Das Jacobische Kriterium der Variationsrechnung und die Oszillationseigenschaften linearer Differentialgleichungen 2. Ordnung

Ohne Zusammenfassung     

Buckling of an axisymmetric vesicle under compression: the effects of resistance to shear

We consider the axisymmetric deformation of an initially spherical,porous vesicle with incompressible membrane having finite resistanceto in-plane shearing, as the vesicle is compressed between parallelplates. We adopt a thin-shell balance-of-forces formulationin which the mechanical properties of the membrane are describedby a single dimensionless parameter, C, which is the ratio ofthe membrane's resistance to shearing to its resistance to bending.This results in a novel free-boundary problem which we solvenumerically to obtain vesicle shapes as a function of plateseparation, h. For small deformations, the vesicle contactseach plate over a small circular area. At a critical value ofplate separation, h_TC, there is a transcritical bifurcationfrom which a new branch of solutions emerges, representing buckledvesicles which contact each plate along a circular curve. Forthe values of C investigated, we find that the transcriticalbifurcation is subcritical and that there is a further saddle-nodebifurcation (fold) along the branch of buckled solutions ath = h_SN (where h_SN > h_TC). The resulting bifurcation structureis commensurate with a hysteresis loop in which a sudden transitionfrom an unbuckled solution to a buckled one occurs as h is decreasedthrough h_TC and a further sudden transition, this time froma buckled solution to an unbuckled one, occurs as h is increasedthrough h_SN. We find that h_SN and h_TC increase with C, thatis, vesicles that resist shear are more prone to buckling.     

Glas, Keramik, feuerfeste Materialien

Ohne Zusammenfassung     

Injection moulding of thermoplastics: Freezing of variable-viscosity fluids.

The injection moulding of thermoplastics involves, during mould filling, flows of hot polymer melts into mould networks, the walls of which are so cold that frozen layers form on them. An analytical study of such flows is presented here for the case when the Graetz number is small and the Nahme number is non-zero and can be large. Thus the flows are fully-developed and temperature differences due to heat generation by viscous dissipation are sufficiently large to cause significant variations in viscosity. Gz Graetz number - h half-height of channel or disc - h ^* half-height of polymer melt region in channel or disc - L length of channel or pipe - m viscosity shear-rate exponent - Na _Q Nahme number based on flowrate - Na _P Nahme number based on pressure drop - Na _PL lower critical value of Nahme number based on pressure drop - Na _PU upper critical value of Nahme number based on pressure drop - Na _P Nahme number based on pressure gradient - p pressure - P pressure drop - Q volumetric flowrate - r radial coordinate in pipe or disc - R radius of pipe - Re Reynolds number - R _i inner radius of disc - R ₀ outer radius of disc - R ^* radius of polymer melt region in pipe - T temperature - T _m melting temperature of polymer - T ₀ reference temperature - T _w wall temperature - u axial velocity in pipe or channel or radial velocity in disc - w width of channel - x axial coordinate in channel - y transverse coordinate in channel or disc - z axial coordinate in pipe - thermal conductivity of molten polymer - thermal conductivity of frozen polymer - heat capacity of molten polymer - viscosity temperature exponent - dimensionless transverse coordinate in channel or disc - ^* dimensionless half-height of polymer melt region in channel or disc - dimensionless temperature - ^* dimensionless wall temperature - µ viscosity of molten polymer - µ ₀ consistency of molten polymer - dimensionless pressure drop - dimensionless pressure gradient - density of molten polymer - dimensionless radial coordinate in pipe or disc - _i dimensionless inner radius of disc - ^* dimensionless radius of polymer melt region in pipe - dimensionless velocity     

Injection moulding of thermoplastics: Freezing of variable-viscosity fluids.

