The Allen–Cahn equation with dynamic boundary conditions and mass constraints

The Allen–Cahn equation, coupled with dynamic boundary conditions, has recently received a good deal of attention. The new issue of this paper is the setting of a rather general mass constraint, which may involve either the solution inside the domain or its trace on the boundary. The system of nonlinear partial differential equations can be formulated as a variational inequality. The presence of the constraint in the evolution process leads to additional terms in the equation and the boundary condition containing a suitable Lagrange multiplier. A well‐posedness result is proved for the related initial value problem. Copyright © 2014 John Wiley & Sons, Ltd.     

Tunable Linear and Nonlinear Optical Properties from Room Temperature Phosphorescent Cyclic Triimidazole-Pyrene Bio-Probe

Organic materials with multiple emissions tunable by external stimuli represent a great challenge. TTPyr, crystallizing in different polymorphs, shows a very rich photophyisics comprising excitation-dependent fluorescence and phosphorescence at ambient conditions, and mechanochromic and thermochromic behavior. Transformation among the different species has been followed by thermal and X-ray diffraction analyses and the emissive features interpreted through structural results and DFT/TDDFT calculations. Particularly intriguing is the polymorph TTPyr(HT), serendipitously obtained at high temperature but stable also at room temperature, whose non-centrosymmetric structure guarantees an SHG efficiency 10 times higher than that of standard urea. Its crystal packing, where only the TT units are strongly rigidified by π-π stacking interactions while the Pyr moieties possess partial conformational freedom, is responsible for the observed dual fluorescence. The potentialities of TTPyr for bioimaging have been successfully established.     

Potassium-doped FePc thin-film on metal surfaces: observation of different empty state occupation

Iron-Phthalocyanine molecules deposited on the Cu(119) vicinal surface form molecular chains along the vicinal surface steps, as deduced by the low-energy electron diffraction (LEED) reconstruction pattern. The work-function lowers at the FePc single-layer completion, due to the formation of an interface dipole. Further FePc deposition induces a different growth morphology, as suggested by the slope discontinuity in the work function variation. Upon depositing potassium onto the FePc thin-film prepared on Cu(119), the K-injected electrons fill up the Fe-d-associated and ligand-π-related orbitals, as observed by means of high-resolution ultraviolet photoelectron spectroscopy.     

A Novel Coherent Multilevel Combined Phase and Polarization Shift Keying Modulation in Twisted Fibers

This article proposes a novel coherent multilevel modulation model that exploits polarization and phase of the field. This model is based on the possibility of coherent systems to use all the four degrees of freedom of the electromagnetic field. The proposed scheme is able, by applying a suitable twisting process to the optical fiber, to physically confine the polarization and the phase of the transmitted field within the phase sphere. In this way, with the same performances of existing systems, the receiver is considerably simplified because there is no longer need of birefringence tracking circuits.     

Relaxation of Multiwell Energies in Linearized Elasticity and Applications to Nematic Elastomers

The relaxation of a free-energy functional which describes the order–strain interaction in nematic elastomers is obtained explicitly. We work in the regime of small strains (linearized kinematics). Adopting the uniaxial order tensor theory (Frank model) to describe the liquid crystal order, we prove that the minima of the relaxed functional exhibit an effective biaxial nematic texture, as in the de Gennes order tensor model. In particular, this implies that, at a sufficiently macroscopic scale, the response of the material is soft even if the order of the system is assumed to be fixed at the microscopic scale. The relaxed energy density satisfies a solenoidal quasiconvexification formula.     

Interface Energy in the Edwards-Anderson Model

We numerically investigate the spin glass energy interface problem in three dimensions. We analyze the energy cost of changing the overlap from −1 to +1 at one boundary of two coupled systems (in the other boundary the overlap is kept fixed to +1). We implement a parallel tempering algorithm that simulates finite temperature systems and works with both cubic lattices and parallelepiped with fixed aspect ratio. We find results consistent with a lower critical dimension D _c =2.5. The results show a good agreement with the mean field theory predictions.     

Au2trien: a dinuclear gold(III) complex with unprecedented structura features

The X-ray structure of a dinuclear gold(III) complex, Au2trien, shows the presence of two square planar gold(III) centers bridged by a nitrogen donor, in a very unusual fashion.     

Protonation equilibria in aqueous solutions of the hydrolysed copolymer of maleic anhydride with cyclopentene

The thermodynamics of proton dissociation of the hydrolysed 1:1 copolymer of maleic anhydride with cyclopentene in aqueous solution has been investigated. Potentiometric, microcalorimetric and dilatometric measurements on the copolymer solutions indicate that the two acidic functions are quite strong and not very different. Relatively poor solvation of vicinal carboxyl groups could account for the behaviour of the copolymer; it could stem from steric hindrances imposed by the cyclopentene residues.     

First evaluation of the thermodynamic properties for spheres to elongated micelles transition of some propanediyl-alpha,omega-bis(dimethylalkylammonium bromide) surfactants in aqueous solution

The apparent and partial molar enthalpies, apparent molar volumes, and adiabatic compressibilities at 298 K of the aqueous solutions of the cationic gemini surfactants propanediyl-alpha,omega-bis(octyldimethylammonium bromide) (8-3-8) and propanediyl-alpha,omega-bis(dodecyldimethylammonium bromide) (12-3-12) have been measured as a function of concentration. The trends of the partial molar enthalpies versus concentration are the first well documented thermodynamic evidence of sphere to rod transition in the micellar phase, involving a detectable quantity of heat, and allow the determination of the change in enthalpy associated with this transition. The changes in enthalpies upon micellization and for the sphere to elongated micelles transition, DeltaH(s)(-->)(r), have been obtained from the experimental data by using a pseudo-phase transition approach: -1.5 kJ mol(-1) for 8-3-8 and -3.9 kJ mol(-1) for 12-3-12. No evidence of the above transition is found in the trends of volumetric properties versus m. The apparent adiabatic molar compressibilities for the compounds under investigation are also reported here for the first time: a negative group contribution for the methylene group is evaluated, when the surfactants are present in solution as a single molecule, reflecting its solvation structure. In the micellar phase, the -CH(2)- group contribution becomes positive. A value of 1.17 x 10(-3) cm(3) bar(-1) mol(-1) for the change in adiabatic molar compressibility upon micellization is obtained. The lower values of the methylene group contributions to the volumetric properties for the monomers support the hypothesis of partial association of the chains before the cmc.