scholarly journals The asymptotic behavior of degenerate oscillatory integrals in two dimensions

2009 ◽  
Vol 257 (6) ◽  
pp. 1759-1798 ◽  
Author(s):  
Michael Greenblatt
Keyword(s):  
Asymptotic Behavior ◽  
Two Dimensions ◽  
Oscillatory Integrals

Accurate calculation of the bound states of the quantum dipole problem in two dimensions

Open Physics ◽  
2012 ◽  
Vol 10 (1) ◽  
Author(s):  
Paolo Amore
Keyword(s):  
Asymptotic Behavior ◽  
Upper Bound ◽  
Ground State ◽  
Bound States ◽  
Two Dimensions ◽  
Accurate Calculation ◽  
Perfect Agreement

AbstractWe present an accurate calculation of the energies of the bound states of the quantumdipole problemin two dimensions using a Rayleigh-Ritz approach. We obtain an upper bound for the energy of the ground state, which is by far the most precise in the literature for this problem. We also obtain an alternative estimate of the fundamental energy of the model performing an extrapolation of the results corresponding to different subspaces. Finally, our calculation of the energies of the first 500 states shows a perfect agreement with the expected asymptotic behavior.

Dispersion of particle systems in Brownian flows

1996 ◽  
Vol 28 (1) ◽  
pp. 53-74 ◽  
Author(s):  
Craig L. Zirbel ◽  
Erhan Çinlar
Keyword(s):  
Asymptotic Behavior ◽  
Incompressible Flows ◽  
Center Of Mass ◽  
Spatial Dimension ◽  
Two Dimensions ◽  
Separation Process ◽  
Particle Systems ◽  
Largest Lyapunov Exponent ◽  
Second Moments ◽  
Pair Separation

We study the dispersion of a collection of particles carried by an isotropic Brownian flow in Of particular interest are the center of mass and the centered spatial second moments. Their asymptotic behavior depends strongly on the spatial dimension and the largest Lyapunov exponent of the flow. We use estimates for the pair separation process to give a fairly complete picture of this behavior as t → ∞. In particular, for incompressible flows in two dimensions, we show that the variance of the center of mass grows sublinearly, while dispersion relative to the center of mass grows linearly.

scholarly journals Homogenization of a 2D Tidal Dynamics Equation

Mathematics ◽  
2020 ◽  
Vol 8 (12) ◽  
pp. 2209
Author(s):  
Giuseppe Cardone ◽  
Aurelien Fouetio ◽  
Jean Louis Woukeng
Keyword(s):  
Asymptotic Behavior ◽  
Two Dimensions ◽  
Tidal Dynamics ◽  
Equivalent Problem ◽  
Sigma Convergence ◽  
Convergence Method

This work deals with the homogenization of two dimensions’ tidal equations. We study the asymptotic behavior of the sequence of the solutions using the sigma-convergence method. We establish the convergence of the sequence of solutions towards the solution of an equivalent problem of the same type.

ON LOGARITHMIC CORRECTIONS IN TWO-DIMENSIONAL PERCOLATION

1993 ◽  
Vol 07 (26) ◽  
pp. 1661-1665
Author(s):  
M. MARSILI ◽  
G. JUG
Keyword(s):  
Asymptotic Behavior ◽  
Critical Exponent ◽  
Transfer Matrix ◽  
Finite Size ◽  
Two Dimensions ◽  
Matrix Analysis ◽  
Two Dimensional ◽  
Site Percolation ◽  
Logarithmic Corrections ◽  
Transfer Matrix Analysis

The possibility of unusual leading logarithmic corrections to the asymptotic behavior of the percolation connectedness length ξ in two dimensions is explored through a finite-size transfer-matrix analysis on strips of widths L≤12. It is found that, for both square-site and triangular-site percolation problems, no such corrections arise and the accepted exact value of the critical exponent ν is recovered.

Dispersion of particle systems in Brownian flows

1996 ◽  
Vol 28 (01) ◽  
pp. 53-74 ◽  
Author(s):  
Craig L. Zirbel ◽  
Erhan Çinlar
Keyword(s):  
Asymptotic Behavior ◽  
Incompressible Flows ◽  
Center Of Mass ◽  
Spatial Dimension ◽  
Two Dimensions ◽  
Separation Process ◽  
Particle Systems ◽  
Largest Lyapunov Exponent ◽  
Second Moments ◽  
Pair Separation

We study the dispersion of a collection of particles carried by an isotropic Brownian flow in Of particular interest are the center of mass and the centered spatial second moments. Their asymptotic behavior depends strongly on the spatial dimension and the largest Lyapunov exponent of the flow. We use estimates for the pair separation process to give a fairly complete picture of this behavior as t → ∞. In particular, for incompressible flows in two dimensions, we show that the variance of the center of mass grows sublinearly, while dispersion relative to the center of mass grows linearly.

scholarly journals Convergence of random oscillatory integrals in the presence of long-range dependence and application to homogenization

2018 ◽  
Vol 38 (2) ◽  
pp. 271-286 ◽  
Author(s):  
Ivan Nourdin ◽  
Atef Lechiheb ◽  
Guangqu Zheng ◽  
Ezzedine Haouala
Keyword(s):  
Asymptotic Behavior ◽  
Long Range ◽  
Elliptic Equations ◽  
Random Coefficients ◽  
Oscillatory Integrals ◽  
Long Range Dependence ◽  
Stochastic Integrals ◽  
Highly Oscillatory

This paper deals with the asymptotic behavior of random oscillatory integrals in the presence of long-range dependence. As a byproduct, we solve the corrector problem in random homogenization of onedimensional elliptic equations with highly oscillatory random coefficients displaying long-range dependence, by proving convergence to stochastic integrals with respect to Hermite processes.

scholarly journals The local sum conjecture in two dimensions

2020 ◽  
Vol 16 (08) ◽  
pp. 1667-1699
Author(s):  
Robert Fraser ◽  
James Wright
Keyword(s):  
Algebraic Geometry ◽  
Elementary Proof ◽  
Exponential Sums ◽  
Research Area ◽  
Two Dimensions ◽  
Oscillatory Integrals ◽  
Newton Polyhedra

The local sum conjecture is a variant of some of Igusa’s questions on exponential sums put forward by Denef and Sperber. In a remarkable paper by Cluckers, Mustata and Nguyen, this conjecture has been established in all dimensions, using sophisticated, powerful techniques from a research area blending algebraic geometry with ideas from logic. The purpose of this paper is to give an elementary proof of this conjecture in two dimensions which follows Varčenko’s treatment of Euclidean oscillatory integrals based on Newton polyhedra for good coordinate choices. Another elementary proof is given by Veys from an algebraic geometric perspective.

Sign in / Sign up

Export Citation Format

Share Document