Simulations of the PDF functions for dilute colloidal suspensions of molecular particles flowing in mesopores with rough surface boundaries

Simulations have been carried out to analyze the dynamics of dilute colloidal suspensions of macromolecular particles in solutions flowing in pores, subject to hydrodynamic forces, Brownian motion and stochastic collisions at rough pore boundaries in a two-dimensional spatial frame. A theoretical model is developed and intensively analyzed for the treatment of the mechanical restitution of the particles due to dynamic collisions at these boundaries. In particular we are able to calculate the Probability distribution functions for the spatial positions and the orientations of rod-like particles inside the pores. The results are presented for different widths of pore channels referenced to the size of a rod-like particle. These simulations are general in the sense that they are developed for confining and open pore channels, rough at the nano scale. The simulations also permit calculating the nematic order parameters for colloidal suspensions; the model calculation is applied for dilute colloidal suspensions of carbon nano-tubes in an aqueous single-stranded DNA solution flowing inside pores. Our calculated nematic order results for dilute suspensions of particles of known lengths flowing inside porous systems should indicate, when coupled to birefringence and dichroism experimental results, the possibility to estimate the pore widths for these systems.     

Boëder PDF Brownian simulations for macromolecular rod-like particles near uneven solid surfaces

A molecular dynamics simulation is presented to calculate the Probability Distribution Functions (PDF) for the spatial positions and angular orientations of macromolecular rod-like particles in dilute solutions, under hydrodynamic flow, in the vicinity of uneven solid boundaries. The Brownian and hydrodynamic restitution model for ideally flat surfaces is generalized to simulate the diffusive collisions between the macromolecular particles and an uneven solid surface. Two types of uneven surfaces are particularly considered: the periodic grating and the random rough, with characteristic profiles of heights and lateral variations. Different from ideally flat surfaces, the simulation results demonstrate that uneven surfaces have characteristic depletion layers, and characteristic and variable PDF. This is the case under varying conditions of hydrodynamic flow, Brownian movement and diffusive collisions. These characteristics uniquely identify Boeder PDF signatures for the uneven surface topography.     

Robust delay-constrained routing in telecommunications

In telecommunications, operators usually use market surveys and statistical models to estimate traffic evolution in networks or to approximate queuing delay functions in routing strategies. Many research activities concentrated on handling traffic uncertainty in network design. Measurements on real world networks have shown significant errors in delay approximations, leading to weak management decisions in network planning. In this work, we introduce elements of robust optimization theory for delay modeling in routing problems. Different types of data uncertainty are considered and linked to corresponding robust models. We study a special case of constraints featuring separable additive functions. Specifically, we consider that each term of the sum is disturbed by a random parameter. These constraints are frequent in network based problems, where functions reflecting real world measurements on links are summed up over end-to-end paths. While classical robust formulations have to deal with the introduction of new variables, we show that, under specific hypotheses, the deterministic robust counterpart can be formulated in the space of original variables. This offers the possibility of constructing tractable robust models. Starting from Soyster’s conservative model, we write and compare different uncertainty sets and formulations offering each a different protection level for the delay constrained routing problem. Computational experiments are developed in order to evaluate the “price of robustness” and to assess the quality of the new formulations.     

Crystallographic report: 2,4‐Diphenyl‐1,3‐bis(4,4,5,5‐tetramethyl[1,3,2] dioxaborolan‐2‐yl)‐buta‐1Z,3E‐diene

The compound comprises a 1Z,3E‐butadiene moiety substituted by two pinacol boronate functional groups. Copyright © 2005 John Wiley & Sons, Ltd.     

Combining valproate and bipyridyl ligands to construct a 0D core‐shell Zn5(μ3‐OH)2 cluster and a 2D layered coordination network with a [Zn3(μ3‐OH)]2 SBU

