All Outputs (51)

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 εx˙(t) = −x(t)+ λ f(x(t − 1)) with ε ≪ 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. 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., Emes, R. D., Harris, D. W., Wattis, J. A., Dryden, I. L., Hodgman, T. C., Brameld, J. M., & 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; 20ppm in feed) or Reporcin (recombin... 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.

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.

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.