Professor Jonathan Wattis' Outputs (53)

DNA charge neutralisation by linear polymers II: reversible binding
Journal Article
Maltsev, E., Wattis, J. A., & Byrne, H. M. DNA charge neutralisation by linear polymers II: reversible binding. Physical Review E, 74,

We model the way in which polymers bind to DNA and neutralise
its charged backbone by analysing the dynamics of the distribution
of gaps along the DNA.
We generalise existing theory for irreversible binding to construct
new deterministic models... Read More about DNA charge neutralisation by linear polymers II: reversible binding.

An introduction to mathematical models of coagulation-fragmentation processes: a discrete deterministic mean-field approach
Journal Article
Wattis, J. A. An introduction to mathematical models of coagulation-fragmentation processes: a discrete deterministic mean-field approach. Physica D: Nonlinear Phenomena, 222,

We summarise the properties and the fundamental mathematical results
associated with basic models which describe
coagulation and fragmentation processes in a deterministic manner
and in which cluster size is a discrete quantity (an integer
multip... Read More about An introduction to mathematical models of coagulation-fragmentation processes: a discrete deterministic mean-field approach.

Exact solutions for cluster-growth kinetics with evolving size and shape profiles
Journal Article
Wattis, J. A. Exact solutions for cluster-growth kinetics with evolving size and shape profiles. Journal of Physics A: Mathematical and General, 39,

In this paper we construct a model for the simultaneous
compaction by which clusters are restructured, and growth
of clusters by pairwise coagulation. The model has the form
of a multicomponent aggregation problem in which the
components are clu... Read More about Exact solutions for cluster-growth kinetics with evolving size and shape profiles.

Symmetry-breaking in chiral polymerisation
Journal Article
Wattis, J. A., & Coveney, P. V. Symmetry-breaking in chiral polymerisation. Origins of Life and Evolution of Biospheres, 35(3),

We propose a model for chiral polymerisation and investigate
its symmetric and asymmetric solutions. The model has a source
species which decays into left- and right-handed types of monomer,
each of which can polymerise to form homochiral chains;... Read More about Symmetry-breaking in chiral polymerisation.

The Becker-Döring equations with monomer input, competition and inhibition
Journal Article
Bolton, C. D., & Wattis, J. A. The Becker-Döring equations with monomer input, competition and inhibition. Journal of Physics A: Mathematical and General, 37,,

We investigate the Becker-Döring model of nucleation with
three generalisations; an input of monomer, an input of inhibitor and finally, we allow the monomers to form two morphologies of cluster. We assume size-independent aggregation and fragmentat... Read More about The Becker-Döring equations with monomer input, competition and inhibition.

Similarity solutions of a Becker-Döring system with time-dependent monomer input
Journal Article
Wattis, J. A. Similarity solutions of a Becker-Döring system with time-dependent monomer input. Journal of Physics A: Mathematical and General, 37,

We formulate the Becker-Döring equations for cluster growth in the presence of a time-dependent source of monomer input.
In the case of size-independent aggregation and ragmentation
rate coefficients we find similarity solutions which are approache... Read More about Similarity solutions of a Becker-Döring system with time-dependent monomer input.

The Becker-Döring equations with exponentially size-dependent rate coefficients
Journal Article
Wattis, J. A., Bolton, C. D., & Coveney, P. V. The Becker-Döring equations with exponentially size-dependent rate coefficients. Journal of Physics A: Mathematical and General, 37,

This paper is concerned with an analysis of the Becker-Döring equations which lie at the heart of a number of descriptions of non-equilibrium phase transitions and related complex dynamical processes. The Becker-Döring theory describes growth and fra... Read More about The Becker-Döring equations with exponentially size-dependent rate coefficients.

Coagulation equations with mass loss
Journal Article
Wattis, J. A., McCartney, D. G., & Gudmundsson, T. Coagulation equations with mass loss. Journal of Engineering Mathematics, 49,

We derive and solve models for coagulation with mass loss
arising, for example, from industrial processes in which
growing inclusions are lost from the melt by colliding with the wall of the vessel. We consider a variety of loss laws and a variety... Read More about Coagulation equations with mass loss.

DNA charge neutralisation by linear polymers I: irreversible binding
Journal Article
Maltsev, E., Wattis, J. A., & Byrne, H. M. DNA charge neutralisation by linear polymers I: irreversible binding. Physical Review E, 74,

We develop a deterministic mathematical model to describe the way
in which polymers bind to DNA by considering the dynamics of the
gap distribution that forms when polymers bind to a DNA plasmid.
In so doing, we generalise existing theory to accou... Read More about DNA charge neutralisation by linear polymers I: irreversible binding.

Coarse-graining and renormalisation group methods for the elucidation of the kinetics of complex nucleation and growth processes
Journal Article
Coveney, P. V., & Wattis, J. A. Coarse-graining and renormalisation group methods for the elucidation of the kinetics of complex nucleation and growth processes. Molecular Physics, 104,

We review our work on generalisations of the Becker-Doring model of cluster-formation as applied to nucleation theory, polymer growth kinetics, and the formation of upramolecular structures in colloidal chemistry. One valuable tool in analysing math... Read More about Coarse-graining and renormalisation group methods for the elucidation of the kinetics of complex nucleation and growth processes.

Discrete breathers in a two-dimensional Fermi-Pasta-Ulam lattice
Journal Article
Butt, I. A., & Wattis, J. A. Discrete breathers in a two-dimensional Fermi-Pasta-Ulam lattice. Journal of Physics A: Mathematical and General, 39,

Using asymptotic methods, we investigate whether discrete
breathers are supported by a two-dimensional Fermi-Pasta-Ulam lattice. A scalar (one-component) two-dimensional
Fermi-Pasta-Ulam lattice is shown to model the charge stored
within an electr... Read More about Discrete breathers in a two-dimensional Fermi-Pasta-Ulam lattice.

Discrete breathers in a two-dimensional hexagonal Fermi-Pasta-Ulam lattice
Journal Article
Butt, I. A., & Wattis, J. A. Discrete breathers in a two-dimensional hexagonal Fermi-Pasta-Ulam lattice

We consider a two-dimensional Fermi-Pasta-Ulam (FPU) lattice
with hexagonal symmetry. Using asymptotic methods based on
small amplitude ansatz, at third order we obtain a eduction to a cubic nonlinear Schr{\"o}dinger equation (NLS) for the breathe... Read More about Discrete breathers in a two-dimensional hexagonal Fermi-Pasta-Ulam lattice.

Asymptotic analysis of combined breather-kink modes in a Fermi-Pasta-Ulam chain
Journal Article
Butt, I. A., & Wattis, J. A. Asymptotic analysis of combined breather-kink modes in a Fermi-Pasta-Ulam chain. Physica D: Nonlinear Phenomena, 231,

We find approximations to travelling breather solutions of the
one-dimensional Fermi-Pasta-Ulam (FPU) lattice. Both bright
breather and dark breather solutions are found. We find that the
existence of localised (bright) solutions depends upon the... Read More about Asymptotic analysis of combined breather-kink modes in a Fermi-Pasta-Ulam chain.