Skip to main content

Research Repository

Advanced Search

Outputs (49)

On the Meaning of Averages in Genome-wide Association Studies: What Should Come Next? (2023)
Journal Article
Rauch, C., Wattis, J., & Bray, S. (2023). On the Meaning of Averages in Genome-wide Association Studies: What Should Come Next?. Organisms, 6(1), 7-22. https://doi.org/10.13133/2532-5876/17811

Identifying the association between phenotypes and genotypes is the fundamental basis of genetic analyses. Although genomic technologies used to generate data have rapidly advanced within the last 20 years, the statistical models used in genome-wide... Read More about On the Meaning of Averages in Genome-wide Association Studies: What Should Come Next?.

Mathematical Models of Chiral Symmetry-breaking – A Review of General Theories, and Adiabatic Approximations of the APED System (2022)
Journal Article
Diniz, P. C., Wattis, J. A., & Da Costa, F. P. (2022). Mathematical Models of Chiral Symmetry-breaking – A Review of General Theories, and Adiabatic Approximations of the APED System. Origins of Life and Evolution of Biospheres, 52(4), 183-204. https://doi.org/10.1007/s11084-022-09631-w

We review the literature surrounding chiral symmetry-breaking in chemical systems, with a focus on understanding the mathematical models underlying these chemical processes. We comment in particular on the toy model of Sandars, Viedma’s crystal grind... Read More about Mathematical Models of Chiral Symmetry-breaking – A Review of General Theories, and Adiabatic Approximations of the APED System.

GIFT: New method for the genetic analysis of small gene effects involving small sample sizes (2022)
Journal Article
Rauch, C., Kyratzi, P., Blott, S., Bray, S., & Wattis, J. A. D. (2023). GIFT: New method for the genetic analysis of small gene effects involving small sample sizes. Physical Biology, 20(1), Article 016001. https://doi.org/10.1088/1478-3975/ac99b3

Small gene effects involved in complex/omnigenic traits remain costly to analyse using current genome-wide association methods (GWAS) because of the number of individuals required to return meaningful association(s), a.k.a. study power. Inspired by f... Read More about GIFT: New method for the genetic analysis of small gene effects involving small sample sizes.

Analysis of phenotype-genotype associations using genomic informational field theory (GIFT) (2022)
Journal Article
Wattis, J. A., Bray, S. M., Kyratzi, P., & Rauch, C. (2022). Analysis of phenotype-genotype associations using genomic informational field theory (GIFT). Journal of Theoretical Biology, 548, Article 111198. https://doi.org/10.1016/j.jtbi.2022.111198

We show how field- and information theory can be used to quantify the relationship between genotype and phenotype in cases where phenotype is a continuous variable. Given a sample population of phenotype measurements, from various known genotypes, we... Read More about Analysis of phenotype-genotype associations using genomic informational field theory (GIFT).

Breather modes of fully nonlinear mass-in-mass chains (2022)
Journal Article
Wattis, J. A. (2022). Breather modes of fully nonlinear mass-in-mass chains. Physical Review E, 105(5), Article 054212. https://doi.org/10.1103/PhysRevE.105.054212

We propose a model for a chain of particles coupled by nonlinear springs in which each mass has an internal mass and all interactions are assumed to be nonlinear. We show how to construct an asymptotic solution of this system using multiple timescale... Read More about Breather modes of fully nonlinear mass-in-mass chains.

Solution classes of the matrix second Painlevé hierarchy (2022)
Journal Article
Gordoa, P. R., Pickering, A., & Wattis, J. (2022). Solution classes of the matrix second Painlevé hierarchy. Physica D: Nonlinear Phenomena, 435, Article 133295. https://doi.org/10.1016/j.physd.2022.133295

We explore the generation of classes of solutions of the matrix second Painlevé hierarchy. This involves the consideration of the application of compositions of auto-Bäcklund transformations to different initial solutions, with the number of distinct... Read More about Solution classes of the matrix second Painlevé hierarchy.

