Dynamic Transitions and Baroclinic Instability for 3D Continuously Stratified Boussinesq Flows

The main objective of this article is to study the nonlinear stability and dynamic transitions of the basic (zonal) shear flows for the three-dimensional continuously stratified rotating Boussinesq model. The model equations are fundamental equations in geophysical fluid dynamics, and dynamics associated with their basic zonal shear flows play a crucial role in understanding many important geophysical fluid dynamical processes, such as the meridional overturning oceanic circulation and the geophysical baroclinic instability. In this paper, first we derive a threshold for the energy stability of the basic shear flow, and obtain a criteria for nonlinear stability in terms of the critical horizontal wavenumbers and the system parameters such as the Froude number, the Rossby number, the Prandtl number and the strength of the shear flow. Next we demonstrate that the system always undergoes a dynamic transition from the basic shear flow to either a spatiotemporal oscillatory pattern or circle of steady states, as the shear strength $\Lambda$ of the basic flow crosses a critical threshold $\Lambda_c$. Also we show that the dynamic transition can be either continuous or catastrophic, and is dictated by the sign of a transition parameter $A$, fully characterizing the nonlinear interactions of different modes. A systematic numerical method is carried out to explore transition in different flow parameter regimes. We find that the system admits only critical eigenmodes with horizontal wave indices $(0,m_y)$. Such modes, horizontally have the pattern consisting of $m_y$-rolls aligned with the x-axis. Furthermore, numerically we encountered continuous transitions to multiple steady states, continuous and catastrophic transitions to spatiotemporal oscillations.Comment: 20 pages, 7 figure

Quasistatic nonlinear viscoelasticity and gradient flows

We consider the equation of motion for one-dimensional nonlinear viscoelasticity of strain-rate type under the assumption that the stored-energy function is $\lambda$-convex, which allows for solid phase transformations. We formulate this problem as a gradient flow, leading to existence and uniqueness of solutions. By approximating general initial data by those in which the deformation gradient takes only finitely many values, we show that under suitable hypotheses on the stored-energy function the deformation gradient is instantaneously bounded and bounded away from zero. Finally, we discuss the open problem of showing that every solution converges to an equilibrium state as time $t \to \infty$ and prove convergence to equilibrium under a nondegeneracy condition. We show that this condition is satisfied in particular for any real analytic cubic-like stress-strain function.Comment: 40 pages, 1 figur

Traveling waves in one-dimensional nonlinear models of strain-limiting viscoelasticity

In this article we investigate traveling wave solutions of a nonlinear differential equation describing the behaviour of one-dimensional viscoelastic medium with implicit constitutive relations. We focus on a subclass of such models known as the strain-limiting models introduced by Rajagopal. To describe the response of viscoelastic solids we assume a nonlinear relationship among the linearized strain, the strain rate and the Cauchy stress. We then concentrate on traveling wave solutions that correspond to the heteroclinic connections between the two constant states. We establish conditions for the existence of such solutions, and find those solutions, explicitly, implicitly or numerically, for various forms of the nonlinear constitutive relation

Logarithmic dimension and bases in whitney spaces

Cataloged from PDF version of article.In generalization of [3] we will give the formula for the logarithmic dimension of any Cantor-type set. We will demonstrate some applications of the logarithmic dimension in Potential Theory. We will construct a polynomial basis in E(K(Λ)) when the logarithmic dimension of a Cantor-type set is smaller than 1. We will show that for any generalized Cantor-type set K(Λ), the space E(K(Λ)) possesses a Schauder basis. Locally elements of the basis are polynomials. The result generalizes theorems 1 and 2 in [12].Şengül, YaseminM.S

