Existence of extremal solutions by approximation to a first-order initial dynamic equation with Carathéodory's conditions and discontinuous non-linearities*

This paper is devoted to the study of the existence of extremal solutions to a first-order initial value problem on an interval of an arbitrary time scale. We prove the existence of extremal solutions for problems satisfying Carathéodory's conditions. Moreover, they are approximated uniformly by a sequence of lower and upper solutions to this problem, respectively.

We also can warrant the existence and approximation of extremal solutions for the problem by relaxing their continuity properties.     

A dislocation dynamics study of the strength of stacking fault tetrahedra. Part I: interactions with screw dislocations

We present a comprehensive dislocation dynamics (DD) study of the strength of stacking fault tetrahedra (SFT) to screw dislocation glide in fcc Cu. Our methodology explicitly accounts for partial dislocation reactions in fcc crystals, which allows us to provide more detailed insights into the dislocation–SFT processes than previous DD studies. The resistance due to stacking fault surfaces to dislocation cutting has been computed using atomistic simulations and added in the form of a point stress to our DD methodology. We obtain a value of 1658.9 MPa, which translates into an extra force resolved on the glide plane that dislocations must overcome before they can penetrate SFTs. In fact, we see they do not, leading to two well differentiated regimes: (i) partial dislocation reactions, resulting in partial SFT damage, and (ii) impenetrable SFT resulting in the creation of Orowan loops. We obtain SFT strength maps as a function of dislocation glide plane-SFT intersection height, interaction orientation, and dislocation line length. In general SFTs are weaker obstacles the smaller the encountered triangular area is, which has allowed us to derive simple scaling laws with the slipped area as the only variable. These laws suffice to explain all strength curves and are used to derive a simple model of dislocation–SFT strength. The stresses required to break through obstacles in the 2.5–4.8-nm size range have been computed to be 100–300 MPa, in good agreement with some experimental estimations and molecular dynamics calculations.     

Globular Polymer Grafts Require a Critical Size for Efficient Molecular Sieving of Enzyme Substrates

A series of 2,2‐bis(hydroxymethyl)propionic acid dendrons of generation 2 through 8 having a strained cyclooctyne at the core and hydroxy groups at the periphery were prepared by a divergent method and used to functionalize azide‐decorated α‐chymotrypsin. The ability of the appended dendrons to selectively block enzyme activity (through a molecular sieving effect) was investigated using a small molecule substrate (benzoyl‐l ‐tyrosine p‐nitroanilide), as well as two proteins of different size (casein and bovine serum albumin). Additionally, the ability of dendrons to block complexation with a chymotrypsin antagonist, α‐antichymotrypsin, was investigated, and it was found that the dendron coating effectively prevented inhibition by this antagonist. We found that a critical generation is required to achieve efficient sieving with bis‐MPA dendrons, which illustrates the importance of macromolecular architecture and size in the shielding of proteins.     

Label-free optical biosensing with slot-waveguides

We demonstrate label-free molecule detection by using an integrated biosensor based on a Si(3)N(4)/SiO(2) slot-waveguide microring resonator. Bovine serum albumin (BSA) and anti-BSA molecular binding events on the sensor surface are monitored through the measurement of resonant wavelength shifts with varying biomolecule concentrations. The biosensor exhibited sensitivities of 1.8 and 3.2 nm/(ng/mm(2)) for the detection of anti-BSA and BSA, respectively. The estimated detection limits are 28 and 16 pg/mm(2) for anti-BSA and BSA, respectively, limited by wavelength resolution.     

On‐Chip Alginate Microencapsulation of Functional Cells

We report the use of a PTFE‐based microfluidic device for the encapsulation of living, therapeutically‐active cells within monodisperse alginate microspheres. We present a novel microfluidic platform and a flexible experimental method for the production of alginate microspheres. Cell lines HEK293, U‐2 OS and PC12 were separately encapsulated using this method, with minimal loss of cell viability.

     

EBC-232 and 323: A Structural Conundrum Necessitating Unification of Five In Silico Prediction and Elucidation Methods

Structurally unique halimanes EBC-232 and EBC-323, isolated from the Australian rainforest plant Croton insularis, proved considerably difficult to elucidate. The two diastereomers, which consist an unusual oxo-6,7-spiro ring system fused to a dihydrofuran, were solved by unification and consultation of five in silico NMR elucidation and prediction methods [i.e., ACDLabs, olefin strain energy (OSE), DP4, DU8+ and TD DFT CD]. Structure elucidation challenges of this nature are prime test case examples for empowering future AI learning in structure elucidation.     

Synthesis and characterization of modular polyphosphonate homopolymers and copolymers

Linear polyphosphonates with the generic formula –[P(Ph)(X)OR′O]_n– (X = S or Se) have been synthesized by polycondensations of P(Ph)(NEt₂)₂ and a diol (HOR′OH = 1,4-cyclohexanedimethanol, 1,4-benzenedimethanol, tetraethylene glycol, or 1,12-dodecanediol) followed by reaction with a chalcogen. Random copolymers have been synthesized by polycondensations of P(Ph)(NEt₂)₂ and mixture of two of the diols in a 2:1:1 mol ratio followed by reaction with a chalcogen. Block copolymers with the generic formula –[P(Ph)(X)OR′O]_{(x + 2)} –[P(Ph)(X)OR′O]_{(x + 3)}– (X = S or Se) have been synthesized by the polycondensations of Et₂N[P(Ph)(X)OR′O]_{(x + 2)}P(Ph)NEt₂ oligomers with HOR′O[P(Ph)(X)OR′O]_{(x + 3)}H oligomers followed by reaction with a chalcogen. The Et₂N[P(Ph)(X)OR′O]_{(x + 2)}P(Ph)NEt₂ oligomers are prepared by the reaction of an excess of P(Ph)(NEt₂)₂ with a diol while the HOR′O[P(Ph)(X)OR′O]_{(x + 3)}H oligomers are prepared by the reaction of P(Ph)(NEt₂)₂ with an excess of the diol. In each case the excess, x is the same and determines the average block sizes. All of the polymers were characterized using ¹H, ¹³C{¹H}, and ³¹P{¹H} NMR spectroscopy, TGA, DSC, and SEC. ³¹P{¹H} NMR spectroscopy demonstrates that the random and block copolymers have the expected arrangements of monomers and, in the case of block copolymers, verifies the block sizes. All polymers are thermally stable up to ~300°C, and the arrangements of monomers in the copolymers (block vs. random) affect their degradation temperatures and T_g profiles. The polymers have weight average MWs of up to 3.8 × 10⁴ Da.