1. GAČR Grant no. 102/08/H081 “Nonstandard application of physical fields” Arindam SARKAR Jiří Chvojka A David LUKÁŠ

2. Journal of Statistical Physics Auto-model based computer simulation of Rayleigh Instability (A.S.) has been supported by GACR Grant no. 102/08/H081 “Nonstandard application of physical fields”.

3. Dispersion relation Dispersion law for the Rayleigh instability plots dimensionless angular frequency against the dimensionless wave-number.

4. Auto-model (a) The original longitudinal and cross sectional configurations of the liquid coated fibre. (b) Detailed cross-sectional shape of the original liquid layer on a fibre and the liquid nodes distribution along the fibre axis after the detachment into individual unduloids at the time of MCSPS=20,000.

5. Dynamics of Rayleigh instability The time versus the droplet numbers for (a) the liquid coating the fibre; (b) the pure liquid jet. Unduloids on the fibre merge and those, which disappeared, are marked in grey.

6. Time versus the droplet numbers The time versus the droplet numbers for the system of liquid coating fibre with the original cross-section sketched. (a) the droplet numbers n ~ MCSPS; (b) ln(n) versus MCSPS with a regression result.

7. Outputs The Rayleigh wavelength l versus the original radius r o as predicted by the analytical theory (solid line) and by the computer simulations (points). (a) is for pure liquid jet and (b) for liquid coating a fibre.

8. Hammersley and Clifford theorem Markov random field

9. Clans and clan functions g Bayes’ rule

10. Clan functions and marginal pobabilitioes

11. Energy function, Hamiltonian and exchange energies Interaction energies E(x i,x j ) in [e.u.] Gas x i = 0Liquid x i = 1Fiber x i = 2 Gas x j = 0-40-1020 Liquid x j = 1-10-26-10 Fiber x j = 220-100

12. ELECTROHYDRODYNAMICS OF FREE LIQUID SURFACE IN A CIRCULAR CLEFT; AN APPLICATION TO ELECTROSPRAYING AND ELECTROSPINNING Journal: Acta Materialia A. Sarkar, Jiří Chvojka a D.Lukáš

16. Journal: Textile Progress Arindam+Jiří+David