Mathematical modelling of earlier stages of COVID-19 transmission dynamics in Ghana (2022)
Journal Article
Acheampong, E., Okyere, E., Iddi, S., Bonney, J. H., Wattis, J. A., Gomes, R. L., & Asamoah, J. K. K. (2022). Mathematical modelling of earlier stages of COVID-19 transmission dynamics in Ghana. Results in Physics, 34, Article 105193. https://doi.org/10.1016/j.rinp.2022.105193

In late 2019, a novel coronavirus, the SARS-CoV-2 outbreak was identified in Wuhan, China and later spread to every corner of the globe. Whilst the number of infection-induced deaths in Ghana, West Africa are minimal when compared with the rest of th... Read More about Mathematical modelling of earlier stages of COVID-19 transmission dynamics in Ghana.

Stochastic fractal and Noether's theorem (2021)
Journal Article
Rahman, R., Nowrin, F., Rahman, M. S., Wattis, J. A. D., & Hassan, M. K. (2021). Stochastic fractal and Noether's theorem. Physical Review E, 103(2), Article 022106. https://doi.org/10.1103/physreve.103.022106

We consider the binary fragmentation problem in which, at any breakup event, one of the daughter segments either survives with probability p or disappears with probability 1 ? p. It describes a stochastic dyadic Cantor set that evolves in time, and e... Read More about Stochastic fractal and Noether's theorem.

Integrability and asymptotic behaviour of a differential-difference matrix equation (2020)
Journal Article
Gordoa, P. R., Pickering, A., & Wattis, J. A. (2021). Integrability and asymptotic behaviour of a differential-difference matrix equation. Physica D: Nonlinear Phenomena, 415, Article 132754. https://doi.org/10.1016/j.physd.2020.132754

In this paper we consider the matrix lattice equation U_{n,t} (U_{n+1} ? U_{n?1} ) = g(n)I, in both its autonomous (g(n) = 2) and nonautonomous (g(n) = 2n ? 1) forms. We show that each of these two matrix lattice equations are integrable. In addition... Read More about Integrability and asymptotic behaviour of a differential-difference matrix equation.

Monte–Carlo simulation of crystallization in single‐chain square‐well homopolymers (2020)
Journal Article
Wicks, T. J., Wattis, J. A. D., & Graham, R. S. (2021). Monte–Carlo simulation of crystallization in single‐chain square‐well homopolymers. Polymer Crystallization, 4(1), Article e10146. https://doi.org/10.1002/pcr2.10146

© 2020 Wiley Periodicals LLC We present Monte–Carlo (MC) simulations of the crystallization transition of single-chain square-well homopolymers, with a continuous description of monomer positions. For long chains with short-ranged interactions this s... Read More about Monte–Carlo simulation of crystallization in single‐chain square‐well homopolymers.

Mathematical modelling of telomere length dynamics (2019)
Journal Article
Wattis, J. A., Qi, Q., & Byrne, H. M. (2019). Mathematical modelling of telomere length dynamics. Journal of Mathematical Biology, 1-38. https://doi.org/10.1007/s00285-019-01448-y

© 2019, The Author(s). Telomeres are repetitive DNA sequences located at the ends of chromosomes. During cell division, an incomplete copy of each chromosome’s DNA is made, causing telomeres to shorten on successive generations. When a threshold leng... Read More about Mathematical modelling of telomere length dynamics.

Asymptotic analysis of breather modes in a two-dimensional mechanical lattice (2019)
Journal Article
Wattis, J., & Alzaidi, A. (2020). Asymptotic analysis of breather modes in a two-dimensional mechanical lattice. Physica D: Nonlinear Phenomena, 401, Article 132207. https://doi.org/10.1016/j.physd.2019.132207

We consider a two-dimensional square lattice in which each node is restricted to the plane of the lattice, but is permitted to move in both directions of the lattice. We assume nodes are connected to nearest neighbours along the lattice directions wi... Read More about Asymptotic analysis of breather modes in a two-dimensional mechanical lattice.

