arXiv subjects

T. G. Myers

Publications and source records attributed to T. G. Myers.

14 recordsLinked to original sources

arXiv2026

One-Positron Quantum Cyclotron

A one-positron quantum cyclotron is realized with a single positron suspended indefinitely in the magnetic field of a Penning trap. This opens the possibility of quantum measurements of the positron magnetic moment at a precision much higher than attained with classical cyclotron motion. Comparing the magnetic moments measured using positron and electron quantum cyclotrons should provide the most stringent test of the fundamental CPT invariance of the Standard Model of particle physics in the lepton sector.

physics.ins-det↗

arXiv2026

On the use of equilibrium models to describe dynamic adsorption regimes

We present a column adsorption model that couples a Pseudo-First-Order (PFO) kinetic formulation with the Sips isotherm framework. Using a traveling wave approximation, we derive analytical solutions for specific operating conditions. Qualitatively, these solutions deviate significantly from their pure Sips counterparts: instead of a smooth, continuous increase in concentration at the column outlet, the PFO-Sips model predicts an abrupt, sudden breakthrough. We validate these analytical solutions against diverse experimental datasets from the literature. The results reveal that the PFO-based model consistently underperforms compared to the original Sips formulation. Furthermore, this validation exposes fundamental inconsistencies within the PFO framework. We demonstrate that despite its widespread use in the literature for almost a century, the PFO model is inherently flawed and structurally unfit for describing column adsorption dynamics.

math-ph↗

arXiv2024

Mathematical modelling of flow and adsorption in a gas chromatograph

In this paper, a mathematical model is developed to describe the evolution of the concentration of compounds through a gas chromatography column. The model couples mass balances and kinetic equations for all components. Both single and multiple-component cases are considered with constant or variable velocity. Non-dimensionalisation indicates the small effect of diffusion. The system where diffusion is neglected is analysed using Laplace transforms. In the multiple-component case, it is demonstrated that the competition between the compounds is negligible and the equations may be decoupled. This reduces the problem to solving a single integral equation to determine the concentration profile for all components (since they are scaled versions of each other). For a given analyte, we then only two parameters need to be fitted to the data. To verify this approach, the full governing equations are also solved numerically using the finite difference method and a global adaptive quadrature method to integrate the Laplace transformation. Comparison with the Laplace solution verifies the high degree of accuracy of the simpler Laplace form. The Laplace solution is then verified against experimental data from BTEX chromatography. This novel method, which involves solving a single equation and fitting parameters in pairs for individual components, is highly efficient. It is significantly faster and simpler than the full numerical solution and avoids the computationally expensive methods that would normally be used to fit all curves at the same time.

cs.CE↗

arXiv2024

A mathematical model for contaminant adsorption in packed columns using nonlinear mass transfer

We propose a mathematical model for describing column adsorption processes where large amounts of contaminant are removed from a carrier gas. The large mass loss causes velocity and pressure to be variables which must then be determined along with the contaminant and gas concentrations and adsorbed quantity. The adsorption rate is described using a Langmuir sink, which is physically more sensible than the linear sink used in a previous study. The proposed model is solved numerically and using a traveling wave approach. The analytical solutions are consistent with previous models with fixed gas velocity and provide excellent agreement when validated against experimental data.

cond-mat.stat-mech↗

arXiv2022

Measurement of the Electron Magnetic Moment

The electron magnetic moment,$-μ/μ_B = g/2 = 1.001 \, 159 \, 652 \, 180 \, 59 \, (13) \, [0.13\, \rm{ppt}]$, is determined 2.2 times more accurately than the value that stood for 14 years. The most precisely determined property of an elementary particle tests the most precise prediction of the Standard Model (SM) to $1$ part in $10^{12}$. The test would improve an order of magnitude if the uncertainty from discrepant measurements of the fine structure constant $α$ is eliminated since the SM prediction is a function of $α$. The new measurement and SM theory together predict $α^{-1}=137.035 \, 999 \, 166 \, (15) \, [0.11 \, \rm{ppb}]$ with an uncertainty ten times smaller than the current disagreement between measured $α$ values.

