On the Domain of Analyticity and Small Scales for the Solutions of the Damped-driven 2D Navier-Stokes Equations

We obtain a logarithmically sharp estimate for the space-analyticity radius of the solutions of the damped-driven 2D Navier-Stokes equations with periodic boundary conditions and relate this to the small scales in this system. This system is inspired by the Stommel--Charney barotropic ocean circulation model

Sharp estimates for the number of degrees of freedom for the damped-driven 2D Navier--Stokes equations

We derive upper bounds for the number of asymptotic degrees (determining modes and nodes) of freedom for the two-dimensional Navier--Stokes system and Navier-Stokes system with damping. In the first case we obtain the previously known estimates in an explicit form, which are larger than the fractal dimension of the global attractor. However, for the Navier--Stokes system with damping our estimates for the number of the determining modes and nodes are comparable to the sharp estimates for the fractal dimension of the global attractor. Our investigation of the damped-driven 2D Navier--Stokes system is inspired by the Stommel--Charney barotropic model of ocean circulation where the damping represents the Rayleigh friction. We remark that our results equally apply to the Stommel--Charney model

Continuous data assimilation for the three-dimensional Brinkman-Forchheimer-extended Darcy model

In this paper we introduce and analyze an algorithm for continuous data assimilation for a three-dimensional Brinkman-Forchheimer-extended Darcy (3D BFeD) model of porous media. This model is believed to be accurate when the flow velocity is too large for Darcy's law to be valid, and additionally the porosity is not too small. The algorithm is inspired by ideas developed for designing finite-parameters feedback control for dissipative systems. It aims to obtaining improved estimates of the state of the physical system by incorporating deterministic or noisy measurements and observations. Specifically, the algorithm involves a feedback control that nudges the large scales of the approximate solution toward those of the reference solution associated with the spatial measurements. In the first part of the paper, we present few results of existence and uniqueness of weak and strong solutions of the 3D BFeD system. The second part is devoted to the setting and convergence analysis of the data assimilation algorithm

Hadamard well-posedness for a hyperbolic equation of viscoelasticity with supercritical sources and damping

Presented here is a study of a viscoelastic wave equation with supercritical source and damping terms. We employ the theory of monotone operators and nonlinear semigroups, combined with energy methods to establish the existence of a unique local weak solution. In addition, it is shown that the solution depends continuously on the initial data and is global provided the damping dominates the source in an appropriate sense.Comment: The 2nd version includes a new proof of the energy identit

Pengaruh Penerapan Sistem Informasi Akuntansi dan Kualitas Audit terhadap Penentuan Opini Audit

This research tested the influence of the implementation of accounting information system and audit quality towards determining audit opinion.This research uses primary data that obtained with questionnaire survey method. The sample gotten by using purposive sampling by choosing accountant that work with Big Four KAP and Non Big Four in Jakarta and Bekasi area. This research uses SEM Model approach, while data processing analysis uses LISREL Software. Tested result model indicates that accounting information system not significant against audit opinion, while audit quality significantly affecting determination of audit opinion. Keywords: information system, audit quality, opinio

Spectral scaling of the Leray-α\alpha model for two-dimensional turbulence

We present data from high-resolution numerical simulations of the Navier-Stokes-$\alpha$ and the Leray-$\alpha$ models for two-dimensional turbulence. It was shown previously (Lunasin et al., J. Turbulence, 8, (2007), 751-778), that for wavenumbers $k$ such that $k\alpha\gg 1$, the energy spectrum of the smoothed velocity field for the two-dimensional Navier-Stokes-$\alpha$ (NS-$\alpha$) model scales as $k^{-7}$. This result is in agreement with the scaling deduced by dimensional analysis of the flux of the conserved enstrophy using its characteristic time scale. We therefore hypothesize that the spectral scaling of any $\alpha$-model in the sub-$\alpha$ spatial scales must depend only on the characteristic time scale and dynamics of the dominant cascading quantity in that regime of scales. The data presented here, from simulations of the two-dimensional Leray-$\alpha$ model, confirm our hypothesis. We show that for $k\alpha\gg 1$, the energy spectrum for the two-dimensional Leray-$\alpha$ scales as $k^{-5}$, as expected by the characteristic time scale for the flux of the conserved enstrophy of the Leray-$\alpha$ model. These results lead to our conclusion that the dominant directly cascading quantity of the model equations must determine the scaling of the energy spectrum.Comment: 11 pages, 4 figure