Bifurcation and symmetry breaking for a class of semilinear elliptic equations in an annulus

In this paper we consider the problem $$\left\{ \begin{array}{ll} -\Delta u=u^p+\lambda u & \quad\hbox{ in }A,\\ u > 0&\quad \hbox{ in }A,\\ u=0 &\quad \hbox{ on }\partial A, \end{array}\right. $$ where A is an annulus of ${\mathbb{R}^N,N\ge2}$ and p?>?1. We prove bifurcation of nonradial solutions from the radial solution in correspondence of a sequence of exponents {p _k } and for expanding annuli.     

On a class of nonlinear integral equations

In this paper we consider abstract equations of the typeK _ν ν +ν =w ₀, in a closed convex subset of a separable Hilbert spaceH. For eachv in the closed convex subset,K _v :H →H is a bounded linear map. As an application of our abstract result we obtain an existence result for nonlinear integral equations of the typeν(s)+ν(s)∫ ₀ ¹ k(s,t)ν(t)dt =W ₀(s) in the spaceL ² [0,1].     

Functional GPCR microarrays

This paper describes G-protein-coupled receptor (GPCR) microarrays on porous glass substrates and functional assays based on the binding of a europium-labeled GTP analogue. The porous glass slides were made by casting a glass frit on impermeable glass slides and then coating with gamma-aminopropyl silane (GAPS). The emitted fluorescence was captured on an imager with a time-gated intensified CCD detector. Microarrays of the neurotensin receptor 1, the cholinergic receptor muscarinic 2, the opioid receptor mu, and the cannabinoid receptor 1 were fabricated by pin printing. The selective agonism of each of the receptors was observed. The screening of potential antagonists was demonstrated using a cocktail of agonists. The amount of activation observed was sufficient to permit determinations of EC50 and IC50. Such microarrays could potentially streamline drug discovery by helping integrate primary screening with selectivity and safety screening without compromising the essential functional information obtainable from cellular assays.     

Entanglement dynamics in two-qubit open system interacting with a squeezed thermal bath via quantum nondemolition interaction

We analyze the dynamics of entanglement in a two-qubit systeminteracting with an initially squeezed thermal environment via aquantum nondemolition system-reservoir interaction, with the systemand reservoir assumed to be initially separable. We compare andcontrast the decoherence of the two-qubit system in the case wherethe qubits are mutually close-by (`collective regime’) or distant(`localized regime’) with respect to the spatial variation of theenvironment. Sudden death of entanglement (as quantified byconcurrence) is shown to occur in the localized case rather than inthe collective case, where entanglement tends to `ring down’.A consequence of the QND character of the interaction is that thetime-evolved fidelity of a Bell state never falls below \(1/\sqrt{2}\),a fact that is useful for quantum communication applicationslike a quantum repeater. Usinga novel quantification of mixed state entanglement, we show thatthere are noise regimes where even though entanglementvanishes, the state is still available forapplications like NMR quantum computation, because of the presenceof a pseudo-pure component.     

Dispersion and reactivity of copper catalysts supported on Al2O3-ZrO2

A series of CuO/Al(2)O(3)-ZrO(2) catalysts with Cu loadings varying from 1.0 to 20 wt % were prepared and characterized by X-ray diffraction (XRD), temperature-programmed reduction (TPR), temperature-programmed desorption (TPD) of CO(2) and NH(3), electron spin resonance (ESR), and Brunauer-Emmett-Teller surface area measurements. The dispersion and metal area of copper were determined by the N(2)O decomposition method. XRD results suggest that the copper oxide is present in a highly dispersed amorphous state at copper loadings < 10 wt % and as a crystalline CuO phase at higher Cu loadings. ESR results suggest the presence of two types of copper species on the Al(2)O(3)-ZrO(2) support. TPR results suggest well-dispersed copper oxide species at low Cu loadings and crystalline copper oxide species at high Cu loadings. Well-dispersed copper oxide species were reduced more easily than large copper oxide species by H(2). The results of CO(2) TPD suggest that the basicity of the catalysts was found to increase with an increase of copper loading up to 5.0 wt % and decreases with a further increase of copper loading. The results of NH(3) TPD suggest that the acidity of the catalysts was found to decrease with an increase of copper loading up to 5.0 wt % and increases with a further increase of copper loading. The catalytic properties were evaluated for the vapor-phase dehydrogenation of cyclohexanol to cyclohexanone and correlated with the results of CO(2) TPD measurements and the dispersion of Cu on the Al(2)O(3)-ZrO(2) support.     

