Special functions associated with a certain fourth-order differential equation

We develop a theory of “special functions” associated with a certain fourth-order differential operator D_m,n\mathcal{D}_{\mu,\nu} on ℝ depending on two parameters μ,ν. For integers μ,ν≥−1 with μ+ν∈2ℕ₀, this operator extends to a self-adjoint operator on L ²(ℝ₊,x ^μ+ν+1 dx) with discrete spectrum. We find a closed formula for the generating functions of the eigenfunctions, from which we derive basic properties of the eigenfunctions such as orthogonality, completeness, L ²-norms, integral representations, and various recurrence relations.     

Validation of an Eulerian Stochastic Fields Solver Coupled with Reaction–Diffusion Manifolds on LES of Methane/Air Non-premixed Flames

Flow, Turbulence and Combustion - The Eulerian stochastic fields (ESF) combustion model can be used in LES in order to evaluate the filtered density function to describe the process of...     

Upper and Lower Bounds for the Synchronizer Performance in Systems with Probabilistic Message Loss

Methodology and Computing in Applied Probability - In this paper, we revisit the performance of the α-synchronizer in distributed systems with probabilistic message loss as introduced in...     

Reactive Nanoparticles Derived from Polysaccharide Phenyl Carbonates

Polysaccharide (PS) based nanoparticles (NP) are of great interest for biomedical applications. A key challenge in this regard is the functionalization of these nanomaterials. The aim of the present work was the development of reactive PS-NP that can be coupled with an amino group containing compounds under mild aqueous conditions. A series of cellulose phenyl carbonates (CPC) and xylan phenyl carbonates (XPC) with variable degrees of substitution (DS) was obtained by homogeneous synthesis. The preparation of PS-NP by self-assembling of these hydrophobic derivatives was studied comprehensively. While CPC mostly formed macroscopic aggregates, XPC formed well-defined spherical NP with diameters around 100 to 200 nm that showed a pronounced long-term stability in water against both particle aggregation as well as cleavage of phenyl carbonate moieties. Using an amino group functionalized dye it was demonstrated that the novel XPC-NP are reactive towards amines. A simple coupling procedure was established that enables direct functionalization of the reactive NP in an aqueous dispersion. Finally, it was demonstrated that dye functionalized XPC-NP are non-cytotoxic and can be employed in advanced biomedical applications.     

Conical surface structures on model thin-film electrodes and tape-cast electrode materials for lithium-ion batteries

A computationally-effective approach for calculating the electromechanical behavior of SWNTs and MWNTs of the dimensions used in nano-electronic devices has been developed. It is a mixed finite element–tight-binding code carefully designed to realize significant time saving in calculating deformation-induced changes in electrical transport properties of the nanotubes. The effect of the MWNT diameter and chirality on the conductance after mechanical deformation was investigated. In case of torsional deformation, results revealed the conductance of MWNTs to depend strongly on the diameter, since bigger MWNTs reach the buckling load under torsion much earlier, their electrical conductivity changes more easily than in small diameter ones. For the same outer diameter, zigzag MWNTs are more sensitive to twisting than armchair MWNTs since the hexagonal cells are oriented in such a way that they oppose less resistance to the buckling deformations due to torsion. Thus small diameter armchair MWNTs should work better if used as conductors, while big diameter zigzag MWNTs are more suitable for building sensors.     

A theoretical description of elastic pillar substrates in biophysical experiments.

Arrays of elastic pillars are used in biophysical experiments as sensors for traction forces. The evaluation of the forces can be complicated if they are coupled to the pillar displacements over large distances. This is the case if many of the pillars are interconnected by elastic linkages as, for example, in fiber networks that are grown on top of pillars. To calculate the traction forces in such a network, we developed a set of nonlinear inhomogeneous equations relating the forces in the linking elements to the resulting pillar deflections. We chose a homogeneous, activated two-dimensional network of cytoskeletal actin filaments to illustrate that a pillar substrate is generally not a force sensor but a force-gradient sensor. In homogeneous networks the forces acting along the filaments can be approximated by analyzing only pillar deflections in the edge zones of the substrate and by integration over the corresponding force gradients.