6 〈 θ ( q ) θ ( − q ) 〉 = k$_{B}$T/Kq $^{2}$. In the semidiscrete represen- tation, we obtain within the time-dependent Ginzburg-Landau framework. In previous work, Stratonovich [5] presented fluctuating equations of motion for harmonic fluctuations in terms of Langevin equations, analyzing these equations within the traceless symmetric basis described here in a straight- forward manner[6]. Our equations of motion contain the necessary nonlinearities and our numerical methodology accounts for them in a computationally straightforward way. We also present, to the best of our knowledge for the first time, a systematic stochastic integration scheme ca- pable of yielding highly accurate solutions of the non- linear equations of nematodynamics. These equations can be applied to study fluctuations of nematic order at the isotropic-nematic interface, pseudo-Casimir interac- tions close to the isotropic-nematic transition, as well as nucleation phenomena in nematogens. The study of these and similar problems is ongoing and will be reported else- where. Fig.(5) shows the angular average of the static correlations of director fluctuations C$_{θ}$ ( q ) = ∑ | q | = q 〈 θ ( q ) θ ( − q ) 〉 . The formally divergent q = 0 mode is excluded both from the numerical data and analytical result. Given that the analytical result is obtained from a linearization about the aligned state whereas the numerical solution is calculated from the equations of motion arising from the full non-linear free energy, the agreement between theory and simulation is satisfactory. The stochastic method of lines thus accurately captures equilibrium fluctuations in the ordered state as well as in the disordered one. The numerical method of solution presented in this paper can be applied to a variety of problems in ne- matodynamics where accounting for fluctuations in ne- matic order are important. To the best of our knowledge, no systematic study of anharmonic fluctuations exists GIM thanks the DST(India) and the Indo-French Cen- tre for the Promotion of Advanced Research (CEFIPRA) for support. VI. ACKNOWLEDGEMENTS V. DISCUSSION AND CONCLUSION [1] P. G. de Gennes and J. Prost, The Physics of Liquid Crystals (Clarendon Press, Oxford, 1993), 2nd ed. [2] T. Moses, J. Reeves, and P. Pirondi, Americal Journal of Physics 75 , 220 (2007). [3] P. G. de Gennes, Molecular Crystals and Liquid Crystals 12 , 193 (1971). [4] E. F. Gramsbergen, L. Longa, and W. H. de Jeu, Physics Reports 135 , 195 (1986). [5] R. Stratonovich, Sov.Phys.JETP 43 , 672 (1976). [6] P. D. Olmsted and P. Goldbart, Phys. Rev. A 41 , 4578 (1990). [7] B. J. Berne and R. Pecora, Dynamic Light Scattering: With Applications to Chemistry, Biology, and Physics (Dover, New York, 2000). [8] A. Cuetos and M. Dijkstra, Phys. Rev. Lett. 98 , 095701 (2007). [9] A. Ajdari, L. Peliti, and J. Prost, Phys. Rev. Lett. 66 , 1481 (1991). [10] F. Schmid, G. Germano, S. Wolfsheimer, and T. Schilling, Macromolecular Symposia 252 , 110 (2007). [11] A. K. Bhattacharjee, G. I. Menon, and R. Adhikari, Phys. Rev. E 78 , 026707 (2008). [12] O. A. Liskovets, J. Diff. Eqs. 1 , 1308 (1965). [13] C. W. Gardiner, Handbook of Stochastic Methods (Springer, Berlin, 1983). [14] G. Maruyama, Rend. Circolo. Math. Palermo 4 , 48 (1955). [15] G. N. Milstein, Numerical integration of stochastic dif- ferential equations (Kluwer, London, 1995). [16] J. Wilkie, Phys. Rev. E 70 , 017701 (2004). [17] M. Abramowitz and I. A. Stegun, Handbook of Mathe- matical Functions: with Formulas, Graphs, and Mathe- matical Tables (Dover, 1964). [18] A. Shinozaki and Y. Oono, Phys. Rev. E 48 , 2622 (1993). [19] M. Patra and M. Karttunen, Numerical Methods for Par- tial Differential Equations 22 , 936 (2005). 〈 θ ( q ) θ ( − q ) 〉 = − k$_{B}$T K L ( q ) . (23)