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KINETIC HIERARCHIES AND MACROSCOPIC LIMITS FOR CRYSTALLINE STEPS IN 1+1 DIMENSIONS
kinetic theory epitaxial growth crystal surface Burton–Cabrera–Frank model particle system Bogoliubov–Born–Green–Kirkwood–Yvon hierarchy closure evaporation-condensation surface diffusion correlation function step chemical potential macroscopic limit propagation of chaos
2015/10/16
We apply methods of kinetic theory to study the passage from particle systems to nonlinear partial differential equations (PDEs) in the context of deterministic crystal surface relaxation. Starting wi...
Some standard numerical problems become intractable in high dimensions.
Yet successes are often achieved in practice. This may be explained in terms
of the underlying target function being somehow s...
Comment on "A new exactly solvable quantum model in $N$ dimensions"
Comment solvable quantum model $N$ dimensions
2011/7/7
We pinpoint that the work about "a new exactly solvable quantum model in $N$ dimensions" by Ballesteros et al. [Phys. Lett. A {\bf 375} (2011) 1431, arXiv:1007.1335] is not a new exactly solvable quan...
A nonconventional strong law of large numbers and fractal dimensions of some multiple recurrence sets
strong law of large numbers nonconventional ergodic averages
2011/1/21
We provide conditions which yield a strong law of large num-bers for expressions of the form 1/N PN n=1 FX(q1(n)), · · · ,X(qℓ(n)) where X(n), n 0’s is a sufficiently fast mixing ve...
Extending a Hybrid Godunov Method for Radiation Hydrodynamics to Multiple Dimensions
Hybrid Godunov Method Radiation Hydrodynamics Multiple Dimensions
2010/12/15
This paper presents a hybrid Godunov method for three-dimensional radiation hydrodynamics.
The multidimensional technique outlined in this paper is an extension of the one-dimensional method that was...