Perturbative analysis of wave interactions in nonlinear systems

This work proposes a new way for handling obstacles to asymptotic integrability in perturbed nonlinear PDEs within the method of Normal Forms - NF - for the case of multi-wave solutions. Instead of including the whole obstacle in the NF, only its resonant part is included, and the remainder is assigned to the homological equation. This leaves the NF intergable and its solutons retain the character of the solutions of the unperturbed equation. We exploit the freedom in the expansion to construct canonical obstacles which are confined to te interaction region of the waves. Fo soliton solutions, e.g., in the KdV equation, the interaction region is a finite domain around the origin; the canonical obstacles then do not generate secular terms in the homological equation. When the interaction region is infifnite, or semi-infinite, e.g., in wave-front solutions of the Burgers equation, the obstacles may contain resonant terms. The obstacles generate waves of a new type, which cannot be written as functionals of the solutions of the NF. When an obstacle contributes a resonant term to the NF, this leads to a non-standard update of th wave velocity.Comment: 13 pages, including 6 figure

Direct photons from relativistic heavy ion collisions at CERN SPS and at RHIC

Assuming QGP as the initial state, we have analyzed the direct photon data, obtained by the WA98 collaboration, in 158 A GeV Pb+Pb collisions at CERN SPS. It was shown, that for small thermalisation time, two loop rate contribute substantially to high $p_T$ photons. We argue that for extremely short thermalisation time scale, the higher loop contribution should not be neglected. For thermalisation time 0.4 fm or greater, when higher loop contribution are not substantial, the initial temperature of the QGP is not large and the system does not produce enough hard $p_T$ photons to fit the WA98 experiment. For initial time in the ranges of 0.4-1.0 fm, WA98 data could be fitted only if the fluid has initial radial velocity in the range of 0.3-0.5c. The model was applied to predict photon spectrum at RHIC energy.Comment: 5 pages, 5 figure

Self-consistency in non-extensive thermodynamics of highly excited hadronic states

The self-consistency of a thermodynamical theory for hadronic sys- tems based on the non-extensive statistics is investigated. We show that it is possible to obtain a self-consistent theory according to the asymptotic bootstrap principle if the mass spectrum and the energy density increase q-exponentially. A direct consequence is the existence of a limiting effective temperature for the hadronic system. We show that this result is in agreement with experiments.Comment: 8 page

THz Metamaterial Characterization Using THz-TDS

The purpose of this chapter is to familiarize the reader with metamaterials and describe terahertz (THz) spectroscopy within metamaterials research. The introduction provides key background information on metamaterials, describes their history and their unique properties. These properties include negative refraction, backwards phase propagation, and the reversed Doppler Effect. The history and theory of metamaterials are discussed, starting with Veselago’s negative index materials work and Pendry’s publications on physical realization of metamaterials. The next sections cover measurement and analyses of THz metamaterials. THz Time-domain spectroscopy (THz-TDS) will be the key measurement tool used to describe the THz metamaterial measurement process. Sample transmission data from a metamaterial THz-TDS measurement is analyzed to give a better understanding of the different frequency characteristics of metamaterials. The measurement and analysis sections are followed by a section on the fabrication process of metamaterials. After familiarizing the reader with THz metamaterial measurement and fabrication techniques, the final section will provide a review of various methods by which metamaterials are made active and/or tunable. Several novel concepts were demonstrated in recent years to achieve such metamaterials, including photoconductivity, high electron mobility transistor (HEMT), microelectromechanical systems (MEMS), and phase change material (PCM)-based metamaterial structures

THz Metamaterial Characterization Using THz-TDS

The purpose of this chapter is to familiarize the reader with metamaterials and describe terahertz (THz) spectroscopy within metamaterials research. The introduction provides key background information on metamaterials, describes their history and their unique properties. These properties include negative refraction, backwards phase propagation, and the reversed Doppler Effect. The history and theory of metamaterials are discussed, starting with Veselago’s negative index materials work and Pendry’s publications on physical realization of metamaterials. The next sections cover measurement and analyses of THz metamaterials. THz Time-domain spectroscopy (THz-TDS) will be the key measurement tool used to describe the THz metamaterial measurement process. Sample transmission data from a metamaterial THz-TDS measurement is analyzed to give a better understanding of the different frequency characteristics of metamaterials. The measurement and analysis sections are followed by a section on the fabrication process of metamaterials. After familiarizing the reader with THz metamaterial measurement and fabrication techniques, the final section will provide a review of various methods by which metamaterials are made active and/or tunable. Several novel concepts were demonstrated in recent years to achieve such metamaterials, including photoconductivity, high electron mobility transistor (HEMT), microelectromechanical systems (MEMS), and phase change material (PCM)-based metamaterial structures