Time-Reversible Hamiltonian Vector Fields with Symplectic Symmetries

This paper deals with the dynamics of time-reversible Hamiltonian vector fields with two degrees of freedom around an elliptic equilibrium point in presence of 1–1 resonance. The main result says that under certain conditions there are two one-parameter families of reversible periodic solutions terminating at the equilibrium.     

First Curl,Then Wrinkle

The excellent properties of elastomers are exploited to trigger wrinkling instabilities in curved shells. Micro‐ and nano‐fibres are produced by electrospinning and UV irradiated: each fibre consists of a soft core and a stiff outer half‐shell. Upon solvent de‐swelling, the fibres curl because the shell and the core have different natural lengths. Wrinkling only starts after the fibre has attained a well‐defined helical shape. A simple analytical model is proposed to find the curling curvature and wrinkle wavelength, as well as the transition between the “curling” and “wrinkling” regimes. This new instability resembles that found in the tendrils of climbing plants as they dry and lignify.

     

Thermoluminescence study of the amorphisation of hexagonal ice by irradiation at 77 K

This paper reports on a thermoluminescence study of D₂O ice I_h. A sample of hexagonal (I_h) ice is irradiated by a 100 MeV X-ray source at 77 K. The emission spectrum that is measured immediately after the end of the irradiation process has the thermoluminescent behaviour of amorphous ice. The kinetic transition is followed to the stable form, taking place at 85 K. The relaxation time of the transition is of the order of 5 minutes. It is concluded that, due to irradiation, a few outer layers of ice I_h are converted to the low-density amorphous form of ice, which then converts to cubic ice. Although complex to quantify, thermoluminescence appears to be, in the present study, particularly sensitive to the time evolution of irradiated samples.     

New Materials for Solid‐Phase Extraction of Trace Elements

Abstract

The development of new sorbents and their application in preconcentration methods for determination of trace elements is a subject of great interest. This review summarizes and discusses several analytical methods involving the preparation and use of new solid‐phase materials. The performance and general properties of sorbents such as carbon nanotubes, imprinted ions, biosorbents, nanoparticles, and fullerene are discussed in detail. The perspective and future trends in the use of these materials are also considered.     

Tunable all-fiber intracavity wavelength converter without external pumps

A new architecture for tunable broadband wavelength conversion in a dispersion-shifted fiber is presented. Conversion is achieved by using four-wave-mixing in a dispersion-shifted fiber in a single fiber-ring cavity. Wide tunability is achieved by the self-generation of two tunable orthogonal pumps in the cavity. This effect is due to the introduction of two tunable fiber Bragg gratings written in high birefringence fibers which act as selective polarization and wavelength filters. The results show conversion efficiencies up to −2 dB with the signal-to-noise ratio of the converted signal up to 26 dB.     

The influence of skew rays on angular losses in air-clad fibres

Detailed experimental transmission properties of high numerical aperture air-clad undoped fibres are presented. Measurements of the angular transmissivity indicate a 15% lower numerical aperture (NA = 0.75) compared to theoretical predictions for the bridge thickness and wavelength ratio of δ/λ = 0.226. The discrepancy is attributed to skew rays that are deliberately launched and which are subject to larger loss rates through diffractive tunnelling in frustrated total internal reflection than meridional rays. Measurements of the angular propagation losses show that light launched at angles less than the critical angle for total internal reflection experiences low initial losses as well as low propagation losses. Light launched at steeper angles experiences a significant initial loss attributed to loss of skew rays within 1.5 m of propagation as well as larger general propagation losses.     

Periodic orbits for a class ofC 1 three-dimensional systems

We studyC ¹ perturbations of a reversible polynomial differential system of degree 4 in\(\mathbb{R}^3 \). We introduce the concept of strongly reversible vector field. If the perturbation is strongly reversible, the dynamics of the perturbed system does not change. For non-strongly reversible perturbations we prove the existence of an arbitrary number of symmetric periodic orbits. Additionally, we provide a polynomial vector field of degree 4 in\(\mathbb{R}^3 \) with infinitely many limit cycles in a bounded domain if a generic assumption is satisfied.     

Spin 1 Fields in Riemann-Cartan Space-Times via Duffin-Kemmer-Petiau Theory

We consider massive spin 1 fields, in Riemann-Cartan space-times, described by Duffin-Kemmer-Petiau theory. We show that this approach induces a coupling between the spin 1 field and the space-time torsion which breaks the usual equivalence with the Proca theory, but that such equivalence is preserved in the context of the Teleparallel Equivalent of General Relativity.     

Inclusion of Benzaldehyde Semicarbazone into β-Cyclodextrin Produces a Very Effective Anticonvulsant Formulation

Aryl semicarbazones can be considered a novel class of compounds presenting anticonvulsant activity. In order to improve the efficiency and bioavailability of benzaldehyde semicarbazone (BS) we used the host–guest strategy and β-cyclodextrin (β-CD) to prepare a BS/β-CD 1:1 inclusion compound, which was characterized by thermal analyses (TG, DTG, DSC), XRD powder pattern diffraction analyses, infrared data and ¹H, ¹³C, 2D-ROESY NMR and ¹H relaxation times. The BS/β-CD inclusion compound was tested in rats using the maximum electroshock (MES) screen. The minimum dose necessary to produce anticonvulsant activity decreased from 100 mg/Kg (ip or vo) for the free semicarbazone to 25 mg/Kg/vo (75%) and 15 mg/Kg/ip (85%), indicating that the host–guest strategy that uses β-CD and BS is very effective and could be successfully employed in the preparation of pharmaceutical formulationof anticonvulsants.     

A variational treatment for general elliptic equations of the flame propagation type: regularity of the free boundary

We develop a variational theory to study the free boundary regularity problem for elliptic operators: Lu=Dj(a_ij(x)Diu)+biui+c(x)u=0$Lu=D_j(a_{ij}(x)D_{i}u)+b_i{u}_i+c(x)u=0$ in {u>0}$\{u>0\}$, 〈a_ij(x)∇u,∇u〉=2$〈a_{ij}(x)\mathrm{\nabla }u,\mathrm{\nabla }u〉=2$ on ∂{u>0}$\partial \{u>0\}$. We use a singular perturbation framework to approximate this free boundary problem by regularizing ones of the form: Luε=βε(uε)$L{u}_{\epsilon }={\beta }_{\epsilon }(u_{\epsilon })$, where βε${\beta }_{\epsilon }$ is a suitable approximation of Dirac delta function δ₀${\delta }_0$. A useful variational characterization to solutions of the above approximating problem is established and used to obtain important geometric properties that enable regularity of the free boundary. This theory has been developed in connection to a very recent line of research as an effort to study existence and regularity theory for free boundary problems with gradient dependence upon the penalization.