Nuclear poly(A) tail size is regulated by Cnot1 during the serum response (2019)
Other
Singhania, R., Thorn, G. J., Williams, K., Gandhi, R. D., Daher, C., Barthet-Barateig, A., …de Moor, C. H. (2019). Nuclear poly(A) tail size is regulated by Cnot1 during the serum response

The poly(A) tail removal from mRNAs introduces a delay between mRNA synthesis and decay. We measured levels and poly(A) tail sizes of serum-induced mRNAs and used mathematical modelling to compare their deadenylation time with the delay in decay and... Read More about Nuclear poly(A) tail size is regulated by Cnot1 during the serum response.

Modelling Emerging Pollutants in Wastewater Treatment: A Case Study using the Pharmaceutical 17??ethinylestradiol (2019)
Journal Article
Acheampong, E., Dryden, I. L., Wattis, J. A., Twycross, J., Scrimshaw, M. D., & Gomes, R. L. (2019). Modelling Emerging Pollutants in Wastewater Treatment: A Case Study using the Pharmaceutical 17??ethinylestradiol. Computers and Chemical Engineering, 128, 477-487. https://doi.org/10.1016/j.compchemeng.2019.06.020

Mathematical modelling can play a key role in understanding as well as quantifying uncertainties surrounding the presence and fate of emerging pollutants in wastewater treatment processes (WWTPs). This paper presents for the first time a simplified e... Read More about Modelling Emerging Pollutants in Wastewater Treatment: A Case Study using the Pharmaceutical 17??ethinylestradiol.

Effects of competition between random sequential nucleation of point-sized seeds and island growth by adsorption of finite-sized grains (2019)
Journal Article
Khanam, A., Wattis, J. A., & Hassan, M. K. (2019). Effects of competition between random sequential nucleation of point-sized seeds and island growth by adsorption of finite-sized grains. Physical Review E, 99(4), https://doi.org/10.1103/PhysRevE.99.042110

We study random sequential adsorption of particles from a pool onto a one-dimensional substrate following ballistic deposition rules with separate nucleation and growth processes occurring simultaneously. Nucleation describes the formation of point-s... Read More about Effects of competition between random sequential nucleation of point-sized seeds and island growth by adsorption of finite-sized grains.

Asymptotic approximations to travelling waves in the diatomic Fermi-Pasta-Ulam lattice (2019)
Journal Article
Wattis, J. A. (2019). Asymptotic approximations to travelling waves in the diatomic Fermi-Pasta-Ulam lattice. Mathematics in Engineering, 1(2), 327-342. https://doi.org/10.3934/mine.2019.2.327

We construct high-order approximate travelling waves solutions of the diatomic Fermi-Pasta-Ulam lattice using asymptotic techniques which are valid for arbitrary mass ratios. Separately small amplitude ansatzs are made for the motion of the lighter a... Read More about Asymptotic approximations to travelling waves in the diatomic Fermi-Pasta-Ulam lattice.

The second Painlevé equation, a related nonautonomous semidiscrete equation, and a limit to the first Painlevé equation: scalar and matrix cases (2018)
Journal Article
Pickering, A., Gordoa, P. R., & Wattis, J. A. (2019). The second Painlevé equation, a related nonautonomous semidiscrete equation, and a limit to the first Painlevé equation: scalar and matrix cases. Physica D: Nonlinear Phenomena, 391, 72-86. https://doi.org/10.1016/j.physd.2018.12.001

In this paper we consider the matrix nonautonomous semidiscrete (or lattice) equation D dtUn = (2n − 1)(Un+1 − Un−1)−1, as well as the scalar case thereof. This equation was recently derived in the context of auto-Bäcklund transformations for a matri... Read More about The second Painlevé equation, a related nonautonomous semidiscrete equation, and a limit to the first Painlevé equation: scalar and matrix cases.

