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.

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.

Homogenization and correctors for the wave equation with periodic coefficients

2014 ◽  
Vol 24 (07) ◽  
pp. 1343-1388 ◽  
Author(s):  
Juan Casado-Díaz ◽  
Julio Couce-Calvo ◽  
Faustino Maestre ◽  
José D. Martín Gómez
Keyword(s):  
Asymptotic Behavior ◽  
Wave Equation ◽  
Space Variable ◽  
Limit Problem ◽  
Almost Periodic ◽  
Wave Problem ◽  
Periodic Coefficients ◽  
Convergence Method

Using the two-scale convergence method, we study the asymptotic behavior of a wave problem in ℝN with periodic coefficients in the space variable and almost-periodic coefficients in the time one. We obtain a nonlocal corrector and show how this implies that the limit problem is nonlocal in general.

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.

scholarly journals Asymptotic modeling of thin plastic oscillating layer

2014 ◽  
Vol 32 (2) ◽  
pp. 95
Author(s):  
Ait Moussa Abdlaziz ◽  
Mohamed Verid Abdelkader
Keyword(s):  
Asymptotic Behavior ◽  
Elasticity Problem ◽  
Asymptotic Behavior Of Solutions ◽  
Interface Conditions ◽  
Asymptotic Modeling ◽  
Limit Problems ◽  
Small Parameters ◽  
Convergence Method ◽  
Thin Plastic

In this paper we study the asymptotic behavior of solutions to a elasticity problem, of a containing structure a plastic thin oscillating layer of thickness and rigidity depending of small parameters $\varepsilon$. We use the epi-convergence method to find the limit problems with interface conditions.

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 Multiscale homogenization of a class of nonlinear equations with applications in lubrication theory and applications

2011 ◽  
Vol 9 (1) ◽  
pp. 17-40 ◽  
Author(s):  
Andreas Almqvist ◽  
Emmanuel Kwame Essel ◽  
John Fabricius ◽  
Peter Wall
Keyword(s):  
Thin Film ◽  
Asymptotic Behavior ◽  
Monotone Operators ◽  
Thin Film Lubrication ◽  
Multiscale Convergence ◽  
Convergence Method ◽  
Bounding Surfaces ◽  
Fundamental Theorems ◽  
Multiscale Homogenization ◽  
Film Lubrication

We prove a homogenization result for monotone operators by using the method of multiscale convergence. More precisely, we study the asymptotic behavior asε→0of the solutionsuεof the nonlinear equationdiv⁡aε(x,∇uε)=div⁡bε, where bothaεandbεoscillate rapidly on several microscopic scales andaεsatisfies certain continuity, monotonicity and boundedness conditions. This kind of problem has applications in hydrodynamic thin film lubrication where the bounding surfaces have roughness on several length scales. The homogenization result is obtained by extending the multiscale convergence method to the setting of Sobolev spacesW01,p(Ω), where1<p<∞. In particular we give new proofs of some fundamental theorems concerning this convergence that were first obtained by Allaire and Briane for the casep=2.

The tangled web of agency

2018 ◽  
Vol 41 ◽  
Author(s):  
Alain Pe-Curto ◽  
Julien A. Deonna ◽  
David Sander
Keyword(s):  
Two Dimensions ◽  
Bad Company

AbstractWe characterize Doris's anti-reflectivist, collaborativist, valuational theory along two dimensions. The first dimension is socialentanglement, according to which cognition, agency, and selves are socially embedded. The second dimension isdisentanglement, the valuational element of the theory that licenses the anchoring of agency and responsibility in distinct actors. We then present an issue for the account: theproblem of bad company.

Sign in / Sign up

Export Citation Format

Share Document