Adhesion-Induced Instability in Asperities

Adhesive forces between two approaching asperities will deform the asperities, and under certain conditions this will result in a sudden runaway deformations leading to a jump-to-contact instability. We present finite element-based numerical studies on adhesion-induced deformation and instability in asperities. We consider the adhesive force acting on an asperity, when it is brought near a rigid half-space, due to van der Waals interaction between the asperity and the half-space. The adhesive force is considered to be distributed over the volume of the asperity (body force), thus resulting in more realistic simulations for the length scales considered. Iteration scheme based on a ``residual stress update'' algorithm is used to capture the effect of deformation on the adhesion force, and thereby the equilibrium configuration and the corresponding force. The numerical results are compared with the previous approximate analytical solutions for adhesion force, deformation of the asperity and adhesion-induced mechanical instability (jump-to-contact). It is observed that the instability can occur at separations much higher,and could possibly explain the higher value of instability separation observed in experiments. The stresses in asperities, particularly in case of small ones, are found to be high enough to cause yielding before jump -to-contact. The effect of roughness is considered by modeling a spherical protrusion on the hemispherical asperity.This small-scale roughness at the tip of the asperities is found to control the deformation behavior at small separations, and hence are important in determining the friction and wear due to the jump-to-contact instability.

Modelling transport processes during microwave heating: A review

The review is concerned with models that analyze transport:processes that occur during microwave heating. Early models on microwave. heating used Lambert's law to describe the microwave power absorption. Over the last decade, models for transport processes have been developed with the microwave power derived from Maxwell's equations. Those models, primarily based on plane waves, have been used for analyzing microwave heating of solids, liquids, emulsions, microwave thawing and drying. The models illustrate phenomena such a resonances, hot spots, edge and runaway heating. The literature on microwave sintering, susceptor heating and microwave assisted synthesis is largely experimental in nature and only key issues are highlighted. To fully appreciate the models for microwave heating, a section on the theory of electromagnetic wave propagation is included, where expressions for the electric field in dielectric slabs and cylinders are presented.

Turbulence and cooling in galaxy cluster cores

We study the interplay between turbulent heating, mixing, and radiative cooling in an idealized model of cool cluster cores. Active galactic nuclei (AGN) jets are expected to drive turbulence and heat cluster cores. Cooling of the intracluster medium (ICM) and stirring by AGN jets are tightly coupled in a feedback loop. We impose the feedback loop by balancing radiative cooling with turbulent heating. In addition to heating the plasma, turbulence also mixes it, suppressing the formation of cold gas at small scales. In this regard, the effect of turbulence is analogous to thermal conduction. For uniform plasma in thermal balance (turbulent heating balancing radiative cooling), cold gas condenses only if the cooling time is shorter than the mixing time. This condition requires the turbulent kinetic energy to be a parts per thousand(3) the plasma internal energy; such high velocities in cool cores are ruled out by observations. The results with realistic magnetic fields and thermal conduction are qualitatively similar to the hydrodynamic simulations. Simulations where the runaway cooling of the cool core is prevented due to mixing with the hot ICM show cold gas even with subsonic turbulence, consistent with observations. Thus, turbulent mixing is the likely mechanism via which AGN jets heat cluster cores. The thermal instability growth rates observed in simulations with turbulence are consistent with the local thermal instability interpretation of cold gas in cluster cores.

The cold mode: a phenomenological model for the evolution of density perturbations in the intracluster medium

Cool cluster cores are in global thermal equilibrium but are locally thermally unstable. We study a non-linear phenomenological model for the evolution of density perturbations in the intracluster medium (ICM) due to local thermal instability and gravity. We have analysed and extended a model for the evolution of an overdense blob in the ICM. We find two regimes in which the overdense blobs can cool to thermally stable low temperatures. One for large t(cool)/t(ff) (t(cool) is the cooling time and t(ff) is the free-fall time), where a large initial overdensity is required for thermal runaway to occur; this is the regime which was previously analysed in detail. We discover a second regime for t(cool)/t(ff) less than or similar to 1 (in agreement with Cartesian simulations of local thermal instability in an external gravitational field), where runaway cooling happens for arbitrarily small amplitudes. Numerical simulations have shown that cold gas condenses out more easily in a spherical geometry. We extend the analysis to include geometrical compression in weakly stratified atmospheres such as the ICM. With a single parameter, analogous to the mixing length, we are able to reproduce the results from numerical simulations; namely, small density perturbations lead to the condensation of extended cold filaments only if t(cool)/t(ff) less than or similar to 10.