scholarly journals Conditioned Two-Dimensional Simple Random Walk: Green’s Function and Harmonic Measure

2019 ◽  
Author(s):  
Serguei Popov
Keyword(s):  
Random Walk ◽  
Green’S Function ◽  
Green's Function ◽  
Harmonic Measure ◽  
Simple Random Walk ◽  
Two Dimensional

scholarly journals DIFFERENTIAL EQUATION APPROACH FOR ONE- AND TWO-DIMENSIONAL LATTICE GREEN'S FUNCTION

2007 ◽  
Vol 21 (02n03) ◽  
pp. 139-154 ◽  
Author(s):  
J. H. ASAD
Keyword(s):  
Differential Equation ◽  
Green’S Function ◽  
Recurrence Relation ◽  
Green's Function ◽  
Two Dimensional ◽  
Dimensional Lattice ◽  
One Dimensional ◽  
The One ◽  
Lattice Green's Function ◽  
Lattice Green’S Function

A first-order differential equation of Green's function, at the origin G(0), for the one-dimensional lattice is derived by simple recurrence relation. Green's function at site (m) is then calculated in terms of G(0). A simple recurrence relation connecting the lattice Green's function at the site (m, n) and the first derivative of the lattice Green's function at the site (m ± 1, n) is presented for the two-dimensional lattice, a differential equation of second order in G(0, 0) is obtained. By making use of the latter recurrence relation, lattice Green's function at an arbitrary site is obtained in closed form. Finally, the phase shift and scattering cross-section are evaluated analytically and numerically for one- and two-impurities.

scholarly journals Chemical Source Inversion Using Assimilated Constituent Observations in an Idealized Two-Dimensional System

2009 ◽  
Vol 137 (9) ◽  
pp. 3013-3025
Author(s):  
Andrew Tangborn ◽  
Robert Cooper ◽  
Steven Pawson ◽  
Zhibin Sun
Keyword(s):  
Kalman Filter ◽  
Green’S Function ◽  
Green's Function ◽  
Transport Model ◽  
Chemical Constituents ◽  
Gaussian Model ◽  
Satellite Observation ◽  
Dimensional System ◽  
Two Dimensional ◽  
Source Inversion

Abstract A source inversion technique for chemical constituents is presented that uses assimilated constituent observations rather than directly using the observations. The method is tested with a simple model problem, which is a two-dimensional Fourier–Galerkin transport model combined with a Kalman filter for data assimilation. Inversion is carried out using a Green’s function method and observations are simulated from a true state with added Gaussian noise. The forecast state uses the same spectral model but differs by an unbiased Gaussian model error and emissions models with constant errors. The numerical experiments employ both simulated in situ and satellite observation networks. Source inversion was carried out either by directly using synthetically generated observations with added noise or by first assimilating the observations and using the analyses to extract observations. Twenty identical twin experiments were conducted for each set of source and observation configurations, and it was found that in the limiting cases of a very few localized observations or an extremely large observation network there is little advantage to carrying out assimilation first. For intermediate observation densities, the source inversion error standard deviation is decreased by 50% to 90% when the observations are assimilated with the Kalman filter before carrying out the Green’s function inversion.

Efficient computation of the two-dimensional periodic Green's function

1999 ◽  
Vol 47 (5) ◽  
pp. 895-897 ◽  
Author(s):  
G.S. Wallinga ◽  
E.J. Rothwell ◽  
K.M. Chen ◽  
D.P. Nyquist
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Two Dimensional ◽  
Efficient Computation

The transient behaviour of the simple random walk in the plane

1988 ◽  
Vol 25 (01) ◽  
pp. 58-69 ◽  
Author(s):  
D. Y. Downham ◽  
S. B. Fotopoulos
Keyword(s):  
Random Walk ◽  
Transient Process ◽  
Asymptotic Form ◽  
Simple Random Walk ◽  
Rectangular Lattice ◽  
Two Dimensional ◽  
Transient Behaviour ◽  
Practical Implications ◽  
Asymptotic Forms

For the simple two-dimensional random walk on the vertices of a rectangular lattice, the asymptotic forms of several properties are well known, but their forms can be insufficiently accurate to describe the transient process. Inequalities with the correct asymptotic form are derived for six such properties. The rates of approach to the asymptotic form are derived. The accuracy of the bounds and some practical implications of the results are discussed.

scholarly journals Evaluating the exfoliation of two-dimensional materials with a Green's function surface model

2020 ◽  
Vol 101 (7) ◽  
Author(s):  
Yipeng An ◽  
Yusheng Hou ◽  
Shijing Gong ◽  
Ruqian Wu ◽  
Chuanxi Zhao ◽  
...  
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Surface Model ◽  
Two Dimensional ◽  
Two Dimensional Materials
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