Adsorption of block copolymers in nanoporous alumina

We have studied the adsorption of end-attaching block copolymer chains inside the cylindrical pores of nanoporous alumina. Highly asymmetric PS-PEO block copolymers, with a small PEO anchoring block and a long PS dangling block, were allowed to adsorb onto porous alumina substrates with an average pore diameter of ∼200 nm from toluene solution. The adsorption process was monitored using FTIR spectroscopy, whereas depth profile analysis was performed by means of XPS and Ar⁺ ion sputtering. It is found that the PS-PEO adsorption kinetics in porous alumina are ∼4 orders of magnitude slower than the corresponding case of a flat alumina substrate. It appears that chains adsorbed near the pore entrance early on tend to form a barrier for chains entering the pore at later times, thereby slowing down the adsorption process significantly. This effect is much more pronounced for large chains whose dimensions are comparable with the pore diameter. The equilibrium adsorbance value is also affected by chain size due to the additional entropic penalty associated with chain confinement, the adsorbance falling substantially when the chain dimensions become comparable with the pore diameter. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 1676–1682, 2010     

Improper hydrogen-bonded cyclohexane C-Hax?Yax contacts: experimental evidence from H NMR spectroscopy of suitable axial cyclohexane models

B3LYP/6-31+G(d,p) calculations predicted the presence of improper hydrogen-bonded C-H_ax?Y_ax contacts of different strength in cyclohexane derivatives;¹ it was predicted that the addition of an appropriate bridging fragment X_ax between an axial substituent Y₁ and a cyclohexane carbon would strengthen the improper hydrogen-bonded contact C-H_ax?Y₁ when the X_ax-Y₁ bond vector bisects the cyclohexane ring. To support the theoretical predictions with experimental evidence for this effect, several 2-substituted adamantane analogues with suitable improper H-bonded C-H_ax?O contacts of different strength were synthesized, as models of the corresponding cyclohexane derivatives, and their ¹H NMR spectra were recorded at 298 K. The ¹H NMR signal separation within the cyclohexane ring γ-CH₂s is increased when the B3LYP/6-31+G(d,p)-calculated strength of the H-bonded C-H_ax?O=C_ax contact interaction is increased.     

Airy trajectory engineering in dynamic linear index potentials

We study the propagation of Airy beams in transversely linear index potentials with a gradient that is dynamically changing along the propagation direction. We find exact solutions in the case of Airy and apodized (Gaussian and exponentially) Airy beams in 1+1 and 2+1 dimensions. More important, we find that the Airy beam can follow any predefined path, in which case the potential gradient is determined as a function of this path.     

Bifurcation near infinity for the Neumann problem with concave–convex nonlinearities

In this Note, we study a class of Neumann parametric elliptic equations driven by a nonhomogeneous differential operator and with a reaction that exhibits competing terms (concave–convex nonlinearities). Using the Ambrosetti–Rabinowitz condition and related topological and variational arguments, we prove a bifurcation result for large values of the parameter.     

Matrix-free interior point method for compressed sensing problems

We consider a class of optimization problems for sparse signal reconstruction which arise in the field of compressed sensing (CS). A plethora of approaches and solvers exist for such problems, for example GPSR, FPC_AS, SPGL1, NestA, $\mathbf{\ell _1\_\ell _s}$ , PDCO to mention a few. CS applications lead to very well conditioned optimization problems and therefore can be solved easily by simple first-order methods. Interior point methods (IPMs) rely on the Newton method hence they use the second-order information. They have numerous advantageous features and one clear drawback: being the second-order approach they need to solve linear equations and this operation has (in the general dense case) an ${\mathcal {O}}(n^3)$ computational complexity. Attempts have been made to specialize IPMs to sparse reconstruction problems and they have led to interesting developments implemented in $\mathbf{\ell _1\_\ell _s}$ and PDCO softwares. We go a few steps further. First, we use the matrix-free IPM, an approach which redesigns IPM to avoid the need to explicitly formulate (and store) the Newton equation systems. Secondly, we exploit the special features of the signal processing matrices within the matrix-free IPM. Two such features are of particular interest: an excellent conditioning of these matrices and the ability to perform inexpensive (low complexity) matrix–vector multiplications with them. Computational experience with large scale one-dimensional signals confirms that the new approach is efficient and offers an attractive alternative to other state-of-the-art solvers.     

Global optimization of general nonconvex problems with intermediate polynomial substructures

This work considers the global optimization of general nonconvex nonlinear and mixed-integer nonlinear programming problems with underlying polynomial substructures. We incorporate linear cutting planes inspired by reformulation-linearization techniques to produce tight subproblem formulations that exploit these underlying structures. These cutting plane strategies simultaneously convexify linear and nonlinear terms from multiple constraints and are highly effective at tightening standard linear programming relaxations generated by sequential factorable programming techniques. Because the number of available cutting planes increases exponentially with the number of variables, we implement cut filtering and selection strategies to prevent an exponential increase in relaxation size. We introduce algorithms for polynomial substructure detection, cutting plane identification, cut filtering, and cut selection and embed the proposed implementation in BARON at every node in the branch-and-bound tree. A computational study including randomly generated problems of varying size and complexity demonstrates that the exploitation of underlying polynomial substructures significantly reduces computational time, branch-and-bound tree size, and required memory.     

The 19F and 31P magnetic resonance spectra of phosphorus trifluoride in nematic solution

The phosphorus and fluorine N.M.R. spectra of PF₃ in a nematic solvent (EBBA) are discussed. The molecular geometry is found to agree with structures obtained from microwave and electron diffraction studies. The sign of the ordering parameter is assumed negative, the signs of the phosphorus fluorine coupling constant and of the chemical shift anisotropies follow from this assumption, and are found to be in agreement with theoretical predictions. The effect of temperature on the isotropic chemical shift of fluorine is discussed.