Behaviour of the extended modified Volterra lattice --reductions to generalised mKdV and NLS equations (2018)
Journal Article
Wattis, J. A., Gordoa, P., & Pickering, A. (2018). Behaviour of the extended modified Volterra lattice --reductions to generalised mKdV and NLS equations. Communications in Nonlinear Science and Numerical Simulation, 65, 98-110. https://doi.org/10.1016/j.cnsns.2018.05.016

We consider the first member of an extended modified Volterra lattice hierarchy. This system of equations is differential with respect to one independent variable and differential-delay with respect to a second independent variable. We use asymptot... Read More about Behaviour of the extended modified Volterra lattice --reductions to generalised mKdV and NLS equations.

Shape of transition layers in a differential--delay equation (2017)
Journal Article
Wattis, J. A. (in press). Shape of transition layers in a differential--delay equation. IMA Journal of Applied Mathematics, https://doi.org/10.1093/imamat/hxx011

We use asymptotic techniques to describe the bifurcation from steady-state to a periodic solution in the singularly perturbed delayed logistic equation ?x?(t) = ?x(t)+ ? f(x(t ? 1)) with ? ? 1. The solution has the form of plateaus of approximatel... Read More about Shape of transition layers in a differential--delay equation.

Monte Carlo simulation of single-chain square-well homopolymers (2017)
Journal Article
Wicks, T. J., Wattis, J. A., & Graham, R. (2018). Monte Carlo simulation of single-chain square-well homopolymers. Manuscript submitted for publication

We present Monte Carlo simulations of the crystallisation transition of single-chain square-well homopolymers. We combine parallel tempering with a non-standard choice of tempering levels, a bespoke biasing strategy and a method to map results betwe... Read More about Monte Carlo simulation of single-chain square-well homopolymers.

Band-gaps in long Josephson junctions with periodic phase-shifts (2017)
Journal Article
Ahmad, S., Susanto, H., & Wattis, J. A. (2017). Band-gaps in long Josephson junctions with periodic phase-shifts. Physics Letters A, 381(13), https://doi.org/10.1016/j.physleta.2017.01.062

We investigate analytically and numerically a long Josephson junction on an infnite domain, having arbitrary periodic phase shift of k, that is, the so-called 0-k long Josephson junction. The system is described by a one-dimensional sine-Gordon equat... Read More about Band-gaps in long Josephson junctions with periodic phase-shifts.

Mitochondrial phosphoenolpyruvate carboxykinase (PEPCK-M) and serine biosynthetic pathway genes are co-ordinately increased during anabolic agent-induced skeletal muscle growth (2016)
Journal Article
Brown, D. M., Williams, H., Ryan, K., Wilson, T., Daniel, Z. C., Mareko, M. H. D., …Parr, T. (2016). Mitochondrial phosphoenolpyruvate carboxykinase (PEPCK-M) and serine biosynthetic pathway genes are co-ordinately increased during anabolic agent-induced skeletal muscle growth. Scientific Reports, 6(1), https://doi.org/10.1038/srep28693

We aimed to identify novel molecular mechanisms for muscle growth during administration of anabolic agents. Growing pigs (Duroc/(Landrace/Large-White)) were administered Ractopamine (a beta-adrenergic agonist; BA; 20 ppm in feed) or Reporcin (recombi... Read More about Mitochondrial phosphoenolpyruvate carboxykinase (PEPCK-M) and serine biosynthetic pathway genes are co-ordinately increased during anabolic agent-induced skeletal muscle growth.

The effects of insulin resistance on individual tissues: an application of a mathematical model of metabolism in humans (2016)
Journal Article
Pearson, T., Wattis, J. A., King, J., McDonald, I., & Mazzatti, D. (in press). The effects of insulin resistance on individual tissues: an application of a mathematical model of metabolism in humans. Bulletin of Mathematical Biology, 78(6), https://doi.org/10.1007/s11538-016-0181-1

Whilst the human body expends energy constantly, the human diet consists of a mix of carbohydrates and fats delivered in a discontinuous manner. To deal with this sporadic supply of energy, there are transport, storage and utilisation mechanisms, for... Read More about The effects of insulin resistance on individual tissues: an application of a mathematical model of metabolism in humans.

