Motion by Mean Curvature from Glauber-Kawasaki Dynamics with Speed Change

Funaki, Tadahisa; Meurs, Patrick; Sethuraman, Sunder; Tsunoda, Kenkichi

doi:10.1007/s10955-022-03044-9

Cited by 4 publications

(17 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This paper fits to the recent paper series [5,6,13,12] on hydrodynamic limits of interacting particle systems. In these papers the particle systems are such that the particle density on the macroscopic scale tends to be close to either of two distinct positive values 0 < α − < α + .…”

Section: Introductionsupporting

confidence: 85%

“…This completes the list of assumptions on the flip rate c. The difference in these assumptions with respect to the previous papers [5,6,13,12] is (UB); in those papers f is instead balanced, i.e. the integral in (UB) is zero.…”

Section: The Glauber-kawasaki Dynamicsmentioning

confidence: 83%

“…In addition to c x (η), one could consider an exchange rate c x,y (η) in the Kawasaki dynamics (called speed change); see e.g. [13]. In the present paper we simply take c x,y (η) ≡ 1, i.e.…”

Section: The Glauber-kawasaki Dynamicsmentioning

confidence: 99%

“…While we keep K constant for now, we will consider K = K(N ) → ∞ as N → ∞ later to observe a sharp interface in the limit. We write √ K rather than K to be consistent with the setting in the previous papers [5,6,13,12].…”

Section: The Glauber-kawasaki Dynamicsmentioning

confidence: 99%

“…While the assumptions on c are similar in the previous papers [5,6,13,12], the assumptions on the exchange rates are different. [12] considers the same generator L K as in (1.2).…”

Section: The Glauber-kawasaki Dynamicsmentioning

confidence: 99%

See 4 more Smart Citations

Constant-speed interface flow from unbalanced Glauber-Kawasaki dynamics

Funaki¹,

Meurs²,

Sethuraman³

et al. 2023

View full text Add to dashboard Cite

We derive the hydrodynamic limit of Glauber-Kawasaki dynamics. The Kawasaki part is simple and describes independent movement of the particles with hard core exclusive interactions. It is speeded up in a diffusive space-time scaling. The Glauber part describes the birth and death of particles. It is set to favor two levels of particle density with a preference for one of the two. It is also speeded up in time, but at a lesser rate than the Kawasaki part. Under this scaling, the limiting particle density instantly takes either of the two favored density values. The interface which separates these two values evolves with constant speed (Huygens' principle).Similar hydrodynamic limits have been derived in four recent papers. The crucial difference with these papers is that we consider Glauber dynamics which has a preferences for one of the two favored density values. As a result, we observe limiting dynamics on a shorter time scale, and the evolution is different from the mean curvature flow obtained in the four previous papers. While several steps in our proof can be adopted from these papers, the proof for the propagation of the interface is new.

show abstract

Section: Introductionsupporting

confidence: 85%

Section: The Glauber-kawasaki Dynamicsmentioning

confidence: 83%

Section: The Glauber-kawasaki Dynamicsmentioning

confidence: 99%

Section: The Glauber-kawasaki Dynamicsmentioning

confidence: 99%

“…While the assumptions on c are similar in the previous papers [5,6,13,12], the assumptions on the exchange rates are different. [12] considers the same generator L K as in (1.2).…”

Section: The Glauber-kawasaki Dynamicsmentioning

confidence: 99%

See 3 more Smart Citations