On uniformly rotating fluid drops trapped between two parallel plates

This contribution is about the dynamics of a liquid bridge between two fixed parallel plates. We consider a mathematical model and present some results from the doctoral thesis [10] of the first author. He showed that there is a Poisson bracket and a corresponding Hamiltonian, so that the model equations are in Hamiltonian form. The result generalizes previous results of Lewis et al. on the dynamics of free boundary problems for "free" liquid drops to the case of a drop between two parallel plates, including, especially the effect of capillarity and the angle of contact between the plates and the free fluid surface. Also, we prove the existence of special solutions which represent uniformly rotating fluid ridges, and we present specific stability conditions for these solutions. These results extend work of Concus and Finn [2] and Vogel [18],[19] on static capillarity problems (see also Finn [5]). Using the Hamiltonian structure of the model equations and symmetries of the solutions, the stability conditions can be derived in a systematic way. The ideas that are described will be useful for other situations involving capillarity and free boundary problems as well

Discrete Routh Reduction

This paper develops the theory of abelian Routh reduction for discrete mechanical systems and applies it to the variational integration of mechanical systems with abelian symmetry. The reduction of variational Runge-Kutta discretizations is considered, as well as the extent to which symmetry reduction and discretization commute. These reduced methods allow the direct simulation of dynamical features such as relative equilibria and relative periodic orbits that can be obscured or difficult to identify in the unreduced dynamics. The methods are demonstrated for the dynamics of an Earth orbiting satellite with a non-spherical $J_2$ correction, as well as the double spherical pendulum. The $J_2$ problem is interesting because in the unreduced picture, geometric phases inherent in the model and those due to numerical discretization can be hard to distinguish, but this issue does not appear in the reduced algorithm, where one can directly observe interesting dynamical structures in the reduced phase space (the cotangent bundle of shape space), in which the geometric phases have been removed. The main feature of the double spherical pendulum example is that it has a nontrivial magnetic term in its reduced symplectic form. Our method is still efficient as it can directly handle the essential non-canonical nature of the symplectic structure. In contrast, a traditional symplectic method for canonical systems could require repeated coordinate changes if one is evoking Darboux' theorem to transform the symplectic structure into canonical form, thereby incurring additional computational cost. Our method allows one to design reduced symplectic integrators in a natural way, despite the noncanonical nature of the symplectic structure.Comment: 24 pages, 7 figures, numerous minor improvements, references added, fixed typo

ErbB2 and bone sialoprotein as markers for metastatic osteosarcoma cells

Osteosarcoma is the most common malignant bone neoplasia occurring in young patients in the first two decades of life, and represents 20% of all primitive malignant bone tumours. At present, treatment of metastatic osteosarcoma is unsatisfactory. High-dose chemotherapy followed by CD34+ leukapheresis rescue may improve these poor results. Neoplastic cells contaminating the apheresis may, however, contribute to relapse. To identify markers suitable for detecting osteosarcoma cells in aphereses we analysed the expression of bone-specific genes (Bone Sialoprotein (BSP) and Osteocalcin) and oncogenes (Met and ErbB2) in 22 patients with metastatic osteosarcoma and six healthy stem cell donors. The expression of these genes in aphereses of patients affected by metastatic osteosarcoma was assessed by RT–PCR and Southern blot analysis. Met and Osteocalcin proved to be not useful markers since they are positive in aphereses of both patients with metastatic osteosarcoma and healthy stem cell donors. On the contrary, BSP was expressed at significant levels in 85% of patients. Moreover, 18% of patients showed a strong and significantly positive (seven to 16 times higher than healthy stem cell donors) ErbB2 expression. In all positive cases, neoplastic tissue also expressed ErbB2. Our data show that ErbB2 can be a useful marker for tumour contamination in aphereses of patients affected by ErbB2-expressing osteosarcomas and that analysis of Bone Sialoprotein expression can be an alternative useful marker

Screening and identification of seed-specific genes using digital differential display tools combined with microarray data from common wheat

<p>Abstract</p> <p>Background</p> <p>Wheat is one of the most important cereal crops for human beings, with seeds being the tissue of highly economic value. Various morphogenetic and metabolic processes are exclusively associated with seed maturation. The goal of this study was to screen and identify genes specifically expressed in the developing seed of wheat with an integrative utilization of digital differential display (DDD) and available online microarray databases.</p> <p>Results</p> <p>A total of 201 unigenes were identified as the results of DDD screening and microarray database searching. The expressions of 6 of these were shown to be seed-specific by qRT-PCR analysis. Further GO enrichment analysis indicated that seed-specific genes were mainly associated with defense response, response to stress, multi-organism process, pathogenesis, extracellular region, nutrient reservoir activity, enzyme inhibitor activity, antioxidant activity and oxidoreductase activity. A comparison of this set of genes with the rice (<it>Oryza sativa</it>) genome was also performed and approximately three-fifths of them have rice counterparts. Between the counterparts, around 63% showed similar expression patterns according to the microarray data.</p> <p>Conclusions</p> <p>In conclusion, the DDD screening combined with microarray data analysis is an effective strategy for the identification of seed-specific expressed genes in wheat. These seed-specific genes screened during this study will provide valuable information for further studies about the functions of these genes in wheat.</p