Necessary conditions for breathers on continuous media to approximate breathers on discrete lattices (2015)
Journal Article
Smith, W., & Wattis, J. (2015). Necessary conditions for breathers on continuous media to approximate breathers on discrete lattices. European Journal of Applied Mathematics, 27(1), https://doi.org/10.1017/S0956792515000273

We start by considering the sine-Gordon partial differential equation (PDE with an arbitrary perturbation. Using the method of Kuzmak-Luke, we investigate those conditions the perturbation must satisfy in order for a breather solution to be a vali... Read More about Necessary conditions for breathers on continuous media to approximate breathers on discrete lattices.

Random sequential adsorption with two components: asymptotic analysis and finite size effects (2015)
Journal Article
Reeve, L., & Wattis, J. A. (2015). Random sequential adsorption with two components: asymptotic analysis and finite size effects. Journal of Physics A: Mathematical and Theoretical, 48(23), Article 235001. https://doi.org/10.1088/1751-8113/48/23/235001

We consider the model of random sequential adsorption (RSA) in which two lengths of rod-like polymer compete for binding on a long straight rigid one-dimensional substrate. We take all lengths to be discrete, assume that binding is irreversible, and... Read More about Random sequential adsorption with two components: asymptotic analysis and finite size effects.

Mathematical modelling of hepatic lipid metabolism (2015)
Journal Article
Pratt, A. C., Wattis, J. A., & Salter, A. M. (2015). Mathematical modelling of hepatic lipid metabolism. Mathematical Biosciences, 262, https://doi.org/10.1016/j.mbs.2014.12.012

The aim of this paper is to develop a mathematical model capable of simulating the metabolic response to a variety of mixed meals in fed and fasted conditions with particular emphasis placed on the hepatic triglyceride element of the model. Model va... Read More about Mathematical modelling of hepatic lipid metabolism.

Behaviour of the extended Toda lattice (2015)
Journal Article
Wattis, J. A., Gordoa, P. R., & Pickering, A. (2015). Behaviour of the extended Toda lattice. Communications in Nonlinear Science and Numerical Simulation, 28, https://doi.org/10.1016/j.cnsns.2015.04.006

We consider the first member of an extended Toda lattice hierarchy. This system of equations is differential with respect to one independent variable and differential-delay with respect to a second independent variable. We use asymptotic analysis to... Read More about Behaviour of the extended Toda lattice.

Scaling behavior near jamming in random sequential adsorption (2015)
Journal Article
Purves, B., Reeve, L., Wattis, J. A., & Mao, Y. (2015). Scaling behavior near jamming in random sequential adsorption. Physical Review E, 91(2), Article 022118. https://doi.org/10.1103/PhysRevE.91.022118

For the Random Sequential Adsorption model, we introduce the ‘availability’ as a new variable corresponding to the number of available locations in which an adsorbate can be accommodated. We investigate the relation of the availability to the coverag... Read More about Scaling behavior near jamming in random sequential adsorption.

Decay of bound states in a sine-Gordon equation with double well potentials (2015)
Journal Article
Ali, A., Susanto, H., & Wattis, J. A. (2015). Decay of bound states in a sine-Gordon equation with double well potentials. Journal of Mathematical Physics, 56, Article 051502. https://doi.org/10.1063/1.4917284

We consider a spatially inhomogeneous sine-Gordon equation with a double-well potential, describing long Josephson junctions with phase-shifts. We discuss the interactions of symmetric and antisymmetric bound states in the system. Using a multiple sc... Read More about Decay of bound states in a sine-Gordon equation with double well potentials.

A mathematical model of the human metabolic system and metabolic flexibility (2014)
Journal Article
Pearson, T., Wattis, J. A., King, J. R., MacDonald, I. A., & Mazzatti, D. (2014). A mathematical model of the human metabolic system and metabolic flexibility. Bulletin of Mathematical Biology, 76(9), https://doi.org/10.1007/s11538-014-0001-4

In healthy subjects some tissues in the human body display metabolic flexibility, by this we mean the ability for the tissue to switch its fuel source between predominantly carbohydrates in the post prandial state and predominantly fats in the fasted... Read More about A mathematical model of the human metabolic system and metabolic flexibility.

