An integrated approach to global synchronization and state estimation for nonlinear singularly perturbed complex networks

This paper aims to establish a unified framework to handle both the exponential synchronization and state estimation problems for a class of nonlinear singularly perturbed complex networks (SPCNs). Each node in the SPCN comprises both 'slow' and 'fast' dynamics that reflects the singular perturbation behavior. General sector-like nonlinear function is employed to describe the nonlinearities existing in the network. All nodes in the SPCN have the same structures and properties. By utilizing a novel Lyapunov functional and the Kronecker product, it is shown that the addressed SPCN is synchronized if certain matrix inequalities are feasible. The state estimation problem is then studied for the same complex network, where the purpose is to design a state estimator to estimate the network states through available output measurements such that dynamics (both slow and fast) of the estimation error is guaranteed to be globally asymptotically stable. Again, a matrix inequality approach is developed for the state estimation problem. Two numerical examples are presented to verify the effectiveness and merits of the proposed synchronization scheme and state estimation formulation. It is worth mentioning that our main results are still valid even if the slow subsystems within the network are unstable

Sudden stoppage of rotor in a thermally driven rotary motor made from double-walled carbon nanotubes

In a thermally driven rotary motor made from double-walled carbon nanotubes, the rotor (inner tube) can be actuated to rotate within the stator (outer tube) when the environmental temperature is high enough. A sudden stoppage of the rotor can occur when the inner tube has been actuated to rotate at a stable high speed. To find the mechanisms of such sudden stoppages, eight motor models with the same rotor but different stators are built and simulated in the canonical NVT ensembles. Numerical results demonstrate that the sudden stoppage of the rotor occurs when the difference between radii is near 0.34 nm at a high environmental temperature. A smaller difference between radii does not imply easier activation of the sudden rotor stoppage. During rotation, the positions and electron density distribution of atoms at the ends of the motor show that a sp(1) bonded atom on the rotor is attracted by the sp(1) atom with the biggest deviation of radial position on the stator, after which they become two sp(2) atoms. The strong bond interaction between the two atoms leads to the loss of rotational speed of the rotor within 1 ps. Hence, the sudden stoppage is attributed to two factors: the deviation of radial position of atoms at the stator's ends and the drastic thermal vibration of atoms on the rotor in rotation. For a stable motor, sudden stoppage could be avoided by reducing deviation of the radial position of atoms at the stator's ends. A nanobrake can be, thus, achieved by adjusting a sp(1) atom at the ends of stator to stop the rotation of rotor quickly.The authors are grateful for financial support from the National Natural-Science-Foundation of China (Grant Nos. 50908190, 11372100)

Non-existence of New Quantum Ergosphere Effect of a Vaidya-type Black Hole

Hawking evaporation of Dirac particles and scalar fields in a Vaidya-type black hole is investigated by the method of generalized tortoise coordinate transformation. It is shown that Hawking radiation of Dirac particles does not exist for $P_1, Q_2$ components but for $P_2, Q_1$ components in any Vaidya-type black holes. Both the location and the temperature of the event horizon change with time. The thermal radiation spectrum of Dirac particles is the same as that of Klein-Gordon particles. We demonstrates that there is no new quantum ergosphere effect in the thermal radiation of Dirac particles in any spherically symmetry black holes.Comment: Latex, 9 pages, no figure, submitted to Mod. Phys. Lett.

Pressure-induced transition in magnetoresistance of single-walled carbon nanotubes

Journal ArticleWe applied hydrostatic pressure (up to 10 GPa) to single-walled carbon nanotube bundles at low temperature (down to 2 K) to measure their magnetoresistance (MR) in a field up to 12 T. We found a pressure-induced transition in MR from positive to negative in the high-field regime. The onset of the transition occurs at ~1:5 GPa, which correlates closely with the tube shape transitions. The characteristics of the high-pressure MR are consistent with a model of pressure-induced two-dimensional weak localization

Elliptic flow of ϕ\phi meson and strange quark collectivity at RHIC

Based on A Multi-Phase Transport (AMPT) model, we have studied the elliptic flow $v_{2}$ of $\phi$ mesons from reconstructed $K^{+}K^{-}$ decay channel at the top Relativistic Heavy Ion Collider energy at Brookhaven National Laboratory. The dependences of $v_{2}$ on transverse momentum $p_T$ and collision centrality are presented and the rescattering effect of $\phi$ mesons in the hadronic phase is also investigated. The results show that experimental measurement of $v_{2}$ for $\phi$ mesons can retain the early collision information before $\phi$ decays and that the $\phi$ $v_2$ value obeys the constituent quark number scaling which has been observed for other mesons and baryons. Our study indicates that the $\phi$ $v_2$ mostly reflects partonic level collectivity developed during the early stage of the nucleus-nucleus collision and the strange and light up/down quarks have developed similar angular anistropy properties at the hadronization.Comment: 5 pages and 5 figures; accepted by Physical Review

Parton Distributions at Hadronization from Bulk Dense Matter Produced at RHIC

We present an analysis of $\Omega$, $\Xi$, $\Lambda$ and $\phi$ spectra from Au+Au collisions at $\sqrt{s_{NN}}=200$ GeV in terms of distributions of effective constituent quarks at hadronization. Consistency in quark ratios derived from various hadron spectra provides clear evidence for hadron formation dynamics as suggested by quark coalescence or recombination models. We argue that the constituent quark distribution reflects properties of the effective partonic degrees of freedom at hadronization. Experimental data indicate that strange quarks have a transverse momentum distribution flatter than that of up/down quarks consistent with hydrodynamic expansion in partonic phase prior to hadronization. After the AMPT model is tuned to reproduce the strange and up/down quark distributions, the model can describe the measured spectra of hyperons and $\phi$ mesons very well where hadrons are formed through dynamical coalescence.Comment: 5 pages, 3 figures, two more paragraph added to address the referee's comment, figure updated to include the KET scale. Accepted version to appear in Phys. Rev.

A Tight Karp-Lipton Collapse Result in Bounded Arithmetic

Cook and Krajíček [9] have obtained the following Karp-Lipton result in bounded arithmetic: if the theory proves , then collapses to , and this collapse is provable in . Here we show the converse implication, thus answering an open question from [9]. We obtain this result by formalizing in a hard/easy argument of Buhrman, Chang, and Fortnow [3]. In addition, we continue the investigation of propositional proof systems using advice, initiated by Cook and Krajíček [9]. In particular, we obtain several optimal and even p-optimal proof systems using advice. We further show that these p-optimal systems are equivalent to natural extensions of Frege systems