Global well-posedness and scattering of the (4+1)-dimensional Maxwell-Klein-Gordon equation

This article constitutes the final and main part of a three-paper sequence, whose goal is to prove global well-posedness and scattering of the energy critical Maxwell-Klein-Gordon equation (MKG) on $\mathbb{R}^{1+4}$ for arbitrary finite energy initial data. Using the successively stronger continuation/scattering criteria established in the previous two papers, we carry out a blow-up analysis and deduce that the failure of global well-posedness and scattering implies the existence of a nontrivial stationary or self-similar solution to MKG. Then, by establishing that such solutions do not exist, we complete the proof.Comment: 64 page

Local well-posedness of the (4+1)-dimensional Maxwell-Klein-Gordon equation at energy regularity

This paper is the first part of a trilogy dedicated to a proof of global well-posedness and scattering of the (4+1)-dimensional mass-less Maxwell-Klein-Gordon equation (MKG) for any finite energy initial data. The main result of the present paper is a large energy local well-posedness theorem for MKG in the global Coulomb gauge, where the lifespan is bounded from below by the energy concentration scale of the data. Hence the proof of global well-posedness is reduced to establishing non-concentration of energy. To deal with non-local features of MKG we develop initial data excision and gluing techniques at critical regularity, which might be of independent interest.Comment: 59 page

Symurban Nanocrystals for Advanced Anti-Pollution Skincare

Several of most common dermatoses worldwide, e.g., psoriasis and atopic dermatitis, are worsened in their clinical picture when the skin is regularly exposed to an increased air pollution level, e.g., particulate matter. This is explainable by the activation of the aryl hydrocarbon receptor (AhR) in the skin, which results in an increased release of proinflammatory cytokines and matrix metalloproteinases. Symurban is a competitive AhR antagonist and thus allows the effective protection of skin. In order to improve its dermal bioavailability as a poorly soluble active agent (0.25 µg/mL), nanocrystals were prepared and evaluated. Nanocrystals are pure active crystals reduced in particle size to the submicron range of 100 to 1000 nm. They feature the properties of nanocrystals, such as increased saturation solubility and dissolution velocity, without having to be declared as nanomaterial. Production methods and parameters were systematically investigated. Wet bead milling at 2000 rpm for 30 min yielded the best results. A z-average of 280 nm was achieved for a 10% Symurban suspension with a polydispersity index of 0.20, indicating a narrow size distribution. For the long-term stabilization of the nanocrystal suspension, the performance of 15 surfactants of different categories and HLB values were investigated and evaluated. It was found that non-ionic surfactants in general were better able to stabilize the system than anionic or amphoteric surfactants. Highest stability of over 12 months at 25 °C was achieved with 2% Plantacare 810 UP, an ECOCERT surfactant with high skin tolerance. The suspension was also chemically long-term stable with >97% of remaining Symurban over 12 months. The saturation solubility of Symurban as nanocrystals was significantly increased from 0.25 to 2.9 μg/mL, which corresponds to a factor of >11. In a case study of one male volunteer with healthy skin conditions, penetration profiles of Symurban nanocrystal hydrogel and commercial anti-pollution serum containing an identical amount of Symurban were determined and compared. After 20 min of exposure, the relative Symurban concentration in the deeper skin layers (tape 19-30) was more than two times higher for nanocrystal hydrogel (16%) than the commercial serum (7%). These results suggest that nanocrystals are a promising delivery system for the poorly soluble anti-pollution agent Symurban

Energy dispersed solutions for the (4+1)-dimensional Maxwell-Klein-Gordon equation

This article is devoted to the mass-less energy critical Maxwell-Klein-Gordon system in 4+1 dimensions. In earlier work of the second author, joint with Krieger and Sterbenz, we have proved that this problem has global well-posedness and scattering in the Coulomb gauge for small initial data. This article is the second of a sequence of three papers of the authors, whose goal is to show that the same result holds for data with arbitrarily large energy. Our aim here is to show that large data solutions persist for as long as one has small energy dispersion; hence failure of global well-posedness must be accompanied with a non-trivial energy dispersion.Comment: 63 page

Reconfigurable dual band microstrip patch antenna for software defined radio applications

In this paper, a reconfigurable microstrip patch antenna with RF pin diode switches is implemented for dual band of 2.4 GHz and 5.6 GHz Software Defined Radio (SDR) applications. For the dual band SDR system, the use of a single antenna with a wide bandwidth to cover both of the bands can be limiting for low power level signal applications due to wideband noise. A reconfigurable nested microstrip patch antenna is designed on a Rogers 5880 RT/DUROID substrate which is fed by a coaxial probe from the back side of the grounded substrate. RF switching circuitry involves four RF pin diodes at each side of the inner patch. The dual bands of 2.4 GHz and 5.6 GHz frequency operation can be simply obtained by switching the PIN diodes on and off. The antenna is well matched and achieves approximately 7 dBi simulated gain at both frequency bands. Simulation results show that the nested patch antenna is suitable for dual band SDR applications