No description available.

Many of the phenomena studied in the natural and social sciences are governed by processes which are discrete and nonlinear in nature, while the most highly developed and commonly used mathematical models are linear and continuous. There are significant differences between the discrete and the continuous, the nonlinear and the linear cases, and the development of mathematical models which exhibit the discrete, nonlinear properties occurring in nature and society is critical to future scientific progress. This thesis presents the basic theory of discrete dynamical systems and stability analysis and explores several applications of this theory to nonlinear systems which model interactions involving economic agents and biological populations. In particular we will explore the stability properties of equilibria associated with inter-species and intergenerational population dynamics in biology and market price and agent composition dynamics in economics.

Ulaanbaatar city is the capital city of Mongolia. Presently more than 50 percent of the Mongolian population lives in Ulaanbaatar city, which comprises of 3% of the country’s land area. Water supply for Ulaanbaatar City is supplied solely from groundwater, which is a limited resource that exhibits slow replenishment. It has been recognized that the increasing water demand will eventually exceed the capacity of the known groundwater resources. Therefore, discovering and developing additional water sources or developing creative alternatives is an important challenge for the city. This challenge is especially critical given the anticipated impacts of climate change. Reuse of wastewater has been proposed as an alternative to reduce the overall water supply demand for the city. The first water reuse regulations in Mongolia were passed in 2018, so the institutional setting on water reuse considered to be very open. The goal of this project was to develop a systems approach to characterize the wastewater reuse and provide a basis for evaluating design alternatives that will reduce the use of groundwater resources. A system dynamics model was developed based on the Vensim modeling software to characterize the water use and wastewater budget for the City of Ulaanbaatar. This approach considered the potential role of wastewater reuse as an approach for maintaining a sustainable water supply. Water supply and wastewater generation were estimated for domestic and industrial use. The focus was on industrial reuse with consideration to the current economic and institutional settings of Mongolia. The model took into account the water requirements for various industries (including tannery, wool, food and beverage, soft beverage and alcohol, paper production and car wash, and thermal power). Two different models were generated to compare the systematic change when reuse is incorporated into the system, and linear growth was considered to provide the most appropriate predictions for future changes in water demand. The analysis and model results showed reuse options were likely limited for domestic supplies, but industrial reuse could provide a 4% reduction in total water demand and significant reductions in water use by power generation facilities.

Residual moisture from incompletely dried aggregates would most likely remain in the Warm Mix Asphalt (WMA) due to its lower production and compaction temperature, resulting in harmful effects on field performance. Dynamic modulus has been recognized as a parameter that reflects the overall behavior of asphalt mixtures and possesses promising correlations with field performance. This study aims to investigate the effects of moisture susceptibility of WMA on dynamic modulus and simulate the field performance with the aid of Mechanistic-Empirical Pavement Design Guide (MEPDG) software. Four distinct sets of WMA specimens were prepared as follows: 1. fully dried aggregates without moisture conditioning; 2. fully dried aggregates with moisture conditioning; 3. incompletely dried aggregates without moisture conditioning; and 4. incompletely dried aggregates with moisture conditioning. Simple Performance Test (SPT) was employed to collect the raw data of dynamic modulus tests and master curves were constructed from the reduced data using Hirsch model. The results show that moisture can negatively influence the dynamic modulus values and moisture conditioning had more effect than residual moisture from incompletely dried aggregates. Two types of distress, fatigue cracking and rutting, were analyzed in the simulation. Moisture can significantly decrease the resistance against rutting and to a lesser extent, the resistance against fatigue cracking.

