#### Filter Results:

- Full text PDF available (68)

#### Publication Year

1995

2017

- This year (7)
- Last 5 years (48)
- Last 10 years (62)

#### Publication Type

#### Co-author

#### Journals and Conferences

#### Key Phrases

#### Organism

Learn More

Nodes are randomly distributed within an annulus (and then a shell) to form a point pattern of communication terminals which are linked stochastically according to the Rayleigh fading of radio-frequency data signals. We then present analytic formulas for the connection probability of these spatially embedded graphs, describing the connectivity behaviour as… (More)

Classical dynamical systems range from purely integrable to purely hyperbolic. For purely integrable systems we have a variety of classical methods, such as separation of the Hamilton-Jacobi equation @1#. For almost integrable systems we have Kolmogorov-Arnold-Moser theory @2#. For purely hyperbolic systems it is possible to obtain much information about… (More)

- Justin P. Coon, Carl P. Dettmann, Orestis Georgiou
- ArXiv
- 2012

We develop a cluster expansion for the probability of full connectivity of high density random networks in confined geometries. In contrast to percolation phenomena at lower densities, boundary effects, which have previously been largely neglected, are not only relevant but dominant. We derive general analytical formulas that show a persistence of… (More)

Thermostats are dynamical equations used to model thermodynamic variables such as temperature and pressure in molecular simulations. For computationally intensive problems such as the simulation of biomolecules, we propose to average over fast momentum degrees of freedom and construct thermostat equations in configuration space. The equations of motion are… (More)

- Mohammud Z. Bocus, Carl P. Dettmann, Justin P. Coon
- IEEE Communications Letters
- 2013

An exponential-type approximation of the first order Marcum Q-function is presented, which is robust to changes in its first argument and can easily be integrated with respect to the second argument. Such characteristics are particularly useful in network connectivity analysis. The proposed approximation is exact in the limit of small first argument of the… (More)

- Carl P. Dettmann, Orestis Georgiou, Justin P. Coon
- ISWCS
- 2015

Ad-hoc networks are often deployed in regions with complicated boundaries. We show that if the boundary is modeled as a fractal, a network requiring line of sight connections has the counterintuitive property that increasing the number of nodes decreases the full connection probability. We characterise this decay as a stretched exponential involving the… (More)

Random geometric networks are mathematical structures consisting of a set of nodes placed randomly within a bounded set V ⊆ R mutually coupled with a probability dependent on their Euclidean separation, and are the classic model used within the expanding field of ad-hoc wireless networks. In order to rank the importance of the network’s communicating nodes,… (More)

- Justin P. Coon, Orestis Georgiou, Carl P. Dettmann
- 2014 12th International Symposium on Modeling and…
- 2014

We consider the probability that a dense wireless network confined within a given convex geometry is fully connected. We exploit a recently reported theory to develop a systematic methodology for analytically characterizing the connectivity probability when the network resides within a convex right prism, a polyhedron that accurately models many geometries… (More)

Recent research has demonstrated the importance of boundary effects on the overall connection probability of wireless networks, but has largely focused on convex domains. We consider two generic scenarios of practical importance to wireless communications, in which one or more nodes are located outside the convex space where the remaining nodes reside.… (More)

- Predrag Cvitanović, Niels Søndergaard, Gergely Palla, Gábor Vattay, Carl P. Dettmann
- Physical review. E, Statistical physics, plasmas…
- 1999

A matrix representation of the evolution operator associated with a nonlinear stochastic flow with additive noise is used to compute its spectrum. In the weak noise limit a perturbative expansion for the spectrum is formulated in terms of local matrix representations of the evolution operator centered on classical periodic orbits. The evaluation of… (More)