On the reduction of repetitive processes into singular and non-singular Roesser models

Multidimensional Systems and Signal Processing - In this paper we present new methods for the reduction of a polynomial system matrix describing a discrete linear repetitive process, to equivalent...     

Mathematical simulation and experimental verification of melting resulting from the coupled effect of natural convection and exothermic heat of mixing

When melting processes are associated with an exothermic heat of mixing, unique coupled transport phenomena take place. In this article, a mathematical model has been developed to simulate these unique coupled heat and mass transfer events. The model was based on the control-volume finite difference approach and on an enthalpy method. In order to verify the mathematical model, a low-temperature physical model was established consisting of ice and sulfuric acid solutions. In this physical model, both temperature and velocity measurements were carried out. The model predictions were compared with experimental measurements, and they were found to be in good agreement. The model was also applied to a high-temperature system, namely, the melting of silicon metal in liquid high carbon iron. The predictions distinguished two periods present in the entire melting process. In the first period, the silicon was heated up. The second period, i.e., free melting period, occurred in tandem with the exothermic reaction, and consequently, the melting process was greatly accelerated. As was the case with the low-temperature physical model, as with the high-temperature system, good agreement was obtained between the predicted results and the experimental measurements.     

The Solution kinetics of zirconium in liquid steel

Zirconium cylinders were immersed into liquid steel and their mass-transfer rates were measured under static and dynamic conditions. The cylinders were suspended from a load cell, and the apparent weight of the dissolving specimen as well as temperatures at various locations in the samples were measured continuously during immersion and recorded with a data acquisition System. From the weight measurements, the mass-transfer rate was deduced. In the assimilation of zirconium in liquid steel two periods were identified, i.e. the steel shell period and the free dissolution period. Immediately upon immersion the steel shell period Starts and when this period ends the free dissolution period commences. During the steel shell period, a shell of frozen steel wraps around the cylinder following its initial immersion. When zirconium cylinders were immersed into liquid steel, a reaction was detected at the steel shell/zirconium interface. This reaction took place almost immediately after immersion. The intermetallic Compounds Fe₂Zr and FeZr₂ were identified as reaction products. The experimentally measured mass transfer rates during the free dissolution, under quiescent and inductively stirred steel baths, were very similar. Under the experimental conditions used, the rate Controlling step of zirconium dissolution in liquid steel is reaction controlled.     

Evaluating Liquefaction Strength of Partially Saturated Sand

A method is presented for evaluating the liquefaction strength of partially saturated sand using the compression wave velocity (P-wave velocity), a new indicator of saturation. Based on laboratory test results, an empirical correlation that relates the liquefaction strength with the pore pressure coefficient B is firstly proposed. The strength is defined as the cyclic stress ratio required to cause liquefaction at a specified number of cycles. With the aid of a theoretical relation between B and the P-wave velocity, an explicit correlation of more interest is then established between the liquefaction strength of sand and its P-wave velocity. A comparison of the predictions using this explicit correlation with laboratory measurements shows a satisfactory agreement. The significance of this method lies in that it makes it possible to evaluate the liquefaction strength of sand as affected by saturation through the measurement of P-wave velocity, which can be made not only in the laboratory but particularly in the field.     

Representation and uniformization of algebraic transductions

This paper explores different means of representation for algebraic transductions, i.e., word relations realized by pushdown transducers. The relevance of this work lies more in its point of view rather than any particular result. We are aiming at giving specific techniques for obtaining, or perhaps explaining, decompositions of algebraic (and incidentally, rational) relations, relying solely on their “machine” definition rather than some complex algebraic apparatus. From this point of view, we are hoping to have demystified the heavy formalism employed in the present literature. Some of the novelties of our work are: the use of “stack languages” and “embeddings,” which eliminate the need of arbitrary context-free languages in our characterizations, the study of uniformizations for algebraic transductions and the use of the so-called stack transductions for exposing the anatomy of pushdown transducers.This work was supported by the Natural Science and Engineering Research Council of Canada grants R220259 and OGP0041630.     

A STUDY ON THE SEPARATION OF DIFFUSION AND SURFACE EMISSION COEFFICIENTS IN WOOD

For a more accurate simulation of the moisture sorption process in wood, the precise separation of surface emission and diffusion coefficients is essential. In this paper, a non-linear simplex technique that was developed to obtain the optimum pair of the surface emission coefficient he, and the diffusion coefficient D from a single sorption curve is presented and tested with experimental data. An easy to use computer program was employed to carry out the evaluation. Data analysis showed that the new method resulted in a more statistically accurate calculation of b_c and D than currently existing methods.     

Stackelberg Strategies for Selfish Routing in General Multicommodity Networks

A natural generalization of the selfish routing setting arises when some of the users obey a central coordinating authority, while the rest act selfishly. Such behavior can be modeled by dividing the users into an α fraction that are routed according to the central coordinator’s routing strategy (Stackelberg strategy), and the remaining 1−α that determine their strategy selfishly, given the routing of the coordinated users. One seeks to quantify the resulting price of anarchy, i.e., the ratio of the cost of the worst traffic equilibrium to the system optimum, as a function of α. It is well-known that for α=0 and linear latency functions the price of anarchy is at most 4/3 (J. ACM 49, 236–259, 2002). If α tends to 1, the price of anarchy should also tend to 1 for any reasonable algorithm used by the coordinator. We analyze two such algorithms for Stackelberg routing, LLF and SCALE. For general topology networks, multicommodity users, and linear latency functions, we show a price of anarchy bound for SCALE which decreases from 4/3 to 1 as α increases from 0 to 1, and depends only on α. Up to this work, such a tradeoff was known only for the case of two nodes connected with parallel links (SIAM J. Comput. 33, 332–350, 2004), while for general networks it was not clear whether such a result could be achieved, even in the single-commodity case. We show a weaker bound for LLF and also some extensions to general latency functions. The existence of a central coordinator is a rather strong requirement for a network. We show that we can do away with such a coordinator, as long as we are allowed to impose taxes (tolls) on the edges in order to steer the selfish users towards an improved system cost. As long as there is at least a fraction α of users that pay their taxes, we show the existence of taxes that lead to the simulation of SCALE by the tax-payers. The extension of the results mentioned above quantifies the improvement on the system cost as the number of tax-evaders decreases. Research of G. Karakostas supported by an NSERC Discovery Grant and MITACS. Research of S. Kolliopoulos partially supported by the University of Athens under the project Kapodistrias.     

Edge Pricing of Multicommodity Networks for Selfish Users with Elastic Demands

We examine how to induce selfish heterogeneous users in a multicommodity network to reach an equilibrium that minimizes the social cost. In the absence of centralized coordination, we use the classical method of imposing appropriate taxes (tolls) on the edges of the network. We significantly generalize previous work (Yang and Huang in Transp. Res. Part B 38:1–15, [2004]; Karakostas and Kolliopoulos in Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science, pp. 268–276, [2004]; Fleischer et al. in Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science, pp. 277–285, [2004]) by allowing user demands to be elastic. In this setting the demand of a user is not fixed a priori but it is a function of the routing cost experienced, a most natural assumption in traffic and data networks. Research supported by MITACS and a NSERC Discovery grant.