• **2D/3D extansion of h****igh order fluid modeling of streamer discharges** (in collaboration with S. Dujko)

1D streamer simulations (ionization waves) showd that high order fluid must be used in highly non-equilibrium situations. Major efforts are put to develop a new numerical moethod to solve the non-linear hyperbolic system and couple it with Poisson’s equation.

•
**Modeling of plasmas formed during operation of a diode pumped alkali laser (DPAL)**
(in collaboration with M.J. Kushner)

•
**Modeling capacitively-coupled RF plasma for the synthesis of silicon nano-crystals **(in collaboration with M.J. Kushner and
S. Girshick)

•
**Design and modeling of RF-trapped, chip-scale Helium ion pump **(in collaboration with M.J. Kushner and Y. Gianchandani)

• **PumpKin tool** (in collaboration with A. Luque and F. J. Gordillo-Vázquez)

We have developed the software tool PumpKin (pathway reduction method for plasmakinetic models) to find all principal pathways, i.e. the important reaction sequences, in a given chemical reaction system. The user should solve first the full chemical reaction system, but only once. The output is later used as an input for PumpKin. PumpKin will analyze the full chemical reaction system, and it will automatically determine all significant pathways in the system, i.e. all pathways with a rate above a user-specified threshold. PumpKin tool is freely available under the GPL license [here].

• **Voltage recovery in super-critical fluids for high-power switching** (in collaboration with J. Zhang,
M. Seeger, E.M. van Veldhuizen and E.J.M. van Heesch)

• **High order fluid modeling of streamer discharges in 1D** (in collaboration with S. Dujko and R.D. White)

Streamer discharges pose basic problems in plasma physics, as they are very transient, far from equilibrium and have high ionization density gradients; they appear in diverse areas of science and technology. The present research focuses on the derivation and numerical implementation of a high order fluid model for streamers. [read more...]

• **Chemistry of positive streamers** (in collaboration with S. Nijdam and E. Takahashi)

During writing about my research, suddenly, I realized that my research interests, or the topics I had worked on, are covering quite wide aspects of theoretical and applied mathematics. Here is the list of areas that I have worked on during my Bachelor and two Master studies:

• **Lattices, Bilattices, Boolean and DeMorgan Algebras**

Under supervision of Prof. Dr. Yu. Movsisyan

• **Variational inequality theory, Monotone operator theory**

B.Sc. thesis at Yerevan State University

• **Parabolic free boundary problems, Existence, Regularity theory**

M.Sc. thesis at Yerevan State University

• **2D incompressible Navier-Stokes equation, Finite element method P2-P1 using characteristics method**

Under supervision of Prof. F. Hecht

• **Mathematical finance: Option pricing, SVI parametrization**

M.Sc. thesis at Paris VI

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