Discrete breathers in honeycomb Fermi-Pasta-Ulam lattices (2014)
Journal Article
Wattis, J. A., & James, L. M. (2014). Discrete breathers in honeycomb Fermi-Pasta-Ulam lattices. Journal of Physics A: Mathematical and Theoretical, 47(34), Article 345101. https://doi.org/10.1088/1751-8113/47/34/345101

We consider the two-dimensional Fermi-Pasta-Ulam lattice with hexagonal honeycomb symmetry, which is a Hamiltonian system describing the evolution of a scalar-valued quantity subject to nearest neighbour interactions. Using multiple-scale analy... Read More about Discrete breathers in honeycomb Fermi-Pasta-Ulam lattices.

Modelling the regulation of telomere length: the effects of telomerase and G-quadruplex stabilising drugs (2013)
Journal Article
Hirt, B. V., Wattis, J. A., & Preston, S. P. (2014). Modelling the regulation of telomere length: the effects of telomerase and G-quadruplex stabilising drugs. Journal of Mathematical Biology, 68(6), 1521-1552. https://doi.org/10.1007/s00285-013-0678-2

Telomeres are guanine-rich sequences at the end of chromosomes which shorten during each replication event and trigger cell cycle arrest and/or controlled death (apoptosis) when reaching a threshold length. The enzyme telomerase replenishes the ends... Read More about Modelling the regulation of telomere length: the effects of telomerase and G-quadruplex stabilising drugs.

Behaviour of the extended Volterra lattice (2013)
Journal Article
Pickering, A., Gordoa, P. R., & Wattis, J. A. (2013). Behaviour of the extended Volterra lattice. Communications in Nonlinear Science and Numerical Simulation, 19(3), https://doi.org/10.1016/j.cnsns.2013.07.009

We investigate the behaviour of solutions of the recently proposed extended Volterra lattice. A variety of methods are used to determine the effects of the new terms on small amplitude equations, and, following approximation of the partial differenti... Read More about Behaviour of the extended Volterra lattice.

The effects of a telomere destabilising agent on cancer cell-cycle dynamics - integrated modelling and experiments (2012)
Journal Article
Hirt, B. V., Wattis, J. A., Preston, S. P., & Laughton, C. A. (2012). The effects of a telomere destabilising agent on cancer cell-cycle dynamics - integrated modelling and experiments. Journal of Theoretical Biology, 295, https://doi.org/10.1016/j.jtbi.2011.10.038

The pentacyclic acridinium salt RHPS4 displays anti-tumour properties in vitro as well as in vivo and is potentially cell-cycle specific. We have collected experimental data and formulated a compartmental model using ordinary differential equations t... Read More about The effects of a telomere destabilising agent on cancer cell-cycle dynamics - integrated modelling and experiments.

Chiral polymerisation and the RNA world (2005)
Journal Article
Wattis, J. A., & Coveney, P. V. (2005). Chiral polymerisation and the RNA world. International Journal of Astrobiology, 4(1), https://doi.org/10.1017/S1473550405002454

The purpose of this paper is to review two mathematical models: one for the formation of homochiral polymers from an originally chirally symmetric system; and the other, to show how, in an RNA-world scenario, RNA can simultaneously act both as inf... Read More about Chiral polymerisation and the RNA world.

Nonlinear breathing modes at a defect (2004)
Journal Article
Wattis, J. A. (2004). Nonlinear breathing modes at a defect. Philosophical Transactions A: Mathematical, Physical and Engineering Sciences, 362,

Recent molecular dynamics (MD) simulations of Cubero et al (1999) of a DNA duplex containing the 'rogue' base difluorotoluene (F) in place of a thymine (T) base show that breathing events can occur on the nanosecond timescale, whereas breathing ev... Read More about Nonlinear breathing modes at a defect.

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.

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.

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.

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.

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.