Active and driven hydrodynamic crystals

Motivated by the experimental ability to produce monodisperse particles in microfluidic devices, we study theoretically the hydrodynamic stability of driven and active crystals. We first recall the theoretical tools allowing to quantify the dynamics of elongated particles in a confined fluid. In this regime hydrodynamic interactions between particles arise from a superposition of potential dipolar singularities. We exploit this feature to derive the equations of motion for the particle positions and orientations. After showing that all five planar Bravais lattices are stationary solutions of the equations of motion, we consider separately the case where the particles are passively driven by an external force, and the situation where they are self-propelling. We first demonstrate that phonon modes propagate in driven crystals, which are always marginally stable. The spatial structures of the eigenmodes depend solely on the symmetries of the lattices, and on the orientation of the driving force. For active crystals, the stability of the particle positions and orientations depends not only on the symmetry of the crystals but also on the perturbation wavelengths and on the crystal density. Unlike unconfined fluids, the stability of active crystals is independent of the nature of the propulsion mechanism at the single-particle level. The square and rectangular lattices are found to be linearly unstable at short wavelengths provided the volume fraction of the crystals is high enough. Differently, hexagonal, oblique, and face-centered crystals are always unstable. Our work provides a theoretical basis for future experimental work on flowing microfluidic crystals.     

On the use of Kronecker's algorithm in the generalized rational interpolation problem

Kronecker's algorithm can be used to solve the generalized rational interpolation problem. In order to present the algorithm, rational forms are used here instead of too restrictive rational fractions. The proposed algorithm is reliable as soon as the functionals that characterize the problem satisfy two precise conditions. These conditions are fulfilled in the modified Hermite rational interpolation problem and, as a consequence, in the special case of the Cauchy problem and of the Padé approximation problem. This reliability covers two properties: on one hand, every rational form resulting from the algorithm is a solution of the problem whereas, on the other hand, every solution of the problem is found by the algorithm (with the exception of a possible reduction of the rational form). However, if the algorithm yields a non-reduced rational form, then the corresponding rational fraction is not a solution of the problem.     

Volume entropy,weighted girths and stable balls on graphs

We prove new isoperimetric inequalities on graphs involving quantities linked with concepts from differential geometry. First, we bound from above the product of the volume entropy (defined as the log of the exponential growth rate of the universal cover) and the girth of weighted graphs in terms of their cyclomatic number. In a second part, we study a natural polyhedron associated to a weighted graph: the stable ball. In particular, we relate the volume of this polyhedron, the weight of the graph and its cyclomatic number. © 2007 Wiley Periodicals, Inc. J Graph Theory 55: 291–305, 2007     

Cleavable Binary Dyads: Simplifying Data Extraction and Increasing Storage Density in Digital Polymers

Digital polymers are uniform macromolecules that store monomer‐based binary sequences. Molecularly stored information is usually extracted from the polymer by a tandem mass spectrometry (MS/MS) measurement, in which the coded chains are fragmented to reveal each bit (i.e. basic coded monomer unit) of the sequence. Here, we show that data‐extraction can be greatly simplified by favoring the formation of MS/MS fragments containing two bits instead of one. In order to do so, digital poly(alkoxyamine phosphodiester)s, containing binary dyads in each repeat unit, were prepared by an orthogonal solid‐phase approach involving successive phosphoramidite and radical‐radical coupling steps. Three different sets of monomers were considered to build these polymers. In all cases, four coded building blocks—two hydroxy‐nitroxides and two phosphoramidite monomers—were required to build the dyads. Among the three studied monomer sets, one combination allowed synthesis of uniform sequence‐coded polymers. The resulting polymers led to clear dyad‐containing fragments in MS/MS and could therefore be efficiently decoded. Additionally, an algorithm was created to detect specific dyad fragments, thus enabling automated sequencing.     

Structure of Diacetato bis (2,4,6 Trimethyl Pyridine) Copper(II)

(2.4.6 trimethyl pyridine)₂ Cu(CH₃COO)₂ has been obtained as violet needles by slow evaporation. The crystals belong to the monoclinic system, space group P2_1/C with two molecules in a unit cell of dimension: a = 7.842 (1), b = 16.384 (2), c = 8.320 (2) Å, β = 101.91 (1)°. The structure was solved by heavy atom method and refined by a least squares method (R = 0.029). The coordination of copper is 4 + 2. The atom arrangements of this structure is very near to the copper acetate one solvated by one water molecule and two 3.4 dimethyl pyridine molecules.     

Approaches to the synthesis of CF2-analogues of 2-deoxy-2-aminoglycosides

The preparation of a fluorinated C-glycosidic analogue of a 2-deoxy-2-acetamido-d-altrose is described. The synthetic sequence involves the addition of a difluoroenoxysilane to a d-glucal, an epoxidation of the resulting unsaturated CF₂-glycoside and a ring-opening reaction with TMSN₃. An Overman rearrangement of the unsaturated intermediate is also described.     

Ab Initio Diabatic energies and dipole moments of the electronic states of RbLi molecule

For all states dissociating below the ionic limit Li^? Rb⁺, we perform a diabatic study for ¹Σ⁺ electronic states dissociating into Rb (5s, 5p, 4d, 6s, 6p, 5d, 7s, 4f) + Li (2s, 2p, 3s). Furthermore, we present the diabatic results for the 1–11 ³σ, 1–8 ^1,3Π, and 1–4 ^1,3Δ states. The present calculations on the RbLi molecule are complementary to previous theoretical work on this system, including recently observed electronic states that had not been calculated previously. The calculations rely on ab‐initio pseudopotential, core polarization potential operators for the core‐valence correlation and full valence configuration interaction approaches, combined to an efficient diabatization procedure. For the low‐lying states, diabatic potentials and permanent dipole moments are analyzed, revealing the strong imprint of the ionic state in the ¹Σ⁺ adiabatic states. The transition dipole moment is used to evaluate the radiative lifetimes of the vibrational levels trapped in the 2 ¹Σ⁺ excited states for the first time. In addition to the bound–bound contribution, the bound–free term has been evaluated using the Franck–Condon approximation and also exactly added to the total radiative lifetime. © 2013 Wiley Periodicals, Inc.     

Structural transitions and melting in LJ(74-78) Lennard-Jones clusters from adaptive exchange Monte Carlo simulations

Phase changes in Lennard-Jones (LJ) clusters containing between 74 and 78 atoms are investigated by means of exchange Monte Carlo simulations in the canonical ensemble. The replica temperatures are self-adapted to facilitate the convergence. Although the 74- and 78-atom clusters have icosahedral global minima, the clusters with 75-77 atoms have decahedral ground-state structures and they undergo a structural transition to icosahedral minima before melting. The structural transitions are characterized by quenching and by looking at the Q4 and Q6 orientational bond order parameters. The transition temperatures are estimated to be 0.114, 0.065, and 0.074 reduced units for LJ75, LJ76, and LJ77, respectively. These values, their ordering and the associated latent heats are compared with other estimates based on the harmonic superposition approach.