arXiv subjects

Nathaniel J. Fuller

Publications and source records attributed to Nathaniel J. Fuller.

4 recordsLinked to original sources

arXiv2025

Detection and Ranging Beyond the Canonical Resolution Limit

The canonical range resolution limit in radar, sonar, and lidar systems is found to be a special case of a more general resolution limit. The general limit indicates that it is possible to surpass the canonical limit in moderate (of order unity) signal-to-noise ratio (SNR) environments by using the signal amplitude and phase information. The canonical limit only considers the bandwidth of the received signal without considering how SNR affects the range resolution. Details present in the signal amplitude, such as attenuation and geometric spreading, can act as additional sources of range information. Previous studies have taken advantage of the relationship between target distance and signal amplitude or phase to achieve higher resolution ranging, and often employ unusual transmit waveforms for this purpose. These methods each provide distinct bounds on range resolution, rather than a unified bound applicable across different systems and applications. We apply ideas from information theory to determine a general lower bound to the smallest resolvable range bin size and corresponding target strength measurements.

physics.app-ph↗

arXiv2021

Quasi-stable Localized Excitations in the β-Fermi Pasta Ulam Tsingou System

The lifetimes of localized nonlinear modes in both the $β$-Fermi-Pasta-Ulam-Tsingou ($β$-FPUT) chain and a cubic $β$-FPUT lattice are studied as functions of perturbation amplitude, and by extension, the relative strength of the nonlinear interactions compared to the linear part. We first recover the well known result that localized nonlinear excitations (LNEs) produced by a bond squeeze can be reduced to an approximate two-frequency solution and then show that the nonlinear term in the potential can lead to the production of secondary frequencies within the phonon band. This can affect the stability and lifetime of the LNE by facilitating interactions between the LNE and a low energy acoustic background which can be regarded as "noise" in the system. In the one dimensional FPUT chain, the LNE is stabilized by low energy acoustic emissions at early times; in some cases allowing for lifetimes several orders of magnitude larger than the oscillation period. The longest lived LNEs are found to satisfy the parameter dependence $\mathcal{A}\sqrtβ\approx1.1$ where $β$ is the relative nonlinear strength and $\mathcal{A}$ is the displacement amplitude of the center particles in the LNE. In the cubic FPUT lattice, the LNE lifetime $T$ decreases rapidly with increasing amplitude $\mathcal{A}$ and is well described by the double log relationship $\log_{10}\log_{10}(T)\approx -(0.15\pm0.01)\mathcal{A}\sqrtβ+(0.62\pm0.02)$.

nlin.PS↗

arXiv2019

Nonlinear normal modes in the $β$-Fermi-Pasta-Ulam-Tsingou chain

Nonlinear normal mode solutions of the $β$-FPUT chain with fixed boundaries are presented in terms of the Jacobi sn function. Exact solutions for the two particle chain are found for arbitrary linear and nonlinear coupling strengths. Solutions for the N-body chain are found for purely nonlinear couplings. Three distinct solution types presented: a linear analogue, a chaotic amplitude mapping, and a localized nonlinear mode. The relaxation of perturbed modes are also explored using $l_{1}$-regularized least squares regression to estimate the free energy functional near the nonlinear normal mode solution. The perturbed modes are observed to decay sigmoidally towards a quasi-equilibrium state and a logarithmic relationship between the perturbation strength and mode lifetime is found.

nlin.PS↗

arXiv2017

Numerical and analytical approaches to an advection-diffusion problem at small Reynolds number and large Péclet number

Obtaining a detailed understanding of the physical interactions between a cell and its environment often requires information about the flow of fluid surrounding the cell. Cells must be able to effectively absorb and discard material in order to survive. Strategies for nutrient acquisition and toxin disposal, which have been evolutionarily selected for their efficacy, should reflect knowledge of the physics underlying this mass transport problem. Motivated by these considerations, in this paper we discuss the results from an undergraduate research project on the advection-diffusion equation at small Reynolds number and large Péclet number. In particular, we consider the problem of mass transport for a Stokesian spherical swimmer. We approach the problem numerically and analytically through a rescaling of the concentration boundary layer. A biophysically motivated first-passage problem for the absorption of material by the swimming cell demonstrates quantitative agreement between the numerical and analytical approaches. We conclude by discussing the connections between our results and the design of smart toxin disposal systems.

physics.bio-ph↗