All Outputs (1650)

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 importance of different timings of excitatory and inhibitory pathways in neural field models
Journal Article
Laing, C., & Coombes, S. (2005). The importance of different timings of excitatory and inhibitory pathways in neural field models

In this paper we consider a neural field model comprised of two distinct populations of neurons, excitatory and inhibitory, for which both the velocities of action potential propagation and the time courses of synaptic processing are different. Using... Read More about The importance of different timings of excitatory and inhibitory pathways in neural field models.

Dendritic cable with active spines: a modeling study in the spike-diffuse-spike framework
Journal Article
Timofeeva, Y., Lord, G., & Coombes, S. (2005). Dendritic cable with active spines: a modeling study in the spike-diffuse-spike framework

The spike-diffuse-spike (SDS) model describes a passive dendritic tree with active dendritic spines. Spine-head dynamics is modelled with a simple integrate-and-fire process, whilst communication between spines is mediated by the cable equation. Her... Read More about Dendritic cable with active spines: a modeling study in the spike-diffuse-spike framework.

Symmetric Interior Penalty DG Methods for the Compressible Navier-Stokes Equations I: Method Formulation
Journal Article
Navier-Stokes Equations I: Method Formulation

In this article we consider the development of discontinuous Galerkin finite element methods for the numerical approximation of the compressible Navier-Stokes equations. For the discretization of the leading order terms, we propose employing the gene... Read More about Symmetric Interior Penalty DG Methods for the Compressible Navier-Stokes Equations I: Method Formulation.

Symmetric Interior Penalty DG Methods for the Compressible Navier-Stokes Equations II: Goal--Oriented A Posteriori Error Estimation
Journal Article
Hartmann, R., & Houston, P. (2005). Symmetric Interior Penalty DG Methods for the Compressible Navier-Stokes Equations II: Goal--Oriented A Posteriori Error Estimation

In this article we consider the application of the generalization of the symmetric version of the interior penalty discontinuous Galerkin finite element method to the numerical approximation of the compressible Navier--Stokes equations. In particular... Read More about Symmetric Interior Penalty DG Methods for the Compressible Navier-Stokes Equations II: Goal--Oriented A Posteriori Error Estimation.

Waves, bumps, and patterns in neural field theories
Journal Article
Coombes, S. (2005). Waves, bumps, and patterns in neural field theories

Neural field models of firing rate activity have had a major impact in helping to develop an understanding of the dynamics seen in brain slice preparations. These models typically take the form of integro-differential equations. Their non-local nat... Read More about Waves, bumps, and patterns in neural field theories.

Enhancing SPH using moving least-squares and radial basis functions
Journal Article
Brownlee, R., Houston, P., Levesley, J., & Rosswog, S. (2005). Enhancing SPH using moving least-squares and radial basis functions

In this paper we consider two sources of enhancement for the meshfree Lagrangian particle method smoothed particle hydrodynamics (SPH) by improving the accuracy of the particle approximation. Namely, we will consider shape functions constructed using... Read More about Enhancing SPH using moving least-squares and radial basis functions.

Discontinuous Galerkin Computation of the Maxwell Eigenvalues on Simplicial Meshes
Journal Article
Buffa, A., Houston, P., & Perugia, I. (2005). Discontinuous Galerkin Computation of the Maxwell Eigenvalues on Simplicial Meshes

This paper is concerned with the discontinuous Galerkin approximation of the Maxwell eigenproblem. After reviewing the theory developed in [5], we present a set of numerical experiments which both validate the theory, and provide further insight reg... Read More about Discontinuous Galerkin Computation of the Maxwell Eigenvalues on Simplicial Meshes.

A posteriori error estimation for discontinuous Galerkin discretizations of H(curl)-elliptic partial differential equations
Journal Article
discretizations of H(curl)-elliptic partial differential equations

We develop the a posteriori error estimation of interior penalty discontinuous Galerkin discretizations for H(curl)-elliptic problems that arise in eddy current models. Computable upper and lower bounds on the error measured in terms of a natural (me... Read More about A posteriori error estimation for discontinuous Galerkin discretizations of H(curl)-elliptic partial differential equations.

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.

Clustering through post inhibitory rebound in synaptically coupled neurons
Journal Article
Chik, D. T. W., Coombes, S., & Wang, Z. D. (2004). Clustering through post inhibitory rebound in synaptically coupled neurons

Post inhibitory rebound is a nonlinear phenomenon present in a variety of nerve cells. Following a period of hyper-polarization this effect allows a neuron to fire a spike or packet of spikes before returning to rest. It is an important mechanism u... Read More about Clustering through post inhibitory rebound in synaptically coupled neurons.

Receptors, sparks and waves in a fire-diffuse-fire framework for calcium release
Journal Article
Coombes, S., Hinch, R., & Timofeeva, Y. (2004). Receptors, sparks and waves in a fire-diffuse-fire framework for calcium release

Calcium ions are an important second messenger in living cells. Indeed calcium signals in the form of waves have been the subject of much recent experimental interest. It is now well established that these waves are composed of elementary stochasti... Read More about Receptors, sparks and waves in a fire-diffuse-fire framework for calcium release.

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.

On the reduction theory of binary forms
Journal Article
Cremona, J. E., & Stoll, M. (2001). On the reduction theory of binary forms

Cremona developed a reduction theory for binary forms of degree 3 and 4 with integer coefficients, the motivation in the case of quartics being to improve 2-descent algorithms for elliptic curves over Q. In this paper we extend some of these result... Read More about On the reduction theory of binary forms.

State sum models for quantum gravity
Journal Article
Barrett, J. W. (2000). State sum models for quantum gravity

This paper reviews the construction of quantum field theory on a 4-dimensional spacetime by combinatorial methods, and discusses the recent developments in the direction of a combinatorial construction of quantum gravity.

Unlinked Embedded Graphs
Journal Article
Barrett, J. W. (2000). Unlinked Embedded Graphs

This paper is a self-contained development of an invariant of graphs embedded in three-dimensional Euclidean space using the Jones polynomial and skein theory. Some examples of the invariant are computed. An unlinked embedded graph is one that contai... Read More about Unlinked Embedded Graphs.