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A chemotaxis-diffusion-convection coupling system for describing a form of buoyant convection in which the fluid develops convection cells and plume patterns will be investigated numerically in this study. Based on the two-dimensional convective chemotaxis-fluid model proposed in the literature, we developed an upwind finite element method to investigate the pattern formation and the hydrodynamical stability of the system. The numerical simulations illustrate different predicted physical regimes in the system. In the convective regime, the predicted plumes resemble B\'enard instabilities. Our numerical results show how structured layers of bacteria are formed before bacterium rich plumes fall in the fluid. The plumes have a well defined spectrum of wavelengths and have an exponential growth rate, yet their position can only be predicted in very simple examples. In the chemotactic and diffusive regimes, the effects of chemotaxis are investigated. Our results indicate that the chemotaxis can stabilize the overall system. A time scale analysis has been performed to demonstrate that the critical taxis Rayleigh number for which instabilities set in depends on the chemotaxis head and sensitivity. In addition, the comparison of the differential systems of chemotaxis-diffusion-convection, double diffusive convection, and Rayleigh-B\'enard convection establishes a set of evidences that even if the physical mechanisms are different at the same time the dimensionless systems are strongly related to each other., Comment: 29 pages, 18 figures, 9 tables

High intensity focused ultrasound (HIFU) has many applications ranging from thermal ablation of cancer to hemostasis. Although focused ultrasound can seal a bleeding site, physical mechanisms of acoustic hemostasis are not fully understood yet. To understand better the interaction between different physical mechanisms involved in hemostasis a mathematical model of acoustic hemostasis is developed. This model comprises the nonlinear Westervelt equation and the bioheat equations in tissue and blood vessel. In the three dimensional domain, the nonlinear hemodynamic equations are coupled with the acoustic and thermal equations. Convected cooling and acoustic streaming effects are incorporated in the modeling study. Several sonication angles and two wound shapes have been studied. The optimal focal point location is at the rear of the wound and the optimal angle is 45$^0$., Comment: 21 pages, 14 figures

The influences of blood vessels and focused location on temperature distribution during high-intensity focused ultrasound (HIFU) ablation of liver tumors is studied. A three-dimensional acoustics-thermal-fluid coupling model is employed to compute the temperature field in the hepatic cancerous region. The model is based on the linear Westervelt and bioheat equations as well as the nonlinear Navier-Stokes equations for the liver parenchyma and blood vessels. The effect of acoustic streaming is also taken into account in the present HIFU simulation study. Different blood vessel diameters and focal point locations were investigated. We found from this three-dimensional numerical study that in large blood vessels both the convective cooling and acoustic streaming can change considerably the temperature field and the thermal lesion near blood vessels. If the blood vessel is located within the beam width, both acoustic streaming and blood flow cooling effects should be taken into account. The predicted temperature difference for the cases considered with and without acoustic streaming effect is 54 % in regions close to the vessel wall. The necrosed volume can be reduced about 30 %, when taking into account acoustic streaming effect., Comment: 19 pages, 16 figures