Lyapunov exponent, universality and phase transition for products of random matrices

Products of $M$ i.i.d. random matrices of size $N \times N$ are related to classical limit theorems in probability theory ($N=1$ and large $M$), to Lyapunov exponents in dynamical systems (finite $N$ and large $M$), and to universality in random matrix theory (finite $M$ and large $N$). Under the two different limits of $M \to \infty$ and $N \to \infty$, the local singular value statistics display Gaussian and random matrix theory universality, respectively. However, it is unclear what happens if both $M$ and $N$ go to infinity. This problem, proposed by Akemann, Burda, Kieburg \cite{Akemann-Burda-Kieburg14} and Deift \cite{Deift17}, lies at the heart of understanding both kinds of universal limits. In the case of complex Gaussian random matrices, we prove that there exists a crossover phenomenon as the relative ratio of $M$ and $N$ changes from $0$ to $\infty$: sine and Airy kernels from the Gaussian Unitary Ensemble (GUE) when $M/N \to 0$, Gaussian fluctuation when $M/N \to \infty$, and new critical phenomena when $M/N \to \gamma \in (0,\infty)$. Accordingly, we further prove that the largest singular value undergoes a phase transition between the Gaussian and GUE Tracy-Widom distributions.Comment: Therems 1.1 stated in a more intuitive way; proofs extensively revised; convergence in trace norm for the critical and subcritical cases added; 35 pages, 3 figure

Geometry of quantum evolution in a nonequilibrium environment

We theoretically study the geometric effect of quantum dynamical evolution in the presence of a nonequilibrium noisy environment. We derive the expression of the time dependent geometric phase in terms of the dynamical evolution and the overlap between the time evolved state and initial state. It is shown that the frequency shift induced by the environmental nonequilibrium feature plays a crucial role in the geometric phase and evolution path of the quantum dynamics. The nonequilibrium feature of the environment makes the length of evolution path becomes longer and reduces the dynamical decoherence and non-Markovian behavior in the quantum dynamics

Design Strategy of Community Greenway Connectivity of High-density Urban Asia – A Case Study on Beijing

In the high-density Asian cities which expand rapidly and witness explosive growth in population, the construction of urban community greenways can effectively mitigate the heavy pressure that human beings impose on natural and humanistic environment. In Beijing, poor connectivity is one of the major challenges community greenway construction faces. This paper performs a field survey on the established community greenways in Beijing and their surrounding communities, finding that greenway connectivity is affected by the problems like interference with motorways and unsound greenway planning system in development process. The survey analysis demonstrates that the poor connectivity of community greenways is embodied between greenway, community and surrounding service facilities. To address the problems above, a detailed study on the strategies that improve connectivity of community greenways is conducted

Probing the topcolor-assisted technicolor model via the single t-quark production at Hadron colliders

In this paper, we systematically study the contribution of the TC2 model to the single t-quark production at the Hadron colliders, specially at the LHC. The TC2 model can contribute to the cross section of the single t-quark production in two different ways. First, the existence of the top-pions and top-higgs can modify the $Wtb$ coupling via their loop contributions, and such modification can cause the correction to the cross sections of all three production modes. Our study shows that this kind of correction is negative and very small in all cases. Thus it is difficult to observe such correction even at the LHC. On the other hand, there exist the tree-level FC couplings in the TC2 model which can also contribute to the cross sections of the $tq$ and $t\bar{b}$ production processes. The resonant effect can greatly enhance the cross sections of the $tq$ and $t\bar{b}$ productions. The first evidence of the single t-quark production has been reported by the $D0$ collaboration and the measured cross section for the single t-quark production of $\sigma(p\bar{p}\to tb+X,tqb+X)$ is compatible at the 10% level with the standard model prediction. Because the light top-pion can make great contribution to the $t\bar{b}$ production, the top-pion mass should be very large in order to make the predicted cross section in the TC2 model be consistent with the Tevatron experiments. More detailed information about the top-pion mass and the FC couplings in the TC2 model should be obtained with the running of the LHC.Comment: 30 pages, 3 tables, 10 figure

Supercritical Water Oxidation for Environmentally Friendly Treatment of Organic Wastes

