Dynamics of a Nonlocal Kuramoto-Sivashinsky Equation

In this paper we study the effects of a ``nonlocal'' term on the global dynamics of the Kuramoto-Sivashinsky equation. We show that the equation possesses a ``family of maximal attractors'' parameterized by the mean value of the initial data. The dimension of the attractor is estimated as a function of the coefficient of the nonlocal term and the width of the periodic domain.Comment: Latex fil

Asymptotic Dynamical Difference between the Nonlocal and Local Swift-Hohenberg Models

In this paper the difference in the asymptotic dynamics between the nonlocal and local two-dimensional Swift-Hohenberg models is investigated. It is shown that the bounds for the dimensions of the global attractors for the nonlocal and local Swift-Hohenberg models differ by an absolute constant, which depends only on the Rayleigh number, and upper and lower bounds of the kernel of the nonlocal nonlinearity. Even when this kernel of the nonlocal operator is a constant function, the dimension bounds of the global attractors still differ by an absolute constant depending on the Rayleigh number.Comment: 13 pages, LaTex fil

Vertical Stacked Field Effect Transistor

The move from planar to FinFET technology is expected to continue in the future. Current options include Nanosheet, Forksheet and Vertical FET architectures. While vertical FET is attractive, the footprint is currently too large. Improvement of the footprint of vertical FETs can be achieved if the vertical transistors can be stacked on top of each other with an easy integration path. The present disclosure relates to an integration solution allowing two vertical FET transistors to be stacked on top of each other using a monolithic process integration flow

A Fair View: The Connection Between PBIS and Title I

This presentation offers a Title I school\u27s early implementation of Positive Behavior Interventions & Supports (PBIS). Initial focus will apply to the universal (Tier I) application, where a shared leadership model utilized the collective experiences of educators and school-based mental health professionals. Secondary discussions will highlight the importance of community-based involvement, with primary examples noted in state-level representatives. Additional topics will highlight the use of the Second Step Curriculum in instilling self-regulation and social skills at a Title I school. This will accompany particular strategies employed in various settings in the school setting (e.g., classroom, cafeteria, hallways, etc.). Participants will witness a modeling of examples for classroom and home use. Final discussions will focus on the cultural components of implementing a PBIS framework. This will involve a year-to-year comparison of office disciplinary referrals (ODRs). Implications for future practice will be offered in a Q&A session

Improving mass conservation in FE approximations of the Navier Stokes equations using continuous velocity fields: A connection between grad-div stabilization and Scott--Vogelius elements

This article studies two methods for obtaining excellent mass conservation in finite element computations of the Navier-Stokes equations using continuous velocity fields. Under mild restrictions, the Scott-Vogelius element pair has recently been shown to be inf-sup stable and have optimal approximation properties, while also providing pointwise mass conservation. We present herein the first numerical tests of this element pair for the time dependent Navier-Stokes equations. We also prove that, again under these mild restrictions, the limit of the grad-div stabilized Taylor-Hood solutions to the Navier-Stokes problem converges to the Scott-Vogelius solution as the stabilization parameter tends to infinity. That is, in this setting, we provide theoretical justification that choosing the parameter large does not destroy the solution. A limiting result is also proven for the general case. Numerical tests are provided which verify the theory, and show how both Scott-Vogelius and grad-div stabilized Taylor-Hood (with large stabilization parameter) elements can provide accurate results with excellent mass conservation for Navier-Stokes approximations

Stable computing with an enhanced physics based scheme for the 3D Navier--Stokes equations

We study extensions of an earlier developed energy and helicity preserving scheme for the 3D Navier-Stokes equations and apply them to a more general class of problems. The scheme is studied together with stabilizations of grad-div type in order to mitigate the effect of the Bernoulli pressure error on the velocity error. We prove stability, convergence, discuss conservation properties, and present numerical experiments that demonstrate the advantages of the scheme