Global attractors for singular perturbations of the Cahn–Hilliard equations

AbstractWe consider the singular perturbations of two boundary value problems, concerning respectively the viscous and the nonviscous Cahn–Hilliard equations in one dimension of space. We show that the dynamical systems generated by these two problems admit global attractors in the phase space H01(0,π)×H-1(0,π), and that these global attractors are at least upper-semicontinuous with respect to the vanishing of the perturbation parameter

Explicit Complex Solutions to the Fresnel Coefficients

Global Navigation Satellite System Reflectometry (GNSS-R) is a microwave remote sensing technique which can be used to derive information about the composition or the properties of ground surfaces. The received power of the GPS signals reflected by the ground is proportional to the magnitude of the reflection Fresnel coefficients In particular, it depends on the incidence angle $\theta$ and on the ground's permittivity $\epsilon$. The knowledge of $\epsilon$ is important for determining various conditions and characteristics of the surface (e.g., soil moisture, salinity, freeze-thaw transitions). The value of $\epsilon$ can be found from the Fresnel reflection coefficients, for a given incidence angle $\theta$. For dispersive media, $\epsilon$ is a complex quantity; we present explicit formulas, which express both $\Re(\varepsilon)$ and $\Im(\varepsilon)$ as a function of the incident angle $\theta$ and of the magnitude of the linearly polarized Fresnel reflection coefficients

Determining Real Permittivity from Fresnel Coefficients in GNSS-R

Global Navigation Satellite System Reflectometry (GNSS-R) can be used to derive information about the composition or the properties of ground surfaces, by analyzing signals emitted by GNSS satellites and reflected from the ground. If the received power is measured with linearly polarized antennas, under the condition of smooth surface, the reflected signal is proportional to the modulus of the perpendicular and parallel polarization Fresnel coefficients, which depend on the incidence angle θ, and on the dielectric constant ε of the soil. In general, ε is a complex number; for non-dispersive soils, the imaginary part of ε can be neglected, and a real value of ε is sought. We solve the real valued problem explicitly giving formulas that can be used to determine the dielectric constant ε and we compare the analytical solution with experimental data in the case of sand soil

Delayed - Choice Entanglement - Swapping with Vacuum-One Photon Quantum States

We report the experimental realization of a recently discovered quantum information protocol by Asher Peres implying an apparent non-local quantum mechanical retrodiction effect. The demonstration is carried out by applying a novel quantum optical method by which each singlet entangled state is physically implemented by a two-dimensional subspace of Fock states of a mode of the electromagnetic field, specifically the space spanned by the vacuum and the one photon state, along lines suggested recently by E. Knill et al., Nature 409, 46 (2001) and by M. Duan et al., Nature 414, 413 (2001). The successful implementation of the new technique is expected to play an important role in modern quantum information and communication and in EPR quantum non-locality studies

Quantitative test of the barrier nucleosome model for statistical positioning of nucleosomes up- and downstream of transcription start sites

The positions of nucleosomes in eukaryotic genomes determine which parts of the DNA sequence are readily accessible for regulatory proteins and which are not. Genome-wide maps of nucleosome positions have revealed a salient pattern around transcription start sites, involving a nucleosome-free region (NFR) flanked by a pronounced periodic pattern in the average nucleosome density. While the periodic pattern clearly reflects well-positioned nucleosomes, the positioning mechanism is less clear. A recent experimental study by Mavrich et al. argued that the pattern observed in S. cerevisiae is qualitatively consistent with a `barrier nucleosome model', in which the oscillatory pattern is created by the statistical positioning mechanism of Kornberg and Stryer. On the other hand, there is clear evidence for intrinsic sequence preferences of nucleosomes, and it is unclear to what extent these sequence preferences affect the observed pattern. To test the barrier nucleosome model, we quantitatively analyze yeast nucleosome positioning data both up- and downstream from NFRs. Our analysis is based on the Tonks model of statistical physics which quantifies the interplay between the excluded-volume interaction of nucleosomes and their positional entropy. We find that although the typical patterns on the two sides of the NFR are different, they are both quantitatively described by the same physical model, with the same parameters, but different boundary conditions. The inferred boundary conditions suggest that the first nucleosome downstream from the NFR (the +1 nucleosome) is typically directly positioned while the first nucleosome upstream is statistically positioned via a nucleosome-repelling DNA region. These boundary conditions, which can be locally encoded into the genome sequence, significantly shape the statistical distribution of nucleosomes over a range of up to ~1000 bp to each side.Comment: includes supporting materia