Absorption and transport properties of ultra-fine cellulose webs

Characterization of transport and absorption properties of nanofiber webs is a challenge, because in many cases the material is soft and cannot withstand the stresses exerted by the standard instruments. In this paper, we report on development of a new technique for materials characterization. We propose to conduct wicking and permeability experiments for full characterization of the nanowebs. As an example, we used electrospun cellulose acetate nanowebs. The wicking experiments showed very good reproducibility, demonstrating the square-root-of-time dependence of wetting front position vs time. The prefactor depends on a product of capillary pressure and materials permeability. We developed a technique to independently measure the permeability of small samples of nanowebs. Wicking and permeability data allow one to estimate the pore size; SEM micrographs confirmed the obtained estimates of pore radius. In general, the proposed method allows one to characterize the transport and absorption parameters of the nanofibrous materials for which the standard procedures are inapplicable.     

Size-selective molecular transport through silica colloidal nanopores

Diffusion rate of dye-labelled PAMAM dendrimers through free-standing silica colloidal crystals was studied as a function of the dendrimer generation and nanopore size to determine the transport selectivity.     

Computational thinking and constructionism: creating difference equations in spreadsheets

The invention of the computer has led to the establishment of a new research paradigm, computation, which has recently become more and more popular in scientific exploration. However, computation is not well represented in high school and university curricula in science and engineering, although it applies to a wide range of disciplines beyond computer science and software engineering. In light of the increasing need to provide students with computational education, this paper presents a novel way to develop computational thinking among students. The proposed approach is based on the implementation of Papert's theory of constructionism in electronic spreadsheets. In this approach, students build their knowledge while constructing the difference equation that describes a physical (or engineering) phenomenon, based on specific cases investigated in the spreadsheet. The method does not require the students to write code or perform complex calculations in the spreadsheet and makes it possible to teach advanced subjects at a relatively early stage. The method is demonstrated through contents taken from the secondary and tertiary curricula in mechanics and electromagnetism.     

Fredholmness and invertibility of Toeplitz operators with matrix almost periodic symbols

We consider Toeplitz operators with symbols that are almost periodic matrix functions of several variables. It is shown that under certain conditions on the group generated by the Fourier support of the symbol, a Toeplitz operator is Fredholm if and only if it is invertible.

     

The Subadditive Ergodic Theorem and generic stretching factors for free group automorphisms

Let F _k be a free group of rank k ≥ 2 with a fixed set of free generators. We associate to any homomorphism φ from F _k to a group G with a left-invariant semi-norm a generic stretching factor, λ(φ), which is a noncommutative generalization of the translation number. We concentrate on the situation where φ: F _k → Aut(X) corresponds to a free action of F _k on a simplicial tree X, in particular, where φ corresponds to the action of F _k on its Cayley graph via an automorphism of F _k . In this case we are able to obtain some detailed “arithmetic” information about the possible values of λ = λ(φ). We show that λ ≥ 1 and is a rational number with 2kλ ∈ ℤ[1/(2k − 1)] for every φ ∈ Aut(F _k ). We also prove that the set of all λ(φ), where φ varies over Aut(F _k ), has a gap between 1 and 1+(2k−3)/(2k ²−k), and the value 1 is attained only for “trivial” reasons. Furthermore, there is an algorithm which, when given φ, calculates λ(φ). The second and the third author were supported by the NSF grant DMS#0404991 and the NSA grant DMA#H98230-04-1-0115.     

Nonlinear convective flows in multilayer fluid system

The nonlinear thermocapillary and buoyant-thermocapillary flows in a three-layer system, filling a closed cavity and subjected to a temperature gradient directed along the interfaces, are investigated. The nonlinear simulations of convective regimes are performed by the finite-difference method. The process of transition of unicell structures into multicell structures is studied.     

Polymerization of ethylene oxide with potassium-graphite inclusion compounds

The polymerization of ethylene oxide (EO) in tetrahydrofuran (THF) initiated by inclusion compounds of potassium in graphite (C₂₄K) at 50°C was studied. During the initial slow stage of the polymerization the catalyst efficiency increases, while during the second rapid stage the reaction proceeds at a constant concentration of the active centers. The influence of the catalyst and monomer concentrations on the concentration of the active centers and on the catalyst efficiency was studied. The existence of the slow stage is explained by diffusion of ethylene oxide between the graphite planes, where both initiation and initial chain growth take place. The diffusion of the growing chains from the catalyst into the solution brings about the formation of a necessary concentration of active centers in the solution, which ensures the rapid growth of the polymer chains under homogeneous conditions. An x-ray study of the catalyst after polymerization shows a strongly disturbed crystal structure of the graphite. Poly-(ethylene oxide) obtained at a higher degree of conversion, does not contain low molecular weight fractions.