14,765 research outputs found
Semi-analytical solution of multilayer diffusion problems with time-varying boundary conditions and general interface conditions
We develop a new semi-analytical method for solving multilayer diffusion
problems with time-varying external boundary conditions and general internal
boundary conditions at the interfaces between adjacent layers. The convergence
rate of the semi-analytical method, relative to the number of eigenvalues, is
investigated and the effect of varying the interface conditions on the solution
behaviour is explored. Numerical experiments demonstrate that solutions can be
computed using the new semi-analytical method that are more accurate and more
efficient than the unified transform method of Sheils [Appl. Math. Model.,
46:450-464, 2017]. Furthermore, unlike classical analytical solutions and the
unified transform method, only the new semi-analytical method is able to
correctly treat problems with both time-varying external boundary conditions
and a large number of layers. The paper is concluded by replicating solutions
to several important industrial, environmental and biological applications
previously reported in the literature, demonstrating the wide applicability of
the work.Comment: 24 pages, 8 figures, accepted version of paper published in Applied
Mathematics and Computatio
Zone Leveling Crystal Growth of Thermoelectric PbTe Alloys with Sb_(2)Te_3 Widmanstätten Precipitates
Unidirectional solidification of PbTe-rich alloys in the pseudobinary PbTe-Sb_(2)Te_3 system using the zone leveling technique enables the production of large regions of homogeneous solid solutions for the formation of precipitate nanocomposites as compared with Bridgman solidification. (PbTe)_(0.940)(Sb_(2)Te_3)_(0.060) and (PbTe)_(0.952)(Sb_(2)Te_3)_(0.048) alloys were successfully grown using (PbTe)_(0.4)(Sb_(2)Te_3)_(0.6) and (PbTe)_(0.461)(Sb_(2)Te_3)_(0.539) as seed alloys, respectively, with 1 mm h^(–1) withdrawal velocity. In the unidirectionally solidified regions of both alloys, Widmanstatten precipitates are formed due to the decrease in solubility of Sb_(2)Te_3 in PbTe. To determine the compositions of the seed alloys for the zone leveling experiments, the solute distribution in solidification in the PbTe-richer part of the pseudobinary PbTe-Sb_(2)Te_3 system has been examined from the concentration profiles in the samples unidirectionally solidified by the Bridgman method
Fast computation of effective diffusivities using a semi-analytical solution of the homogenization boundary value problem for block locally-isotropic heterogeneous media
Direct numerical simulation of diffusion through heterogeneous media can be
difficult due to the computational cost of resolving fine-scale
heterogeneities. One method to overcome this difficulty is to homogenize the
model by replacing the spatially-varying fine-scale diffusivity with an
effective diffusivity calculated from the solution of an appropriate boundary
value problem. In this paper, we present a new semi-analytical method for
solving this boundary value problem and computing the effective diffusivity for
pixellated, locally-isotropic, heterogeneous media. We compare our new solution
method to a standard finite volume method and show that equivalent accuracy can
be achieved in less computational time for several standard test cases. We also
demonstrate how the new solution method can be applied to complex heterogeneous
geometries represented by a grid of blocks. These results indicate that our new
semi-analytical method has the potential to significantly speed up simulations
of diffusion in heterogeneous media.Comment: 29 pages, 4 figures, 5 table
Correlations between the interfacial chemistry and current-voltage behavior of n-GaAs/liquid junctions
Correlations between the surface chemistry of etched, (100) oriented n-GaAs electrodes and their subsequent photoelectrochemical behavior have been probed by high-resolution x-ray photoelectron spectroscopy. GaAs photoanodes were chemically treated to prepare either an oxide-free near stoichiometric surface, a surface enriched in zero-valent arsenic (As0), or a substrate-oxide terminated surface. The current-voltage (I-V) behavior of each surface type was subsequently monitored in contact with several electrolytes
Space shuttle nonmetallic materials age life prediction
The chemiluminescence from samples of polybutadiene, Viton, Teflon, Silicone, PL 731 Adhesive, and SP 296 Boron-Epoxy composite was measured at temperatures from 25 to 150 C. Excellent correlations were obtained between chemiluminescence and temperature. These correlations serve to validate accelerated aging tests (at elevated temperatures) designed to predict service life at lower temperatures. In most cases, smooth or linear correlations were obtained between chemiluminescence and physical properties of purified polymer gums, including the tensile strength, viscosity, and loss tangent. The latter is a complex function of certain polymer properties. Data were obtained with far greater ease by the chemiluminescence technique than by the conventional methods of study. The chemiluminescence from the Teflon (Halon) samples was discovered to arise from trace amounts of impurities, which were undetectable by conventional, destructive analysis of the sample
Quark spin coupling in baryons - revisited
A direct connection can be made between mixing angles in negative parity
baryons and the spin coupling of constituent quarks. The mixing angles do not
depend on spectral data. These angles are recalculated for gluon exchange and
pion exchange between quarks. For pion exchange the results of Glozman and
Riska are corrected. The experimental data on mixing are very similar to those
derived from gluon exchange but substantially different from the values
obtained for pion exchange.Comment: 10 pages, RevTex; a sign error is corrected, spin-orbit results are
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