Quantum radiation from superluminal refractive index perturbations

We analyze in detail photon production induced by a superluminal refractive index perturbation in realistic experimental operating conditions. The interaction between the refractive index perturbation and the quantum vacuum fluctuations of the electromagnetic field leads to the production of photon pairs.Comment: 4 page

On the Higher Poisson Structures of the Camassa–Holm Hierarchy

We find a generating series for the higher Poisson structures of the nonlocal Camassa–Holm hierarchy, following the method used by Enriques, Orlov, and third author for the KdV case

Spacetime geometries and light trapping in travelling refractive index perturbations

In the framework of transformation optics, we show that the propagation of a locally superluminal refractive index perturbation (RIP) in a Kerr medium can be described, in the eikonal approximation, by means of a stationary metric, which we prove to be of Gordon type. Under suitable hypotheses on the RIP, we obtain a stationary but not static metric, which is characterized by an ergosphere and by a peculiar behaviour of the geodesics, which are studied numerically, also accounting for material dispersion. Finally, the equation to be satisfied by an event horizon is also displayed and briefly discussed.Comment: 14 pages, 7 figure

Integer solutions of integral inequalities and H-invariant Jacobian Poisson structures

We study the Jacobian Poisson structures in any dimension invariant with respect to the discrete Heisenberg group. The classification problem is related to the discrete volume of suitable solids. Particular attention is given to dimension 3 whose simplest example is the Artin-Schelter-Tate Poisson tensors

Structural characterization of En-1, a cold-adapted protein pheromone isolated from the Antarctic ciliate Euplotes nobilii.

The second of two diffusible cell signal proteins (pheromones) purified from a wild-type strain of the Antarctic ciliate, Euplotes nobilii, has been determined by automated Edman degradation of the whole molecule and peptides generated by its chymotryptic digestion. The proposed sequence of 52 amino acids of this new pheromone, designated En-1, is: NPEDWFTPDT10CAYGDSNTAW20TTCTTPGQTC30YTCCSSCFDV40VGEQACQMSA50QC. In common with the previously determined 60-amino-acid sequence of the other pheromone, En-2, it bears eight cysteines in conserved positions (presumably linked into four conserved intrachain disulfide bonds), and physicochemical features of potential significance for cold adaptation, such as a reduced hydrophobicity, an increased solvent accessibility, and an improved local backbone flexibility. However, En-1 diverges from En-2 for having evolved a threonine cluster in the place of a glycine cluster to apparently make more flexible a region that is likely functionally important

Structural characterization of a protein pheromone from a cold-adapted (Antarctic) single-cell eukaryote, the ciliate Euplotes nobilii

Free-living species of ciliated Protozoa control their vegetative (mitotic) proliferation and mating (sexual) processes by diffusible, cell type-specific protein signals (pheromones). One of these molecules, designated En-2, was isolated from a species, Euplotes nobilii, living in the stably cold marine waters of Antarctica, and its complete amino acid sequence of 60 residues was determined by automated Edman degradation of the whole protein and peptides generated by trypsin digestion. The proposed sequence is : DIEDFYTSETCPYKNDSQLA20- WDTCSGGTGNCGTVCCGQCF40SFPVSQSCAGMADSNDCPNA60. The En-2 structure appears to be characterized by an adaptive insertion of a glycine-rich motif potentially capable to confer more flexibility to a functionally critical region of the molecule

Reply to Comment on: Hawking radiation from ultrashort laser pulse filaments

A comment by R. Schutzhold et al. raises possible concerns and questions regarding recent measurements of analogue Hawking radiation. We briefly reply to the opinions expressed in the comment and sustain that the origin of the radiation may be understood in terms of Hawking emission

Birkhoff strata of the Grassmannian Gr(2)\mathrm{^{(2)}}: Algebraic curves

Algebraic varieties and curves arising in Birkhoff strata of the Sato Grassmannian Gr${^{(2)}}$ are studied. It is shown that the big cell $\Sigma_0$ contains the tower of families of the normal rational curves of all odd orders. Strata $\Sigma_{2n}$, $n=1,2,3,...$ contain hyperelliptic curves of genus $n$ and their coordinate rings. Strata $\Sigma_{2n+1}$, $n=0,1,2,3,...$ contain $(2m+1,2m+3)-$plane curves for $n=2m,2m-1$ $(m \geq 2)$ and $(3,4)$ and $(3,5)$ curves in $\Sigma_3$, $\Sigma_5$ respectively. Curves in the strata $\Sigma_{2n+1}$ have zero genus.Comment: 14 pages, no figures, improved some definitions, typos correcte