Geometric gradient-flow dynamics with singular solutions

The gradient-flow dynamics of an arbitrary geometric quantity is derived using a generalization of Darcy’s Law. We consider flows in both Lagrangian and Eulerian formulations. The Lagrangian formulation includes a dissipative modification of fluid mechanics. Eulerian equations for self-organization of scalars, 1-forms and 2-forms are shown to reduce to nonlocal characteristic equations. We identify singular solutions of these equations corresponding to collapsed (clumped) states and discuss their evolution.     

Vlasov moments, integrable systems and singular solutions

The Vlasov equation governs the evolution of the single-particle probability distribution function (PDF) for a system of particles interacting without dissipation. Its singular solutions correspond to the individual particle motions. The operation of taking the moments of the Vlasov equation is a Poisson map. The resulting Lie-Poisson Hamiltonian dynamics of the Vlasov moments is found to be integrable is several cases. For example, the dynamics for coasting beams in particle accelerators is associated by a hodograph transformation to the known integrable Benney shallow-water equation. After setting the context, the Letter focuses on geodesic Vlasov moment equations. Continuum closures of these equations at two different orders are found to be integrable systems whose singular solutions characterize the geodesic motion of the individual particles.     

Geometry of Vlasov kinetic moments: A bosonic Fock space for the symmetric Schouten bracket

The dynamics of Vlasov kinetic moments is shown to be Lie-Poisson on the dual Lie algebra of symmetric contravariant tensor fields. The corresponding Lie bracket is identified with the symmetric Schouten bracket and the moment Lie algebra is related with a bundle of bosonic Fock spaces, where creation and annihilation operators are used to construct the cold plasma closure. Kinetic moments are also shown to define a momentum map, which is infinitesimally equivariant. This momentum map is the dual of a Lie algebra homomorphism, defined through the Schouten bracket. Finally the moment Lie-Poisson bracket is extended to anisotropic interactions.     

Synthesis and conformational studies of peptidomimetics containing a new bifunctional diketopiperazine scaffold acting as a beta-hairpin inducer

A practical synthesis of a new bifunctional diketopiperazine (DKP) scaffold 1, formally derived from the cyclization of L-aspartic acid and (S)-2,3-diaminopropionic acid, is reported. DKP-1 bears a carboxylic acid and an amino functionalities in a cis relationship, which have been used to grow peptide sequences. Tetra-, penta-, and hexapeptidomimetic sequences were prepared by solution-phase peptide synthesis (Boc strategy). Conformational analysis of these derivatives was carried out by a combination of 1H NMR spectroscopy, IR spectroscopy, CD spectroscopy, and computer modeling, and reveals the formation of beta-hairpin mimics involving 10-membered and 18-membered H-bonded rings and a reverse turn of the growing peptide chain.     

Synthetic Receptors with Micromolar Affinity for Chloride in Water

A water-soluble coordination cage was obtained by reaction of Pd(NO₃)₂ with a 1,3-di(pyridin-3-yl)benzene ligand featuring a short PEG chain. The cavity of the metal-organic cage contains one nitrate anion, which is readily replaced by chloride. The apparent association constant for chloride binding in buffered aqueous solution is K_a=1.8(±0.1)×10⁵ M⁻¹. This value is significantly higher than what has been reported for other macrocyclic chloride receptors. The heavier halides Br⁻ and I⁻ compete with binding or self-assembly, but the receptor displays very good selectivity over common anions such as phosphate, acetate, carbonate, and sulfate. A further increase of the chloride binding affinity by a factor of 3 was achieved using a fluorinated dipyridyl ligand.     

Water dissociation at MgO sub-monolayers on silver: a periodic model study

A hybrid-exchange DFT hamiltonian and a periodic slab model have been employed to simulate water dissociation at the border of sub-monolayer MgO films deposited on Ag(100). Non-polar and polar borders have been considered, but the reaction energy is higher in the former case. The O-1s core level shifts and the O-H vibrational frequencies have been calculated and shown to be compatible with recent XPS and HREELS data, respectively [Savio et al., J. Chem. Phys., 2003, 119, 12053].     

Recent Advances in the Synthesis of Polyamine Derivatives and Their Applications

Biogenic polyamines (PAs) are involved in the growth and development of normal cells, and their intracellular concentration is stable. The concentration of PAs in cancer cells is significantly increased to promote and sustain their rapid proliferation. Over the years, synthetic PAs, which differ in their structure, have demonstrated high antitumor activity and are involved in clinical trials. The chemical synthesis of PAs and their conjugates require the correct choice of synthetic pathways—methods for constructing conjugates and the orthogonal protection of amino groups. The most common methods of synthesis of PA conjugates are acylation of regioselectively protected PAs or their alkylation under the conditions of the Fukuyama reaction. One of the most promising methods of PA synthesis is the use of a multicomponent Ugi reaction, which allows various PAs to be obtained in high yields. In this review, we describe and analyze various approaches that are used in the synthesis of polyamines and their conjugates.