Deterministic and Stochastic Becker–Döring Equations: Past and Recent Mathematical Developments

@article{Hingant2016DeterministicAS,
  title={Deterministic and Stochastic Becker–D{\"o}ring Equations: Past and Recent Mathematical Developments},
  author={Erwan Hingant and Romain Yvinec},
  journal={arXiv: Mathematical Physics},
  year={2016},
  pages={175-204}
}
Becker and Dorimy introduced their equations in 1935 to describes nucleation in supersaturated vapors. Since then, these equations have been popularized to a wide range of applications and Slemrod in 2000 said they “provide perhaps the simplest kinetic model to describe [...] phase transitions”. In this survey we attempt to give an overview of the results obtained on these equations in the parts decades until today. Particularly we gathered results on both deterministic and stochastic versions… 
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17 Citations
Background Citations
9
Methods Citations
4
Results Citations
1

17 Citations

Quasi-stationary distribution and metastability for the stochastic Becker-Döring model

We study a stochastic version of the classical Becker-Doring model, a well-known kinetic model for cluster formation that predicts the existence of a long-lived metastable state before a…

Temporal oscillations in Becker–Döring equations with atomization

We prove that time-periodic solutions arise via Hopf bifurcation in a finite closed system of coagulation-fragmentation equations. The system we treat is a variant of the Becker–Döring equations, in…

The Becker-D\"oring process: law of large numbers and non-equilibrium potential

In this note, we prove a law of large numbers for an infinite chemical reaction network for phase transition problems called the stochastic Becker-Doring process. Under a general condition on the…

Oscillations in a Becker-Döring Model with Injection and Depletion

We study the Becker–Döring bubblelator, a variant of the Becker–Döring coagulation-fragmentation system that models the growth of clusters by gain or loss of monomers. Motivated by models of gas…

A Functional Central Limit Theorem for the Becker–Döring Model

We investigate the fluctuations of the stochastic Becker–Döring model of polymerization when the initial size of the system converges to infinity. A functional central limit problem is proved for the…

A Functional Central Limit Theorem for the Becker–Döring Model

  • Wen Sun
  • Mathematics
    Journal of Statistical Physics
  • 2018
We investigate the fluctuations of the stochastic Becker–Döring model of polymerization when the initial size of the system converges to infinity. A functional central limit problem is proved for the…

On a modified Becker–Döring model for two-phase materials

This work reconsiders the Becker–Döring model for nucleation under isothermal conditions in the presence of phase transitions. Based on thermodynamic principles, a modified model is derived where the…

On a modified Becker–Döring model for two-phase materials

This work reconsiders the Becker–Döring model for nucleation under isothermal conditions in the presence of phase transitions. Based on thermodynamic principles, a modified model is derived where the…

Fokker-Planck Approach of Ostwald Ripening: Simulation of a Modified Lifshitz-Slyozov-Wagner System with a Diffusive Correction

A well-balanced scheme for the modified Lifshitz--Slyozov equation, which incorporates a size-diffusion term and uses the Fokker--Planck structure of the equation.

The initial-boundary value problem for the Lifshitz–Slyozov equation with non-smooth rates at the boundary

We prove existence and uniqueness of solutions to the initial-boundary value problem for the Lifshitz–Slyozov equation (a nonlinear transport equation on the half-line), focusing on the case of…

References

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