Existence,nonexistence and multiplicity results for nonlocal Dirichlet problems

In this paper we establish various existence, nonexistence and multiplicity results for fully nonlinear Dirichlet problems associated to nonlocal Hamilton–Jacobi equations. This study is accomplished by a careful analysis of the principal eigenvalues of the elliptic operator. Resonance phenomena and anti maximum principles are also established.     

The notion of motion: covariational reasoning and the limit concept

This paper investigates outcomes of building students’ intuitive understanding of a limit as a function's predicted value by examining introductory calculus students’ conceptions of limit both before and after instruction. Students’ responses suggest that while this approach is successful at reducing the common limit equals function value misconception of a limit, new misconceptions emerged in students’ responses. Analysis of students’ reasoning indicates a lack of covariational reasoning that coordinates changes in both x and y may be at the root of the emerging limit reached near x = c misconception. These results suggest that although dynamic interpretations of limit may be intuitive for many students, care must be taken to foster a dynamic conception that is both useful at the introductory calculus level and is in line with the formal notion of limit learned in advanced mathematics. In light of the findings, suggestions for adapting the pedagogical approach used in this study are provided.     

Carboxysome-Inspired Electrocatalysis using Enzymes for the Reduction of CO2 at Low Concentrations**

The electrolysis of dilute CO₂ streams suffers from low concentrations of dissolved substrate and its rapid depletion at the electrolyte-electrocatalyst interface. These limitations require first energy-intensive CO₂ capture and concentration, before electrolyzers can achieve acceptable performances. For direct electrocatalytic CO₂ reduction from low-concentration sources, we introduce a strategy that mimics the carboxysome in cyanobacteria by utilizing microcompartments with nanoconfined enzymes in a porous electrode. A carbonic anhydrase accelerates CO₂ hydration kinetics and minimizes substrate depletion by making all dissolved carbon available for utilization, while a highly efficient formate dehydrogenase reduces CO₂ cleanly to formate; down to even atmospheric concentrations of CO₂. This bio-inspired concept demonstrates that the carboxysome provides a viable blueprint for the reduction of low-concentration CO₂ streams to chemicals by using all forms of dissolved carbon.     

Controlled Annealing in Adaptive Multicomponent Gels

We use a pH-driven annealing process to convert between co-assembled and self-sorted networks in multicomponent gels. The initially formed gels at low pH are co-assembled, with the two components coexisting within the same self-assembled structures. We use an enzymatic approach to increase the pH, resulting in a gel-to-sol transition, followed by a hydrolysis to lower the pH once again. As the pH decreases, a self-sorted network is formed by a two-stage gelation process determined by the pK_a of each component. This approach can be expanded to layered systems to generate many varied systems by changing composition and rates of pH change, adapting their microstructure and so allowing access to a far greater range of morphologies and complexity than can be achieved in single component systems.     

Synthesis and Application of Low Molecular Weight PEI-Based Copolymers for siRNA Delivery with Smart Polymer Blends

Polyethylenimine (PEI) is a commonly used cationic polymer for small-interfering RNA (siRNA) delivery due to its high transfection efficiency at low commercial cost. However, high molecular weight PEI is cytotoxic and thus, its practical application is limited. In this study, different formulations of low molecular weight PEI (LMW-PEI) based copolymers polyethylenimine-g-polycaprolactone (PEI–PCL) (800 Da–40 kDa) and PEI–PCL–PEI (5–5–5 kDa) blended with or without polyethylene glycol-b-polycaprolactone (PEG–PCL) (5 kDa-4 kDa) are investigated to prepare nanoparticles via nanoprecipitation using a solvent displacement method with sizes ≈100 nm. PEG–PCL can stabilize the nanoparticles, improve their biocompatibility, and extend their circulation time in vivo. The nanoparticles composed of PEI–PCL–PEI and PEG–PCL show higher siRNA encapsulation efficiency than PEI–PCL/PEG–PCL based nanoparticles at low N/P ratios, higher cellular uptake, and a gene silencing efficiency of ≈40% as a result of the higher molecular weight PEI blocks. These results suggest that the PEI–PCL–PEI/PEG–PCL nanoparticle system could be a promising vehicle for siRNA delivery at minimal synthetic effort.     

Numerical simulation of boundary-layer transition at Mach two

The linear and early nonlinear stages of boundary-layer transition at free-stream Mach numberM ==2.0 are investigated by direct numerical simulation of the compressible Navier-Stokes equations. Results from simulations with a large computational box and small-amplitude random initial conditions are compared with linear stability theory. The growth rates of oblique waves are reproduced correctly. Two-dimensional waves show a growth that is modulated in time, indicating the presence of an extra unstable mode which moves supersonically relative to the free stream. Further simulations are conducted to investigate the nonlinear development of two- and three-dimensional disturbances The transition due to oblique disturbance waves is the most likely cause of transition at this Mach number, and is found to lead to the development of strong streamwise vortices.     

Early Membrane Responses to Magnetic Particles are Predictors of Particle Uptake in Neural Stem Cells

Magnetic particles (MPs) offer several advantages for neural cell therapy, but limited particle uptake by neural cells is a barrier to translation. It is recently proved that tailoring particle physicochemical properties (by enhancing their iron content) dramatically improves uptake in neural stem cells (NSCs)—a major transplant population. High‐throughput screening of particles with varying physicochemical properties can therefore aid in identifying particles with optimal uptake features, but research is hampered by the lack of simple methodologies for studying neural cell membrane responses to nanoparticle platforms. A high‐resolution–high throughput method has been used to study early membrane responses of primary rodent NSCs to particles of variant magnetite loading, to attempt to correlate these responses with known particle internalization profiles. Membrane imaging is enhanced through sequential staining with osmium (O) and thiocarbohydrazide (T), a method termed OTOTO, combined with field‐emission scanning electron microscopy (FESEM). A five‐point classification system was used to systematically evaluate early MP‐induced membrane responses to particles possessing distinct physicochemical properties. Significantly different profiles of membrane activation were noted that correlate with particle uptake profiles. It is suggested that our method can serve as a valuable predictor of particle internalization in neural cells for diverse particle platforms.