کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
1156302 958819 2009 23 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Marcus–Lushnikov processes, Smoluchowski’s and Flory’s models
کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات (عمومی)
پیش نمایش صفحه اول مقاله
Marcus–Lushnikov processes, Smoluchowski’s and Flory’s models
چکیده انگلیسی

The Marcus–Lushnikov process is a finite stochastic particle system in which each particle is entirely characterized by its mass. Each pair of particles with masses xx and yy merges into a single particle at a given rate K(x,y)K(x,y). We consider a strongly gelling   kernel behaving as K(x,y)=xαy+xyαK(x,y)=xαy+xyα for some α∈(0,1]α∈(0,1]. In such a case, it is well-known that gelation occurs, that is, giant particles emerge. Then two possible models for hydrodynamic limits of the Marcus–Lushnikov process arise: the Smoluchowski equation, in which the giant particles are inert, and the Flory equation, in which the giant particles interact with finite ones.We show that, when using a suitable cut-off coagulation kernel in the Marcus–Lushnikov process and letting the number of particles increase to infinity, the possible limits solve either the Smoluchowski equation or the Flory equation.We also study the asymptotic behaviour of the largest particle in the Marcus–Lushnikov process without cut-off and show that there is only one giant particle. This single giant particle represents, asymptotically, the lost mass of the solution to the Flory equation.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Stochastic Processes and their Applications - Volume 119, Issue 1, January 2009, Pages 167–189
نویسندگان
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