arXiv subjects

Daniel G. Cocks

Publications and source records attributed to Daniel G. Cocks.

10 recordsLinked to original sources

arXiv2021

An improved set of electron-THFA cross sections refined through a neural network-based analysis of swarm data

We review experimental and theoretical cross sections for electron transport in $\alpha$-tetrahydrofurfuryl alcohol (THFA) and, in doing so, propose a plausible complete set. To assess the accuracy and self-consistency of our proposed set, we use the pulsed-Townsend technique to measure drift velocities, longitudinal diffusion coefficients and effective Townsend first ionisation coefficients for electron swarms in admixtures of THFA in argon, across a range of density-reduced electric fields from 1 Td to 450 Td. These measurements are then compared to simulated values derived from our proposed set using a multi-term solution of Boltzmann's equation. We observe discrepancies between the simulation and experiment, which we attempt to address by employing a neural network model that is trained to solve the inverse swarm problem of unfolding the cross sections underpinning our experimental swarm measurements. What results from our neural network-based analysis is a refined set of electron-THFA cross sections, which we confirm is of higher consistency with our swarm measurements than that we initially proposed. We also use our data base to calculate electron transport coefficients in pure THFA, across a range of reduced electric fields from 0.001 Td to 10,000 Td.

physics.plasm-ph↗

arXiv2020

Global stability properties of a class of renewal epidemic models with variable susceptibility

We investigate the global dynamics of a renewal-type epidemic model with variable susceptibility. We show that in this extended model there exists a unique endemic equilibrium and prove that it is globally asymptotically stable when $R_0 > 1$, i.e. when it exists. We also show that the infection-free equilibrium, which exists always, is globally asymptotically stable for $R_0 \leq 1$.

math.DS↗

arXiv2020

Self-consistent electron-THF cross sections derived using data-driven swarm analysis with a neural network model

We present a set of self-consistent cross sections for electron transport in gaseous tetrahydrofuran (THF), that refines the set published in our previous study [J. de Urquijo et al., J. Chem. Phys. 151, 054309 (2019)] by proposing modifications to the quasielastic momentum transfer, neutral dissociation, ionisation and electron attachment cross sections. These adjustments are made through the analysis of pulsed-Townsend swarm transport coefficients, for electron transport in pure THF and in mixtures of THF with argon. To automate this analysis, we employ a neural network model that is trained to solve this inverse swarm problem for realistic cross sections from the LXCat project. The accuracy, completeness and self-consistency of the proposed refined THF cross section set is assessed by comparing the analysed swarm transport coefficient measurements to those simulated via the numerical solution of Boltzmann's equation.

physics.plasm-ph↗

arXiv2019

Determining cross sections from transport coefficients using deep neural networks

We present a neural network for the solution of the inverse swarm problem of deriving cross sections from swarm transport data. To account for the uncertainty inherent to this somewhat ill-posed inverse problem, we train the neural network using cross sections from the LXCat project, paired with associated transport coefficients found by the numerical solution of Boltzmann's equation. The use of experimentally measured and theoretically calculated cross sections for training encourages the network to avoid unphysical solutions, such as those containing spurious energy-dependent oscillations. We successfully apply this machine learning approach to simulated swarm data for electron transport in helium, separately determining its elastic momentum transfer and ionisation cross sections to within an accuracy of $4\%$ over the range of energies considered. Our attempt to extend our method to argon was less successful, although the reason for that observation is well-understood. Finally, we explore the feasibility of simultaneously determining cross sections of helium using this approach. We have some success here, determining elastic, total $n=2$ excitation and ionisation cross sections to $10\%$, $20\%$ and $25\%$ accuracy, respectively. We are unsuccessful in properly unfolding the separate $n=2$ singlet and triplet excitation cross sections of helium, but this is as expected given their similar threshold energies.

physics.plasm-ph↗

arXiv2017

Global stability of the multi-strain Kermack-McKendrick (renewal) epidemic model

We extend a recent investigation by Meehan et al. (2019) regarding the global stability properties of the general Kermack-McKendrick (renewal) model to the multi-strain case. We demonstrate that the basic reproduction number of each strain $R_{0j}$ represents a sharp threshold parameter such that when $R_{0j} \leq 1$ for all $j$ each strain dies out and the infection-free equilibrium is globally asymptotically stable; whereas for $R_{01} \equiv \mathrm{max}_j\, R_{0j} > 1$ the endemic equilibrium point $\bar{P}^1$, at which only the fittest strain (i.e. strain 1) remains in circulation, becomes globally asymptotically stable.

