Global analysis of the shadow Gierer-Meinhardt system with general linear boundary conditions in a random environment

The global analysis of the shadow Gierer-Meinhardt system with multiplicative white noise and general linear boundary conditions is investigated in this paper. For this reaction-diffusion system, we employ a fixed point argument to prove local existence and uniqueness. Our results on global existence are based on \emph{a priori} estimates of solutions.     

Amplification of terahertz radiation in carbon nanotubes

We investigate theoretically the feasibility of amplification of terahertz radiation in aligned achiral carbon nanotubes, a zigzag (12,0) and an armchair (10,10) in comparison with a superlattice using a combination of a constant direct current (dc) and a high-frequency alternate current (ac) electric fields. The electric current density expression is derived using the semiclassical Boltzmann transport equation with a constant relaxation time. The electric field is applied along the nanotube axis. Analysis of the current density versus electric field characteristics reveals a negative differential conductivity behavior at high frequency, as well as photon assisted peaks. The photon assisted peaks are about an order of magnitude higher in the carbon nanotubes compared to the superlattice. These strong phenomena in carbon nanotubes can be used to obtain domainless amplification of terahertz radiation at room temperature.     

Multifunctional surfaces with discrete functionalized regions for biological applications

In this paper we describe a method for creating multifunctional glass surfaces presenting discrete patches of different proteins on an inert PEG-functionalized background. Microcontact printing is used to stamp the substrate with octadecyltrichlorosilane to define the active regions. The substrate is then back-filled with PEG-silane {[[2-methoxypoly(ethyleneoxy)]propyl]trimethoxysilane} to define passive regions. A microfluidics device is subsequently affixed to the substrate to deliver proteins to the active regions, with as many channels as there are proteins to be patterned. Examples of trifunctional surfaces are given which present three terminating functional groups, i.e., protein 1, protein 2, and PEG. These surfaces should be broadly useful in biological studies, as patch size is well established to influence cell viability, growth, and differentiation. Three examples of cellular interactions with the surfaces are demonstrated, including the capture of cells from a single cell suspension, the selective sorting of cells from a mixed suspension, and the adhesion of cells to ligand micropatches at critical shear stresses. Within these examples, we demonstrate that the patterned immobilized proteins are active, as they retain their ability to interact with either antibodies in solution or receptors presented by cells. When appropriate (e.g., for E-selectin), proteins are patterned in their physiological orientations using a sandwich immobilization technique, which is readily accommodated within our method. The protein surface densities are highly reproducible in the patches, as supported by fluorescence intensity measurements. Potential applications include biosensors based on the interaction of cells or of marker proteins with protein patches, fundamental studies of cell adhesion as a function of patch size and shear stress, and studies of cell differentiation as a function of surface cues.     

3D Nitrogen-Doped Graphene Encapsulated Metallic Nickel–Iron Alloy Nanoparticles for Efficient Bifunctional Oxygen Electrocatalysis

It is extremely desirable to explore high-efficient, affordable and robust oxygen electrocatalysts toward rechargeable Zn–air batteries (ZABs). A 3D porous nitrogen-doped graphene encapsulated metallic Ni₃Fe alloy nanoparticles aerogel (Ni₃Fe-GA₁) was constructed through a facile hydrothermal assembly and calcination process. Benefiting from 3D porous configuration with great accessibility, high electrical conductivity, abundant active sites, optimal nitrogen content and strong electronic interactions at the Ni₃Fe/N-doped graphene heterointerface, the obtained aerogel showed outstanding catalytic performance toward the oxygen evolution reaction (OER) and oxygen reduction reaction (ORR). Specifically, it exhibited an overpotential of 239 mV to attain 10 mA cm⁻² for OER, simultaneously providing a positive onset potential of 0.93 V within a half-wave potential of 0.8 V for ORR. Accordingly, when employed in the aqueous ZABs, Ni₃Fe-GA₁ achieved higher power density and superior reversibility than Pt/C−IrO₂ catalyst, making it a potential candidate for rechargeable ZABs.