Sum and product separabilities of multivariable functions and applications

Necessary and sufficient conditions for reducibility of certain classes of multivariable polynomials are considered. The special case when a polynomial in that class can be factored into a finite product of single variable polynomials is investigated. A set of necessary and sufficient conditions for decomposing a multivariable p.r.f. into a sum of single variable p.r.f.'s is given. Examples to illustrate applications of sum and product separabilities of functions are given.     

Feedback factorizing control of 3-D transfer functions via a canonical state-space model

The problem factorizing (separating) the transfer function of a given SISO 3-D discrete system, ie of a system depending on three independent variables, is considered. The 3-D system is assumed to be available in its transfer function representation, which is converted to a canonical state-space model by a simple inspection procedure. Then applying state-feedback to this canonical model we choose the feedback matrix gain (under certain conditions) such that the transfer function of the closed-loop system has the desireed factorized form, ie a product of three 1-D transfer functions each one being dependent on a single variable. The method is illustrated by a nontrivial numerical example.     

The diffusion of moisture in sorbent solids part II. activated alumina

Ordinary and thermal diffusion of moisture in activated alumina are investigated using a new diffusion cell design and scheme of analysis reported earlier. The specific form of the mass flux equation has a pronounced effect on the magnitude of the associated thermal diffusion ratio. In the case of activated alumina-moist air, if a partial pressure gradient is used, then the thermal diffusion term is small if not zero.Free, Knudsen and surface diffusion all play a part in the diffusion through activated alumina. However, surface diffusion makes the major contribution and for this reason the model in this case can be simplified to a two parameter surface model.The activation energy for surface diffusion is constant and is approximately equal to the mean isosteric heat of absorption. In addition, mean pore radius, turtuosity, and other physical constants are computed from the least square fit of experimental data. Furthermore, the model is theoretically consistent over the entire concentration range (0≦ C_A ≦ C_Asat).A new fact about activated alumina (Grade F1) it that it does not transfer moisture in a nonisothermal condition so long as the partial pressures of moisture on the two sides of the pellet are the same. There appears to be no previous report of this fact in the periodical literature.     

Dynamics of the atmosphere of Jupiter

Atmospheric jets and vortices on Jupiter persist for decades in the presence of vigorous turbulence which might be expected to destroy organized flows. The penetration depth of the jets into the planet has been a major question, and new data from the NASA Galileo entry probe suggest that they are not shallow atmospheric phenomena. Numerical simulations and Galileo orbiter data promise further progress in the near future.     

Geometrical effects in microfluidic-based microarrays for rapid, efficient single-cell capture of mammalian stem cells and plant cells

In this paper, a detailed numerical and experimental investigation into the optimisation of hydrodynamic micro-trapping arrays for high-throughput capture of single polystyrene (PS) microparticles and three different types of live cells at trapping times of 30 min or less is described. Four different trap geometries (triangular, square, conical, and elliptical) were investigated within three different device generations, in which device architecture, channel geometry, inter-trap spacing, trap size, and trap density were varied. Numerical simulation confirmed that (1) the calculated device dimensions permitted partitioned flow between the main channel and the trap channel, and further, preferential flow through the trap channel in the absence of any obstruction; (2) different trap shapes, all having the same dimensional parameters in terms of depth, trapping channel lengths and widths, main channel lengths and widths, produce contrasting streamline plots and that the interaction of the fluid with the different geometries can produce areas of stagnated flow or distorted field lines; and (3) that once trapped, any motion of the trapped particle or cell or a shift in its configuration within the trap can result in significant increases in pressures on the cell surface and variations in the shear stress distribution across the cell’s surface. Numerical outcomes were then validated experimentally in terms of the impact of these variations in device design elements on the percent occupancy of the trapping array (with one or more particles or cells) within these targeted short timeframes. Limitations on obtaining high trap occupancies in the devices were shown to be primarily a result of particle aggregation, channel clogging and the trap aperture size. These limitations could be overcome somewhat by optimisation of these device design elements and other operational variables, such as the average carrier fluid velocity. For example, for the 20 μm polystyrene microparticles, the number of filled traps increased from 32% to 42% during 5–10 min experiments in devices with smaller apertures. Similarly, a 40%–60% reduction in trapping channel size resulted in an increase in the amount of filled traps, from 0% to almost 90% in 10 min, for the human bone marrow derived mesenchymal stem cells, and 15%–85% in 15 min for the human embryonic stem cells. Last, a reduction of the average carrier fluid velocity by 50% resulted in an increase from 80% to 92% occupancy of single algae cells in traps. Interestingly, changes in the physical properties of the species being trapped also had a substantial impact, as regardless of the trap shape, higher percent occupancies were observed with cells compared to single PS microparticles in the same device, even though they are of approximately the same size. This investigation showed that in microfluidic single cell capture arrays, the trap shape that maximizes cell viability is not necessarily the most efficient for high-speed single cell capture. However, high-speed trapping configurations for delicate mammalian cells are possible but must be optimised for each cell type and designed principally in accordance with the trap size to cell size ratio.     

Cyclic olefin copolymer based microfluidic devices for biochip applications: Ultraviolet surface grafting using 2-methacryloyloxyethyl phosphorylcholine

This report studies the surface modification of cyclic olefin copolymer (COC) by 2-methacryloyloxyethyl phosphorylcholine (MPC) monomer using photografting technique for the purpose of biointerface applications, which demonstrate resistance to both protein adsorption and cell adhesion in COC-based microfluidic devices. This is essential because the hydrophobic nature of COC can lead to adsorption of specific compounds from biological fluids in the microchannel, which can affect the results during fluidic analysis and cause clogging inside the microchannel. A correlation was found between the irradiation time and hydrophobicity of the modified substrate. Static water contact angle results show that the hydrophilicity property of the MPC-grafted substrate improves with increasing irradiation time. The contact angle of the modified surface decreased to 20 ± 5° from 88 ± 3° for the untreated substrate. The surface characterization of the modified surface was evaluated using x-ray photoelectron spectroscopy (XPS) and Fourier transform infrared spectroscopy (FTIR spectroscopy). Attenuated total reflection-FTIR and XPS results show the presence of the phosphate group (P-O) on modified COC substrates, indicating that the hydrophilic MPC monomer has successfully grafted on COC. Finally, it was demonstrated that cell adhesion and protein adsorption on the MPC modified COC specimen has reduced significantly.