Flows in networks : an algorithmic approach

**Authors:**Marcon, Alister Justin**Date:**2013-05-01**Subjects:**Graph theory , Network analysis (Planning) , Algorithms , Mathematical optimization , System analysis**Type:**Thesis**Identifier:**uj:7507 , http://hdl.handle.net/10210/8364**Description:**M.Sc. (Mathematics) , In Chapter 1, we consider the relevant theory pertaining to graphs and digraphs that will be used in the study of flows in networks. Warshall’s algorithm for reachability is also considered since it will allow us to ascertain whether some paths exist in some instance. In Chapter 2, we explore flows and cuts in networks. We define the basic concepts of source, sink, intermediate vertices, capacity, costs and lower-bounds. Feasible flows are defined, as well as the value of a flow. Cuts in capacitated networks are explored and further theory relating the value of a flow and cuts is given. We considered the problem of determining a maximal flow. In particular, we consider augmentations of the flow—this allows us to give a characterization of a maximal flow. The important Max-flow Min-cut theorem is also considered. After having explored the relevant theory, we move on to methods of finding a maximal flow for a given s-t network that has a capacity on each of its arcs. Firstly, we consider zero-one and unit-capacity networks since these play a role in the applications of maximal flows in Chapter 4. We, then, compile the relevant theory and algorithms in order to implement two augmenting path finding algorithms.**Full Text:**

**Authors:**Marcon, Alister Justin**Date:**2013-05-01**Subjects:**Graph theory , Network analysis (Planning) , Algorithms , Mathematical optimization , System analysis**Type:**Thesis**Identifier:**uj:7507 , http://hdl.handle.net/10210/8364**Description:**M.Sc. (Mathematics) , In Chapter 1, we consider the relevant theory pertaining to graphs and digraphs that will be used in the study of flows in networks. Warshall’s algorithm for reachability is also considered since it will allow us to ascertain whether some paths exist in some instance. In Chapter 2, we explore flows and cuts in networks. We define the basic concepts of source, sink, intermediate vertices, capacity, costs and lower-bounds. Feasible flows are defined, as well as the value of a flow. Cuts in capacitated networks are explored and further theory relating the value of a flow and cuts is given. We considered the problem of determining a maximal flow. In particular, we consider augmentations of the flow—this allows us to give a characterization of a maximal flow. The important Max-flow Min-cut theorem is also considered. After having explored the relevant theory, we move on to methods of finding a maximal flow for a given s-t network that has a capacity on each of its arcs. Firstly, we consider zero-one and unit-capacity networks since these play a role in the applications of maximal flows in Chapter 4. We, then, compile the relevant theory and algorithms in order to implement two augmenting path finding algorithms.**Full Text:**

Die assessering van gemeenskappe vanuit die lewende sisteemteorie

- Delport, Catharina Sophia Louisa

**Authors:**Delport, Catharina Sophia Louisa**Date:**2014-04-24**Subjects:**System theory , Social systems , System analysis , Decision making**Type:**Thesis**Identifier:**http://ujcontent.uj.ac.za8080/10210/381702 , uj:10903 , http://hdl.handle.net/10210/10410**Description:**M.A. (Social Work) , The research resulted from the lack of reliable and valid measurement instruments on community functioning. Operationalization of community functioning is complicated by the general character of widely used theories es related to communities in South Africa. Measurement is severely hampered by insufficient conceptualization. In the exploration of social service theory, the Living System Theory was selected as the theoretical underpinning for the research. Living System Theory offers a framework for processes and structures to critically and systematically describe, analyse, explain and interpret communities. Operationalization of community functioning was greatly expedited by the selection of the Living System Theory in view of its detailed description and universal character. In this study the term community from the Living System Theory, is conceptualized to In new synthesis and is also analysed systematically. In the systematic analyses of a community it was concluded that six relevant assessment areas occur in community context, namely: physical structures; transport; communication; decision-making; policy; and product/service. All six identified assessment areas were analysed systematically, but for the purposes of this study only decision-making was operationalized...**Full Text:**

**Authors:**Delport, Catharina Sophia Louisa**Date:**2014-04-24**Subjects:**System theory , Social systems , System analysis , Decision making**Type:**Thesis**Identifier:**http://ujcontent.uj.ac.za8080/10210/381702 , uj:10903 , http://hdl.handle.net/10210/10410**Description:**M.A. (Social Work) , The research resulted from the lack of reliable and valid measurement instruments on community functioning. Operationalization of community functioning is complicated by the general character of widely used theories es related to communities in South Africa. Measurement is severely hampered by insufficient conceptualization. In the exploration of social service theory, the Living System Theory was selected as the theoretical underpinning for the research. Living System Theory offers a framework for processes and structures to critically and systematically describe, analyse, explain and interpret communities. Operationalization of community functioning was greatly expedited by the selection of the Living System Theory in view of its detailed description and universal character. In this study the term community from the Living System Theory, is conceptualized to In new synthesis and is also analysed systematically. In the systematic analyses of a community it was concluded that six relevant assessment areas occur in community context, namely: physical structures; transport; communication; decision-making; policy; and product/service. All six identified assessment areas were analysed systematically, but for the purposes of this study only decision-making was operationalized...**Full Text:**