Supercritical water oxidation is a promising, environment-friendly technology to efficiently deal with a wide variety of organic wastes such as wastewaters, industrial and municipal sludge, etc. As for the two key problems, i.e., corrosion and salt plugging, generally encountered in supercritical water oxidation plants, this chapter firstly reported the related mechanism analysis, solutions, research status, and development trends, respectively. From the perspectives of corrosion prevention and control, safety and automatic control, economic improvements, and development of novel reactors, a number of advanced technologies and equipment such as on-line desalination in supercritical water, new operation scheme assisted secondary traditional treatment, produced-gas recovery and oxygen reuse and novel TWM reactor, etc., were introduced systematically. Finally, this chapter summarizes the implementation status of industrial plants and the technological features of several firms being active in the construction of full-scale supercritical water oxidation plants. This chapter will provide very valuable information for the researchers and engineers who are interested in supercritical water oxidation for the harmless treatment of organic pollutants

The Wetting of Leaf Surfaces and Its Ecological Significances

Leaf wettability, indicating the affinity for water on leaf surfaces, is a common phenomenon for plants in a wide variety of habitats. The contact angle (θ) of water on leaves measured at the gas, solid and liquid interface is an index of surface wettability. Leaves are termed as “super-hydrophilic” if θ 110°, the leaves are classified as being non-wettable, while θ > 130° for highly non-wettable and θ > 150° for super-hydrophobic. Both internal and external factors can influence leaf wettability. The chemical composition and structure of leaf surfaces are internal causes, but the external environment can also influence wettability by affecting the structure and composition of the surface. The main internal factors that affecting leaf wettability include the content and microstructure of the epidermal wax, the number, size and pattern of trichomes, stomatal density, the shape of epidermal cells, and leaf water status. The leaf contact angles increased with the increasing of leaf wax content. However, studies have shown that the contact angles were more dependent on the complexity of wax structure than on the absolute amount. For trichomes, there are three types of interaction between trichomes and water droplets, including (1) low trichomes density: no apparent influence of trichomes on the location of surface moisture, droplet formation and retention ; (2) medium trichomes density: trichomes appear to circle surface moisture into patches; (3) high trichomes density: trichomes appear to hold water droplets above the trichomes. In some cases, a higher stomatal density was accompanied with a higher contact angles. While, it was also observed that there was no significant correlation between contact angle and stomatal density for some species. For the effects of epidermal cells on leaf wettability, it was generally considered that the combination of a dense layer of surface wax and the convex epidermal cells was what created a hydrophobic leaf surface. However, the influence of leaf water content on contact angle of water droplets on different leaf surfaces was complex, e.g., contact angles increased with decreasing of leaf water content, contact angle remained to be constant with different leaf water content

Universality for products of random matrices I: Ginibre and truncated unitary cases

Recently, the joint probability density functions of complex eigenvalues for products of independent complex Ginibre matrices have been explicitly derived as determinantal point processes. We express truncated series coming from the correlation kernels as multivariate integrals with singularity and investigate saddle point method for such a type of integrals. As an application, we prove that the eigenvalue correlation functions have the same scaling limits as those of the single complex Ginibre ensemble, both in the bulk and at the edge of the spectrum. We also prove that the similar results hold true for products of independent truncated unitary matrices.Comment: 41 pages; revised upon the suggestions of the anonymous referees; to appear in International Mathematics Research Notices. in IMRN 201

System Reliability Evaluation Based on Convex Combination Considering Operation and Maintenance Strategy

The approaches to the system reliability evaluation with respect to the cases, where the components are independent or the components have interactive relationships within the system, were proposed in this paper. Starting from the higher requirements on system operational safety and economy, the reliability focused optimal models of multiobjective maintenance strategies were built. For safety-critical systems, the pessimistic maintenance strategies are usually taken, and, in these cases, the system reliability evaluation has also to be tackled pessimistically. For safety-uncritical systems, the optimistic maintenance strategies were usually taken, and, in these circumstances, the system reliability evaluation had also to be tackled optimistically, respectively. Besides, the reasonable maintenance strategies and their corresponding reliability evaluation can be obtained through the convex combination of the above two cases. With a high-speed train system as the example background, the proposed method is verified by combining the actual failure data with the maintenance data. Results demonstrate that the proposed study can provide a new system reliability calculation method and solution to select and optimize the multiobjective operational strategies with the considerations of system safety and economical requirements. The theoretical basis is also provided for scientifically estimating the reliability of a high-speed train system and formulating reasonable maintenance strategies