Jets from active galactic nuclei in the centers of galaxy clusters inflate cavities of low density relativistic plasma and drive shock and sound waves into the intracluster medium. When these waves overrun previously inflated cavities, they form a di
fferentially rotating vortex through the Richtmyer-Meshkov instability. The dissipation of energy captured in the vortex can contribute to the feedback of energy into the atmospheres of cool core clusters. Using a series of hydrodynamic simulations we investigate the efficiency of this process: we calculate the kinetic energy in the vortex by decomposing the velocity field into its irrotational and solenoidal parts. Compared to the two-dimensional case, the 3-dimensional Richtmyer-Meshkov instability is about a factor of 2 more efficient. The energy in the vortex field for weak shocks is E_vortex ~ rho_ICM v_shock^2 V_bubble (with dependence on the geometry, density contrast, and shock width). For strong shocks, the vortex becomes dynamically unstable, quickly dissipating its energy via a turbulent cascade. We derive a number of diagnostics for observations and laboratory experiments of shock-bubble interactions, like the shock-vortex standoff distance, which can be used to derive lower limits on the Mach number. The differential rotation of the vortex field leads to viscous dissipation, which is sufficiently efficient to react to cluster cooling and to dissipate the vortex energy within the cooling radius of the cluster for a reasonable range of vortex parameters. For sufficiently large filling factors (of order a few percent or larger), this process could thus contribute significantly to AGN feedback in galaxy clusters.
Strained coherent heteroepitaxy of III-V semiconductor films such as In$_x$Ga$_{1-x}$As/GaAs has potential for electronic and optoelectronic applications such as high density logic, quantum computing architectures, laser diodes, and other optoelectro
nic devices. Crystal symmetry can have a large effect on the morphology of these films and their spatial order. Often the formation of group IV strained heterostructures such as Ge deposited on Si is analyzed using analytic models based on the Asaro-Tiller-Grinfeld instability. However, the governing dynamics of III-V 3D heterostructure formation has different symmetry and is more anisotropic. The additional anisotropy appears in both the surface energy and the diffusivity. Here, the resulting anisotropic governing dynamics are studied to linear order. The resulting possible film morphologies are compared with experimentally observed In$_x$Ga$_{1-x}$As/GaAs films. Notably it is found that surface-energy anisotropy plays a role at least as important as surface diffusion anisotropy if not more so, in contrast to previous suppositions.
Epitaxial self-assembled quantum dots (SAQDs) are of both technological and fundamental interest, but their reliable manufacture still presents a technical challenge. To better understand the formation, morphology and ordering of epitaxial self-assem
bled quantum dots (SAQDs), it is essential to have an accurate model that can aid further experiments and predict the trends in SAQD formation. SAQDs form because of the destabilizing effect of elastic mismatch strain, but most analytic models and some numerical models of SAQD formation either assume an elastically homogeneous anisotropic film-substrate system or assume an elastically heterogeneous isotropic system. In this work, we perform the full film-substrate elastic calculation. Then we incorporate the elasticity calculation into a stochastic linear growth model. We find that using homogeneous elasticity can cause errors in the elastic energy density as large as 26%, and for typical modeling parameters lead to errors of about 11% in the estimated value of average dot spacing. We also quantify the effect of elastic heterogeneity on the order estimates of SAQDs and confirm previous finding on the possibility of order enhancement by growing a film near the critical film height.
Heteroepitaxial self-assembled quantum dots (SAQDs) will allow breakthroughs in electronics and optoelectronics. SAQDs are a result of Stranski-Krastanow growth whereby a growing planar film becomes unstable after an initial wetting layer is formed.
Common systems are Ge$_{x}$Si$_{1-x}$/Si and In$_{x}$Ga$_{1-x}$As/GaAs. For applications, SAQD arrays need to be ordered. The role of crystal anisotropy, random initial conditions and thermal fluctuations in influencing SAQD order during early stages of SAQD formation is studied through a simple stochastic model of surface diffusion. Surface diffusion is analyzed through a linear and perturbatively nonlinear analysis. The role of crystal anisotropy in enhancing SAQD order is elucidated. It is also found that SAQD order is enhanced when the deposited film is allowed to evolve at heights near the critical wetting surface height that marks the onset of non-planar film growth.
Epitaxial self-assembled quantum dots (SAQDs) are of interest for nanostructured optoelectronic and electronic devices such as lasers, photodetectors and nanoscale logic. Spatial order and size order of SAQDs are important to the development of usabl
e devices. It is likely that these two types of order are strongly linked; thus, a study of spatial order will also have strong implications for size order. Here a study of spatial order is undertaken using a linear analysis of a commonly used model of SAQD formation based on surface diffusion. Analytic formulas for film-height correlation functions are found that characterize quantum dot spatial order and corresponding correlation lengths that quantify order. Initial atomic-scale random fluctuations result in relatively small correlation lengths (about two dots) when the effect of a wetting potential is negligible; however, the correlation lengths diverge when SAQDs are allowed to form at a near-critical film height. The present work reinforces previous findings about anisotropy and SAQD order and presents as explicit and transparent mechanism for ordering with corresponding analytic equations. In addition, SAQD formation is by its nature a stochastic process, and various mathematical aspects regarding statistical analysis of SAQD formation and order are presented.
