Morse coding for a Fuchsian group of a finite covolume

We consider the Morse coding of the geodesic flow on the hyperbolic plane $H$ with respect to a Dirichlet fundamental domain $D$ of a Fuchsian group $\Gamma$. The main theorem states that the codes of all the generic geodesics constitute a $k$-step topological Markov chain, if and only if the fundamental domain $D$ is an ideal polygon (i.e. has all of its vertices on the absolute).Comment: 11 pages, 4 figure

Premagic and Ideal Flow Matrices

Several interesting properties of a special type of matrix that has a row sum equal to the column sum are shown with the proofs. Premagic matrix can be applied to strongly connected directed network graph due to its nodes conservation flow. Relationships between Markov Chain, ideal flow and random walk on directed graph are also discussed

Cross-layer Congestion Control, Routing and Scheduling Design in Ad Hoc Wireless Networks

This paper considers jointly optimal design of crosslayer congestion control, routing and scheduling for ad hoc wireless networks. We first formulate the rate constraint and scheduling constraint using multicommodity flow variables, and formulate resource allocation in networks with fixed wireless channels (or single-rate wireless devices that can mask channel variations) as a utility maximization problem with these constraints. By dual decomposition, the resource allocation problem naturally decomposes into three subproblems: congestion control, routing and scheduling that interact through congestion price. The global convergence property of this algorithm is proved. We next extend the dual algorithm to handle networks with timevarying channels and adaptive multi-rate devices. The stability of the resulting system is established, and its performance is characterized with respect to an ideal reference system which has the best feasible rate region at link layer. We then generalize the aforementioned results to a general model of queueing network served by a set of interdependent parallel servers with time-varying service capabilities, which models many design problems in communication networks. We show that for a general convex optimization problem where a subset of variables lie in a polytope and the rest in a convex set, the dual-based algorithm remains stable and optimal when the constraint set is modulated by an irreducible finite-state Markov chain. This paper thus presents a step toward a systematic way to carry out cross-layer design in the framework of “layering as optimization decomposition” for time-varying channel models

Transitory powder flow dynamics during emptying of a continuous mixer

This article investigates the emptying process of a continuous powder mixer, from both experimental and modelling points of view. The apparatus used in this work is a pilot scale commercial mixer Gericke GCM500, for which a specific experimental protocol has been developed to determine the hold up in the mixer and the real outflow. We demonstrate that the dynamics of the process is governed by the rotational speed of the stirrer, as it fixes characteristic values of the hold-up weight, such as a threshold hold-up weight. This is integrated into a Markov chain matrix representation that can predict the evolution of the hold-up weight, as well as that of the outflow rate during emptying the mixer. Depending on the advancement of the process, the Markov chain must be considered as non-homogeneous. The comparison of model results with experimental data not used in the estimation procedure of the parameters contributes to validating the viability of this model. In particular, we report results obtained when emptying the mixer at variable rotational speed, through step changes