arXiv subjects

D. J. Ratliff

Publications and source records attributed to D. J. Ratliff.

5 recordsLinked to original sources

arXiv2026

Understanding Non-Gaussian Chorus Wave Statistics via the Benjamin-Feir Index

We derive an extended wave action model for equatorial chorus waves, identifying a wave activity index (a version of the Benjamin-Feir index, BFI) which indicates non-Gaussian frequency spectra emerge when BFI$>$0.5. Global maps of this index indicate the night and dawn sectors ($0<{\rm MLT}<9)$ of the magnetosphere as the primary region for non-Gaussian wave statistics to emerge. Comparisons with events measured by the Van Allen probe A demonstrate good qualitative agreement whilst identifying key aspects for model refinement. A key strength of our model that our work highlights is its ability to account for the asymmetric frequency spectra characteristic of non-Gaussian chorus. This work ultimately establishes the first wave activity index that distinguishes Gaussian and non-Gaussian wave scenarios from first principles, providing the groundwork for a threshold-based quantification for use in space weather modelling.

physics.plasm-ph↗

arXiv2026

Tuning polymer architecture for quasicrystal self-assembly

Using computer simulations and theory, we investigate the ultrasoft interactions between dendrimers formed of a central polymer connected by stiff linkers to a corona of flexible polymers, forming `pompoms' at the ends of the linkers. We show that the resulting coarse-grained interaction potential between pairs of dendrimers exhibits tunable lengthscale competition based on properties of the core and corona polymers. We present a simple model for this pair potential, which we confirm using accelerated Monte Carlo methods. We then demonstrate the connection between dendrimer structure and mesoscopic phases by presenting parameter choices that result in stable dodecagonal quasicrystals, and show that the size of the region in the phase diagram where quasicrystals are stable can be controlled by tuning details of the polymer architecture alone. These results pave the way for experimental realization of soft matter quasicrystals by identifying what overall molecular architecture leads to their stability.

cond-mat.soft↗

arXiv2021

Kink-antikink stripe interactions in the two-dimensional sine-Gordon equation

The main focus of the present work is to study quasi-one-dimensional kink-antikink stripes embedded in the two-dimensional sine-Gordon equation. Using variational techniques, we reduce the interaction dynamics between a kink and an antikink stripe on their respective time and space dependent widths and locations. The resulting reduced system of coupled equations is found to accurately describe the width and undulation dynamics of a single kink stripe as well as that of interacting ones. As an aside, we also discuss two related topics: the computational identification of the kink center and its numerical implications and alternative perturbative and multiple scales approaches to the transverse direction induced dynamics for a single kink stripe in the two-dimensional realm.

nlin.PS↗

arXiv2019

Which wavenumbers determine the thermodynamic stability of soft matter quasicrystals?

For soft matter to form quasicrystals an important ingredient is to have two characteristic lengthscales in the interparticle interactions. To be more precise, for stable quasicrystals, periodic modulations of the local density distribution with two particular wavenumbers should be favored, and the ratio of these wavenumbers should be close to certain special values. So, for simple models, the answer to the title question is that only these two ingredients are needed. However, for more realistic models, where in principle all wavenumbers can be involved, other wavenumbers are also important, specifically those of the second and higher reciprocal lattice vectors. We identify features in the particle pair interaction potentials which can suppress or encourage density modes with wavenumbers associated with one of the regular crystalline orderings that compete with quasicrystals, enabling either the enhancement or suppression of quasicrystals in a generic class of systems.

cond-mat.soft↗

arXiv2018

Dispersive Dynamics in the Characteristic Moving Frame

A mechanism for dispersion to automatically arise from the dispersionless Whitham Modulation equations (WMEs) is presented, relying on the use of a moving frame. The speed of this is chosen to be one of the characteristics which emerge from the linearisation of the Whitham system, and assuming these are real (and thus the WMEs are hyperbolic) morphs the WMEs into the Korteweg - de Vries (KdV) equation in the boosted co-ordinate. Strikingly, the coefficients of the KdV equation are universal, in the sense that they are determined by abstract properties of the original Lagrangian density. Two illustrative examples of the theory are given to illustrate how the KdV may be constructed in practice. The first being a revisitation of the derivation of the KdV equation from shallow water flows, to highlight how the theory of this paper fits into the existing literature. The second is a complex Klein-Gordon system, providing a case where the KdV equation may only arise with a moving frame.

nlin.PS↗