Mathematical modeling bond graph

A mathematical model for molecular complexity, such as the one developed by Bertz [21], has merit in helping to organize those properties which contribute to a heuristic idea of this subject. Using the language of graph theory [22] such a model will include a hierarchy of types of nodes (atoms) and of types of edges (bonds), as well as various other concepts such... 

The bond-graph network of liquid membrane process can be successfully exploited for modeling the separation and transport ability of complex reaction-diffusion phenomena. However, such models involving appropriate mathematical formulations are especially useful in predicting the system s response to the changes in operating conditions and specific characteristics of the liquid membrane components. In general, such models are not... 

Graph theory offers many useful characterizations of molecules. If the molecular property is bond additive, the modeling by graphs is quite adequate. Graph theory, even when not explicitly mentioned, has been behind many successful mathematical or quantum-chemical models. For example, Hameka studied the magnetic susceptibility of alkanes from a quantum-chemical point of view. " However, the very same quantum-chemical model can be translated without difficulties in the graph theoretical terms when it leads to even simpler expressions for the same magnetic susceptibilities. """"" ... 

Bonding in clusters and condensed cluster compounds that extend in one, two and three dimensions Principles of bonding and reactivity in transition metal cluster compounds Mathematical cluster chemistry Graph-theory derived models for the skeletal chemical bonding in organometallic metal carbonyl clusters... 

Clearly, for FDI it is necessary that a system is structurally observable. As switches temporarily disconnect and reconnect model parts they change the structure of a hybrid system model. Consequently, control properties, i.e. structural observability and structural controllability as well as characteristics of the mathematical model derived fl om the bond graph, i.e. the number of state variables, or the index of a DAE system become system mode dependent. Chapters briefly addresses these issues by confining to switched LTI systems and provides some small illustrating examples. 

Borutzky, W. (2014). Bond graph model-based system mode identification and mode-dependent fault thresholds for hybrid systems. Mathematical and Computer Modelling of Dynamical Systems, 20(06), 585-616. 

In [9], it is suggested to explicitly represent considered degradation phenomena in a nominal bond graph of the system once a mathematical model for them is available. However, if a mathematical model of a degradation process derived from first principles is not available, if a nominal parameter in the constitutive equation of an element is then replaced by a function of time so that measured data is fitted and can be extrapolated into the future, a bond graph representation might be a problem. If a resistance becomes time-varying as of sometime point to then this may be simply captured by a nonlinear modulated resistor. If the nominal capacitance Co in the constitutive equation q t) = Co e(t) of a capacitor is replaced by a time-dependent capacitance C t) then... 

Bond graph modelling cannot only support the generation of state space models for the simulation of the dynamic behaviour of a system. Bond graphs can serve as core model representation from which various forms of mathematical models can be directly generated such as... 

The bond graph model in LFT form of the multi-port RS equivalent to the mathematical model of (3.13) is given in Fig. 3.6a. 

Jardin, A., Marquis-Favre, W., Thomasset, D. Bond graph sizing of mechatronic systems Coupling of inverse modelling with dynamic optimization. In The 6th Vienna International Conference on Mathematical Modelling, pages 1929-1938, Vienna, Austria, February, 11—13 2009. 

In (9.26), the lower the number of break variables, the easier it is to solve this system. The purpose of the following algorithms is to open all the existing causal loops in the bond graph by means of the minimum number of break variables. In a later step, the mathematical model will be automatically obtained based on these break variables. These algorithms have been conceived to deal with one-dimensional and multi-bond graph systems. 

Before applying these algorithms, the bond graph model must be causally augmented. In [13, 14] an improved causality assignment procedure is explained. Causality will drive the search of ZCPs. Two algorithms are used to obtain the mathematical models of bond graph systems. 

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