Solid phase synthesis of a molecular library of pyrimidines, pyrazoles, and isoxazoles with biological potential

A small molecular library of 40 pyrimidine, pyrazole, and isoxazole derivatives, bearing structural features for a promising binding of therapeutically interesting enzymes, was designed and prepared. An efficient and straightforward solid phase synthesis was envisaged and carried out on a Rink amide resin. The assistance of microwave heating in any step reduced the reaction time, increased the reaction yields, and allowed an easy work-up and purification of the targeted compounds.     

Polarized Absorption,Spontaneous and Stimulated Blue Light Emission of J‐type Tetraphenylbutadiene Monocrystals

Blue amplified spontaneous emission at room temperature is demonstrated from the exposed face of the strongly emitting organic semiconductor 1,1,4,4‐tetraphenyl‐1,3‐butadiene in single crystal form. The symmetry of the crystal and calculation of lattice sums indicate the J‐type organization of the molecular transition moments. The minimum in the lowest exciton dispersion branch, from which emission takes place, is found at the edge of the Brillouin zone leading to a dominant vibronic emission since the zero‐phonon line is forbidden. The observed gain narrowed line is attributed to the vibronic replica which becomes amplified with increased pumping. The reported emission is along the normal to the exposed crystal face, important for the development of vertical cavity geometry lasers based on organic single crystals. The threshold excitation fluence of 400 μJ cm^?2 is comparable to other organic crystalline systems, even if the amplification path is much reduced as a consequence of the vertical geometry. Considering these relevant aspects, the optical characterization of this material is provided. The polarized absorption spectra are reported and the properties of the lowest‐energy excitonic state investigated. Calculation of the electronic transitions for the isolated molecule, lattice sums for the transition at lowest energy, and the symmetry of the crystal allow attributing the largest face of the samples and the observed optical bands in the spectra. Polarized time‐resolved spectra are also reported allowing to identify the intrinsic excitonic emission.     

Entropically Driven Self‐Assembly of Lysinibacillus sphaericus S‐Layer Proteins Analyzed Under Various Environmental Conditions

S‐Layer proteins are an example of bionanostructures that can be exploited in nanofabrication. In addition to their ordered structure, the ability to self‐assembly is a key feature that makes them a promising technological tool. Here, in vitro self‐assembly kinetics of SpbA was investigated, and found that it occurs at a rate that is dependent on temperature, its concentration, and the concentration of calcium ions and sodium chloride. The activation enthalpy (120.81 kJ · mol^?1) and entropy (129.34 J · mol^?1 · K^?1) obtained infers that the incorporation of monomers incurs in a net loss of hydrophobic surface. By understanding how the protein monomers drive the self‐assembly at different conditions, the rational optimization of this process was feasible.

     

A multidimensional real Schwarz Lemma for the Hilbert metric

We present a real multidimensional version of the Schwarz Lemma on a bounded convex domain D of ℝ ⁿ endowed with the Hilbert metric. We provide as an application an extension of a Birkhoff’s Theorem on mappings contracting the Hilbert metric.     

Floating and sinking: the imprint of massive scalars around rotating black holes

We study the coupling of massive scalar fields to matter in orbit around rotating black holes. It is generally expected that orbiting bodies will lose energy in gravitational waves, slowly inspiraling into the black hole. Instead, we show that the coupling of the field to matter leads to a surprising effect: because of superradiance, matter can hover into "floating orbits" for which the net gravitational energy loss at infinity is entirely provided by the black hole's rotational energy. Orbiting bodies remain floating until they extract sufficient angular momentum from the black hole, or until perturbations or nonlinear effects disrupt the orbit. For slowly rotating and nonrotating black holes floating orbits are unlikely to exist, but resonances at orbital frequencies corresponding to quasibound states of the scalar field can speed up the inspiral, so that the orbiting body sinks. These effects could be a smoking gun of deviations from general relativity.     

Thermal momentum distribution from path integrals with shifted boundary conditions

For a thermal field theory formulated in the grand canonical ensemble, the distribution of the total momentum is an observable characterizing the thermal state. We show that its cumulants are related to thermodynamic potentials. In a relativistic system, for instance, the thermal variance of the total momentum is a direct measure of the enthalpy. We relate the generating function of the cumulants to the ratio of (a) a partition function expressed as a Matsubara path integral with shifted boundary conditions in the compact direction and (b) the ordinary partition function. In this form the generating function is well suited for Monte Carlo evaluation, and the cumulants can be extracted straightforwardly. We test the method in the SU(3) Yang-Mills theory and obtain the entropy density at three different temperatures.     

Real-time digital holographic microscopy of multiple and arbitrarily oriented planes

Digital holographic microscopy is used to numerically refocus a recorded hologram at an arbitrary axial distance. However, as a straightforward property of coherent light fields, image reconstruction on an arbitrary tilted plane could be directly obtained by a rotation in k-space. We demonstrate that this property allows the real-time microscopic inspection of particle distribution over three mutually orthogonal planes at the same time. As a straightforward application we use the proposed technique for real-time monitoring of fluid flow over the three cross sections of a microfluidic channel.     

Spherical and non-spherical bubbles in cosmological phase transitions

The cosmological remnants of a first-order phase transition generally depend on the perturbations that the walls of expanding bubbles originate in the plasma. Several of the formation mechanisms occur when bubbles collide and lose their spherical symmetry. However, spherical bubbles are often considered in the literature, in particular for the calculation of gravitational waves. We study the steady state motion of bubble walls for different bubble symmetries. Using the bag equation of state, we discuss the propagation of phase transition fronts as detonations and subsonic or supersonic deflagrations. We consider the cases of spherical, cylindrical and planar walls, and compare the energy transferred to bulk motions of the relativistic fluid. We find that the different wall geometries give similar perturbations of the plasma. For the case of planar walls, we obtain analytical expressions for the kinetic energy in the bulk motions. As an application, we discuss the generation of gravitational waves.     

Complete minimal hypersurfaces in quaternionic hyperbolic space

We construct new examples of embedded, complete minimal hypersurfaces in quaternionic hyperbolic space and also some minimal foliations. We introduce fans and construct analytic deformations of bisectors.