L’intérêt pour la modélisation et la commande des engins volants s’est accru de manière significative au cours de ces dernières années. La complexité et les possibilités des engins volants s’accroissent rapidement et la gamme des missions qu’elles doivent réaliser se développe. Cependant afin que les drones puissent atteindre ce potentiel, certains défis techniques doivent être surmontés, notamment l’étude et l’intégration de la flexibilité structurelle, la prise en compte des phénomènes aérodynamiques, et l’élaboration de stratégies de commandes adaptées. Le travail présenté s’inscrit dans ce cadre et porte spécifiquement sur deux types de drones : -Les plus légers que l’air : Application à la modélisation et commande d’un dirigeable souple. -Les plus lourds que l’air : Application à la modélisation et commande d’un quadrirotor flexible : le XSF. Nous présentons dans un premier temps un modèle global d’engins volants flexibles autonomes. On admet que ces objets volants subissent de grands déplacements et de petites déformations élastiques. Le formalisme utilisé est basé sur l’approche de Newton-Euler, approche souvent utilisée dans le cas d’objets volants rigides. Dans cette étude nous généralisons le formalisme de corps rigides existant en y incluant l’effet de la flexibilité, sans pour autant détruire la méthodologie globale, et ce au moyen d’une technique hybride lagrangienne-eulerienne. La flexibilité apparaît dans le système dynamique global par le moyen d’un nombre réduit de degrés de liberté supplémentaires issus d’une synthèse modale. Cette technique permet de faciliter par la suite l’élaboration d’algorithmes de commande et de stabilisation. Le phénomène des masses ajoutées est également pris en considération. Une méthode originale de traitement analytique de ce phénomène a été établie pour un corps flexible en grands mouvements. Elle est basée sur la notion de potentiel flexible, et sur le développement de l’énergie cinétique du fluide sous l’effet d’un mouvement global du corps flexible. Cette méthode a permis de mettre en évidence le couplage rigide-flexible dans la matrice des masses ajoutées pour un traitement global d’un dirigeable flexible. On présente aussi le modèle dynamique et aérodynamique du quadrirotor flexible XSF conçu au laboratoire IBISC et destiné à un concours interuniversitaire sur les microdrones. Une technique robuste " Backstepping " est réalisée pour la stabilisation du dirigeable flexible au voisinage d’un point cible. Et une stratégie de contrôle de PID a été proposée pour la stabilisation de l’XSF. La stratégie de commande est contrainte par l’impératif d’optimisation du rapport précision/portabilité, pour que les algorithmes développés puissent être intégrés dans l’informatique embarquée de ces engins volants. Une validation numérique est présentée à la fin du rapport. / The interest of dynamic modeling and control of the autonomous flying objects increased significantly during these last years. Complexity and capability of these flying objects are expanding rapidly now, and the range of missions their designed to support is growing. In order to fulfil this requirement, it is necessary, in one hand, to introduce the effect of the structural flexibility and the aerodynamic phenomenon in the dynamic model, and in the other hand, to build a suitable strategy of command and stabilization for these flying objects. The work is registered within this framework, and relates two types of engines: - Lighter than air vehicle: Application on the modelling and control of flexible airship. - Heavier than air vehicle: Application on the modelling and control of flexible micro-drone. We present a general model of autonomous flexible flying engine undergoing great overall motion and small elastic displacements. The formalism used is based on the Newton- Euler approach, which is frequently used for rigid flying objects. In this study we generalize the existing formalisms for rigid bodies, by including the effect of flexibility without destroying the total methodology. A modal synthesis is used. A hybrid method based on the energetic principles and Lagrange equations is presented. The phenomenon of the added masses is also taken into account. In order to integrate the fluid-structure interaction of a flexible airship, we develop an original analytical formulation of the problem using both the new notion of flexible flow potential, and the development of the kinetic energy of the air constrained by the motion and the vibration of the airship. This method allows to put in an obvious place the coupling "overall motion - flexibility" in the added mass matrix. We also present the dynamic and aerodynamic model of a flexible quadrirotor called XSF, designed in the IBISC laboratory and intended for an interuniversity competition for microdrones. A robust methodology based on the " Backstepping " control is realized to stabilize the airship around a desired position, and a PID controller is proposed to stabilise the XSF. The strategy of command is compelled by imperative to optimize the ratio precision/portability, to allow an easy insertion of the developed algorithms in the embedded electronics. A numerical validation is presented in the end of this report.

本文嘗試建立一個無限期的兩部門小型開放經濟模型。本模型的特 用一 個收益函數(或稱 GNP 函數)，代表一般化的兩部門生產 討進口限額政 策對資本累積和經常帳的影響。本文同時探討採倥B政策和放寬進口限額 兩種政策，並得到不少新的結論。例如cksher-Ohlin 模型中，若政府放 寬限額政策，並不會影響國內璊妒矕薛▼躑□F這與傳統靜態理論強調限 額量的多寡會影響國孝祭蚺j不相同。同時，對資本累積、經常帳之影響 必須視財貨K集度而定。若進口財為資本(勞力)密集財，資本存量減少(增 常帳不定(惡化)，動態福利水準上升。但在特定要素模型下，B則會使國 內價格下降，資本累積增加，經常帳惡化。

<p>Dynamic Air Diffuser</p>

We present a dynamic optimization approach for perishable products in a competitive and dynamically changing market. We build a general optimization framework that ties together the competetive and the dynamic nature of pricing. This approach also allows differential pricing for large customers as well as demand learning for the seller. We analyze special cases of the model and illustrate the policies numerically. / Singapore-MIT Alliance (SMA)

In this paper, we introduce a fluid model of dynamic pricing and inventory management for make-to-stock manufacturing systems. Instead of considering a traditional model that is based on how price affects demand, we consider a model that relies on how price and level of inventory affect the time a unit of product remains in inventory. Our motivation is based on the observation that in inventory systems, a unit of product incurs a delay before being sold. This delay depends on the unit price of the product, prices of competitors, and the level of inventory of this product. Moreover, delay data is not hard to acquire and is internally controlled and monitored by the manufacturer. It is interesting to notice that this delay is similar to travel times incurred in a transportation network. The model of this paper includes joint pricing, production and inventory decisions in a competitive, capacitated multi-product dynamic environment. In particular, in this paper we (i) introduce a model for dynamic pricing and inventory control that uses delay rather then demand data and establish connections with traditional demand models, (ii) study analytical properties of this model, (iii) establish conditions under which the model has a solution and finally, (iv) establish an algorithm that solves efficiently a discretized version of the model.

Steel plate shear walls have typically been analyzed using quasi static and monotonic pushover analysis; however, dynamic excitations during an earthquake elicit different behaviour from the structure due to the nature of the loading. This report outlines the design and analysis of a steel plate shear wall according to NBCC and S16-09 requirements. For lateral loading, wind and seismic forces are considered. The NBCC recognizes two procedures for determining seismic loading, the equivalent static force procedure and dynamic analysis. An analytical model was created in SAP2000® using capacity design principals and the strip model. The dynamic analysis uses bi-directional tension strips to resist load reversals and was validated against a finite element analysis using ABAQUS®. The dynamic analysis provided an effective means of designing the steel plate shear wall. The equivalent static force procedure resulted in a similar design; however, the structure required stiffening to meet the deflection requirements.