Supramolecular interactions between beta-cyclodextrin and hydrophobically end-capped poly(ethylene glycol)s: a quartz crystal microbalance study

In this study, the supramolecular interactions occurring between beta-cyclodextrin-based surfaces and macromolecular chains modified at one end with naphthyl, adamantyl, or phenyladamantyl hydrophobic groups were investigated by means of a quartz crystal microbalance. beta-Cyclodextrin-functionalized gold electrodes were obtained through the amide-coupling reaction between mono-6-deoxy-6-amino-beta-cyclodextrin and 11-mercaptoundecanoic acid self-assembled monolayer allowing the reproducible preparation of densely grafted surfaces with host properties. The interaction data obtained for the three different modified poly(ethylene glycol)s are in good agreement with our previous studies performed by high performance liquid chromatography and surface plasmon resonance. This evidences that the driving force for the supramolecular interaction is based on the inclusion of the hydrophobic terminal group of the chains within the cyclodextrin cavities. The reversibility of the inclusion process was proven through the regeneration of the original host properties of the sensing surfaces using sodium dodecylsulfate as a competitor for the desorption of the poly(ethylene glycol) chains.     

Noise-like pulses generated at high harmonics in a partially-mode-locked km-long Raman fiber laser

We present a 5-km-long Raman fiber laser that delivers pulses at high harmonics of the fundamental cavity repetition rate, up to 1 GHz. The observed nanosecond pulses that propagate in an anomalous dispersion regime possess a complex noise-like structure with a coherence time of around 1 picosecond.     

Homogenization of variational problems in manifold valued <Emphasis Type="Italic">BV</Emphasis>-spaces

This paper extends the result of Babadjian and Millot (preprint, 2008) on the homogenization of integral functionals with linear growth defined for Sobolev maps taking values in a given manifold. Through a Γ-convergence analysis, we identify the homogenized energy in the space of functions of bounded variation. It turns out to be finite for BV-maps with values in the manifold. The bulk and Cantor parts of the energy involve the tangential homogenized density introduced in Babadjian and Millot (preprint, 2008), while the jump part involves an homogenized surface density given by a geodesic type problem on the manifold.     

Multiple four-wave mixing in optical fibers: 1.5-3.4-THz femtosecond pulse sources and real-time monitoring of a 20-GHz picosecond source

In this work, we report recent progress on the design of all-fibered ultra-high repetition-rate pulse sources for telecommunication applications around 1550 nm. The sources are based on the non-linear compression of an initial beat-signal through a multiple four-wave mixing process taking place into an optical fiber. We experimentally demonstrate real-time monitoring of a 20 GHz pulse source having an integrated phase noise 0.01 radian by phase locking the initial beat note against a reference RF oscillator. Based on this technique, we also experimentally demonstrate a well-separated high-quality 110 fs pulse source having a repetition rate of 2 THz. Finally, we show that with only 1.4 m of standard single mode fiber, we can achieve a twofold increase of the repetition rate, up to 3.4 THz, through the self-imaging Talbot effect. Experimental results are supported by numerical simulations based on the generalized non-linear Schrödinger equation.     

Material voids in elastic solids with anisotropic surface energies

This work discusses the role of highly anisotropic interfacial energy for problems involving a material void in a linearly elastic solid. Using the calculus of variations it is shown that important qualitative features of the equilibrium shape of the void may be deduced from smoothness and convexity properties of the interfacial energy.     

Unilateral gradient flow of the Ambrosio–Tortorelli functional by minimizing movements

Motivated by models of fracture mechanics, this paper is devoted to the analysis of a unilateral gradient flow of the Ambrosio–Tortorelli functional, where unilaterality comes from an irreversibility constraint on the fracture density. Solutions of such evolution are constructed by means of an implicit Euler scheme. An asymptotic analysis in the Mumford–Shah regime is then carried out. It shows the convergence towards a generalized heat equation outside a time increasing crack set. In the spirit of gradient flows in metric spaces, a notion of curve of maximal unilateral slope is also investigated, and analogies with the unilateral slope of the Mumford–Shah functional are also discussed.     

A two-gradient approach for phase transitions in thin films

Motivated by solid-solid phase transitions in elastic thin films, we perform a Γ-convergence analysis for a singularly perturbed energy related to second order phase transitions in a domain of vanishing thickness. Under a two-wells assumption, we derive a sharp interface model with an interfacial energy depending on the asymptotic ratio between the characteristic length scale of the phase transition and the thickness of the film. In each case, the interfacial energy is determined by an explicit optimal profile problem. This asymptotic problem entails a nontrivial dependance on the thickness direction when the phase transition is created at the same rate as the thin film, while it shows a separation of scales if the thin film is created at a faster rate than the phase transition. The last regime, when the phase transition is created at a faster rate than the thin film, is more involved. Depending on growth conditions of the potential and the compatibility of the two phases, we either obtain a sharp interface model with scale separation, or a trivial situation driven by rigidity effects.     

Regenerative 40 Gbit/s wavelength converter based on similariton generation

We present an all-optical regeneration technique based on spectral filtering of self-similar parabolic pulses (similaritons). In particular, we demonstrate numerically and experimentally that ghost pulses, which occur in the zero bit slots of telecommunication pulse trains, can be effectively suppressed. These results are obtained with a 40 Gbit/s pulse train.     

Dark-soliton-like pulse-train generation from induced modulational polarization instability in a birefringent fiber

Theory and experiments show that the nonlinear development of the modulational polarization instability of an intense light beam in a normally dispersive, low-birefringence optical fiber leads to ultrashort dark-soliton-like trains with repetition rates in the terahertz range in the polarization orthogonal to the pump.     

Novel Monolithic Stationary Phase with Surface-Grafted Triphenyl Selector for Reversed-Phase Capillary Electrochromatography

A triphenylmethylamine-functionalized monolithic capillary column was newly designed for reversed-phase capillary electrochromatographic applications. Incorporation of the three phenyl rings-containing selector (also referred to as trityl selector) was achieved through post-polymerization functionalization of a generic monolithic matrix bearing nucleophilic-sensitive hydroxysuccinimide moieties. Such a 3D polymer matrix was obtained through UV-induced in situ free radical copolymerization of N-acryloxysuccinimide and ethylene dimethacrylate. The separation properties of the trityl monolithic capillary column were initially evaluated vis-à-vis polycyclic aromatic hydrocarbons, as model hydrophobic compounds, and compared to the separation ability of a benzylamine-functionalized monolithic capillary column prepared using the same generic monolithic matrix. Electrochromatographic separation of phenols and anilines was also considered, and our preliminary results suggest the occurrence of hydrophobic interactions due to the aromatic and non-polar nature of the surface-grafted trityl selector. The triphenyl monolithic capillary column exhibited relative standard deviation values (% RSD) below 4.1 % for the here-studied chromatographic parameters, namely, retention factor, selectivity, resolution, and efficiency.