Describing function-based control synthesis for a nonlinear hydraulic drive system

**Authors:**Heyns, Louis Jacobus**Date:**2014-03-13**Subjects:**Hydraulic engineering , System analysis**Type:**Thesis**Identifier:**uj:4338 , http://hdl.handle.net/10210/9688**Description:**M.Ing. , Experimental tests have indicated that limit cycles are likely to occur in hydraulic drive systems, where backlash in the actuator seals is the dominant nonlinearity'. This study primarily deals with the analysis and synthesis of existing hydraulic drive systems to eliminate limit cycles and with establishing a design tool for the design of hydraulic drives with the object of avoiding limit cycles. Most analytical results were verified experimentally. The most general methods for the design of practical nonlinear systems are discussed. It is concluded that some form of synthesis and analysis is necessary, and that the need exists for general methods to evaluate the stability of nonlinear systems and design tools for nonlinear system design. Ageneral procedure of system analysis is given. Amathematical model of the system needs to be obtained, which can be done with the aid of bond graphs. Simulations of complex systems are recommended to verify system performance only. The first procedure of system analysis that should be followed is to systematically identify elements of the system which are not related to the cause of the limit cycle. Experimental testing is a good first step in identifying the non-critical elements. Signal flow diagrams enable the engineer quickly to determine all feedback loops of a complicated system which might be critical. Block diagrams are necessary for the application of nonlinear analysis and synthesis techniques. Hydraulic resonance, where the actuator seal acts as an oscillating mechanism, is identified as a possible cause of the limit cycle. An unusual application of the describing function, where the describing function is applied to optimize the hydraulic supply, is discussed. The transfer function of flow in a hydraulic pipe is given. With the use of the describing function, the gain margin can be studied versus different parameters of the plant. This gives insight into slightly damped conditions of the hydraulic supply that might be the cause of a limit cycle in the system. A control gain does not change the dynamic behaviour of the hydraulic supply, but only amplifies certain natural modes of the system. The design application of the describing function to nonlinear hydraulic drives is discussed. Procedures to eliminate an existing limit cycle and to design a nonlinear hydraulic drive system are proposed. Most important of all, is to design the system so that the natural frequencies of the mechanical structure and the hydraulic supply do not have any common multiples.**Full Text:**

**Authors:**Heyns, Louis Jacobus**Date:**2014-03-13**Subjects:**Hydraulic engineering , System analysis**Type:**Thesis**Identifier:**uj:4338 , http://hdl.handle.net/10210/9688**Description:**M.Ing. , Experimental tests have indicated that limit cycles are likely to occur in hydraulic drive systems, where backlash in the actuator seals is the dominant nonlinearity'. This study primarily deals with the analysis and synthesis of existing hydraulic drive systems to eliminate limit cycles and with establishing a design tool for the design of hydraulic drives with the object of avoiding limit cycles. Most analytical results were verified experimentally. The most general methods for the design of practical nonlinear systems are discussed. It is concluded that some form of synthesis and analysis is necessary, and that the need exists for general methods to evaluate the stability of nonlinear systems and design tools for nonlinear system design. Ageneral procedure of system analysis is given. Amathematical model of the system needs to be obtained, which can be done with the aid of bond graphs. Simulations of complex systems are recommended to verify system performance only. The first procedure of system analysis that should be followed is to systematically identify elements of the system which are not related to the cause of the limit cycle. Experimental testing is a good first step in identifying the non-critical elements. Signal flow diagrams enable the engineer quickly to determine all feedback loops of a complicated system which might be critical. Block diagrams are necessary for the application of nonlinear analysis and synthesis techniques. Hydraulic resonance, where the actuator seal acts as an oscillating mechanism, is identified as a possible cause of the limit cycle. An unusual application of the describing function, where the describing function is applied to optimize the hydraulic supply, is discussed. The transfer function of flow in a hydraulic pipe is given. With the use of the describing function, the gain margin can be studied versus different parameters of the plant. This gives insight into slightly damped conditions of the hydraulic supply that might be the cause of a limit cycle in the system. A control gain does not change the dynamic behaviour of the hydraulic supply, but only amplifies certain natural modes of the system. The design application of the describing function to nonlinear hydraulic drives is discussed. Procedures to eliminate an existing limit cycle and to design a nonlinear hydraulic drive system are proposed. Most important of all, is to design the system so that the natural frequencies of the mechanical structure and the hydraulic supply do not have any common multiples.**Full Text:**

Beheertegnieke vir stelsels met meer as een nie-lineariteit

**Authors:**Gouws, Johan**Date:**2014-09-30**Subjects:**Automatic control , Control theory , Nonlinear theories , System analysis**Type:**Thesis**Identifier:**uj:12428 , http://hdl.handle.net/10210/12215**Description:**M.Ing. (Electrical & Electronic Engineering) , Please refer to full text to view abstract**Full Text:**

**Authors:**Gouws, Johan**Date:**2014-09-30**Subjects:**Automatic control , Control theory , Nonlinear theories , System analysis**Type:**Thesis**Identifier:**uj:12428 , http://hdl.handle.net/10210/12215**Description:**M.Ing. (Electrical & Electronic Engineering) , Please refer to full text to view abstract**Full Text:**

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