A bifurcation problem governed by the boundary condition II

In this work we consider the problem u = a(x)u^p in on , where is a smooth bounded domain, isthe outward unit normal to , is regarded as a parameter and0 < p < 1. We consider both cases where a(x) > 0 in or a(x) is allowed to vanish in a whole subdomain ₀ of . Ourmain results include existence of non-negative non-trivial solutionsin the range 0 < < ₁, where ₁ is characterized by meansof an eigenvalue problem, uniqueness and bifurcation from infinityof such solutions for small , and the appearance of dead coresfor large enough .     

Experimental investigation of primary and secondary features in high-mach-number shock-bubble interaction

Experiments to study the compression and unstable evolution of an isolated soap-film bubble containing helium, subjected to a strong planar shock wave (M=2.95) in ambient nitrogen, have been performed in a vertical shock tube of square internal cross section using planar laser diagnostics. The early phase of the interaction process is dominated by the formation of a primary vortex ring due to the baroclinic source of vorticity deposited during the shock-bubble interaction, and the mass transfer from the body of the bubble to the vortex ring. The late time (long after shock interaction) study reveals the presence of a secondary baroclinic source of vorticity at high Mach number which is responsible for the formation of counterrotating secondary and tertiary vortex rings and the subsequent larger rate of elongation of the bubble.     

Predictions of novel two-photon absorption bands in fluorescent proteins

By means of time-dependent density functional theory, we calculate the two-photon cross-sections for the lowest relevant excitations in some model chromophores of intrinsically fluorescent proteins. The two-photon strength of the first, one-photon active transition varies among the various chromophores, in line with experimental findings. Interestingly, additional transitions with large two-photon cross-sections are found in the 500-700 nm region arising from near-resonant enhancement, as revealed by few-state model analysis. Multiphoton excitation of fluorescent proteins in this spectral region can lead to relevant application for bioimaging.     

Recoverable PEG-supported copper catalyst for highly stereocontrolled nitroaldol condensation

A new poly(ethylene glycol)-modified DAT2-Cu(OAc)2 complex smoothly catalyzes a base-free nitroaldol condensation in a highly enantioselective manner (ee up to 93%) also in reagent-grade solvent and in the presence of air. Effective recovery and recycling (up to five runs) of supported catalysts are documented.     

Transport of chloride and carboxyfluorescein through phospholipid vesicle membranes by heptapeptide amphiphiles

Seven synthetic anion transporters (SAT) of the general form R(2)N-COCH(2)OCH(2)CO-(Gly)(3)-Pro-(Gly)(3)-OR' were prepared. Three pairs of compounds each contained twin n-hexyl, n-decyl, and n-octadecyl (R) groups at the N-terminus and one contained twin n-tetradecyl groups. Three of the compounds were C-terminated by benzyl and three by heptyl (R') residues. The ability of these compounds to mediate ion release from phospholipid vesicles was assessed. Chloride release was measured by ion selective electrode measurements and by chloride quenching of the fluorescent dye lucigenin. Transport of the anion carboxyfluorescein (CF) was measured by fluorescence dequenching. Differences in both the C- (R') and N-terminal (R) residues within the ionophores affected anion transport. The chloride release data acquired by ion selective electrode and fluorescence methods were similar but not identical. A possible carrier mechanism for Cl(-) transport was discredited. Both Cl(-) and CF anions were released from vesicles by these compounds. The results of CF and Cl(-) transport showed good consistency when the ionophore's N-terminal chains were either decyl or octadecyl but not when they were hexyl. The transport of CF and Cl(-) appears to be fundamentally different when R is C(6) compared to C(10) or C(18). Differences between the behavior of SATs with Cl(-) and CF were also reflected in negative ion mass spectrometric studies.     

Neumann boundary conditions for a nonlocal nonlinear diffusion operator. Continuous and discrete models

Let be a nonnegative, smooth function with , supported in , symmetric, , and strictly increasing in . We consider the Neumann boundary value problem for a nonlocal, nonlinear operator that is similar to the porous medium, and we study the equation

We prove existence and uniqueness of solutions and a comparison principle. We find the asymptotic behaviour of the solutions as : they converge to the mean value of the initial data. Next, we consider a discrete version of the above problem. Under suitable hypotheses we prove that the discrete model has properties analogous to the continuous one. Moreover, solutions of the discrete problem converge to the continuous ones when the mesh parameter goes to zero. Finally, we perform some numerical experiments.

     

Magnetically Active Carbon Nanotubes at Work

Endohedral and exohedral assembly of magnetic nanoparticles (MNPs) and carbon nanotubes (CNTs) recently gave birth to a large body of new hybrid nanomaterials (MNPs–CNTs) featuring properties that are otherwise not in reach with only the graphitic or metallic cores themselves. These materials feature enhanced magnetically guided motions (rotation and translation), magnetic saturation and coercivity, large surface area, and thermal stability. By guiding the reader through the most significant examples in this Concept paper, we describe how researchers in the field engineered and exploited the synergistic combination of these two types of nanoparticles in a large variety of current and potential applications, such as magnetic fluid hyperthermia therapeutics and in magnetic resonance imaging to name a few.     

Carbon–Phosphorus Coupling from C^N Cyclometalated AuIII Complexes

With the aim of exploiting new organometallic species for cross-coupling reactions, we report here on the Au^III-mediated C_aryl−P bond formation occurring upon reaction of C^N cyclometalated Au^III complexes with phosphines. The [Au(C^N)Cl₂] complex 1 featuring the bidentate 2-benzoylpyridine (C^CON) scaffold was found to react with PTA (1,3,5-triaza-7-phosphaadamantane) under mild conditions, including in water, to afford the corresponding phosphonium 5 through C−P reductive elimination. A mechanism is proposed for the title reaction based on in situ ³¹P{¹H} NMR and HR-ESI-MS analyses combined with DFT calculations. The C−P coupling has been generalized to other C^N cyclometalated Au^III complexes and other tertiary phosphines. Overall, this work provides new insights into the reactivity of cyclometalated Au^III compounds and establishes initial structure–activity relationships to develop Au^III-mediated C−P cross-coupling reactions.