physics.atom-ph↗

arXiv2022

Magnetic nanodrug delivery in non-Newtonian blood flows

With the goal of determining strategies to maximise drug delivery to a specific site in the body, we developed a mathematical model for the transport of drug nanocarriers (nanoparticles) in the bloodstream under the influence of an external magnetic field. Under the assumption of long (compared to the radius) blood vessels the Navier-Stokes equations are reduced, to a simpler model consistently with lubrication theory. Under these assumptions, analytical results are compared for Newtonian, power-law, Carreau and Ellis fluids, and these clearly demonstrate the importance of shear thinning effects when modelling blood flow. Incorporating nanoparticles and a magnetic field to the model we develop a numerical scheme and study the particle motion for different field strengths. We demonstrate the importance of the non-Newtonian behaviour: for the flow regimes investigated in this work, consistent with those in blood micro vessels, we find that the field strength needed to absorb a certain amount of particles in a non-Newtonian fluid has to be larger than the one needed in a Newtonian fluid. Specifically, for one case examined, a two times larger magnetic force had to be applied in the Ellis fluid than in the Newtonian fluid for the same number of particles to be absorbed through the vessel wall. Consequently, models based on a Newtonian fluid can drastically overestimate the effect of a magnetic field. Finally, we evaluate the particle concentration at the vessel wall and compute the evolution of the particle flux through the wall for different permeability values, as that is important when assessing the efficacy of drug delivery applications. The insights from our work bring us a step closer to successfully transferring magnetic nanoparticle drug delivery to the clinic.

physics.flu-dyn↗

arXiv2020

Switchable Damping for a One-Particle Oscillator

The possibility to switch the damping rate for a one-electron oscillator is demonstrated, for an electron that oscillates along the magnetic field axis in a Penning trap. Strong axial damping can be switched on to allow this oscillation to be used for quantum nondemolition detection of the cyclotron and spin quantum state of the electron. Weak axial damping can be switched on to circumvent the backaction of the detection motion that has limited past measurements. The newly developed switch will reduce the linewidth of the cyclotron transition of one-electron by two orders of magnitude.

quant-ph↗

arXiv2020

Mass transfer from a fluid flowing through a porous media

A mathematical model is developed for the process of mass transfer from a fluid flowing through a packed column. Mass loss, whether by absorption or adsorption, may be significant. This is appropriate for example when removing contaminants from flue gases. With small mass loss the model reduces to a simpler form which is appropriate to describe the removal of contaminants/pollutants from liquids. A case study is carried out for the removal of CO2 from a gas mixture passing over activated carbon. Using the experimental parameter values it is shown, via non-dimensionalisation, that certain terms may be neglected from the governing equations, resulting in a form which may be solved analytically using a travelling wave substitution. From this all important quantities throughout the column may be described; concentration of gaseous materials, amount of material available for mass transfer, fluid velocity and pressure. Results are verified by comparison with experimental data for the breakthrough curve (the amount of carbon measured at the column outlet). The advantage of the analytical expression over a purely numerical solution is that it can easily be used to optimise the process. In the final section we demonstrate how the model may be further reduced when small amounts of contaminant are removed. The model is shown to exhibit better agreement than established models when compared to experimental data for the removal of amoxicillin and congo red dye from water.

cond-mat.other↗

arXiv2020

Mathematical modelling of carbon capture in a packed column by adsorption

A mathematical model of the process of carbon capture in a packed column by adsorption is developed and analysed. First a detailed study is made of the governing equations. Due to the complexity of the internal geometry it is standard practice to average these equations. Here the averaging process is revisited. This shows that there exists a number of errors and some confusion in the standard systems studied in the literature. These errors affect the parameter estimation, with consequences when the experimental set-up is modified or scaled-up. Assuming, as a first approximation, an isothermal model the gas concentration equation is solved numerically. Excellent agreement with data from a pressure swing adsorption experiment is demonstrated. A new analytical solution (valid away from the inlet) is obtained. This provides explicit relations for quantities such as the amount of adsorbed gas, time of first breakthrough, total process time and width and speed of the reaction zone, showing how these depend on the operating conditions and material parameters. The relations show clearly how to optimise the carbon capture process. By comparison with experimental data the analytical solution may also be used to calculate unknown system parameters.