The injection moulding of thermoplastics involves, during mould filling, flows of hot polymer melts into mould networks, the walls of which are so cold that frozen layers form on them. An analytical study of such flows is presented here for the case when the Graetz and Nahme numbers are large and the Pearson number is small. Thus the flows are developing and temperature differences due to heat generation by viscous dissipation are sufficiently large to cause significant variations in viscosity (but the difference between the entry temperature of the polymer to a specific part of the mould network and the melting temperature of the polymer is not). Br Brinkman number - Gz Graetz number - h half-height of channel or disc - h ^* half-height of polymer melt region in channel or disc - L length of channel or pipe - m viscosity shear-rate exponent - Na Nahme number - p pressure - P pressure drop - Pe Péclet number - Pn Pearson number - Q volumetric flowrate - r radial coordinate in pipe or disc - R radius of pipe - Re Reynolds number - R _i inner radius of disc - R _o outer radius of disc - R ^* radius of polymer melt region in pipe - T temperature - T _ad adiabatic temperature rise - T _e entry polymer melt temperature - T _m melting temperature of polymer - T _max maximum temperature - T ₀ reference temperature - T _w wall temperature - flow-average temperature rise - u _r radial velocity in pipe or disc - u _x axial velocity in channel - u _y transverse velocity in channel or disc - u _z axial velocity in pipe - w width of channel - x axial coordinate in channel or modified radial coordinate in disc - y transverse coordinate in channel or disc - z axial coordinate in pipe - thermal conductivity of molten polymer - thermal conductivity of frozen polymer - scaled dimensionless axial coordinate in channel or pipe or radial coordinate in disc - ₀ undetermined integration constant - heat capacity of molten polymer - viscosity temperature exponent - dimensionless transverse coordinate in channel or disc - ^* dimensionless half-height of polymer melt region in channel or disc - H ^* scaled dimensionless half-height of polymer melt region in channel or disc or radius of polymer melt region in pipe - dimensionless temperature - ^* dimensionless wall temperature - scaled dimensionless temperature - numerical constant - µ viscosity of molten polymer - µ ₀ consistency of molten polymer - dimensionless pressure gradient - scaled dimensionless pressure gradient - density of molten polymer - dimensionless radial coordinate in pipe or disc - _i dimensionless inner radius of disc - ^* dimensionless radius of polymer melt region in pipe - dimensionless streamfunction - scaled dimensionless streamfunction - dummy variable - streamfunction - similarity variable - similarity variable     

Llama-derived single-domain antibodies for the detection of botulinum A neurotoxin

Single-domain antibodies (sdAb) specific for botulinum neurotoxin serotype A (BoNT A) were selected from an immune llama phage display library derived from a llama that was immunized with BoNT A toxoid. The constructed phage library was panned using two methods: panning on plates coated with BoNT A toxoid (BoNT A Td) and BoNT A complex toxoid (BoNT Ac Td) and panning on microspheres coupled to BoNT A Td and BoNT A toxin (BoNT A Tx). Both panning methods selected for binders that had identical sequences, suggesting that panning on toxoided material may be as effective as panning on bead-immobilized toxin for isolating specific binders. All of the isolated binders tested were observed to recognize bead-immobilized BoNT A Tx in direct binding assays, and showed very little cross-reactivity towards other BoNT serotypes and unrelated protein. Sandwich assays that incorporated selected sdAb as capture and tracer elements demonstrated that all of the sdAb were able to recognize soluble (“live”) BoNT A Tx and BoNT Ac Tx with virtually no cross-reactivity with other BoNT serotypes. The isolated sdAb did not exhibit the high degree of thermal stability often associated with these reagents; after the first heating cycle most of the binding activity was lost, but the portion of the protein that did refold and recover antigen-binding activity showed only minimal loss on subsequent heating and cooling cycles. The binding kinetics of selected binders, assessed by both an equilibrium fluid array assay as well as surface plasmon resonance (SPR) using toxoided material, gave dissociation constants (K _D ) in the range 2.2 × 10⁻¹¹ to 1.6 × 10⁻¹⁰ M. These high-affinity binders may prove beneficial to the development of recombinant reagents for the rapid detection of BoNT A, particularly in field screening and monitoring applications.     

Spectral beam combining of 2 μm Tm fiber laser systems

Output beams from three independently frequency-stabilized thulium master-oscillator power-amplifier fiber laser systems were spectrally combined using a plane-ruled metal diffraction grating. Two laser channels were frequency-stabilized with guided mode resonance filters and the third was stabilized using a plane-ruled metal diffraction grating. The systems had output wavelengths between 1984 and 2015 nm, each with a spectral width of 100-450 pm and output powers between 40-120 W. The combined beam had powers up to 49 W and was 32% efficient with respect to the launched pump power.     

Amorphous BeN as a new solid host for rare‐earth‐related luminescent materials

Beryllium‐nitride (BeN) thin films were prepared by sputtering a Be target in an atmosphere of pure nitrogen. The films were doped with samarium simply by placing a piece of Sm metal on the surface of the Be target. Under these deposition conditions the films present an amorphous structure and an optical bandgap of approx. 4 eV. They also exhibit visible light emission due to Sm³⁺ ions as a result of either photon or electron excitation. The present experimental results show that amorphous BeN films are suitable, and efficient, III‐nitride hosts for rare‐earth doping purposes. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)