Forced Symmetry Breaking from SO(3) to SO(2) for Rotating Waves on the Sphere

We consider a small SO(2)-equivariant perturbation of a reaction-diffusion system on the sphere, which is equivariant with respect to the group SO(3) of all rigid rotations. We consider a normally hyperbolic SO(3)-group orbit of a rotating wave on the sphere that persists to a normally hyperbolic SO(2)-invariant manifold $M(\epsilon)$. We investigate the effects of this forced symmetry breaking by studying the perturbed dynamics induced on $M(\epsilon)$ by the above reaction-diffusion system. We prove that depending on the frequency vectors of the rotating waves that form the relative equilibrium SO(3)u_{0}, these rotating waves will give SO(2)-orbits of rotating waves or SO(2)-orbits of modulated rotating waves (if some transversality conditions hold). The orbital stability of these solutions is established as well. Our main tools are the orbit space reduction, Poincare map and implicit function theorem

Femtosecond spectroscopic study of carminic acid–DNA interactions

Photo-excited carminic acid and carminic acid–DNA complexes in a buffer solution at pH 7 have been examined using a variety of spectroscopy techniques, that are in particular, the femtosecond resolved fluorescence upconversion and transient absorption spectroscopy. The observation of dual fluorescence emission, one peaks at 470 nm and the other at 570 nm, indicates to an excited-state (S1) intramolecular proton transfer (ESIPT). A detailed analysis of the transient absorption measurements of an aqueous carminic-acid solution at pH 7 yielded four lifetimes for the excited-state (S1): 8, 15, 33 and 46 ps. On the other hand, only two lifetimes, 34 and 47 ps, were observed by fluorescence upconversion spectroscopy because of the detection limitation to the long wavelength edge of the carminic-acid spectrum. The four S1 lifetimes were ascribed to the coexistence of respectively two tautomer (normal and tautomer) forms of carminic acid, in the non-dissociated state (CAH) and in the deprotonated state (CA−). The fluorescence upconversion measurements of carminic acid–DNA complexes exhibited a prolongation of the fluorescence lifetimes. This effect was accepted as evidence for the formation of intercalation complexes between the carminic acid and the DNA. The intercalative binding of the carminic acid to DNA was confirmed by the fluorescence titration experiments resulting to a binding constant of 2 × 105 M−1 that is typical for anthracycline–DNA complexes

All-Fiber DBR-Based Sensor Interrogation System for Measuring Acoustic Waves

We investigate the use of all-fiber distributed Bragg reflector (DBR) lasers for fiber optic sensing. We measure the steady-state strain response and show that it is very similar to that for a simple fiber Bragg grating (FBG). The lasers can be wavelength multiplexed and support multisensor operation without crosstalk. We also verify the principle of wavelength-to-power mapping, which can simplify sensor interrogation. Finally, we demonstrate that all-fiber DBR lasers can be used to detect acoustic waves

Global existence for semilinear reaction-diffusion systems on evolving domains

We present global existence results for solutions of reaction-diffusion systems on evolving domains. Global existence results for a class of reaction-diffusion systems on fixed domains are extended to the same systems posed on spatially linear isotropically evolving domains. The results hold without any assumptions on the sign of the growth rate. The analysis is valid for many systems that commonly arise in the theory of pattern formation. We present numerical results illustrating our theoretical findings.Comment: 24 pages, 3 figure

A Review of Recent Results on Simultaneous Interrogation of Multiple Fiber Bragg Grating-Based Sensors Using Microwave Photonics

We review recent results on exploiting microwave photonics to enable simultaneous interrogation of multiple fiber Bragg grating (FBG)-based sensors. In particular, we describe the use of (1) microwave photonic filtering and (2) chirped microwave pulse generation and compression as a means to map the wavelength (spectral) changes in the response of FBG-based sensors (specifically, an in-fiber Fabry-Pérot cavity sensor based on FBGs, FBG sensors directly, and a linearly chirped FBG sensor) to applied temperature (or strain) to the power of a radio-frequency signal (i.e., a wavelength-to-power mapping) or to the correlation peak of the compressed microwave signal. The approaches support high-resolution and high-speed interrogation and can be suitable for large scale sensing networks