Browsing by Subject "Relaxation phenomena"
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Item NMR relaxation in synthetic porous media(Texas Tech University, 1999-05) Xu, XinweiDue to their central importance in interpreting NMR logs, the NMR relaxation mechanisms in rocks are being thoroughly investigated by the industry. The bulk fluid response and the surface relaxivity are currently better characterized than is the diffusional relaxation. This latter T2 relaxation mechanism is due to the diffusion of the molecules across the strong internal field gradients generated by the susceptibility contrast between rock and pore fluid when the rock is placed in a magnetic field. The CPMG T2 measurement sequence is unable to refocus the spins effectively, since they see a time-varying internal field. This contributes an additional signal loss mechanism that is not present in a simple Ti measurement. To better characterize this diffusional loss mechanism, the T2 relaxation in synthetic mono-disperse porous media were measured in the lab at room temperature as a function of pore size at 2 MHz. Since the samples were oil-wet, decane was used as the pore fluid. The results are compared to higher field data (85 MHz) and to the relaxation of brine in Berea sandstone at low field. The author observed diffusional relaxation for these samples. As expected, the mono-disperse samples could be characterized by a single exponential decay constant. For small values of the refocusing time T (the inter-echo CPMG pulse spacing or interpulse spacing time), the T2 rate was proportional to t. For large values of x, the T2 relaxation was independent of the refocusing time x. Over the entire x regime, this T2 loss mechanism had a very well-characterized simple inverse dependence on pore radius.Item Relaxation in harmonic oscillator systems and wave propagation in negative index materials(2009-05) Chimonidou, Antonia; Sudarshan, E. C. G.This dissertation is divided up into two parts, each examining a distinct theme. The rst part of our work concerns itself with open quantum systems and the relaxation phenomena arising from the repeated application of an interaction Hamiltonian on systems composed of quantum harmonic oscillators. For the second part of our work, we shift gears and investigate the wave propagation in left-handed media, or materials with simultaneously negative electric permeability and magnetic permeability . Each of these two parts is complete within its own context. In the rst part of this dissertation, we introduce a relaxation-generating model which we use to study the process by which quantum correlations are created when an interaction Hamiltonian is repeatedly applied to bipartite harmonic oscillator systems for some characteristic time interval . The two important time scales which enter our results are discussed in detail. We show that the relaxation time obtained by the application of this repeated interaction scheme is proportional to both the strength of interaction and to the characteristic time interval . Through discussing the implications of our model, we show that, for the case where the oscillator frequencies are equal, the initial Maxwell-Boltzmann distributions of the uncoupled parts evolve to a new Maxwell-Boltzmann distribution through a series of transient Maxwell-Boltzmann distributions, or quasi-stationary, non-equilibrium states. We further analyze the case in which the two oscillator frequencies are unequal and show how the application of the same model leads to a non-thermal steady state. The calculations are exact and the results are obtained through an iterative process, without using perturbation theory. In the second part of this dissertation, we examine the response of a plane wave incident on a at surface of a left-handed material, a medium characterized by simultaneously negative electric permittivity and magnetic permeability . We do this by solving Maxwell's equations explicitly. In the literature up to date, it has been assumed that negative refractive materials are necessarily frequency dispersive. We propose an alternative to this assumption by suggesting that the requirement of positive energy density can be relaxed, and discuss the implications of such a proposal. More speci cally, we show that once negative energy solutions are accepted, the requirement for frequency dispersion is no longer needed. We further argue that, for the purposes of discussing left-handed materials, the use of group velocity as the physically signi cant quantity is misleading, and suggest that any discussion involving it should be carefully reconsidered.