arXiv subjects

Andrew Zangwill

Publications and source records attributed to Andrew Zangwill.

11 recordsLinked to original sources

arXiv2025

Aubry-Andr\'e Localization Transition for an Active Undulator

The transport of deformable self-propelling objects like bacteria, worms, snakes, and robots through heterogeneous environments is poorly understood. In this paper, we use experiment, simulation, and theory to study a snake-like robot as it undulates without sensory feedback through a narrow channel containing a linear array of boulder-like hemispherical obstacles. The profile of the boulder landscape approximates a one-dimensional potential introduced by Aubry and Andr\'e (AA) to study wave function localization in aperiodic lattices. The AA model provides a deterministically disordered alternative to the better-known phenomenon of Anderson localization, which occurs in truly random disordered lattices. When the boulder landscape is strictly periodic, the robot can pass completely through the channel. But if the landscape is sufficiently aperiodic, the robot becomes trapped and fails to exit the channel. The metrics we use to quantify this transition -- including exponential distributions of robot position when localized -- agree well with earlier experimental and theoretical work on a localization transition that occurs when quantum waves interact with the AA potential. A theoretical treatment of the robot's motion using resistive force theory modified to include spatially varying drag forces reproduces the behavior we observe. Further, our results indicate that the transition is generated by large fluctuations in the driving torques required for self-propulsion. These results point to a potentially fundamental connection between classical and quantum wave mechanics and the locomotion of undulators. Our study illustrates how analogies with models from condensed matter physics and wave optics can lead to the discovery of principles of self-propulsion in non-periodic landscapes.

physics.bio-ph↗

arXiv2018

The dynamics of scattering in undulatory active collisions

Natural and artificial self-propelled systems must manage environmental interactions during movement. Such interactions, which we refer to as active collisions, are fundamentally different from momentum-conserving interactions studied in classical physics, largely because the internal driving of the locomotor can lead to persistent contact with heterogeneities. Here, we experimentally and numerically study the effects of active collisions on a laterally-undulating sensory-deprived robophysical model, whose dynamics are applicable to self-propelled systems across length scales and environments. The robot moves via spatial undulation of body segments, with a nearly-linear center-of-geometry trajectory. Interactions with a single rigid post scatter the robot, and these deflections are proportional to the head-post contact duration. The distribution of scattering angles is smooth and strongly-peaked directly behind the post. Interactions with a single row of evenly-spaced posts (with inter-post spacing $d$) produce distributions reminiscent of far-field diffraction patterns: as $d$ decreases, distinct secondary peaks emerge as large deflections become more likely. Surprisingly, we find that the presence of multiple posts does not change the nature of individual collisions; instead, multi-modal scattering patterns arise from multiple posts altering the likelihood of individual collisions to occur. As $d$ decreases, collisions near the leading edges of the posts become more probable, and we find that these interactions are associated with larger deflections. Our results, which highlight the surprising dynamics that can occur during active collisions of self-propelled systems, can inform control principles for locomotors in complex terrain and facilitate design of task-capable active matter.

physics.class-ph↗

arXiv2014

The education of Walter Kohn and the creation of density functional theory

The theoretical solid-state physicist Walter Kohn was awarded one-half of the 1998 Nobel Prize in Chemistry for his mid-1960's creation of an approach to the many-particle problem in quantum mechanics called density functional theory (DFT). In its exact form, DFT establishes that the total charge density of any system of electrons and nuclei provides all the information needed for a complete description of that system. This was a breakthrough for the study of atoms, molecules, gases, liquids, and solids. Before DFT, it was thought that only the vastly more complicated many-electron wave function was needed for a complete description of such systems. Today, fifty years after its introduction, DFT (in one of its approximate forms) is the method of choice used by most scientists to calculate the physical properties of materials of all kinds. In this paper, I present a biographical essay of Kohn's educational experiences and professional career up to and including the creation of DFT.

physics.hist-ph↗

arXiv2011

Model and Simulations of the Epitaxial Growth of Graphene on Non-Planar 6H-SiC Surfaces

