Homogeneous Cooling States¶are not always¶Good Approximations to Granular Flows

A widespread belief in the study of granular flow is the existence of “homogeneous cooling states”, i.e., self-similar solutions which would attract all solutions, faster than the equilibrium solution does. In most cases, the existence of these self-similar solutions is an open problem. Here we consider a one-dimensional model, which has been used for some years, and for which simple self-similar solutions do exist. However, we prove that the approximation is quite poor. Our proof makes use of the powerful and simple tools of mass transportation, and exploits the structure of the evolution equation, seen as a nonlinear transport equation.     

Impact of concentration self-quenching on the charge generation yield of fullerene based donor-bridge-acceptor compounds in the solid state

A fullerene based Donor-Bridge-Acceptor (DBA) compound, incorporating a π-extended tetrathiafulvalene electron donor, is investigated with respect to its photophysics in solution versus solid state. Solid films of neat DBA are compared with blend films where the DBA compound is diluted in the inert, low dielectric, polymer poly(styrene). It is found that the moderate intermolecular electronic coupling and donor-acceptor separation (22 ?) in this case leads to the generation of more dissociated, intermolecular charges than a mixture of the donor and acceptor reference compounds. However, the increased intermolecular interactions in the solid state lead to the excited state of the fullerene suffering from concentration self-quenching. This is found to severely affect the charge generation yield in solid films. The impact of competing intra and intermolecular interactions in the solid state upon the film photophysics is analysed in terms of a kinetic model which includes both the effects of concentration self-quenching and the impact of film composition upon the dielectric stabilisation of charge separated states. We conclude that both concentration self-quenching and dielectric stabilisation are critical in determining the photophysics of the blend films, and discuss strategies based upon our observations to enhance the charge photogeneration properties of organic films and photovoltaic devices based upon DBA compounds.     

Separation of complex sugar mixtures on a hydrolytically stable bidentate urea‐type stationary phase for hydrophilic interaction near ultra high performance liquid chromatography

A stationary phase bearing both bridged bis‐ureido and free amino groups (USP‐HILIC‐NH₂–2.5SP) for high‐speed hydrophilic interaction liquid chromatography separations was prepared using a one‐pot two‐step procedure starting from 2.5 μm totally porous silica particles. Highly polar compounds, such as polyols, hydroxybenzoic acids, and sugars, were successfully analyzed in shorter times and with higher peak efficiency, when compared to results obtained with a bidentate urea‐type column packed with 5 μm particles. Increased sugarophilicity and better peak shape were attested for the USP‐HILIC‐NH₂–2.5SP column (100 × 3.2 mm id) when compared with two commercially available UHPLC columns, namely an acquity BEH amide packed with totally porous 1.7 μm microparticles and a HILIC Kinetex column packed with core–shell 2.6 μm particles. Finally, the new column was employed in the separation of complex mixture of sugars (mono‐, di‐, and oligosaccharides) and in the analysis of beer samples. The resulting chromatograms showed good selectivity and overall resolution, while the catalyzing effect of the free amino moieties resulted in excellent peak shapes and in the absence of split peaks due to sugar anomerization phenomena.     

Asymptotic Information-Theoretic Detection of Dynamical Organization in Complex Systems

The identification of emergent structures in complex dynamical systems is a formidable challenge. We propose a computationally efficient methodology to address such a challenge, based on modeling the state of the system as a set of random variables. Specifically, we present a sieving algorithm to navigate the huge space of all subsets of variables and compare them in terms of a simple index that can be computed without resorting to simulations. We obtain such a simple index by studying the asymptotic distribution of an information-theoretic measure of coordination among variables, when there is no coordination at all, which allows us to fairly compare subsets of variables having different cardinalities. We show that increasing the number of observations allows the identification of larger and larger subsets. As an example of relevant application, we make use of a paradigmatic case regarding the identification of groups in autocatalytic sets of reactions, a chemical situation related to the origin of life problem.     

Creating permanent 3D arrangements of isolated cells using holographic optical tweezers

We report the creation of permanent 3D configurations of cells, at predefined positions, within a gelatin matrix. The technique used holographic optical tweezers to manipulate individual E. coli within a solution comprising monomer precursors. The matrix was then set and after the laser beam was removed, we were able to demonstrate that the structures remained intact for many days. We were also able to demonstrate that, in the presence of appropriate nutrients, the E. coli survived within the gelatin matrix for several days. The technique could have a number of potential future applications, including the arrangement of a variety of different cell types in complex architectures, as motifs for promoting tissue differentiation and growth within the field of cell engineering.     

Chain folding in single crystals of tetrafluoroethylene copolymers

Molecular-mechanics calculations are performed on model folds proposed in the literature for single crystals of polytetrafluoroethylene crystallized in the phase stable below 19°C, in order to evaluate how they are modified when a fluorine atom is substituted by a bulky group, as occurs in fluorinated copolymers of tetrafluoroethylene. Only intramolecular effects are taken into account (isolated-chain model). An exhaustive analysis has been carried out of tetrafluoroethylene-hexafluoropropylene copolymer. Moreover, the lower energy folds found for such a copolymer have been examined for copolymers with chlorotrifluoroethylene and perfluoroalkylvinylethers, as comonomers. Our calculations show that all the considered comonomers can be arranged in the model folds proposed for the homopolymer, according to the imposed geometric constraints.     

A linear hyperbolic system and an optimal control problem

We prove a theorem of existence, uniqueness, and continuous dependence for a linear hyperbolic system with Darboux-type conditions under assumptions on the coefficients, which are in a sense the most general possible. Moreover, an application of this result to an optimal control problem is given.     

Balls have the worst best Sobolev inequalities

Using transportation techniques in the spirit of Cordero-Erausquin, Nazaret and Villani [7], we establish an optimal non parametric trace Sobolev inequality, for arbitrary locally Lipschitz domains in ℝⁿ. We deduce a sharp variant of the Brézis-Lieb trace Sobolev inequality [4], containing both the isoperimetric inequality and the sharp Euclidean Sobolev embedding as particular cases. This inequality is optimal for a ball, and can be improved for any other bounded, Lipschitz, connected domain. We also derive a strengthening of the Brézis-Lieb inequality, suggested and left as an open problem in [4]. Many variants will be investigated in a companion article [10].