Boundary layer analysis of the Navier-Stokes equations with Generalized Navier boundary conditions

We study the weak boundary layer phenomenon of the Navier-Stokes equations in a 3D bounded domain with viscosity, $\epsilon > 0$, under generalized Navier friction boundary conditions, in which we allow the friction coefficient to be a (1, 1) tensor on the boundary. When the tensor is a multiple of the identity we obtain Navier boundary conditions, and when the tensor is the shape operator we obtain conditions in which the vorticity vanishes on the boundary. By constructing an explicit corrector, we prove the convergence of the Navier-Stokes solutions to the Euler solution as the viscosity vanishes. We do this both in the natural energy norm with a rate of order $\epsilon^{3/4}$ as well as uniformly in time and space with a rate of order $\epsilon^{3/8 - \delta}$ near the boundary and $\epsilon^{3/4 - \delta'}$ in the interior, where $\delta, \delta'$ decrease to 0 as the regularity of the initial velocity increases. This work simplifies an earlier work of Iftimie and Sueur, as we use a simple and explicit corrector (which is more easily implemented in numerical applications). It also improves a result of Masmoudi and Rousset, who obtain convergence uniformly in time and space via a method that does not yield a convergence rate.Comment: Additional references and several typos fixe

Kerr electro-optic measurements and nonuniform electric field reconstructions

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1999.Includes bibliographical references (p. 341-343).by Tza-Jing Gung.Ph.D

Equipoise: An Animated Short Film About Positiveness and Negativity.

Equipoise is an animated short about positiveness, negativity and the opposite but complementary relationship between them. The two opposite attitudes of an individual’s personality not only affect but also establish emotions, decisions and behaviors. Positiveness reinforces positive thinking while pessimistic assumptions and hardship are driven by negativity. A person who has an imbalanced mind may live in pain or lead to high risks. To have a great mental condition, both positiveness and negativity have to be involved to establish the balance. However, the importance of negativity, in one case, pessimism was frequently ignored as a result of education that focuses on positiveness or optimism for most of the time. The animated short Equipoise depicts the complementarity of two forces and introduces the concept of balance from an objective standpoint. The two forces are balancing for different circumstances and no matter who is leading, the other is always supporting

Pattern discovery in sequence databases : algorithms and applications to DNA/protein classification

Sequence databases comprise sequence data, which are linear structural descriptions of many natural entities. Approximate pattern discovery in a sequence database can lead to important conclusions or prediction of new phenomena. Traditional database technology is not suitable for accomplishing the task, and new techniques need to be developed. In this dissertation, we propose several new techniques for discovering patterns in sequence databases. Our techniques incorporate pattern matching algorithms and novel heuristics for discovery and optimization. Experimental results of applying the techniques to both generated data and DNA/proteins show the effectiveness of the proposed techniques. We then develop several classifiers using our pattern discovery algorithms and a previously published fingerprint technique. When we apply the classifiers to classify DNA and protein sequences, they give information that is complementary to the best classifiers available today

PENERAPAN MODEL PEMBELAJARAN KOOPERATIF TIPE MAKE A MATCH BERBANTUAN MULTIMEDIA UNTUK MENINGKATKAN HASIL BELAJAR PPKn SISWA KELAS VC SD WIDIATMIKA TAHUN PELAJARAN 2020/2021

Penelitian ini bertujuan untuk meningkatkan hasil belajar PPKn dengan menggunakan model pembelajaran kooperatif tipe make a match berbantuan multimedia. Jenis penelitiannya adalah penelitian tindakan kelas. Teknik pengumpulan data menggunakan lembar observasi pelaksanaan pembelajaran, tes, dan catatan lapangan. Berdasarkan perhitungan nilai keterlaksanaan pembelajaran peningkatan hasil belajar tersebut ditunjukkan pada perolehan nilai pra siklus dengan rata-rata kelas 67,12, persentase ketuntasan 23,08% mengalami kenaikan pada siklus I dengan nilai rata-rata kelas 75,96, persentase ketuntasan 76,92% dan pada siklus II dengan nilai rata-rata kelas 82,69 persentase ketuntasan 100%. Hasil tersebut juga menunjukkan bahwa penelitian tindakan kelas ini mencapai indikator ketuntasan yang ditentukan yaitu 80%. Dapat disimpulkan bahwa penerapan model pembelajaran kooperatif tipe make a match berbantuan multimedia dapat meningkatkan hasil belajar PPKn siswa kelas VC SD Widiatmika

