Metastability of finite state Markov chains: a recursive procedure to identify slow variables for model reduction

Consider a sequence $(\eta^N(t) :t\ge 0)$ of continuous-time, irreducible Markov chains evolving on a fixed finite set $E$, indexed by a parameter $N$. Denote by $R_N(\eta,\xi)$ the jump rates of the Markov chain $\eta^N_t$, and assume that for any pair of bonds $(\eta,\xi)$, $(\eta',\xi')$ $\arctan \{R_N(\eta,\xi)/R_N(\eta',\xi')\}$ converges as $N\uparrow\infty$. Under a hypothesis slightly more restrictive (cf. \eqref{mhyp} below), we present a recursive procedure which provides a sequence of increasing time-scales \theta^1_N, \dots, \theta^{\mf p}_N, $\theta^j_N \ll \theta^{j+1}_N$, and of coarsening partitions \{\ms E^j_1, \dots, \ms E^j_{\mf n_j}, \Delta^j\}, 1\le j\le \mf p, of the set $E$. Let \phi_j: E \to \{0,1, \dots, \mf n_j\} be the projection defined by \phi_j(\eta) = \sum_{x=1}^{\mf n_j} x \, \mb 1\{\eta \in \ms E^j_x\}. For each 1\le j\le \mf p, we prove that the hidden Markov chain $X^j_N(t) = \phi_j(\eta^N(t\theta^j_N))$ converges to a Markov chain on \{1, \dots, \mf n_j\}

Stationary states of boundary driven exclusion processes with nonreversible boundary dynamics

We prove a law of large numbers for the empirical density of one-dimensional, boundary driven, symmetric exclusion processes with different types of non-reversible dynamics at the boundary. The proofs rely on duality techniques

Electrospinning of poly(ethylene-co-vinyl alcohol) nanofibres encapsulated with Ag nanoparticles for skin wound healing

Copyright © 2011 Chao Xu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.Skin wound healing is an urgent problem in clinics and military activities. Although significant advances have been made in its treatment, there are several challenges associated with traditional methods, for example, limited donor skin tissue for transplantation and inflammation during long-term healing time. To address these challenges, in this study we present a method to fabricate Poly(ethylene-co-vinyl alcohol) (EVOH) nanofibres encapsulated with Ag nanoparticle using electrospinning technique. The fibres were fabricated with controlled diameters (59nm-3m) by regulating three main parameters, that is, EVOH solution concentration, the electric voltage, and the distance between the injection needle tip (high-voltage point) and the fibre collector. Ag was added to the nanofibres to offer long-term anti-inflammation effect by slow release of Ag nanoparticles through gradual degradation of EVOH nanofibre. The method developed here could lead to new dressing materials for treatment of skin wounds. © 2011 Chao Xu et al.The work was partially supported by the National Natural Science Foundation of China (nos. 10825210, 10872157, and 31050110125) and the National 111 Project of China (no. B06024)

Reliability-based optimal design of water distribution networks

A considerable amount of research has been carried out on the reliability analysis and optimal design of water distribution systems, and it has been reported that each of the above problems is very difficult to solve (Eiger et al. 1994; Wagner et al. 1988). The authors are therefore to be commended for their work, which directly incorporated a sophisticated probabilistic reliability model into an optimization routine. The paper had other interesting and useful aspects, which, unfortunately, will not be elaborated upon here

Dynamically encircling exceptional points: in situ control of encircling loops and the role of the starting point

The most intriguing properties of non-Hermitian systems are found near the exceptional points (EPs) at which the Hamiltonian matrix becomes defective. Due to the complex topological structure of the energy Riemann surfaces close to an EP and the breakdown of the adiabatic theorem due to non-Hermiticity, the state evolution in non-Hermitian systems is much more complex than that in Hermitian systems. For example, recent experimental work [Doppler et al. Nature 537, 76 (2016)] demonstrated that dynamically encircling an EP can lead to chiral behaviors, i.e., encircling an EP in different directions results in different output states. Here, we propose a coupled ferromagnetic waveguide system that carries two EPs and design an experimental setup in which the trajectory of state evolution can be controlled in situ using a tunable external field, allowing us to dynamically encircle zero, one or even two EPs experimentally. The tunability allows us to control the trajectory of encircling in the parameter space, including the size of the encircling loop and the starting/end point. We discovered that whether or not the dynamics is chiral actually depends on the starting point of the loop. In particular, dynamically encircling an EP with a starting point in the parity-time-broken phase results in non-chiral behaviors such that the output state is the same no matter which direction the encircling takes. The proposed system is a useful platform to explore the topology of energy surfaces and the dynamics of state evolution in non-Hermitian systems and will likely find applications in mode switching controlled with external parameters.Comment: 15 pages, 11 figure