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A moving boundary problem arising from the diffusion of oxygen in absorbing tissue
Approximate analytical and numerical solutions of a partial differential equation are obtained which describe the
diffusion of oxygen in an absorbing medium. Essential
mathematical difficulties are associated with the presence
of a moving boundary which marks the furthest penetration
of oxygen into the medium and also with the need to allow
for an initial distribution of oxygen through the medium
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A method for solving moving boundary problems in heat flow Part I: Using cubic splines
A new approach to a heat-flow problem involving a moving boundary makes use of a grid system which moves with the boundary. The necessary interpolations are performed by using cubic splines. The method smooths out irregularities in the motion of the boundary which were evident in previous calculations based on a fixed grid system
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A method for solving moving boundary problems in heat flow part ii: Using cubic polynomials
A moving grid system has been used to get the solution of the moving boundary problem discussed earlier in Part I, but basing the necessary interpolations on ordinary cubic polynomials rather than splines. The computations are much more economical and the results obtained are also found to he more satiafactory
Modeling of Transient Trapping of Fatty Acid Tails in Phospholipids
We present the derivation of a new model to describe neutron spin echo
spectroscopy and quasi-elastic neutron scattering data on liposomes. We compare
the new model with existing approaches and benchmark it with experimental data.
The analysis indicates the importance of including all major contributions into
modeling of the intermediate scattering function. Simultaneous analysis of the
experimental data on lipids with full contrast and tail contrast matched
samples, reveals highly confined lipid tail motion. A comparison of their
dynamics demonstrates the statistical independ-ence of tail-motion and
height-height correlation of the membrane. A more detailed analysis indi-cates
that lipid tails are subject to relaxations in a potential with cylindrical
symmetry, in addition to the undulation and diffusive motion of the liposome.
Despite substantial differences in the chemis-try of the fatty acid tails, the
observation indicates a universal behavior. The analysis of partially
deuterated systems confirms the strong contribution of the lipid tail to the
intermediate scattering function. Within the time range from 5 to 100 ns, the
intermediate scattering function can be de-scribed by the height-height
correlation function. The existence of the fast-localized tail motion and the
contribution of slow translational diffusion of liposomes determines the
intermediate scattering function for t 100 ns, respectively.
Taking into account the limited time window lowers the bending moduli by a
factor of 1.3 (DOPC) to 2 (DMPC) compared to the full range.Comment: 33 pages, 5 figures, published in Soft Matte
Fe and N self-diffusion in non-magnetic Fe:N
Fe and N self-diffusion in non-magnetic FeN has been studied using neutron
reflectivity. The isotope labelled multilayers, FeN/57Fe:N and Fe:N/Fe:15N were
prepared using magnetron sputtering. It was remarkable to observe that N
diffusion was slower compared to Fe while the atomic size of Fe is larger
compared to N. An attempt has been made to understand the diffusion of Fe and N
in non-magnetic Fe:N
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