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Dr. Yuri L. Vasenin
The solvers for subset decisions for complex problem modelling
Scientific Toys Software



  • Computational experiments on the basis of non-stationary models of the electric arc cathode spot with the self-consistent description of the near electrode plasma sheath processes.
  • Physical processes on the metal surface covered by dense plasma, taking into account surface dynamics, peculiarities of the electron emission mechanism, plasma formation and so on.
  • Physical and mathematical models for computer simulation of the thermal processes in arc electrodes and weld pool.
It was developed physical and mathematical models, written and debugged codes for more than 20 computer programs for computational experiments /data treatment /visualization of results. Short descriptions of selected projects presented below.

Numerical calculation of the thermo-field electron emission in most general quasi-classical approach. It is determined also energy distribution of the emitted electrons, so it is possible calculate average energy of the emitted electrons and Nottingham potential. It was used the Bethe-Zommerfield free-electron model for the metal electrons distribution on energy. The calculation performs in a range of the surface temperature Tc and electrical field field strength Ec: 0< Tc < 6000 K, and 0 < Ec< 10^8 V/cm, that is cover both thermionic and field electron emission without additional analysis of usefulness analytical equations for known Richardson-Schottky and Fowler-Nordheim approximations for electron current densities.
It is possible to change the program for:
  1. tunneling probability calculation by direct solving of the 1D Shrodinger equation instead of the given by WKB approximation for the potential barrier formed by image force of funneling electron and external electrical field;
  2. calculation of the MIM (metal-insulator-metal) structures (with p.1);
  3. use in calculation of the experimentally measured distributions of the metal electrons on energy for given cathode material;
  4. the near surface potential barrier modification (with p.1) for the metal covered by monatomic/thin dielectric layers of external materials.

Program for the experimental/numerical calculations data treatment - 2D inter/extrapolation and smoothing with the interactive visual control while the data in preparation to be used in the library collection files or for using in calculation at intermediate values of dependent on 2 parameters.

Program for the calculation of the boundary conditions within the cathode spot of the metal vapor arc. The energy balance on the surface, current density , pressure, erosion, ionic an electron currents and many others parameters can be calculated for the metals: Al, Fe, Cu, Ni, Ti, W, Mo,...
Results of computations for Cu electrode presented in articles:
"The Energy Balance Structure on the Cathode Surface of the Metal Vapor Arc"
(spot_bal.pdf, 214 627 Bytes)
"Boundary Conditions for Plasma Jet Footpoint on Vacuum Arc Cathode"
(spot_ft.pdf, 140 455 Bytes)

computer modeling of the non-stationary thermal processes within the vacuum arc cathode. It was taken into account surface and solid/liquid phase transition border movement for the problem in 1D (spherical symmetry - SPOT1D) and 2D (cylindrical symmetry - SPOT2D) description approach. Boundary conditions are self-consistent with the near electrode plasma parameters and dependent on electrode surface temperature and the near cathode potential fall.
Results of computations for Cu electrode presented in articles:
"A One Dimensional (1D) Non �Stationary Model for Cathode Spot of the Metal Vapor Arc"
(spot_1d.pdf, 183 839 Bytes)
"A Two Dimensional (2D) Approach for Cathode Spot Modelling"
(spot_2d.pdf, 170 099 Bytes)

multicomponent PLasma Ionic Composition Calculator - solver for the system up to 13x10 of nonlinear transcendent equation set, namely Saha equations with taking into account the lowering of the ionization potential (due to small non-ideality of the plasma), equations for quasi-neutrality of plasma and Dalton's low for partial pressure of given chemical elements.

Program for computational experiments with results visualization developed for optimization of the wire welding/melting processes with the time dependent electric current, applied voltage and wire supply.

modeling of thermal processes in piping repair by brazing. The computational program has been developed for numerical experiments on the basis of solving of the non-stationary 2D heat transportation within tubes/layer with taking into account the melting/solidification border movement within the brazing layer. Optimal geometrical parameters (Tube ON Tube with overlapping - TONT,Coupling ON Tube - CONT) and conditions of the brazed joint heating can be determined, as well as time and energy required ateXtreme conditions (XCONT) for performance of brazing.
(The whole project was carried out in collaboration with Dr. and results was published in: PWJ, no.4, 2001)

modeling of 3D non-stationary heat propagation process with taking into account the melting process (into the case of metal piece). Complex geometry can be constructed by using the approximation by cubic sub-pieces.

The Sots software series can be used for parameters evaluation within the complex problem/systems by modeling and simulation of the more simple problem.


The programs of the SToySseries was prepared for work on personal computers,
compatible with the IBM PC and OS Windows 9x/ NT/ ME /2000 ...
(minimal requirement: MS DOS 5.0 on IBM PC i80286+i80287 <= tested & work (!) due to used by SToyS very effective codes/algoritms)
Computational programs was realized on C/C++ and FORTRAN languages.
All STOYS products are subject for modification and adaptation (on request) to meet   your goals.
For more information
onSToyS series call:
The author page Dr. Yuri L. Vasenin
Tel.(380 44) 261 5349, Fax: (380 44) 268 0486,
Paton Welding Institute, 11 Bozhenko St., Kiev 03680, Ukraine
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