Global controllability between steady supercritical flows in channel networks

We consider a tree‐like network of open channels with outflow at the root. Controls are exerted at the boundary nodes of the network except for the root. In each channel, the flow is modelled by the de St. Venant equations. The node conditions require the conservation of mass and the conservation of energy. We show that the states of the system can be controlled within the entire network in finite time from a stationary supercritical initial state to a given supercritical terminal state with the same orientation. During this transition, the states stay in the class of C1‐functions, so no shocks occur. Copyright 2004 John Wiley & Sons, Ltd.     

Axial resonances in the open and hidden charm sectors

A SU(4) flavor symmetrical Lagrangian is constructed for the interaction of the pseudo-scalar mesons with the vector mesons. SU(4) symmetry is broken to SU(3) by suppression of terms in the Lagrangian where the interaction should be driven by charmed mesons. Chiral symmetry can be restored by setting this new SU(4) symmetry-breaking parameters to zero. Unitarization in coupled channels leads to the dynamical generation of resonances. Many known axial resonances can be identified including the new controversial X(3872) and the structure found recently by Belle around 3875MeV in the hidden charm sector. Also new resonances are predicted, some of them with exotic quantum numbers.     

Cross-ladder effects in Bethe-Salpeter and light-front equations

The Bethe-Salpeter (BS) equation in Minkowski space for scalar particles is solved for a kernel given by a sum of ladder and cross-ladder exchanges. The solution of corresponding light-front (LF) equation, where we add the time-ordered stretched boxes, is also obtained. Cross-ladder contributions are found to be very large and attractive, whereas the influence of stretched boxes is negligible. Both approaches --BS and LF-- give very close results.     

Linearly implicit time stepping methods for numerical weather prediction

The efficient time integration of the dynamic core equations for numerical weather prediction (NWP) remains a key challenge. One of the most popular methods is currently provided by implementations of the semi-implicit semi-Lagrangian (SISL) method, originally proposed by Robert (J. Meteorol. Soc. Jpn., 1982). Practical implementations of the SISL method are, however, not without certain shortcomings with regard to accuracy, conservation properties and stability. Based on recent work by Gottwald, Frank and Reich (LNCSE, Springer, 2002), Frank, Reich, Staniforth, White and Wood (Atm. Sci. Lett., 2005) and Wood, Staniforth and Reich (Atm. Sci. Lett., 2006) we propose an alternative semi-Lagrangian implementation based on a set of regularized equations and the popular Störmer–Verlet time stepping method in the context of the shallow-water equations (SWEs). Ultimately, the goal is to develop practical implementations for the 3D Euler equations that overcome some or all shortcomings of current SISL implementations.     

Metastability of solitary roll wave solutions of the St. Venant equations with viscosity

We study by a combination of numerical and analytical Evans function techniques, the stability of solitary wave solutions of the St. Venant equations for viscous shallow water flow down an incline, and related models. Our main result is to exhibit examples of metastable solitary waves for the St. Venant equations, with stable point spectrum indicating coherence of the wave profile but unstable essential spectrum indicating oscillatory convective instabilities shed in its wake. We propose a mechanism based on “dynamic spectrum” of the wave profile, by which a wave train of solitary pulses can stabilize each other by de-amplification of convective instabilities as they pass through successive waves. We present numerical time evolution studies supporting these conclusions, which bear also on the possibility of stable periodic solutions close to the homoclinic. For the closely related viscous Jin-Xin model, by contrast, for which the essential spectrum is stable, we show using the stability index of Gardner-Zumbrun that solitary wave pulses are always exponentially unstable, possessing point spectra with positive real part.     

Strong approximation and a central limit theorem for St. Petersburg sums

The St. Petersburg paradox (Bernoulli, 1738) concerns the fair entry fee in a game where the winnings are distributed as $P(X=2^k)=2^{?k},k=1,2,\dots$. The tails of $X$ are not regularly varying and the sequence $S_n$ of accumulated gains has, suitably centered and normalized, a class of semistable laws as subsequential limit distributions (Martin-Löf, 1985; Csörg? and Dodunekova, 1991). This has led to a clarification of the paradox and an interesting and unusual asymptotic theory in past decades. In this paper we prove that $S_n$ can be approximated by a semistable Lévy process $\{L\left(n\right),n\ge 1\}$ with a.s. error $O\left(\sqrt{n}{(logn)}^{1+\epsilon }\right)$ and, surprisingly, the error term is asymptotically normal, exhibiting an unexpected central limit theorem in St. Petersburg theory.     

单分散二氧化硅微球的制备及表面化学修饰

采用St(o)ber法在醇-水混合体系中,以正硅酸乙酯(TEOS)作为硅源,在氨水催化作用下制备SiO2纳米微球,分析了不同浓度的氨水、TEOS、乙醇和温度对SiO2微球形貌及粒径的影响,并利用透射电镜对其形貌和粒径进行表征.最后引入具有疏水基团的十六烷基三甲氧基硅烷对SiO2微球表面进行修饰,并采用FT-IR和测量接触角对修饰的SiO2微球进行分析.结果表明:SiO2微球粒径随氨水浓度的增加而增大;随TEOS、乙醇浓度和温度的升高先增大后减小;并通过FT-IR和测量接触角证明疏水基团成功接枝到SiO2微球表面.     

Electromagnetic form factor via Bethe-Salpeter amplitude in Minkowski space

For a relativistic system of two scalar particles, we find the Bethe-Salpeter amplitude in Minkowski space and use it to compute the electromagnetic form factor. The comparison with Euclidean space calculation shows that the Wick rotation in the form factor integral induces errors which increase with the momentum transfer Q². At JLab domain (Q ² = 10 GeV^2/c²), they are about 30%. Static approximation results in an additional and more significant error. On the contrary, the form factor calculated in light-front dynamics is almost indistinguishable from the Minkowski space one.     

微孔羟基磷灰石/聚(甲基丙烯酸甲酯-苯乙烯)复合微球的制备及其吸附性能

以微孔纳米羟基磷灰石(HAP)为无机载体,甲基丙烯酸甲酯(MMA)和苯乙烯(St)为聚合单体,采用悬浮聚合法制备了HAP/P(MMA-St)复合微球。研究了影响球体粒度及其分布的主要因素和微球的吸附性能。结果表明,表面活性剂用量(质量分数,下同)为1‰,MMA用量为2%,HAP用量为30%,转速为300r/min时复合微球的合格球收率最高,为86.4%。当微球中HAP的质量分数为36.07%时,HAP/P(MMA-St)微球对牛血清蛋白的最大吸附量Qe=18.70mg/g,比未加HAP时,增加了4.65mg/g。