We prove that the spectral gap of the Swendsen-Wang dynamics for the random-cluster model on arbitrary graphs with m edges is bounded above by 16m logm times the spectral gap of the single-bond (or heat-bath) dynamics. This and the corresponding lower bound (from [U12]) imply that rapid mixing of these two dynamics is equivalent. Using the known lower bound on the spectral gap of the Swendsen-W...

We study a random graph model which is a superposition of the bond percolation model on Zd with probability p of an edge, 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 describ...

Engineering systems are frequently abstracted to models with discontinuous behaviour (such as a switch or contact), and a hybrid model is one which contains continuous and discontinuous behaviours. Bond graphs are an established physical modelling method, but there are several methods for constructing switched or ‘hybrid’ bond graphs, developed for either qualitative ‘structural’ analysis or ef...

Mathematical models of cardiac action potentials have become increasingly important in the study of heart disease and pharmacology, but concerns linger over their robustness during long periods of simulation, in particular due to issues such as model drift and non-unique steady states. Previous studies have linked these to violation of conservation laws, but only explored those issues with resp...

We investigate what happens to the third order ferromagnetic phase transition displayed by the Ising model on various dynamical planar lattices (ie coupled to 2D quantum gravity) when we introduce annealed bond disorder in the form of either antiferromagnetic couplings or null couplings. We also look at the effect of such disordering for the Ising model on general φ and φ Feynman diagrams. Subm...

Bond graphs have established themselves as a reliable tool for modeling physical systems. Multi-bonds are a bondgraphic extension that provides a general approach to modeling all kinds of multi-dimensional processes in continuous physical systems. This paper presents a Modelica library for modeling multi-bond graphs and their application to three-dimensional mechanical systems. A set of bondgra...

The pace of innovation in Cyber-Physical Systems (CPSs) drives the need for multi-disciplinary methods and tools to support rapid and accurate assessment of design alternatives. In this chapter, the authors describe collaborative models (co-models) that link Discrete-Event (DE) models of control software with Continuous-Time (CT) models of controlled plant. They present methods and tools for co...

We study the statistical properties of the scattering matrix associated with generic quantum graphs. The scattering matrix is the quantum analogue of the classical evolution operator on the graph. For the energy-averaged spectral form factor of the scattering matrix we have recently derived an exact combinatorial expression. It is based on a sum over families of periodic orbits which so far cou...

The concept of arithmetic-geometric index was recently introduced in chemical graph theory, but it has proven to be useful from both a theoretical and practical point view. aim this paper is obtain new bounds the characterize extremal graphs with respect them. Several are based on other indices, such as second variable Zagreb or general atom-bond connectivity index), some them involve parameter...

We study the statistical properties of the scattering matrix associated with generic quantum graphs. The scattering matrix is the quantum analogue of the classical evolution operator on the graph. For the energy-averaged spectral form factor of the scattering matrix we have recently derived an exact combinatorial expression. It is based on a sum over families of periodic orbits which so far cou...