On Decomposition Theorems for Hardy Spaces on Domains in ℂn and Applications

Hardy spaces of analytic functions are studied both on strongly pseudoconvex domains in ℂⁿ and on domains of finite type in ℂ². Duality theorems, atomic decompositions, and factorization of functions are treated. Mapping properties of certain Hankel operators are studied.     

An evolutionary method for optimization of plate buckling resistance

Optimization of plate buckling resistance is very complicated, because the in-plane stress resultants in the prebuckled state of a plate are functions of thickness distribution. This paper discusses the problem of finding the optimum thickness distribution of isotropic plate structures, with a given volume and layout, that would maximise the buckling load. A simple numerical method using the finite-element analysis is presented to obtain the optimum thickness distribution. Optimum designs of compression-loaded rectangular plates with different boundary conditions and plate aspect ratios are obtained by using the proposed method. Optimum designs from earlier studies and the methods of buckling analysis used to attain these results are discussed and compared with the designs from the proposed method. This paper also examines the reliability of the optimality criterion generally used for plate buckling optimization, which is based on the uniform strain energy density.     

Delaunay graphs are almost as good as complete graphs

LetS be any set ofN points in the plane and let DT(S) be the graph of the Delaunay triangulation ofS. For all pointsa andb ofS, letd(a, b) be the Euclidean distance froma tob and let DT(a, b) be the length of the shortest path in DT(S) froma tob. We show that there is a constantc (≤((1+√5)/2) π≈5.08) independent ofS andN such that $$\frac{{DT(a,b)}}{{d(a,b)}}< c.$$      

Layered droplet microstructures in sheared emulsions: finite-size effects

We investigate the influence of confinement on the steady state microstructure of emulsions sheared between parallel plates, in a regime where the average droplet dimension is comparable to the gap width between the confining walls. Utilizing droplet velocimetry, we find that the droplets can organize into discrete layers under the influence of shear. The number of layers decreases from two (at relatively higher shear rates) to one (at lower shear rates), as the drops grow slightly larger due to coalescence. We argue that the layering and overall composition profile may be controlled by the interplay of droplet collisions (which can cause separation of droplet centers in the velocity gradient direction), droplet migration toward the centerline (due to wall effects), and droplet packing constraints. We also study the effects of mixture composition on droplet microstructure, and summarize these results in the form of a morphology diagram in the parameter space of mass fraction and shear rate. We find that formation of strings of the suspended phase (reported earlier by our group in flow-visualization studies on confined emulsions) is observed over a broad composition window. We also find a stable (nontransient) morphology wherein the droplets are arranged in highly ordered pearl-necklace chain structures.     

On the Frequency of Zeros of Solutions of Second Order Linear Differential Equations

We consider the equation \(\rm f^{\prime\prime}+{A}(z){f}=0\) with linearly independent solutions f₁,₂, where A(z) is a transcendental entire function of finite order. Conditions are given on A(z) which ensure that max{λ(f₁),λ(f₂)} = ∞, where λ(g) denotes the exponent of convergence of the zeros of g. We show as a special case of a further result that if P(z) is a non-constant, real, even polynomial with positive leading coefficient then every non-trivial solution of \(\rm f^{\prime\prime}+{e}^P{f}=0\) satisfies λ(f) = ∞. Finally we consider the particular equation \(\rm f^{\prime\prime}+({e}^Z-K){f}=0\) where K is a constant, which is of interest in that, depending on K, either every solution has λ(f) = ∞ or there exist two independent solutions f₁, f₂ each with λ(f_i) ≤ 1.     

‘Sacrificial’ supramolecular assembly and pressure-induced polymerization: toward sequence-defined functionalized nanothreads

Limited supramolecular strategies have been utilized to synthesize sequence-defined polymers, despite the prominence of noncovalent interactions in materials design. Herein, we illustrate the utility of ‘sacrificial’ aryl-perfluoroaryl supramolecular synthons to synthesize sp³-hybridized nanothreads from sp²-enriched reactants. Our strategy features A–B reactant pairs in the form of a phenol:pentafluorophenol co-crystal that is preorganized for an electronically-biased and sequence-defined polymerization. The polymerization, initiated at 12 GPa, affords an alternating copolymer featuring exogenous –OH functionalities. The external substitution is confirmed through IR spectroscopy. Importantly, the inclusion of the functional unit provides the first experimental glimpse at reaction mechanism: keto–enol tautomerization that can only occur during cycloaddition is observed through IR spectroscopy. Our approach realizes the first example of a functionalized nanothread and attains sequence definition through sacrificial supramolecular preorganization and presents a further approach for de novo design of complex nanothreads.

Supramolecular synthons are exploited to synthesize –OH functionalized sp³-rich sequence-defined nanothreads using pressure-induced polymerization of a phenol:pentafluorophenol co-crystal.      

Transfer hydrogenation using recyclable polyurea-encapsulated palladium: efficient and chemoselective reduction of aryl ketones

A robust and recyclable palladium catalyst [Pd0EnCat] has been prepared by ligand exchange of polyurea-encapsulated palladium(II) acetate with formic acid, resulting in deposition of Pd(0) in the support material; Pd0EnCat is shown to be a highly efficient transfer hydrogenation catalyst for chemoselective reduction of a wide range of aryl ketones to benzyl alcohols.     

Rapid biomass analysis

New, rapid, and inexpensive methods that monitor the chemical composition of corn stover and corn stover-derived samples are a key element to enabling the commercialization of processes that convert stover to fuels and chemicals. These new techniques combine near infrared (NIR) spectroscopy and projection to latent structures (PLS) multivariate analysis to allow the compositional analysis of hundreds of samples in 1 d at a cost of about $10 each. The new NIR/PLS rapid analysis methods can also be used to support a variety of research projects that would have been too costly to pursue by traditional methods.     

Influence of structure and solubility of chain transfer agents on the RAFT control of dispersion polymerisation in scCO2

Reversible addition–fragmentation chain transfer (RAFT) dispersion polymerisation of methyl methacrylate (MMA) is performed in supercritical carbon dioxide (scCO₂) with 2-(dodecylthiocarbonothioylthio)-2-methylpropionic acid (DDMAT) present as chain transfer agent (CTA) and surprisingly shows good control over PMMA molecular weight. Kinetic studies of the polymerisation in scCO₂ also confirm these data. By contrast, only poor control of MMA polymerisation is obtained in toluene solution, as would be expected for this CTA which is better suited for acrylates. In this regard, we select a range of CTAs and use them to determine the parameters that must be considered for good control in dispersion polymerisation in scCO₂. A thorough investigation of the nucleation stage during the dispersion polymerisation reveals an unexpected “in situ two-stage” mechanism that strongly determines how the CTA works. Finally, using a novel computational solvation model, we identify a correlation between polymerisation control and degree of solubility of the CTAs. All of this ultimately gives rise to a simple, elegant and counterintuitive guideline to select the best CTA for RAFT dispersion polymerisation in scCO₂.

RAFT dispersion polymerisation of methyl methacrylate is performed in scCO₂ with 2-(dodecylthiocarbonothioylthio)-2-methylpropionic acid (DDMAT) present as chain transfer agent (CTA) and surprisingly shows good control over PMMA molecular weight.