On Integrability and Exact Solvability in Deterministic and Stochastic Laplacian Growth

We review applications of theory of classical and quantum integrable systems to the free-boundary problems of fluid mechanics as well as to corresponding problems of statistical mechanics. We also review important exact results obtained in the theory of multi-fractal spectra of the stochastic models related to the Laplacian growth: Schramm-Loewner and Levy-Loewner evolutions

A particle flow specific boundary element formulation for microfluidic applications

This paper was presented at the 4th Micro and Nano Flows Conference (MNF2014), which was held at University College, London, UK. The conference was organised by Brunel University and supported by the Italian Union of Thermofluiddynamics, IPEM, the Process Intensification Network, the Institution of Mechanical Engineers, the Heat Transfer Society, HEXAG - the Heat Exchange Action Group, and the Energy Institute, ASME Press, LCN London Centre for Nanotechnology, UCL University College London, UCL Engineering, the International NanoScience Community, www.nanopaprika.eu.In this study, a special formulation to obtain velocities of particles flowing within a microchannel is presented. The formulation is based on boundary element method, and the large system matrices resulting from the analysis is reduced to a system of linear equations with the unknowns being the rigid-body motion parameters of the particles. This reduction is achieved through matrix multiplications which increases computational efficiency when compared with the solution of a large system of equations. Since the formulation involves mainly matrix multiplications, parallelization is straightforward. With the presented algorithm, only the position of the particle(s) are tracked through the solution of their rigid-body velocities and an explicit time integration to obtain displacements. Due to the boundary-only nature of the boundary element method, the particle flow in close proximity to the channel walls are very effectively modeled without any need for specific model. The presented method is given in 2D, where the 3D formulation is straightforward. To demonstrate the applicability of the method, besides some benchmark problems, two fundamental processes, namely flow cytometry and hydrodynamic-based particle separation, are studied. It is observed that present formulation offers an efficient numerical model to be used for the simulation of the particle trajectory for 2D microfluidic applications and can easily be extended for 3D multiphysics simulations

Simulations of electromagnetic effects in high frequency capacitively coupled discharges using the Darwin approximation

The Darwin approximation is investigated for its possible use in simulation of electromagnetic effects in large size, high frequency capacitively coupled discharges. The approximation is utilized within the framework of two different fluid models which are applied to typical cases showing pronounced standing wave and skin effects. With the first model it is demonstrated that Darwin approximation is valid for treatment of such effects in the range of parameters under consideration. The second approach, a reduced nonlinear Darwin approximation-based model, shows that the electromagnetic phenomena persist in a more realistic setting. The Darwin approximation offers a simple and efficient way of carrying out electromagnetic simulations as it removes the Courant condition plaguing explicit electromagnetic algorithms and can be implemented as a straightforward modification of electrostatic algorithms. The algorithm described here avoids iterative schemes needed for the divergence cleaning and represents a fast and efficient solver, which can be used in fluid and kinetic models for self-consistent description of technical plasmas exhibiting certain electromagnetic activity