Numerical calculations of turbulent reacting flow in a gas-turbine combustor

A numerical study for confined, axisymmetrical, turbulent diffusion flames is presented. Local mean gas properties are predicted by solving the appropriate conservation equations in the finite difference form with the corresponding boundary conditions. The k-epsilon two-equation turbulence model is employed to describe the turbulent nature of the flow. A two-step kinetic model is assumed to govern the reaction mechanism. The finite reaction rate is the smaller of an Arrhenius type of reaction rate and a modified version of eddy-breakup model. Reasonable agreement is observed between calculations and measurements, but to obtain better agreement, more work is needed on improvements of the above mathematical models. However, the present numerical study offers an improvement in the analysis and design of the gas turbine combustors

Mean field equations, hyperelliptic curves and modular forms: II

A pre-modular form $Z_n(\sigma; \tau)$ of weight $\tfrac{1}{2} n(n + 1)$ is introduced for each $n \in \Bbb N$, where $(\sigma, \tau) \in \Bbb C \times \Bbb H$, such that for $E_\tau = \Bbb C/(\Bbb Z + \Bbb Z \tau)$, every non-trivial zero of $Z_n(\sigma; \tau)$, namely $\sigma \not\in E_\tau[2]$, corresponds to a (scaling family of) solution to the mean field equation \begin{equation} \tag{MFE} \triangle u + e^u = \rho \, \delta_0 \end{equation} on the flat torus $E_\tau$ with singular strength $\rho = 8\pi n$. In Part I (Cambridge J. Math. 3, 2015), a hyperelliptic curve $\bar X_n(\tau) \subset {\rm Sym}^n E_\tau$, the Lam\'e curve, associated to the MFE was constructed. Our construction of $Z_n(\sigma; \tau)$ relies on a detailed study on the correspondence $\Bbb P^1 \leftarrow \bar X_n(\tau) \to E_\tau$ induced from the hyperelliptic projection and the addition map. As an application of the explicit form of the weight 10 pre-modular form $Z_4(\sigma; \tau)$, a counting formula for Lam\'e equations of degree $n = 4$ with finite monodromy is given in the appendix (by Y.-C. Chou).Comment: 32 pages. Part of content in previous versions is removed and published separately. One author is remove

The internet milieu: individualization within a globalised community

Communication technologies have become deeply embedded in our lives, mediating the ways in which information is presented. Due to the global nature of this channel of communication, the world has shrunk and members of the internet may share similar cultural norms of thinking and behaving. Yet, paradoxically, the Internet is personal in that each individual has an interactive opportunity in choosing the options that can expand the breadth and depth of the information they are reading, who they interact with, and the means to achieve that interaction. These options can be expressed through a variety of media techniques. This paper is based on a study of selected websites hosted in English. It looks at language use in the Internet and illustrates the paradoxes between global and individual mediations of meanin

The Effect of Congressional Sessions on the Stock Market in Emerging Democracy: the Case of Taiwan

Political uncertainty, Congressional effect, Volatility asymmetry, EGARCH-M

Buoyancy effects on the vapor condensation rate on a horizontal liquid surface

The results are presented of a numerical study of the effects of buoyancy on the direct condensation of saturated or nearly saturated vapor on a horizontal liquid surface in a cylindrical tank. The liquid motion beneath the liquid-vapor interface is induced by an axisymmetric laminar jet of subcooled liquid. Analysis and numerical results show that the dominant parameter which determines the influence of buoyancy on the condensation rate is the Richardson number. However, the effect of buoyancy on the condensation rate cannot be quantified in terms of the Richardson number alone. The critical value of the Richardson number below which the condensation rate is not significantly reduced depends on the Reynolds number as well as the Prandtl number