Min-max theory,Willmore conjecture and the energy of links

In this paper we give an overview of some aspects of the min-max theory of minimal surfaces, and discuss recent applications to conformally invariant problems in Geometry and Topology. The goal is to explain what the proofs of the Willmore conjecture for surfaces and the Freedman-He-Wang conjecture for links share in common. This is based on joint work of the authors [19] and on joint work of I. Agol and the authors [1].     

Braided reinforced composite rods for the internal reinforcement of concrete

This paper reports on the development of braided reinforced composite rods as a substitute for the steel reinforcement in concrete. The research work aims at understanding the mechanical behaviour of core-reinforced braided fabrics and braided reinforced composite rods, namely concerning the influence of the braiding angle, the type of core reinforcement fibre, and preloading and postloading conditions. The core-reinforced braided fabrics were made from polyester fibres for producing braided structures, and E-glass, carbon, HT polyethylene, and sisal fibres were used for the core reinforcement. The braided reinforced composite rods were obtained by impregnating the core-reinforced braided fabric with a vinyl ester resin. The preloading of the core-reinforced braided fabrics and the postloading of the braided reinforced composite rods were performed in three and two stages, respectively. The results of tensile tests carried out on different samples of core-reinforced braided fabrics are presented and discussed. The tensile and bending properties of the braided reinforced composite rods have been evaluated, and the results obtained are presented, discussed, and compared with those of conventional materials, such as steel. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 44, No. 4, pp. 327–338, May–June, 2008.     

Couette flow from a thirteen field theory with slip and jump boundary conditions

Received March 12, 2001 / Published online: June 1, 2001     

Local entropic effects of polymers grafted to soft interfaces

In this paper, we study the equilibrium properties of polymer chains end-tethered to a fluid membrane. The loss of conformational entropy of the polymer results in an inhomogeneous pressure field that we calculate for Gaussian chains. We estimate the effects of excluded volume through a relation between pressure and concentration. Under the polymer pressure, a soft surface will deform. We calculate the deformation profile for a fluid membrane and show that close to the grafting point, this profile assumes a cone-like shape, independently of the boundary conditions. Interactions between different polymers are also mediated by the membrane deformation. This pair-additive potential is attractive for chains grafted on the same side of the membrane and repulsive otherwise. Received 20 April 2000     

Mesophase formation and thermal behavior of catanionic mixtures of gemini surfactants with sodium alkylsulfates

The thermal behavior for three homologous series of cationic geminis surfactants of the type n-2-n, alkanediyl-α,ω-bis(alkyldimethylammonium bromide), with n = 12, 14, 16, and 18, and sodium alkyl sulfates, SC _m S, with m = 12, 14, and 16, is reported here. The cationic/anionic molar ratio is kept at 1:2 (equicharged mixtures), and salt is also present. Polarizing light microscopy and differential scanning calorimetry show a stepwise fusion for the mixtures with appearance of several mesophases between the crystalline structures and the isotropic liquid. A main endothermic transition is observed, associated with partial chain melting and consequent loss of crystalline order, followed by a transition to a smectic liquid crystal. The phase transition thermodynamics is interpreted in terms of an interplay between van der Waals chain–chain interactions and ionic head group interactions.     

How different are two chemical structures?

We extend the scope of a recent method for superimposing two molecules ( J. Chem. Phys. 2009, 131, 124126-1-124126-10 ) to include the identification of chiral structures. This methodology is tested by applying it to several organic molecules and water clusters that were subjected to geometry optimization. The accuracy of four simpler, non-superimposing approaches is then analyzed by comparing pairs of structures for argon and water clusters. The structures considered in this work were obtained by a Markovian walk in the coordinate space. First, a random geometry is generated, and then, the iterative application of a mutation operator ensures the creation of increasingly dissimilar structures. The discriminating power of the non-superimposing approaches is tested by comparing the corresponding dissimilarity measures with the root-mean-square distance obtained from the superimposing method. Finally, we showcase the application of those methods to characterize the diversity of solutions in global geometry optimization by evolutionary algorithms.     

Generation and characterization of low‐energy structures in atomic clusters

Factors relevant for controlling the structures determined in the local optimization of argon clusters are investigated. In particular, the role of volume and shape for the box where initial structures are generated is assessed. A thorough characterization of the optimization is also presented, based on a nearest‐neighbor analysis, in clusters ranging from 30 to 55 atoms. This includes the assessment of the degree of preservation of aspects of the initial randomly generated structure in the final optimized counterpart, and the correlation between optimized energy and the number of nearest neighbors and average departure from the diatomic reference distance. The usefulness of this analysis to explore the energy landscape of atomic clusters is also highlighted. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

The Role of the Eu<Superscript>3+</Superscript> Concentration on the SrMoO<Subscript>4</Subscript>:Eu Phosphor Properties: Synthesis,Characterization and Photophysical Studies

SrMoO₄ doped with rare earth are still scarce nowadays and have attracted great attention due to their applications as scintillating materials in electro-optical like solid-state lasers and optical fibers, for instance. In this work Sr_1−xEu_xMoO₄ powders, where x = 0.01; 0.03 and 0.05, were synthesized by Complex Polymerization (CP) Method. The structural and optical properties of the SrMoO₄:Eu³⁺ were analyzed by powder X-ray diffraction patterns, Fourier Transform Infra-Red (FTIR), Raman Spectroscopy, and through Photoluminescent Measurements (PL). Only a crystalline scheelite-type phase was obtained when the powders were heat-treated at 800 °C for 2 h, 2θ = 27.8° (100% peak). The excitation spectra of the SrMoO₄:Eu³⁺ (λ_Em. = 614 nm) presented the characteristic band of the Eu^3 + 5L₆ transition at 394 nm and a broad band at around 288 nm ascribed to the charge-transfer from the O (2p) state to the Mo (4d) one in the SrMoO₄ matrix. The emission spectra of the SrMoO₄:Eu³⁺ powders (λ_Exc. = 394 and 288 nm) show the group of sharp emission bands among 523–554 nm and 578–699 nm, assigned to the ⁵D₁→⁷F_{0,1and 2} and ⁵D₀→⁷F_{0,1,2,3 and 4}, respectively. The band related to the ⁵D₀→⁷F₀ transition indicates the presence of Eu³⁺ site without inversion center. This hypothesis is strengthened by the fact that the band referent to the ⁵D₀→⁷F₂ transition is the most intense in the emission spectra.     

Moreau–Yosida Regularization of Maximal Monotone Operators of Type (D)

We propose a Moreau–Yosida regularization for maximal monotone operators of type (D), in non-reflexive Banach spaces. It generalizes the classical Moreau–Yosida regularization as well as Brezis–Crandall–Pazy’s extension of this regularization to strictly convex (reflexive) Banach spaces with strictly convex duals. Our main results are obtained by making use of recent results by the authors on convex representations of maximal monotone operators in non-reflexive Banach spaces.