Overcomplete mechanisms of plastic collapse

The analysis of regular mechanisms of plastic collapse for plane frames may be done by simple statics. By contrast, the solutions of analogous problems for space frames require the use of deformation equations; the mere formation of a collapse mechanism does not make the collapsing portion of a frame soluble by statics alone. Further, the number of plastic hinges for regular collapse of a plane frame is determinable, but no rule can be constructed for the number of hinges in a space frame; indeed, space frames can collapse by mechanisms which appear to have more degrees of freedom than are necessary, and are in this sense over-complete.     

A beam summation algorithm for wave radiation and guidance in stratified media

A Gaussian beams summation (GBS) algorithm for tracking source excited wave fields in plane stratified media is presented. In the present application the medium is described by layers with constant gradient of the wave speed, and the GB propagators are calculated recursively in a closed form. The algorithm is calibrated for numerical efficacy and accuracy by defining simple physical criteria for choosing the expansion parameters (the beam collimation and the spectral discretization and truncation) that allow for sparse representation of the source-excited angular spectrum of beams. It is validated for a source-excited example in layered media, where it provides a smooth and physically meaningful solution under multipath and caustic conditions and remains accurate for long propagation ranges where phase error tends to accumulate.     

Preparation of isatoates from isatoic anhydride

A wide variety of alkyl isatoates can be prepared in good yield from the high temperature reaction of isatoic anhydride with alcohols. Isatoates were found to undergo an apparent high temperature rearrangement reaction. Proposed reaction schemes are presented for the formation of isatoates and the subsequent rearrangement reaction.     

Controlled synthesis of cell-laden microgels by radical-free gelation in droplet microfluidics

Micrometer-sized hydrogel particles that contain living cells can be fabricated with exquisite control through the use of droplet-based microfluidics and bioinert polymers such as polyethyleneglycol (PEG) and hyperbranched polyglycerol (hPG). However, in existing techniques, the microgel gelation is often achieved through harmful reactions with free radicals. This is detrimental for the viability of the encapsulated cells. To overcome this limitation, we present a technique that combines droplet microfluidic templating with bio-orthogonal thiol-ene click reactions to fabricate monodisperse, cell-laden microgel particles. The gelation of these microgels is achieved via the nucleophilic Michael addition of dithiolated PEG macro-cross-linkers to acrylated hPG building blocks and does not require any initiator. We systematically vary the microgel properties through the use of PEG linkers with different molecular weights along with different concentrations of macromonomers to investigate the influence of these parameters on the viability and proliferation of encapsulated yeast cells. We also demonstrate the encapsulation of mammalian cells including fibroblasts and lymphoblasts.