Starting from the proposed zinc carboxylate cluster tetrakis(μ‐2‐propylpentanoato)dizinc(II), Zn₂(μ₂‐valp)₄ ( I ), of valproic acid, a branched short‐chain fatty acid, and bipyridine ligands, two new mixed‐ligand coordination compounds, namely, bis(2,2′‐bipyridine)di‐μ₃‐hydroxido‐hexakis(μ‐2‐propylpentanoato)bis(2‐propylpentanoato)pentazinc(II), [Zn₅(C₈H₁₅O₂)₈(OH)₂(C₁₀H₈N₂)₂] ( II ), and poly[[bis(μ‐4,4′‐bipyridine)di‐μ₃‐hydroxido‐octakis(μ‐2‐propylpentanoato)bis(2‐propylpentanoato)hexazinc(II)] dimethylformamide disolvate], {[Zn₆(C₈H₁₅O₂)₁₀(OH)₂(C₁₀H₈N₂)₂]·2C₃H₇NO}_n ( III ), were synthesized. Compound II is a core‐shell‐type zero‐dimensional discrete Zn₅(μ₃‐OH)₂ metal–organic cluster with Zn ions in double‐triangle arrangements that share one Zn ion coincident with an inversion centre. The cluster contains three crystallographically non‐equivalent Zn ions exhibiting three different coordination geometries (tetrahedral, square pyramidal and octahedral). The cluster cores are well separated and embedded in a protective shell of the aliphatic branched short chains of valproate. As a result, there is no specific interaction between the discrete clusters. Conversely, compound III , a 2D layered coordination network with a secondary building unit (SBU), is formed by Zn₆(μ₃‐OH)₂ clusters exhibiting a chair‐like hexagonal arrangement. This SBU is formed from two Zn₃(μ₃‐OH) trimers related by inversion symmetry and connected by two syn–anti bridging carboxylate groups. Each SBU is connected by four 4,4′‐bipyridine ligands producing a 6³‐hcb net topology. 2D coordination layers are sandwiched within layers of dimethylformamide molecules that do not interact strongly with the network due to the hydrophobic protection provided by the valproate ligands.     

Twistor Operators and Eigenvalues of the Dirac Operator on Compact Quaternion-Kähler Spin Manifolds

Quaternion-Kähler twistor operators are introduced. Using these operators with the Lichnerowicz formula, we get lower bounds for the square of the eigenvalues of the Dirac operator in terms of the eigenvalues of the fundamental 4-form.     

A spinorial characterization of hyperspheres

Let M be a compact orientable n-dimensional hypersurface, with nowhere vanishing mean curvature H, immersed in a Riemannian spin manifold ${\overline{M}}$ admitting a non trivial parallel spinor field. Then the first eigenvalue ${\lambda_1(D_{M}^{H})}$ (with the lowest absolute value) of the Dirac operator ${D_{M}^{H}}$ corresponding to the conformal metric ${\langle\;,\;\rangle^{H}=H^{2}\,\langle\;,\;\rangle}$ , where ${\langle\;,\;\rangle}$ is the induced metric on M, satisfies ${\left|\lambda_1(D_{M}^{H})\right|\le \frac{n}{2}}$ . By applying the Bourguignon-Gauduchon first variational formula, we obtain a necessary condition for ${\left|\lambda_1(D_{M}^{H})\right|=\frac{n}{2}}$ . As a consequence, we prove that round hyperspheres are the only hypersurfaces of the Euclidean space satisfying the equality in the Bär inequality $$\lambda_1(D_{M})^{2}\le \frac{n^{2}}{4{vol}(M)}\int_{M} H^{2}\, dV,$$ where D _M stands now for the Dirac operator of the induced metric.     

Keto-coumarin scaffold for photoinitiators for 3D printing and photocomposites

The purposes of this paper are moving toward (a) the development of a new series of photoinitiators (PIs) which are based on the keto-coumarin (KC) core, (b) the introduction of light-emitting diodes (LEDs) as inexpensive and safe sources of irradiation, (c) the study of the photochemical mechanisms through which the new PIs react using different techniques such as Fourier transform infrared, UV–visible or fluorescence spectroscopy, and so on, (d) the use of such compounds (presenting good reactivity and excellent photopolymerization initiating abilities) for two specific and high added value applications: 3D printing (@405 nm) and preparation of thick glass fiber photocomposites with excellent depth of cure, and finally (e) the comparison of the performance of these KC derivatives versus other synthesized coumarin derivatives. In this study, six well-designed KC derivatives ( KC-C , KC-D , KC-E , KC-F , KC-G , and KC-H ) are examined as high-performance visible-light PIs for the cationic polymerization of epoxides as well as the free-radical polymerization of acrylates upon irradiation with LED@405 nm. Excellent polymerization rates are obtained using two different approaches: a photo-oxidation process in combination with an iodonium (Iod) salt and a photo-reduction process when associated with an amine (N-phenylglycine or ethyl 4-(dimethylamino)benzoate). High final reactive conversions were obtained. A full picture of the involved photochemical mechanisms is provided.     

On two classes of finite supersoluble groups

Let ? be a complete set of Sylow subgroups of a finite group G, that is, a set composed of a Sylow p-subgroup of G for each p dividing the order of G. A subgroup H of G is called ?-S-semipermutable if H permutes with every Sylow p-subgroup of G in ? for all p?π(H); H is said to be ?-S-seminormal if it is normalized by every Sylow p-subgroup of G in ? for all p?π(H). The main aim of this paper is to characterize the ?-MS-groups, or groups G in which the maximal subgroups of every Sylow subgroup in ? are ?-S-semipermutable in G and the ?-MSN-groups, or groups in which the maximal subgroups of every Sylow subgroup in ? are ?-S-seminormal in G.