Metastable Periodic Patterns in Singularly Perturbed Delayed Equations

We consider the scalar delayed differential equation epsilon(x) over dot(t) = -x(t) + f(x(t-1)), where epsilon > 0 and f verifies either df/dx > 0 or df/dx < 0 and some other conditions. We present theorems indicating that a generic initial condition with sign changes generates a solution with a transient time of order exp(c/epsilon), for some c > 0. We call it a metastable solution. During this transient a finite time span of the solution looks like that of a periodic function. It is remarkable that if df/dx > 0 then f must be odd or present some other very special symmetry in order to support metastable solutions, while this condition is absent in the case df/dx < 0. Explicit epsilon-asymptotics for the motion of zeroes of a solution and for the transient time regime are presented.

Electrochemical Control of the Time-Dependent Intensity Fluctuations in Surface-Enhanced Raman Scattering (SERS)

Time-dependent fluctuations in surface-enhanced Raman scattering (SERS) intensities were recorded from a roughened silver electrode immersed in diluted solutions of rhodamine 6G (R6G) and congo red (CR). These fluctuations were attributed to a small number of SERS-active molecules probing regions of extremely high electromagnetic field (hot spots) at the nanostructured surface. The time-dependent distribution of SERS intensities followed a tailed statistics at certain applied potentials, which has been linked to single-molecule dynamics. The shape of the distribution was reversibly tuned by the applied voltage. Mixtures of both dyes, R6G and CR, at low concentrations were also investigated. Since R6G is a cationic dye and CR is an anionic dye, the statistics of the SERS intensity distribution of either dye in a mixture were independently controlled by adjusting the applied potential. The potential-controlled distribution of SERS intensities was interpreted by considering the modulation of the surface coverage of the adsorbed dye by the interfacial electric field. This interpretation was supported by a two-dimensional Monte Carlo simulation that took into account the time evolution of the surface configuration of the adsorbed species and their probability to populate a hypothetical hot spot. The potential-controlled SERS dynamics reported here is a first step toward the spectroelectrochemical investigation of redox processes at the single-molecule level by SERS.

Amazonian Vegetable Oils and Fats: Fast Typification and Quality Control via Triacylglycerol (TAG) Profiles from Dry Matrix-Assisted Laser Desorption/Ionization Time-of-Flight (MALDI-TOF) Mass Spectrometry Fingerprinting

Amazonian oils and fats display unique triacylglycerol (TAG) profiles and, because of their economic importance as renewable raw materials and use by the cosmetic and food industries, are often subject to adulteration and forgery. Representative samples of these oils (andiroba, Brazil nut, buriti, and passion fruit) and fats (cupuacu, murumuru, and ucuba) were characterized without pre-separation or derivatization via dry (solvent-free) matrix-assisted laser desorption/ionization time-of-flight mass spectrometry (MALDI-TOF MS). Characteristic profiles of TAG were obtained for each oil and tat. Dry MALDI-TOF MS provides typification and direct and detailed information, via TAG profiles, of their variable combinations of fatty acids. A database from spectra could be developed and may be used for their fast and reliable typification, application screening, and quality control.