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#### Uniqueness of steady-state solutions for thermodynamically consistent Becker-Döring models

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Ssemaganda, V., Holstein, K., & Warnecke, G. (2011). Uniqueness of steady-state
solutions for thermodynamically consistent Becker-Döring models.* Journal of Mathematical Physics,*
*52*(8), 083304. doi:10.1063/1.3626943.

Cite as: http://hdl.handle.net/11858/00-001M-0000-0013-A5FD-7

##### Abstract

Dreyer and Duderstadt [J. Stat. Phys. 123, 1 (2006)]10.1007/s10955-006-9024-z proposed a modification of the standard mass-conserving Becker-Döring model. In this paper we solve for steady-state solutions to two versions of the Becker-Döring model. One is the modified mass-conserving model introduced by Dreyer and Duderstadt. The second one, which is a new version, is a modification of the so called constant free molecule Becker-Döring model. For practical purposes, there is a maximum cluster of size ν allowed in the system. For each version we study the two known truncations to finite system size. One is given by a zero flux to larger cluster sizes out of the system. The second one is obtained by setting the number of clusters larger than ν to zero. For each model and each truncation we determine the unique steady states by studying the null space of the flux matrix. The zero flux truncation gives equilibrium steady-states whereas the zero particle number truncation leads to non-equilibrium steady-states.
© 2011 American Institute of Physics