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This paper deals with the application of steam to enhance the recovery from petroleum reservoirs. We formulate a mathematical and numerical model that simulates coinjection of volatile oil with steam into a porous rock in a one-dimensional setting. We utilize the mathematical theory of conservation laws to validate the numerical simulations. This combined numerical and analytical approach reveals the detailed mechanism for thermal displacement of oil mixtures discovered in laboratory experiments. We study the structure of the solution, determined by the speeds and amplitudes of the several nonlinear waves involved. Thus we show that the oil recovery depends critically on whether the boiling-point of the volatile oil is around the water boiling temperature, or much below or above it. These boiling-point ranges correspond to three types of wave structures. When the boiling point of the volatile oil is near the boiling point of water, the striking result is that the speed of the evaporation front is equal or somewhat larger than the speed of the steam condensation front. Thus the volatile oil condenses at the location where the steam condenses too, yielding virtually complete oil recovery. Conversely, if the boiling point is too high or too low, there is incomplete recovery. The condensed volatile oil stays at the steam condensation location because the steam condensation front is a physical shock.

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Recently, B. Roth and M. Woods [7] suggested a reexamination of MCG interpretation through currents transversal to the wave propagation direction. They also gave a formula J'(theta) for the dependence of the current intensity on the angle theta between straight fibers and the plane wave front. Here we study more general situations, including current injection at multiple points and curved fibers. We conclude that transversal currents are always present locally, in spite of electric pattern complexity and fiber curvature. Moreover, the J'(theta) relation holds locally. Nevertheless, computations indicate that macroscopically the far magnetic field may be similar to the one generated by a current dipole parallel to the wave propagation direction.

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Com a finalidade de estudar o processo de ativação tecidual durante o "flutter atrial", foi desenvolvido um protocolo experimental para acompanhar de forma controlada a propagação circular da frente de onda de ativação elétrica em tecido isolado de coração de coelho através da técnica não-invasiva de detecção do campo magnético. As medidas foram feitas com blindagem magnética e com parâmetros de posição do tecido sob controle. Estudos da mgnitude e fase dos seis primeiros da série de Fourier foram realizados para melhorar a relação sinal/ruído e através de um processamento por mínimos quadráticos foi localizado o dipolo circular equivalente. A frente de onda de despolarização descreveu um movimento circular, caracterizando o padrão reentrante como mecanismo subjacente à arritmia

Abstract - ln order to study the tissue activation process during atrial flutter, an animal experimentation protocol has been developed to allow controlled studies of circular motion of the evolution front in rabbit atrium tissue through the non-invasive magnetic field detection technique. The measurement were performed inside a shielded chamber with the tissue position parameters under control. Noise-free time series were obtained by using the magnitude and phase of the first six harmonics of the Fourier Series and the position of the center of the equivalent circulating dipole were calculated using a least square procedure. The electrical activation of the tissue indeed appeared to move along a circular path, characterizing the rotating pattern of propagation as the underlying mechanism ofthe arrhythmia.

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