MICRO BUBBLE FORMATION AND BUBBLE DISSOLUTION IN DOMESTIC WET CENTRAL HEATING SYSTEMS

16 % of the carbon dioxide emissions in the UK are known to originate from wet domestic central heating systems. Contemporary systems make use of very efficient boilers known as condensing boilers that could result in efficiencies in the 90-100% range. However, research and development into the phenomenon of micro bubbles in such systems has been practically non-existent. In fact, such systems normally incorporate a passive deaerator that is installed as a ‘default’ feature with no real knowledge as to the micro bubble characteristics and their effect on such systems. High saturation ratios are known to occur due to the widespread use of untreated tap water in such systems and due to the inevitable leakage of air into the closed loop circulation system during the daily thermal cycling. The high temperatures at the boiler wall result in super saturation conditions which consequently lead to micro bubble nucleation and detachment, leading to bubbly two phase flow. Experiments have been done on a test rig incorporating a typical 19 kW domestic gas fired boiler to determine the expected saturation ratios and bubble production and dissolution rates in such systems

Variational formulas of higher order mean curvatures

In this paper, we establish the first variational formula and its Euler-Lagrange equation for the total $2p$-th mean curvature functional $\mathcal {M}_{2p}$ of a submanifold $M^n$ in a general Riemannian manifold $N^{n+m}$ for $p=0,1,...,[\frac{n}{2}]$. As an example, we prove that closed complex submanifolds in complex projective spaces are critical points of the functional $\mathcal {M}_{2p}$, called relatively $2p$-minimal submanifolds, for all $p$. At last, we discuss the relations between relatively $2p$-minimal submanifolds and austere submanifolds in real space forms, as well as a special variational problem.Comment: 13 pages, to appear in SCIENCE CHINA Mathematics 201

[Colored solutions of Yang-Baxter equation from representations of U_{q}gl(2)]

We study the Hopf algebra structure and the highest weight representation of a multiparameter version of $U_{q}gl(2)$. The commutation relations as well as other Hopf algebra maps are explicitly given. We show that the multiparameter universal ${\cal R}$ matrix can be constructed directly as a quantum double intertwiner, without using Reshetikhin's transformation. An interesting feature automatically appears in the representation theory: it can be divided into two types, one for generic $q$, the other for $q$ being a root of unity. When applying the representation theory to the multiparameter universal ${\cal R}$ matrix, the so called standard and nonstandard colored solutions $R(\mu,\nu; {\mu}', {\nu}')$ of the Yang-Baxter equation is obtained.Comment: [14]pages, latex, no figure

Black Holes, Entropy Bound and Causality Violation

The gravity/gauge theory duality has provided us a way of studying QCD at short distances from straightforward calculations in classical general relativity. Among numerous results obtained so far, one of the most striking is the universality of the ratio of the shear viscosity to the entropy density. For all gauge theories with Einstein gravity dual, this ratio is \eta/s=1/4\pi. However, in general higher-curvature gravity theories, including two concrete models under discussion - the Gauss-Bonnet gravity and the (Riemann)^2 gravity - the ratio \eta/s can be smaller than 1/4\pi (thus violating the conjecture bound), equal to 1/4\pi or even larger than 1/4\pi. As we probe spacetime at shorter distances, there arises an internal inconsistency in the theory, such as a violation of microcausality, which is correlated with a classical limit on black hole entropy.Comment: 8 pages, no figures; Invited contribution to appear in the Proceedings of the 75 Years since Solvay, Singapore, Nov 2008, (World Scientific, Singapore, 2009