Continuous Data Assimilation with Stochastically Noisy Data

We analyze the performance of a data-assimilation algorithm based on a linear feedback control when used with observational data that contains measurement errors. Our model problem consists of dynamics governed by the two-dimension incompressible Navier-Stokes equations, observational measurements given by finite volume elements or nodal points of the velocity field and measurement errors which are represented by stochastic noise. Under these assumptions, the data-assimilation algorithm consists of a system of stochastically forced Navier-Stokes equations. The main result of this paper provides explicit conditions on the observation density (resolution) which guarantee explicit asymptotic bounds, as the time tends to infinity, on the error between the approximate solution and the actual solutions which is corresponding to these measurements, in terms of the variance of the noise in the measurements. Specifically, such bounds are given for the the limit supremum, as the time tends to infinity, of the expected value of the $L^2$-norm and of the $H^1$ Sobolev norm of the difference between the approximating solution and the actual solution. Moreover, results on the average time error in mean are stated

A connection between the Camassa-Holm equations and turbulent flows in channels and pipes

In this paper we discuss recent progress in using the Camassa-Holm equations to model turbulent flows. The Camassa-Holm equations, given their special geometric and physical properties, appear particularly well suited for studying turbulent flows. We identify the steady solution of the Camassa-Holm equation with the mean flow of the Reynolds equation and compare the results with empirical data for turbulent flows in channels and pipes. The data suggests that the constant $\alpha$ version of the Camassa-Holm equations, derived under the assumptions that the fluctuation statistics are isotropic and homogeneous, holds to order $\alpha$ distance from the boundaries. Near a boundary, these assumptions are no longer valid and the length scale $\alpha$ is seen to depend on the distance to the nearest wall. Thus, a turbulent flow is divided into two regions: the constant $\alpha$ region away from boundaries, and the near wall region. In the near wall region, Reynolds number scaling conditions imply that $\alpha$ decreases as Reynolds number increases. Away from boundaries, these scaling conditions imply $\alpha$ is independent of Reynolds number. Given the agreement with empirical and numerical data, our current work indicates that the Camassa-Holm equations provide a promising theoretical framework from which to understand some turbulent flows.Comment: tex file, 29 pages, 4 figures, Physics of Fluids (in press

Statistical Properties of Nonlinear Shell Models of Turbulence from Linear Advection Models: Rigorous Results

In a recent paper it was proposed that for some nonlinear shell models of turbulence one can construct a linear advection model for an auxiliary field such that the scaling exponents of all the structure functions of the linear and nonlinear fields coincide. The argument depended on an assumption of continuity of the solutions as a function of a parameter. The aim of this paper is to provide a rigorous proof for the validity of the assumption. In addition we clarify here when the swap of a nonlinear model by a linear one will not work.Comment: 7 pages, 4 figures, submitted to Nonlinearit

Hemimandibulektomi pada kasus ameloblastoma dengan fistula kulit

Ameloblastoma merupakan jenis tumor odontogenik yang bersifat jinak, tumbuh lambat dan lokal invasive. Umumnya, tumor ini tidak menimbulkan rasa nyeri sehingga adanya tumor ini tidak segera diketahui oleh penderita. Pada kasus ini penderita merasakan nyeri oleh karena adanya infeksi dan menyebabkan fistula kulit. Dilaporkan tindakan hemimandibulektomi pada ameloblastoma dengan fistula kulit mandibula dekstra. Pasien laki-Iaki 25 tahun, keluhan benjolan pada rahang bawah kanan yang pernah dioperasi di Lampung tahun 2001, pada tahun 2003 benjolan tumbuh lagi, dan dirasakan semakin membesar serta mengeluarkan nanah. Hasil operasi penyembuhan luka baik. Maj. Ked. Gi. 200613(2):169-172 Ameloblastoma is an odontogenic tumor which characterized as slowly grow and locally invasive. Generally, the tumor does not cause painful, therefore, patient does not know the real condition. In this case, the patient felt painful because of infection which lead skin fistula. It is reported the case of ameloblastoma with skin fistula dextra mandibula of a male 25 years old patient treated with hemimandibulectomy. Previously, it was operated in Lampung at 2001. However at 2003 the swelling condition relapse, grow bigger, producing pus. Progress of this operation is good. Maj. Ked. Gi. 200613(2):169-17

Penerapan Program Typing Master Dalam Meningkatkan Kecepatan Dan Ketelitian Pengetikan 10 Jari Buta

State Polytechnic of Sriwijaya Palembang is a vocational education Institution which in the lecture activities more practical rather than theoretical, as well as within the Department of Business Administration. Department of Business Administration is a subject that study a lot in the areas of secretarial and office including the practice of typing. During this time students at the Business Administration Department trained 10 finger blind typing skills by using a manual typewriter and electronic typewriter. In accordance with current technological developments every company is already using technology such as computers. Therefore, students should be able to follow the development of the technology that is the way to learn to type fast 10-finger blind which should still pay attention to precision and accuracy. There are several kinds of programs that can be used for learning in typing speed, one of which is a master typing program. Typing master\u27s program is often used in polytechnic typing speed competition in Indonesia, unfortunately; only few business administration departments used this master typing program recently. Therefore, with this program it can be known the strengths and weaknesses of this typing master program