Numerical solution to the Saffman-Taylor finger problem with kinetic undercooling regularisation

The Saffman-Taylor finger problem is to predict the shape and,in particular, width of a finger of fluid travelling in a Hele-Shaw cell filled with a different, more viscous fluid. In experiments the width is dependent on the speed of propagation of the finger, tending to half the total cell width as the speed increases. To predict this result mathematically, nonlinear effects on the fluid interface must be considered; usually surface tension is included for this purpose. This makes the mathematical problem suffciently diffcult that asymptotic or numerical methods must be used. In this paper we adapt numerical methods used to solve the Saffman-Taylor finger problem with surface tension to instead include the effect of kinetic undercooling, a regularisation effect important in Stefan melting-freezing problems, for which Hele-Shaw flow serves as a leading order approximation when the specific heat of a substance is much smaller than its latent heat. We find the existence of a solution branch where the finger width tends to zero as the propagation speed increases, disagreeing with some aspects of the asymptotic analysis of the same problem. We also find a second solution branch, supporting the idea of a countably infinite number of branches as with the surface tension problem.

Categorisation of activities of daily living of lower limb amputees during short-term use of a portable kinetic recording system : a preliminary study

The purpose of this preliminary study was to determine the relevance of the categorization of the load regime data to assess the functional output and usage of the prosthesis of lower limb amputees. The objectives were a) to introduce a categorization of load regime, b) to present some descriptors of each activity, and c) to report the results for a case. The load applied on the osseointegrated fixation of one transfemoral amputee was recorded using a portable kinetic system for 5 hours. The periods of directional locomotion, localized locomotion, and stationary loading occurred 44%, 34%, and 22% of recording time and each accounted for 51%, 38%, and 12% of the duration of the periods of activity, respectively. The absolute maximum force during directional locomotion, localized locomotion, and stationary loading was 19%, 15%, and 8% of the body weight on the anteroposterior axis, 20%, 19%, and 12% on the mediolateral axis, and 121%, 106%, and 99% on the long axis. A total of 2,783 gait cycles were recorded. Approximately 10% more gait cycles and 50% more of the total impulse than conventional analyses were identified. The proposed categorization and apparatus have the potential to complement conventional instruments, particularly for difficult cases.

The FAM deubiquitylating enzyme localizes to multiple points of protein trafficking in epithelia, where it associates with E-cadherin and β-catenin

Ubiquitylation is a necessary step in the endocytosis and lysosomal trafficking of many plasma membrane proteins and can also influence protein trafficking in the biosynthetic pathway. Although a molecular understanding of ubiquitylation in these processes is beginning to emerge, very little is known about the role deubiquitylation may play. Fat Facets in mouse (FAM) is substrate-specific deubiquitylating enzyme highly expressed in epithelia where it interacts with its substrate, β-catenin. Here we show, in the polarized intestinal epithelial cell line T84, FAM localized to multiple points of protein trafficking. FAM interacted with β-catenin and E-cadherin in T84 cells but only in subconfluent cultures. FAM extensively colocalized with β-catenin in cytoplasmic puncta but not at sites of cell-cell contact as well as immunoprecipitating with β-catenin and E-cadherin from a higher molecular weight complex (~500 kDa). At confluence FAM neither colocalized with, nor immunoprecipitated, β-catenin or E-cadherin, which were predominantly in a larger molecular weight complex (~2 MDa) at the cell surface. Overexpression of FAM in MCF-7 epithelial cells resulted in increased β-catenin levels, which localized to the plasma membrane. Expression of E-cadherin in L-cell fibroblasts resulted in the relocalization of FAM from the Golgi to cytoplasmic puncta. These data strongly suggest that FAM associates with E-cadherin and β-catenin during trafficking to the plasma membrane.

Aromatic l-amino acid decarboxylase : histochemical localization in rat kidney and lack of effect of dietary potassium or sodium loading on enzyme distribution

Utilizing a mono-specific antiserum produced in rabbits to hog kidney aromatic L-amino acid decarboxylase (AADC), the enzyme was localized in rat kidney by immunoperoxidase staining. AADC was located predominantly in the proximal convoluted tubules; there was also weak staining in the distal convoluted tubules and collecting ducts. An increase in dietary potassium or sodium intake produced no change in density or distribution of AADC staining in kidney. An assay of AADC enzyme activity showed no difference in cortex or medulla with chronic potassium loading. A change in distribution or activity of renal AADC does not explain the postulated dopaminergic modulation of renal function that occurs with potassium or sodium loading.

Kinetic study of goethite dehydration and the effect of aluminium substitution on the dehydrate

Goethite and Al-substituted goethite were synthesized and were characterized using XRD and XRF. The kinetic study of goethite dehydrate was investigated by TG and DTG at different heating rates (2, 5, 10, 15, 20 ◦C/min) and the effect of Al substitution for Fe on dehydrate was studied. The results showed that two types of absorbed water with the same Ed values of 3.4, 6.2 kJ/mol were confirmed on goethite and Alsubstituted goethite. Three types of hydroxyl units were proved, one being on the surface and the other two being in the structure of goethite. The substitution of Al for Fe in the structure of goethite decreases the desorption rate of hydroxyl, increases the dehydroxylation temperature, broadens the desorption peaks in DTG curves, and improves the Ed values from 19.4, 20.4, 26.1 kJ/mol to 21.6, 30, 33.6 kJ/mol when Al substitution comes to 9.1%.