Symmetries in the representation of grain boundary-plane distributions

Symmetries play a crucial role in the theoretical analysis and visualization of the five macroscopic grain boundary parameters, including the misorientation (three parameters) and the orientation of the boundary-plane (two parameters). The symmetry aspects of the misorientation spaces are very well documented and in this article all possible boundary-plane symmetries are enumerated for the 32 crystallographic point groups. It is observed that the boundary-plane spaces exhibit a wide variety of point group symmetries, which depend both on the crystallographic point group and on the corresponding misorientation (i.e. location in the fundamental zone). The list of symmetries presented here should serve as a guide for graphical representations of not only the distributions of boundary-plane orientations but also for the representation of boundary-plane related properties such as energy, mobility etc.     

Control over Kinetic and Thermodynamically Driven Pathways of Crystallization to Yield Cofacial and Slipped-Stack Dimers in Single Crystals

Control over the molecular packing in the solid state is of utmost importance in regulating the bulk optical properties of organic semiconductors. The electronic coupling between the molecules makes it possible to improve the properties of the bulk materials. This work reports an example of control over the selective formation of polymorphic single crystals of donor–acceptor-type small-molecule compound 25TR by 1) kinetic or 2) thermodynamic course of crystallisation to yield slipped stack (S) and cofacial (C) dimers in the single crystals. The distinct optical characteristics of the C-dimer and S-dimer are summarised. Both forms show significant excitonic interactions in the solid state, and the S-dimeric form has strong yellowish orange fluorescence, whereas the C-dimeric form is non-fluorescent in the crystalline state. DFT calculations and differential scanning calorimetric experiments revealed that the C-dimer polymorph is the thermodynamically stable form with a free energy offset of 0.43 eV in comparison with the S-dimer. Interestingly, the thermodynamically driven non-fluorescent single crystal was found to be convertible to its fluorescent form irreversibly by thermal trigger. The charge-carrier-transport characteristics of these two polymorphs were computed by using the Marcus–Hush formalism. The computations of the charge-carrier-transport behaviour revealed that the S-dimer ( 25TR_(R) ) is ambipolar, whereas the C-dimer ( 25TR_(Y) ) is predominantly n-type.     

Bio-Templated Chiral Zeolitic Imidazolate Framework for Enantioselective Chemoresistive Sensing

Chiral metal–organic frameworks (MOFs) have gained rising attention as ordered nanoporous materials for enantiomer separations, chiral catalysis, and sensing. Among those, chiral MOFs are generally obtained through complex synthetic routes by using a limited choice of reactive chiral organic precursors as the primary linkers or auxiliary ligands. Here, we report a template-controlled synthesis of chiral MOFs from achiral precursors grown on chiral nematic cellulose-derived nanostructured bio-templates. We demonstrate that chiral MOFs, specifically, zeolitic imidazolate framework (ZIF), unc -[Zn(2-MeIm)₂, 2-MeIm=2-methylimidazole], can be grown from regular precursors within nanoporous organized chiral nematic nanocelluloses via directed assembly on twisted bundles of cellulose nanocrystals. The template-grown chiral ZIF possesses tetragonal crystal structure with chiral space group of P4₁, which is different from traditional cubic crystal structure of I-43 m for freely grown conventional ZIF-8. The uniaxially compressed dimensions of the unit cell of templated ZIF and crystalline dimensions are signatures of this structure. We observe that the templated chiral ZIF can facilitate the enantiotropic sensing. It shows enantioselective recognition and chiral sensing abilities with a low limit of detection of 39 μM and the corresponding limit of chiral detection of 300 μM for representative chiral amino acid, D- and L- alanine.     

Nanoparticle films as electrodes: voltammetric sensitivity to the nanoparticle energy gap

Electron-transfer reactions of redox solutes at electrode/solution interfaces are facilitated when their formal potentials match, or are close to, the energy of an electronic state of the electrode. Metal electrodes have a continuum of electronic levels, and redox reactions occur without restraint over a wide span of electrode potentials. This paper shows that reactions on electrodes composed of films of metal nanoparticles do have constraints when the nanoparticles are sufficiently small and molecule-like so as to exhibit energy gaps, and resist electron transfers with redox solutes at potentials within the energy gap. When solute formal potentials are near the electronic states of the nanoparticles in the film, electron-transfer reactions can occur. The electronic states of the nanoparticle film electrodes are reflected in the formal potentials of the electrochemical reactions of the dissolved nanoparticles at naked metal electrodes. These ideas are demonstrated by voltammetry of aqueous solutions of the redox solutes methyl viologen, ruthenium hexammine, and two ferrocene derivatives at films on electrodes of 1.1 nm core diameter Au nanoparticles coated with protecting monolayers of phenylethanethiolate ligands. The methyl viologen solute is unreactive at the nanoparticle film electrode, having a formal potential lying in the nanoparticle's energy gap. The other solutes exhibit electron transfers, albeit slowed by the electron hopping resistance of the nanoparticle film. The nanoparticles are not linked together, being insoluble in the aqueous medium; a small amount of an organic additive (acetonitrile) facilitates observing the redox solute voltammetry.