EXHIBITION STAND OF ARCHITECTURE IN A GLOBAL DESIGN ENVIRONMENT: ICONIC BUILDINGS

Abstract. Globalization and consumption culture have had an impact on the urban fabric as well as on all other areas. Consumption culture plays a key role not only in social and economic life but also in physical and spatial transformation of urban space. Urban actors have developed various strategies to enable cities to survive in this environment. In this process within the global economy, cities have started hosting new avenues that promote consumption, the most salient examples of which are iconic buildings. Cities today use iconic buildings to vie with each other, to gain advantage over their competitors and to create impressive images. This process began with the Sydney Opera House, and architecture has been increasingly involved in it to build landmark structures to highlight the values of cities and to create brand cities. The aim of this study is to reveal the characteristics of iconic buildings that are increasing in number and playing an important role in the creation of brand cities.The problem is addressed by the identification of features, concepts and situations related to iconic buildings, and the analysis of an iconic building. A literature review was conducted to highlight the significant aspects of iconic buildings. Iconic buildings are mostly associated with globalization, urban space, famous architects and buildings, and means and architectural understandings. These concepts are addressed with a focus on the Heydar Aliyev Center designed by architect Zaha Hadid. Even though iconic buildings are designed as physically unique and different, their aims and design approaches are similar.However, buildings that claim to be original will start, after a period of time, to look like each other and sometimes lose their value due to globalization and rapid spread of consumption cultureKeywords: Globalization, Brand City, Architecture, Iconic Buildings, Zaha Hadi

Exactly solvab q-extended nonlinear classical and quantum models

Thesis (Master)--Izmir Institute of Technology, Mathematics, Izmir, 2011Includes bibliographical references (leaves: 207-213)Text in English; Abstract: Turkish and Englishxii, 246 leavesIn the present thesis we study q-extended exactly solvable nonlinear classical and quantum models. In these models the derivative operator is replaced by q-derivative, in the form of finite difference dilatation operator. It requires introducing q-numbers instead of standard numbers, and q-calculus instead of standard calculus. We start with classical q-damped oscillator and q-difference heat equation. Exact solutions are constructed as q-Hermite and Kampe-de Feriet polynomials and Jackson q-exponential functions. By q-Cole-Hopf transformation we obtain q-nonlinear heat equation in the form of Burgers equation. IVP for this equation is solved in operator form and q-shock soliton solutions are found. Results are extended to linear q-Schrödinger equation and nonlinear q-Maddelung fluid. Motivated by physical applications, then we introduce the multiple q-calculus. In addition to non-symmetrical and symmetrical q-calculus it includes the new Fibonacci calculus, based on Binet-Fibonacci formula. We show that multiple q-calculus naturally appears in construction of Q-commutative q-binomial formula, generalizing all well-known formulas as Newton, Gauss, and noncommutative ones. As another application we study quantum two parametric deformations of harmonic oscillator and corresponding q-deformed quantum angular momentum. A new type of q-function of two variables is introduced as q-holomorphic function, satisfying q-Cauchy-Riemann equations. In spite of that q-holomorphic function is not analytic in the usual sense, it represents the so-called generalized analytic function. The q-traveling waves as solutions of q-wave equation are derived. To solve the q-BVP we introduce q-Bernoulli numbers, and their relation with zeros of q-Sine function

Barış'ın kemiklerini sızlatmasınlar

Taha Toros Arşivi, Dosya No: 67-Barış MançoUnutma İstanbul projesi İstanbul Kalkınma Ajansı'nın 2016 yılı "Yenilikçi ve Yaratıcı İstanbul Mali Destek Programı" kapsamında desteklenmiştir. Proje No: TR10/16/YNY/010

A review on the effects of special teaching methods 2 lesson to teacher candidates in terms of their performances

AbstractIn recent years, teachers have a big responsibility to actualize the aims of education. In teaching learning environment teachers’ roles are changing continuously and becoming more important. The developments in education technologies do not reduce the importance of teacher role for figuring out the needs of our age but a significant change has been done (Sezgin, 2003). In order to reach this aim; teachers, who are responsible for guiding, to the next generations and having a big impact on figuring the future, should gain necessary qualifications. It is assessed that; students’ attainments in terms of teaching performance during the application period within Special Teaching Methods 2 lesson, is for Elementary Math's Teaching 4th year 7th term students