%0 Journal Article %1 swift1977hydrodynamic %A Swift, J. %A Hohenberg, P. C. %D 1977 %I American Physical Society %J Physical Review A %K 35q35-pdes-in-connection-with-fluid-mechanics 37-02-dynamical-systems-and-ergodic-theory-research-exposition 37c29-dynamical-systems-homoclinic-and-heteroclinic-orbits 37n10-dynamical-systems-in-fluid-mechanics-oceanography-fluid-mechanics 37n20-dynamical-systems-in-other-branches-of-physics 76e06-hydrodynamic-stability-convection %N 1 %P 319--328 %R 10.1103/PhysRevA.15.319 %T Hydrodynamic fluctuations at the convective instability %U https://link.aps.org/doi/10.1103/PhysRevA.15.319 %V 15 %X The effects of thermal fluctuations on the convective instability are considered. It is shown that the Langevin equations for hydrodynamic fluctuations are equivalent, near the instability, to a model for the crystallization of a fluid in equilibrium. Unlike the usual models, however, the free energy of the present system does not possess terms cubic in the order parameter, and therefore the system undergoes a second-order transition in mean-field theory. The effects of fluctuations on such a model were recently discussed by Brazovskii, who found a first-order transition in three dimensions. A similar argument also leads to a discontinuous transition for the convective model, which behaves two dimensionally for sufficiently large lateral dimensions. The magnitude of the jump is unobservably small, however, because of the weakness of the thermal fluctuations being considered. The relation of the present analysis to the work of Graham and Pleiner is discussed.

@article{swift1977hydrodynamic, abstract = {The effects of thermal fluctuations on the convective instability are considered. It is shown that the Langevin equations for hydrodynamic fluctuations are equivalent, near the instability, to a model for the crystallization of a fluid in equilibrium. Unlike the usual models, however, the free energy of the present system does not possess terms cubic in the order parameter, and therefore the system undergoes a second-order transition in mean-field theory. The effects of fluctuations on such a model were recently discussed by Brazovskii, who found a first-order transition in three dimensions. A similar argument also leads to a discontinuous transition for the convective model, which behaves two dimensionally for sufficiently large lateral dimensions. The magnitude of the jump is unobservably small, however, because of the weakness of the thermal fluctuations being considered. The relation of the present analysis to the work of Graham and Pleiner is discussed.}, added-at = {2021-05-20T03:42:25.000+0200}, author = {Swift, J. and Hohenberg, P. C.}, biburl = {https://www.bibsonomy.org/bibtex/24191c904ece2111121479c3bd5579247/gdmcbain}, doi = {10.1103/PhysRevA.15.319}, interhash = {df9e3bfe523c591ddc38432df6d115c1}, intrahash = {4191c904ece2111121479c3bd5579247}, journal = {Physical Review A}, keywords = {35q35-pdes-in-connection-with-fluid-mechanics 37-02-dynamical-systems-and-ergodic-theory-research-exposition 37c29-dynamical-systems-homoclinic-and-heteroclinic-orbits 37n10-dynamical-systems-in-fluid-mechanics-oceanography-fluid-mechanics 37n20-dynamical-systems-in-other-branches-of-physics 76e06-hydrodynamic-stability-convection}, month = jan, number = 1, numpages = {0}, pages = {319--328}, publisher = {American Physical Society}, timestamp = {2021-05-20T03:42:25.000+0200}, title = {Hydrodynamic fluctuations at the convective instability}, url = {https://link.aps.org/doi/10.1103/PhysRevA.15.319}, volume = 15, year = 1977 }