Phenomenological Analysis of pppp and pˉp\bar{p}p Elastic Scattering Data in the Impact Parameter Space

We use an almost model-independent analytical parameterization for $pp$ and $\bar{p}p$ elastic scattering data to analyze the eikonal, profile, and inelastic overlap functions in the impact parameter space. Error propagation in the fit parameters allows estimations of uncertainty regions, improving the geometrical description of the hadron-hadron interaction. Several predictions are shown and, in particular, the prediction for $pp$ inelastic overlap function at $\sqrt{s}=14$ TeV shows the saturation of the Froissart-Martin bound at LHC energies.Comment: 15 pages, 16 figure

Studies on Temperature and Strain Sensitivities of a Few-mode Critical Wavelength Fiber Optic Sensor

This paper studied the relationship between the temperature/strain wavelength sensitivity of a fiber optic in-line Mach-Zehnder Interferometer (MZI) sensor and the wavelength separation of the measured wavelength to the critical wavelength (CWL) in a CWL-existed interference spectrum formed by interference between LP01 and LP02 modes. The in-line MZI fiber optic sensor has been constructed by splicing a section of specially designed few-mode fiber (FMF), which support LP01 and LP02 modes propagating in the fiber, between two pieces of single mode fiber. The propagation constant difference, Δβ, between the LP01 and LP02 modes, changes non-monotonously with wavelength and reaches a maximum at the CWL. As a result, in sensor operation, peaks on the different sides of the CWL then shift in opposite directions, and the associated temperature/strain sensitivities increase significantly when the measured wavelength points become close to the CWL, from both sides of the CWL. A theoretical analysis carried out has predicted that with this specified FMF sensor approach, the temperature/strain wavelength sensitivities are governed by the wavelength difference between the measured wavelength and the CWL. This conclusion was seen to agree well with the experimental results obtained. Combining the wavelength shifts of the peaks and the CWL in the transmission spectrum of the SFS structure, this study has shown that this approach forms the basis of effective designs of high sensitivity sensors for multi-parameter detection and offering a large measurement range to satisfy the requirements needed for better industrial measurements

Gamma-Ray Burst Afterglows: Effects of Radiative Corrections and Nonuniformity of the Surrounding Medium

The afterglow of a gamma-ray burst (GRB) is commonly thought to be due to continuous deceleration of a relativistically expanding fireball in the surrounding medium. Assuming that the expansion of the fireball is adiabatic and that the density of the medium is a power-law function of shock radius, viz., $n_{ext}\propto R^{-k}$, we analytically study the effects of the first-order radiative correction and the nonuniformity of the medium on a GRB afterglow. We first derive a new relation among the observed time, the shock radius and the fireball's Lorentz factor: $t_\oplus=R/4(4-k)\gamma^2c$, and also derive a new relation among the comoving time, the shock radius and the fireball's Lorentz factor: $t_{co}=2R/(5-k)\gamma c$. We next study the evolution of the fireball by using the analytic solution of Blandford and McKee (1976). The radiation losses may not significantly influence this evolution. We further derive new scaling laws both between the X-ray flux and observed time and between the optical flux and observed time. We use these scaling laws to discuss the afterglows of GRB 970228 and GRB 970616, and find that if the spectral index of the electron distribution is $p=2.5$, implied from the spectra of GRBs, the X-ray afterglow of GRB970616 is well fitted by assuming $k=2$.Comment: 17 pages, no figures, Latex file, MNRAS in pres

Flat lens without optical axis: Theory of imaging

We derive a general theory for imaging by a flat lens without optical axis. We show that the condition for imaging requires a material having elliptic dispersion relations with negative group refraction, equivalent to an effective anisotropic refractive index n(theta). Imaging can be achieved with both negative (n0) refractive indices. The Veselago-Pendry lens is a special case with isotropic negative refractive index of n(theta)=-1. Realizations of the imaging conditions using anisotropic media and inhomogeneous media, particularly photonic crystals, are discussed. Numerical examples of imaging and requirements for sub-wavelength imaging are also presented.Comment: 5 pages, 4 figure