Synthesis, structural analysis, and visualization of a library of dendronized polyphenylacetylenes

A library of eleven high cis-content cis-transoidal polyphenylacetylenes (PPAs) dendronized with self-assembling dendrons was prepared from a library of fifteen convergently synthesized macromonomers. Using [Rh(C triple bond CPh)(nbd)(PPh(3))(2)] (nbd=2,5-norbornadiene) in the presence of 10 equiv of N,N-dimethylaminopyridine, predictive control over molecular weight and narrow molecular weight distribution are obtained. The PPA backbone serves as a helical scaffold for the self-assembling dendrons. The dendron primary structure dictates the diameter of the cylindrical PPAs in bulk, both in the self-organized hexagonal columnar (Phi(h)) lattice determined by X-ray diffraction (XRD) and in monolayers on highly ordered pyrolytic graphite (HOPG) and mica visualized by atomic force microscopy (AFM). Thermal and bulk phase characteristics of the cylindrical PPAs reinforces the generality that flexible polymer backbones adopt a helical conformation within the cylindrical macromolecules generated by polymers jacketed with self-assembling dendrons.     

Exploring and expanding the structural diversity of self-assembling dendrons through combinations of AB, constitutional isomeric AB2, and AB3 biphenyl-4-methyl ether building blocks

General, efficient and inexpensive methods for the synthesis of dendritic building blocks methyl 3',4'-dihydroxybiphenyl-4-carboxylate, 3',5'-dihydroxybiphenyl-4-carboxylate, and methyl 3',4',5'-trihydroxybiphenyl-4-carboxylate were elaborated. In all syntheses the major step involved an inexpensive Ni(II)-catalyzed Suzuki cross-coupling reaction. These three building blocks were employed together with methyl 4'-hydroxybiphenyl-4-carboxylate in a convergent iterative strategy to synthesize seven libraries containing up to three generations of 3',4'-, 3',5'-, and 3',4',5'-substituted biphenyl-4-methyl ether based amphiphilic dendrons. These dendrons self-assemble into supramolecular dendrimers that self-organize into periodic assemblies. Structural and retrostructural analysis of their assemblies demonstrated that these dendrons self-assemble into hollow and non-hollow supramolecular dendrimers exhibiting dimensions of up to twice those reported for architecturally related dendrons based on benzyl ether repeat units. These new dendrons expand the structural diversity and demonstrate the generality of the concept of self-assembling dendrons based on amphiphilic arylmethyl ethers.     

Aspects on the Functional Optimization of an Industrial Robot Structure Implemented in Military Logistical Activities

The authors of the present paper outline aspects on the optimization of the a TR-type industrial robot structure movements in order to generate the manipulation space to a flexible manufacturing cell with a parallel organization designed for the pallet and container operation of paint-filled recipients. The paper contains the direct and inverted geometrical modelling of the robot structure using the 3*3 rotation matrix method and the algebra method. After knowing the characteristic point movement of the prehension device, graphics for the variation of the TR robot's general coordinates and for the trajectory of the prehension device's characteristic point of its work space were performed by using the Mathematica 6.0 soft. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the disk theorem

We construct an example of a 2-dimensional Stein normal space X with one singular point x ₀ such that X\{x ₀} is simply connected and it satisfies the disk condition. This answers a question raised by Forn?ss and Narasimhan. We also prove that any increasing union of Stein open sets contained in a Stein space of dimension 2 satisfies the disk condition. Starting from the above example we exhibit, without using deformation theory, a new type of 2-dimensional holes which cannot be filled.     

Convergence of a semi-Lagrangian scheme for the reduced Vlasov–Maxwell system for laser–plasma interaction

The subject matter of this paper concerns the numerical approximation of reduced Vlasov–Maxwell models by semi-Lagrangian schemes. Such reduced systems have been introduced recently in the literature for studying the laser–plasma interaction. We recall the main existence and uniqueness results on these topics, we present the semi-Lagrangian scheme and finally we establish the convergence of this scheme.     

Approximating the Riemann-Stieltjes integral in terms of generalised trapezoidal rules

Error bounds in approximating the Riemann-Stieltjes integral in terms of some new generalised trapezoidal rules are given. Applications for approximating the Riemann integral of a two-function product are provided as well.     

Minimization of vectors of curvilinear functionals on the second order jet bundle: sufficient efficiency conditions

Strongly motivated by its possible applications in Mechanics, in our previous work (Pitea and Postolache (Optim. Lett. doi:10.1007/s11590-010-0272-0, 2011)), we initiated an optimization theory for the second order jet bundle. We considered the problem of minimization of vectors of curvilinear functionals (well known as mechanical work), thought as multi-time multi-objective variational problems, subject to PDE and/or PDI constraints. Within this framework, we introduced necessary conditions. As natural continuation of our results in Pitea and Postolache (Optim. Lett. doi:10.1007/s11590-010-0272-0, 2011), the present work introduces a study of sufficient efficiency conditions. While the background in Sect. 2 is introductory, the theory in Sect. 3 is new as a whole, containing our results.     

Coherent acoustic wave propagation in media with pair-correlated spheres

Propagation of plane compressional waves in a non-viscous fluid with a dense distribution of identical spherical scatterers is investigated. The analysis is based on the multiple scattering approach proposed by Fikioris and Waterman, and is generalized to include arbitrary choice of the pair-correlation functions used to represent the distribution of the scatterers. A closed form solution for the effective wavenumber as a function of the concentration of pair-correlated finite-size spheres is derived up to the second order. In the limit of uncorrelated point-scatterers, this solution is identical to that obtained by Lloyd and Berry. Different pair-correlation functions are exemplified and compared, and the resulting differences discussed.     

View factors in a finite length axysymmetric cylindrical annulus enclosure

View factor – defined as fraction of total outgoing radiation from surface 1 intercepted by surface 2 – is a key concept in solving the radiative heat transfer in systems of surfaces. Analytical forms of the view factor have been developed by means of integration for many conventional systems of 2D and 3D surfaces in various spatial positions. However, little investigation has been carried out for situations in which there is no complete visibility between the surfaces involved in radiative exchange due to configuration of 3D surfaces or due to presence of interposing object that obstruct partially the mutual visibility.Radiative heat exchange was modeled in a finite length cylindrical annulus consisting of non-isothermal diffusely-emitting surfaces. The canonical definition of the view factor was extended by means of an analytical approach to both 3D and 2D surfaces with shading effects (incomplete mutual visibility) and numerical algorithms were developed in order to calculate view factors values and test view factor algebra rules. The system considered in this paper was an axysymmetric cylindrical annulus – frequently used in many heat transfer applications. View factor values for various surface elements were calculated by means of numerical integration. View factor algebra rules – summation and reciprocity – were verified.     

Energy dissipation characteristics of particle sloshing in a rotating cylinder

A study on the energy dissipation characteristics of granular materials flowing/sloshing in a rotating container is presented here. The objective is to develop a configuration for control of excessive structural oscillations, similar to those of tuned vibration absorbers and tuned sloshing absorbers. The effectiveness of energy dissipation through granular flow is primarily determined experimentally. A computational model is developed to understand the flow behavior and energy dissipation in this system. A promising kinematic match of the particle behavior is demonstrated between the numerical predictions and the experimental observations. The use of the granular flow in a rotating drum for vibration control is being investigated for the first time.