On Secular Resonances of Small Bodies in the Planetary Systems

We investigate the secular resonances for massless small bodies and Earth-like planets in several planetary systems. We further compare the results with those of Solar System. For example, in the GJ 876 planetary system, we show that the secular resonances $\nu_1$ and $\nu_2$ (respectively, resulting from the inner and outer giant planets) can excite the eccentricities of the Earth-like planets with orbits 0.21 AU $\leq a <$ 0.50 AU and eject them out of the system in a short timescale. However, in a dynamical sense, the potential zones for the existence of Earth-like planets are in the area 0.50 AU $\leq a \leq$ 1.00 AU, and there exist all stable orbits last up to $10^5$ yr with low eccentricities. For other systems, e.g., 47 UMa, we also show that the Habitable Zones for Earth-like planets are related to both secular resonances and mean motion resonances in the systems.Comment: 8 pages, 3 figures, accepted to IAU236. Proceeding of IAU 236: Near Earth Objects, Our Celestial Neighbors: Opportunity and Risk, in pres

CFD modelling of double-skin facades with venetian blinds

This paper describes CFD modelling of Double Skin Façades (DSF) with venetian blinds inside the façade cavity. The 2-D modelling work investigates the coupled convective, conductive and radiative heat transfer through the DSF system. The angles of the venetian blind can be adjusted and a series of angles (0, 30, 45, 60 and 80 degrees) has been modelled. The modelling results are compared with the measurements from a section of façade tested within a solar simulator and with predictions from a component based nodal model. Agreement between the three methods is generally good. Discrepancies in the results are generally caused by the simplification of the CFD model resulting less turbulence mixing within the façade cavity. The CFD simulation output suggests that the presence of the venetian blinds has led up to 35 percent enhancement in natural ventilation flow for the façade cavity and 75 percent reduction in heat loads for the internal environment. It was also found that little changes of the convective heat transfer coefficients on the glazing surfaces have been caused by the venetian blinds with different angles

Higher Fock State Contributions to the Generalized Parton Distribution of Pion

We discuss the higher Fock state (q \bar q g) contributions to the nonzero value of the pion GPD at the crossover point x = zeta between the DGLAP and ERBL regions. Using the phenomenological light-front constituent quark model, we confirm that the higher Fock state contributions indeed give a nonzero value of the GPD at the crossover point. Iterating the light-front quark model wave function of the lowest q \bar q Fock state with the Bethe-Salpeter kernel corresponding to the one-gluon-exchange, we include all possible time-ordered q \bar q g Fock state contributions and obtain the pion GPD satisfying necessary sum rules and continuity conditions.Comment: References adde

Power Set of Some Quasinilpotent Weighted shifts on lpl^p

For a quasinilpotent operator $T$ on a Banach space $X$, Douglas and Yang defined $k_x=\limsup\limits_{z\rightarrow 0}\frac{\ln\|(z-T)^{-1}x\|}{\ln\|(z-T)^{-1}\|}$ for each nonzero vector $x\in X$, and call $\Lambda(T)=\{k_x: x\ne 0\}$ the power set of $T$. $\Lambda(T)$ have a close link with $T$'s lattice of hyperinvariant subspaces. This paper computes the power set of quasinilpotent weighted shifts on $l^p$ for $1\leq p< \infty$. We obtain the following results: (1) If $T$ is an injective quasinilpotent forward unilateral weighted shift on $l^p(\mathbb{N})$, then $\Lambda(T)=\{1\}$ when $k_{e_0}=1$, where $\{e_n\}_{n=0}^{\infty}$ be the canonical basis for $l^p(\mathbb{N})$; (2) There is a class of backward unilateral weighted shifts on $l^p(\mathbb{N})$ whose power set is $[0,1]$; (3) There exists a bilateral weighted shift on $l^p(\mathbb{Z})$ with power set $[\frac{1}{2},1]$ for $1<p<\infty$.Comment: 22 page