Convective instability of 3-D fluid-saturated geological fault zones heated from below

We conduct a theoretical analysis to investigate the convective instability of 3-D fluid-saturated geological fault zones when they are heated uniformly from below. In particular, we have derived exact analytical solutions for the critical Rayleigh numbers of different convective flow structures. Using these critical Rayleigh numbers, three interesting convective flow structures have been identified in a geological fault zone system. It has been recognized that the critical Rayleigh numbers of the system have a minimum value only for the fault zone of infinite length, in which the corresponding convective flow structure is a 2-D slender-circle flow. However, if the length of the fault zone is finite, the convective flow in the system must be 3-D. Even if the length of the fault zone is infinite, since the minimum critical Rayleigh number for the 2-D slender-circle flow structure is so close to that for the 3-D convective flow structure, the system may have almost the same chance to pick up the 3-D convective flow structures. Also, because the convection modes are so close for the 3-D convective flow structures, the convective flow may evolve into the 3-D finger-like structures, especially for the case of the fault thickness to height ratio approaching zero. This understanding demonstrates the beautiful aspects of the present analytical solution for the convective instability of 3-D geological fault zones, because the present analytical solution is valid for any value of the ratio of the fault height to thickness. Using the present analytical solution, the conditions, under which different convective flow structures may take place, can be easily determined

Energy expenditure during overfeeding

The large inter-individual variation in weight gain during standardized overfeeding together with a weight gain that is often less than theoretically calculated from the energy excess suggest that there are differences between persons in the capacity to regulate energy expenditure and hence metabolic efficiency. Adaptive thermogenesis is defined as the regulated production of heat in response to environmental changes in temperature and diet, resulting in metabolic inefficiency. The question is whether adaptive thermogenesis can be identified in overfeeding experiments. From the numerous human overfeeding experiments we selected those studies that applied suitable protocols and measurement techniques. Five studies claimed to have found evidence for adaptive thermogenesis based on weight gains smaller than expected or unaccounted increases in thermogenesis above obligatory costs. Results from the other 11 studies suggest there is no adaptive thermogenesis as weight gains were proportional to the amount of overfeeding and the increased thermogenesis was associated with theoretical costs of an increased body size and a larger food intake. These results show that in humans, evidence for adaptive thermogenesis is still inconsistent. However, they do not rule out the existence, but emphasize that if present, adaptive changes in energy expenditure may be too small to measure considering measurement errors, errors in assumptions made and small (day-to-day) differences in physical activity. In addition, it is not clear in which component or components of total energy expenditure adaptive changes can occur and whether components can overlap due to measurement limitations

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