Numerical simulation of stochastic dynamics of vortex filaments under action of random (Langevin) force is fulfilled. Calculations are performed on base of the full Biot-Savart law for different intensities of the Langevin force. A new algorithm, which is based on consideration of crossing lines, is used for vortex reconnection procedure. After some transient period the vortex tangle develops into the stationary state characterizing by the developed fluctuations of various physical quantities, such as total length, energy etc. We tested this state to learn whether or not it the thermodynamic equilibrium is reached. With the use of a special treatment, so called method of weighted histograms, we process the distribution energy of the vortex system. The results obtained demonstrate that the thermodynamical equilibrium state with the temperature obtained from the fluctuation dissipation theorem is really reached.
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Donnelly, R.J., Quantized Vortices in Helium II, Cambridge University Press, 1991.
Williams, G.A., Vortex-Loop Phase Transitions in Liquid Helium, Cosmic Strings, and High-Tc Superconductors, Phys. Rev. Lett., 1999, vol. 82, no. 6, p. 1201.
Nemirovskii, S.K. and Fiszdon, W., Chaotic Quantized Vortices and Hydrodynamic Processes Superfluid Helium, Rev. Mod. Phys., 1995, vol. 67,no. 1, p. 37.
Chorin, A., Voticity and Turbulence, New-York: Springer-Verlag, 1994.
Nemirovskii, S.K., Thermodynamic Equilibrium in the System of Chaotic Quantized Vortices in a Weakly Imperfect Bose Gas, Teoretical and Matematical Physics, 2004, vol. 141, no. 1, p. 141.
Zinn-Justin, J., Quantum Field Theory and Critical Phenomena, Oxford: Claberson Press, 1992.
Kondaurova, L.P. and Nemirovskii, S.K., Full Biot-Savart Numerical Simulation of Vortices in HeII, J. Low Temperature Physics, 2005, vol. 138, nos. 3/4, p. 555.
Ferrenberg, A.M. and Swendsen, R.H., New Monte Carlo Technique for Studying Phase Transitions, Phys. Rev. Lett., 1988, vol. 61, p. 2635.
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Kondaurova, L.P., Nemirovskii, S.K. Numerical simulation of stochastic motion of vortex loops under action of random force. Evidence of the thermodynamic equilibrium state. J. Engin. Thermophys. 18, 65–68 (2009). https://doi.org/10.1134/S1810232809010081
- Direct Numerical Simulation
- Vortex Ring
- Vortex Line
- Probability Density Distribution