional invivo lung morphometry, which gives spatial information about features and airway geometry much smaller than the imaging voxel size. The extraordinarily long T1 of 3He provides the opportunity to use stimulated echoes to probe long diffusion times and distances. Preliminary evidence indicates that for distances significantly larger than a pulmonary acinus (≥ 1 cm), the measured diffusivity is severely restricted (near 0.02 cm2/s) and is dominated by diffusion through collateral routes. This implies that the longrange ADC measurement of 3He in lungs is an exquisitely sensitive measure of collateral airway paths.

The rapid-acquisition of q-space data from 1H2O undergoing restricted diffusion in suspensions of red blood cells (RBCs) is made possible using a recently implemented pulse sequence, where the phase cycling of the radio-frequency pulses is reduced by using unbalanced pairs of bipolar magnetic field-gradient pulses. The q-space plots obtained with this pulse sequence show a shift in the position of the first diffraction minimum when compared to data from classical pulsed field gradient stimulated echo experiments. Diffusion simulations were used to investigate the effect of the additional delay introduced by the bipolar gradient pulses on the form of the q-space plots. RBCs of normal discocyte shape align with an external magnetic field, and the angular dependence of q-space spectra from suspensions of RBCs was examined using a linear combination of gradients applied along the y- and z-axes. The resulting q-space plots showed a gradual disappearance of the first diffraction minimum as the angle at which the gradients were applied was changed from 0° (along the z-axis) to~40°, beyond which the q-space plots showed no diffraction features. These experimental results were also evident in Monte-Carlo random walk simulations of diffusion in RBCs with field-gradients applied at varying angles with respect to cells aligned with B0.

No description available.

No description available.

No description available.

The science of diffusion had its beginnings in the nineteenth century, although the blacksmiths and metal artisans of antiquity already, used diffusion phenomena to make such objects as hardened iron swords and gilded bronze wares. Diffusion as a scientific discipline is based on several cornerstones. The most important ones are: (i) The continuum theory of diffusion originating from the work of the German physiologist Adolf Fick, who was inspired by elegant experiments on diffusion in gases and of salt in water performed by the Scotsman Thomas Graham. (ii) The Brownian motion, observed for the first time by the Scotish botanist Robert Brown, was interpreted decades later by the famous German-Jewish physicist Albert Einstein and almost at the same time by the Polish physicist Marian von Smoluchowski. Their theory related the mean square displacement of atoms to the diffusion coefficient. This provided the statistical cornerstone of diffusion and bridged the gap between mechanics and thermodynamics. The Einstein-Smoluchowski relation was verified in tedious experiments by the French Nobel laureate Jean Baptiste Perrin and his coworkers. (iii) Solid-state diffusion was first studied systematically on the example of gold in lead by the British metallurgist Roberts-Austen in 1896. Using a natural radioisotope of lead the Austro-Hungarian Georg von Hevesy and his coworkers performed for the first time studies of self-diffusion in liquid and solid lead around 1920. (iv) The atomistics of diffusion in materials had to wait for the birthday of solid-state physics, heralded by the experiments of the German Nobel laureate Max von Laue. Equally important was the perception of the Russian and German scientists Jakov Frenkel and Walter Schottky, reinforced by the experiments of the American metallurgist Ernest Kirkendall, that point defects play an important role for the properties of crystalline substances, most notably for those controlling diffusion and the many properties that stem from it. (v) The American physicist and twofold Nobel laureate John Bardeen was the first who pointed out the role of correlation in defect-mediated diffusion in solids, an aspect, which was treated in great detail by the American physicist John Manning. (vi) The first systematic studies of grain-boundary diffusion, a transport phenomenon of fundamental as well as technological importance, were initiated by the American materials scientist David Turnbull.

The understanding of human mobility and the development of qualitative models as well as quantitative theories for it is of key importance to the research of human infectious disease dynamics on large geographical scales. In our globalized world, mobility and traffic have reached a complexity and volume of unprecedented degree. Long range human mobility is now responsible for the rapid geographical spread of emergent infectious diseases. Multiscale human mobility networks exhibit two prominent features: (1) Networks exhibit a strong heterogeneity, the distribution of weights, traffic fluxes and populations sizes of communities range over many orders of magnitude. (2) Although the interaction magnitude in terms of traffic intensities decreases with distance, the observed power-laws indicate that long range interactions play a significant role in spatial disease dynamics. We will review how the topological features of traffic networks can be incorporated in models for disease dynamics and show, that the way topology is translated into dynamics can have a profound impact on the overall disease dynamics. We will also introduce a class of spatially extended models in which the impact and interplay of both spatial heterogeneity as well as long range spatial interactions can be investigated in a systematic fashion. Our analysis of multiscale human mobility networks is based on a proxy network of dispersing US dollar bills, which we incorporated in a model to produce real-time epidemic forecasts that projected the spatial spread of the recent outbreak of Influenza A(H1N1).