q-bio.PE↗

arXiv2017

Global stability properties of renewal epidemic models

We investigate the global dynamics of a general Kermack-McKendrick-type epidemic model formulated in terms of a system of renewal equations. Specifically, we consider a renewal model for which both the force of infection and the infected removal rates are arbitrary functions of the infection age, $\tau$, and use the direct Lyapunov method to establish the global asymptotic stability of the equilibrium solutions. In particular, we show that the basic reproduction number, $R_0$, represents a sharp threshold parameter such that for $R_0\leq 1$, the infection-free equilibrium is globally asymptotically stable; whereas the endemic equilibrium becomes globally asymptotically stable when $R_0 > 1$, i.e. when it exists.

q-bio.PE↗

arXiv2016

Coupled, multi-strain epidemic models of mutating pathogens

We introduce and analyze coupled, multi-strain epidemic models designed to simulate the emergence and dissemination of mutant (e.g. drug-resistant) pathogen strains. In particular, we investigate the mathematical and biological properties of a general class of multi-strain epidemic models in which the infectious compartments of each strain are coupled together in a general manner. We derive explicit expressions for the basic reproduction number of each strain and highlight their importance in regulating the system dynamics (e.g. the potential for an epidemic outbreak) and the existence of nonnegative endemic solutions. Importantly, we find that the basic reproduction number of each strain is independent of the mutation rates between the strains --- even under quite general assumptions for the form of the infectious compartment coupling. Moreover, we verify that the coupling term promotes strain coexistence (as an extension of the competitive exclusion principle) and demonstrate that the strain with the greatest reproductive capacity is not necessarily the most prevalent. Finally, we briefly discuss the implications of our results for public health policy and planning.

q-bio.PE↗

arXiv2014

Long-range states in excited ultracold 3He-4He dimers

Long-range bound states of the excited heteronuclear 3He*--4He* system that dissociate to either 3He(1s2s 3S_1) + 4He(1s2p 3P_j) or 3He(1s2p 3P_j) + 4He(1s2s 3S_1), where j=0, 1, 2, are investigated using both single-channel and multichannel calculations in order to analyse the effects of Coriolis and non-adiabatic couplings. The multichannel calculations predict two groups of resonances above the lowest asymptotic energy. One of these groups dissociates to an atomic pair with the 2p excitation on the fermionic atom and the other dissociates to two asymptotes which correspond to the 2p excitation on either atom. Many of these resonances could be identified with levels in the single-channel calculation although the differences in energies were large. The total parity was found to have a significant influence on the ability to make these identifications. No purely bound states were found, although several resonances with line widths smaller than 1 MHz were obtained.

physics.atm-clus↗

arXiv2011

Photoassociation spectroscopy of ultracold metastable ^3He dimers

The bound states of the fermionic ^3He(2 ^3S_1)+ ^3He(2 ^3P_j)system, where j=0,1,2, are investigated using the recently available ab initio short-range ${}^{1,3,5}\Sigma^{+}_{g,u}$ and ${}^{1,3,5}\Pi_{g,u}$ potentials computed by Deguilhem et al. (J. Phys. B: At. Mol. Opt. Phys., 2009, 42, 015102). Single-channel and multichannel calculations have been undertaken in order to investigate the effects of Coriolis and non-adiabatic couplings. The possible experimental observability of the theoretical levels is assessed using criteria based upon the short-range character of each level and their coupling to metastable ground states. Purely long-range levels have been identified and 30 short-range levels near five asymptotes are suggested for experimental investigation.

physics.atm-clus↗

arXiv2009

Photoassociation spectra and the validity of the dipole approximation for weakly bound dimers

Photoassociation (PA) of ultracold metastable helium to the 2s2p manifold is theoretically investigated using a non-perturbative close-coupled treatment in which the laser coupling is evaluated without assuming the dipole approximation. The results are compared with our previous study [Cocks and Whittingham, Phys. Rev. A 80, 023417 (2009)] that makes use of the dipole approximation. The approximation is found to strongly affect the PA spectra because the photoassociated levels are weakly bound, and a similar impact is predicted to occur in other systems of a weakly bound nature. The inclusion or not of the approximation does not affect the resonance positions or widths, however significant differences are observed in the background of the spectra and the maximum laser intensity at which resonances are discernable. Couplings not satisfying the dipole selection rule |J-1| <= J' <= |J+1| do not lead to observable resonances.

physics.atom-ph↗