cond-mat.other↗

arXiv2019

Towards an Improved Test of the Standard Model's Most Precise Prediction

The electron and positron magnetic moments are the most precise prediction of the standard model of particle physics. The most accurate measurement of a property of an elementary particle has been made to test this result. A new experimental method is now being employed in an attempt to improve the measurement accuracy by an order of magnitude. Positrons from a "student source" now suffice for the experiment. Progress toward a new measurement is summarized.

quant-ph↗

arXiv2019

Does mathematics contribute to the nanofluid debate?

Recent experimental evidence has clearly demonstrated that nanofluids do not provide the greatly enhanced heat transfer predicted in the past. Despite seemingly conclusive proof there is still a great deal of current mathematical research asserting the opposite result. In this paper we scrutinise the mathematical work and demonstrate that the disagreement can be traced to a number of issues. These include the incorrect formulation of the governing equations; the use of parameter values orders of magnitude different to the true values (some requiring nanoparticle volume fractions greater than unity and nanoparticles smaller than atoms); model choices that are based on permitting a reduction using similarity variables as opposed to representing an actual physical situation; presentation of results using different scalings for each fluid.

physics.flu-dyn↗

arXiv2019

Optical diffraction from isolated nanoparticles

When subjected to monochromatic incident light a nanoparticle will emit light which then interferes with the incident beam. With sufficient contrast and sufficiently close to the particle this interference pattern may be recorded with a pointed optical fiber in collection mode. It is shown that the analytic dipole model accurately reproduces the observed interference pattern. Using this model and measuring only the lengths of the first two major axes of the observed elliptical fringes we are able to reproduce and quantify the fringe pattern. Importantly, we are able to locate the nanoparticle, with respect to the fibre, using only visible light in a simple experimental setup. For the case described where the image plane is of the order microns above the substrate, hence the fringe number is large, it is shown that the prediction for the particle location and fringe number is insensitive to measurement errors. The phase shift of the scattered wave, a quantity that is notoriously difficult to measure, is easily determined from the theory however it is very sensitive to errors.

physics.optics↗

arXiv2019

Nanocrystal growth via the precipitation method

A mathematical model to describe the growth of an arbitrarily large number of nanocrystals from solution is presented. First, the model for a single particle is developed. By non-dimensionalising the system we are able to determine the dominant terms and reduce it to the standard pseudo-steady approximation. The range of applicability and further reductions are discussed. An approximate analytical solution is also presented. The one particle model is then generalised to $N$ well dispersed particles. By setting $N=2$ we are able to investigate in detail the process of Ostwald ripening. The various models, the $N$ particle, single particle and the analytical solution are compared against experimental data, all showing excellent agreement. By allowing $N$ to increase we show that the single particle model may be considered as representing the average radius of a system with a large number of particles. Following a similar argument the $N=2$ model could describe an initially bimodal distribution. The mathematical solution clearly shows the effect of problem parameters on the growth process and, significantly, that there is a single controlling group. The model provides a simple way to understand nanocrystal growth and hence to guide and optimise the process.

cond-mat.mes-hall↗

arXiv2017

A slip-based model for the size-dependent effective thermal conductivity of nanowires

The heat flux across a nanowire is computed based on the Guyer-Krumhansl equation. Slip conditions with a slip length depending on both temperature and nanowire radius are introduced at the outer boundary. An explicit expression for the effective thermal conductivity is derived and compared to existing models across a given temperature range, providing excellent agreement with experimental data for Si nanowires.

cond-mat.mes-hall↗