Stability of Vortex Solutions to an Extended Navier-Stokes System

We study the long-time behavior an extended Navier-Stokes system in $\R^2$ where the incompressibility constraint is relaxed. This is one of several "reduced models" of Grubb and Solonnikov '89 and was revisited recently (Liu, Liu, Pego '07) in bounded domains in order to explain the fast convergence of certain numerical schemes (Johnston, Liu '04). Our first result shows that if the initial divergence of the fluid velocity is mean zero, then the Oseen vortex is globally asymptotically stable. This is the same as the Gallay Wayne '05 result for the standard Navier-Stokes equations. When the initial divergence is not mean zero, we show that the analogue of the Oseen vortex exists and is stable under small perturbations. For completeness, we also prove global well-posedness of the system we study.Comment: 24 pages, 1 figure, updated to add authors' contact information and to address referee's comment

Spray combustion at normal and reduced gravity in counterflow and co-flow configurations

Liquid fuel dispersion in practical systems is typically achieved by spraying the fuel into a polydisperse distribution of droplets evaporating and burning in a turbulent gaseous environment In view of the nearly insurmountable difficulties of this two-phase flow, a systematic study of spray evaporation and burning in configurations of gradually increasing levels of complexity, starting from laminar sprays to fully turbulent ones, would be useful. A few years ago we proposed to use an electrostatic spray of charged droplets for this type of combustion experiments under well-defined conditions. In the simplest configuration, a liquid is fed into a small metal tube maintained at several kilovolts relative to a ground electrode few centimeters away. Under the action of the electric field, the liquid meniscus at the outlet of the capillary takes a conical shape, with a thin jet emerging from the cone tip (cone-jet mode). This jet breaks up farther downstream into a spray of charged droplets - the so-called ElectroSpray (ES). Several advantages distinguish the electrospray from alternative atomization techniques: (1) it can produce quasi-monodisperse droplets over a phenomenal size range; (2) the atomization, that is strictly electrostatic, is decoupled from gas flow processes, which provides some flexibility in the selection and control of the experimental conditions; (3) the Coulombic repulsion of homopolarly charged droplets induces spray self-dispersion and prevents droplet coalescence; (4) the ES provides the opportunity of studying regimes of slip between droplets and host gas without compromising the control of the spray properties; and (5) the compactness and potential controllability of this spray generation system makes it appealing for studies in reduced-gravity environments aimed at isolating the spray behavior from natural convection complications. With these premises, in March 1991 we initiated a series of experiments under NASA sponsorship (NAG3-1259 and 1688) in which the ES was used as a research tool to examine spray combustion in counter-flow and co-flow spray diffusion flames, as summarized below. The ultimate objective of this investigation is to examine the formation and burning of sprays of liquid fuels, at both normal and reduced gravity, first in laminar regimes and then in turbulent ones

Analysis of mixed elliptic and parabolic boundary layers with corners

We study the asymptotic behavior at small diffusivity of the solutions, u??, to a convection-diffusion equation in a rectangular domain. The diffusive equation is supplemented with a Dirichlet boundary condition, which is smooth along the edges and continuous at the corners. To resolve the discrepancy, on ???, between u?? and the corresponding limit solution, u0, we propose asymptotic expansions of u?? at any arbitrary, but fixed, order. In order to manage some singular effects near the four corners of , the so-called elliptic and ordinary corner correctors are added in the asymptotic expansions as well as the parabolic and classical boundary layer functions. Then, performing the energy estimates on the difference of u?? and the proposed expansions, the validity of our asymptotic expansions is established in suitable Sobolev spaces.open

DiactTOD: Learning Generalizable Latent Dialogue Acts for Controllable Task-Oriented Dialogue Systems

Dialogue act annotations are important to improve response generation quality in task-oriented dialogue systems. However, it can be challenging to use dialogue acts to control response generation in a generalizable way because different datasets and tasks may have incompatible annotations. While alternative methods that utilize latent action spaces or reinforcement learning do not require explicit annotations, they may lack interpretability or face difficulties defining task-specific rewards. In this work, we present a novel end-to-end latent dialogue act model (DiactTOD) that represents dialogue acts in a latent space. DiactTOD, when pre-trained on a large corpus, is able to predict and control dialogue acts to generate controllable responses using these latent representations in a zero-shot fashion. Our approach demonstrates state-of-the-art performance across a wide range of experimental settings on the MultiWOZ dataset, including zero-shot, few-shot, and full data fine-tuning with both end-to-end and policy optimization configurations.Comment: SIGDial 202