The purpose of the matching interdiction problem in a weighted graph is to find two vertices such that the weight of the maximum matching in the graph without these vertices is minimized. An approximate solution for this problem has been presented. In this paper, we consider dendrimers as graphs such that the weights of edges are the bond lengths. We obtain the maximum matching in some types of...

This paper discusses a bond–graph model library implemented in Modelica. Modelica is a new language for physical systems modeling with main objective to facilitate exchange of models and simulation specifications. Bond graphs are a domain–independent way of modeling the dynamics of physical systems. Besides the presentation of the Modelica basic bond– graph library, also an application example ...

then the size of the largest component in p-bond-percolation with p = 1+O(n ) d−1 is roughly n. In Physics jargon, this condition implies that there exists a scaling window with a mean-field width of n around the critical probability pc = 1 d−1 . A consequence of our theorems is that if {Gn} is a transitive expander family with girth at least ( 2 3 + ǫ) logd−1 n then {Gn} has the above scaling ...

We consider bond percolation on random graphs with given degrees and bounded average degree. In particular, we consider the order of the largest component after the random deletion of the edges of such a random graph. We give a rough characterisation of those degree distributions for which bond percolation with high probability leaves a component of linear order, known usually as a giant compon...

Some interdisciplinury issues concerning artificial intelligence (AI) are explored in relation to modelling in physics and engineering. A short survey is given of‘ automated qualitative reasoning about physical systems, which in recent years has become an active research area in AI, and has been partly influenced by system dynamics. The conceptual aspects of‘ the A I approach to physical scienc...

Efficient energy transduction is one driver of evolution; and thus understanding biomolecular energy transduction is crucial to understanding living organisms. As an energy-orientated modelling methodology, bond graphs provide a useful approach to describing and modelling the efficiency of living systems. This paper gives some new results on the efficiency of metabolism based on bond graph mode...

We study a random graph model which is a superposition of bond percolation on Zd with parameter p, and a classical random graph G(n, c/n). We show that this model, being a homogeneous random graph, has a natural relation to the so-called “rank 1 case” of inhomogeneous random graphs. This allows us to use the newly developed theory of inhomogeneous random graphs to describe the phase diagram on ...

We note that it is possible to construct a bond vertex model that displays q-state Potts criticality on an ensemble of φ random graphs of arbitrary topology, which we denote as “thin” random graphs in contrast to the fat graphs of the planar diagram expansion. Since the four vertex model in question also serves to describe the critical behaviour of the Ising model in field, the formulation reve...

Compartmental network modelling is compared with the bond graph approach. Whilst both approaches build on the conservation principle, the compartmental network approach is on a slightly higher level and more compact. Also no analogies must be used, the concepts of physics are used directly in connection whilst system theoretical arguments define consistency and solvability, being roughly equiva...

Given a set S of vertices in a graph, the cocycle determined by S is the set of edges joining a vertex in S to a vertex not in S. A bond is a minimal non-empty cocycle. We characterise graphs that admit an orientation under which every bond of even cardinality has a prescribed directed parity.