Certain geological features have been interpreted as evidence of channelized magma flow in the mantle, which is a compacting porous medium. Aharonov et al. (J. Geophys. Res., vol. 100 (B10), 1995, pp. 20433–20450) developed a simple model of reactive porous flow and numerically analysed its instability to channels. The instability relies on magma advection against a chemical solubility gradient and the porosity-dependent permeability of the porous host rock. We extend the previous analysis by systematically mapping out the parameter space. Crucially, we augment numerical solutions with asymptotic analysis to better understand the physical controls on the instability. We derive scalings for the critical conditions of the instability and analyse the associated bifurcation structure. We also determine scalings for the wavelengths and growth rates of the channel structures that emerge. We obtain quantitative theories for and a physical understanding of, first, how advection or diffusion over the reactive time scale sets the horizontal length scale of channels and, second, the role of viscous compaction of the host rock, which also affects the vertical extent of channelized flow. These scalings allow us to derive estimates of the dimensions of emergent channels that are consistent with the geologic record.

Time series of daily precipitation, at Valentia, Ireland, are examined using conditioned chain-dependent processes. The conditioning is carried out using two different indices of large-scale atmospheric circulation. The first conditioning index relates to mean monthly sea level pressure (SLP), conditioned as either above or below the historic monthly mean. The second conditioning index is based on the geostrophic wind direction (GWD), conditioned as being inside or outside the historic storm quadrant for the month. For each conditioning index, there are two conditioned daily models and they differ in the parameters that relate to both occurrence and intensity and therefore to changes in the distribution of monthly total precipitation. The results of conditioning the daily precipitation on SLP are compared with conditioning on GWD. The GWD conditioned model gave similar results to the SLP conditioned model for the wetter months, but performed poorly for the summer season. Combining the two SLP conditioned daily models into an induced model, which is a mixture of the two chain dependent processes, produces a variance for monthly total precipitation that is closer to the observed value than the unconditioned chain-dependent model.

Ceramic joining has become an area of widespread and increasing engineering importance as the aerospace, automotive, chemicals, metals, and utilities industries seek improved performance at higher temperature and in more corrosive service environments. The brittle nature of ceramics, the difficulty of fabricating near net-shape components, the expense of ceramic machining (requiring diamondtipped cutting tools), and the lack of reliable in-process nondestructive evaluation (NDE) methods have driven the development of a variety of joining techniques. This article discusses recent advances in ceramic joining using microwave energy as a fast, efficient means to obtain joints indistinguishable from as received material.

Ceramic materials of engineering interest include oxides such as Al2O3 and Al6Si2O13 (mullite), Si3N4, and SiC. Joining applications include attachment of components such as piston liners, combustor cans and turbine rotors in high-efficiency engines; fabrication of tube assemblies for high-temperature, high-pressure heat exchangers and temperature and corrosion resistant radiant burners; and installation of hermetic seals for vacuum system components. The most common joints are mechanical attachments which take advantage of the coefficient of thermal expansion (CTE) difference between ceramics and metals. Ceramic-ceramic and ceramicmetal joining methods using metallic, glassy, and glass-ceramic interlayers and diffusion bonding have also been successfully demonstrated in recent years.

The ability to provide rapid and volumetric heating of the parts to be joined makes microwave joining attractive. The feasibility and simplicity of this approach was first demonstrated at Los Alamos National Laboratory in 1985 by Meek and Blake, who used a home microwave oven to join Al2O3 to itself and to metal with a borosilicate glass interlayer.

Microwave joining of sintered silicon carbide, both to itself and reaction bonded silicon carbide, has been accomplished in a single mode rectangular resonant cavity. Several approaches using different interlayer materials were employed to join sintered silicon carbide. Effective joining of reaction bonded silicon carbide to itself and sintered silicon carbide was accomplished without the use of any interlayer material in the single mode resonant cavity as well as in a multi-mode oven. Specimens cut from 0.95 cm diameter rods were joined in the single mode cavity, whereas a variety of arbitrary shapes and larger specimens (of reaction bonded silicon carbide) were joined in the multi-mode oven.

An explicit formula is derived for the variance normalizing constant in the central limit theorem for chain-dependent processes. As an application to meteorology, a specific chain-dependent process is proposed as a probabilistic model for the sequence of daily amounts of precipitation. This model is a generalization of the commonly used Markov chain model for the occurrence of precipitation.