We study step flow growth of epitaxial graphene on 6H-SiC using a one dimensional kinetic Monte Carlo model. The model parameters are effective energy barriers for the nucleation and propagation of graphene at the SiC steps. When the model is applied to graphene growth on vicinal surfaces, a strip width distribution is used to characterize the surface morphology. Additional kinetic processes are included to study graphene growth on SiC nano-facets. Our main result is that the original nano-facet is fractured into several nano-facets during graphene growth. This phenomenon is characterized by the angle at which the fractured nano-facet is oriented with respect to the basal plane. The distribution of this angle across the surface is found to be related to the strip width distribution for vicinal surfaces. As the terrace propagation barrier decreases, the fracture angle distribution changes continously from two-sided Gaussian to one-sided power-law. Using this distribution, it will be possible to extract energy barriers from experiments and interpret the growth morphology quantitatively.

cond-mat.mes-hall↗

arXiv2011

A model for the epitaxial growth of graphene on 6H-SiC

We introduce a kinetic model for the growth of epitaxial graphene on 6H-SiC. The model applies to vicinal surfaces composed of half-unit-cell height steps where experiment shows that step flow sublimation of SiC promotes the formation and growth of graphene strips parallel to the step edges. The model parameters are effective energy barriers for the nucleation and subsequent propagation of graphene at the step edges. Using both rate equations and kinetic Monte Carlo simulations, two distinct growth regimes emerge from a study of the layer coverage and distribution of top-layer graphene strip widths as a function of total coverage, vicinal angle, and the model parameters. One regime is dominated by the coalescence of strips. The other regime is dominated by a novel "climb-over" process which facilitates the propagation of graphene from one terrace to the next. Comparing our results to scanning microscopy studies will provide the first quantitative insights into the kinetics of growth for this unique epitaxial system.

cond-mat.mes-hall↗

arXiv2010

Novel growth mechanism of epitaxial graphene on metals

Graphene, a hexagonal sheet of $sp^2$-bonded carbon atoms, has extraordinary properties which hold immense promise for future nanoelectronic applications. Unfortunately, the popular preparation methods of micromechanical cleavage and chemical exfoliation of graphite do not easily scale up for application purposes. Epitaxial graphene provides an attractive alternative, though there are many challenges, not least of which is the absence of an understanding of the complex atomistic assembly kinetics of graphene. Here, we present a simple rate theory of epitaxial graphene growth on close-packed metal surfaces. Based on recent low-energy electron-diffraction microscopy experiments (LEEM) \cite{loginova09}, our theory supposes that graphene islands grow predominantly by the addition of five-atom clusters, rather than solely by the capture of diffusing carbon atoms. With suitably chosen kinetic parameters, our theory produces a time-dependent carbon adatom density that is in quantitative agreement with measured data. The temperature-dependence of this adatom density at the onset of nucleation leads us to predict that the smallest stable precursor to graphene growth is an immobile island composed of six five-atom clusters. Our findings provide a starting point for more detailed simulations which will yield important input to developing strategies for the large-scale production of epitaxial graphene.

cond-mat.mes-hall↗

arXiv2010

Phase Field Modelling of Submonolayer Epitaxial Growth

We report simulations of submonolayer epitaxial growth using a continuum phase field model. The island density and the island size distribution both show scaling behavior. When the capillary length is small, the island size distribution is consistent with irreversible aggregation kinetics. As the capillary length increases, the island size distribution reflects the effects of reversible aggregation. These results are in quantitative agreement with other simulation methods and with experiments. However, the scaling of the island total density does not agree with known results. The reasons are traced to the mechanisms of island nucleation and aggregation in the phase field model.

cond-mat.mes-hall↗

arXiv2009

Step-edge instability during epitaxial growth of graphene from SiC(0001)

The unique electronic properties of graphene offer the possibility that it could replace silicon when microelectronics evolves to nanoelectronics. Graphene grown epitaxially on silicon carbide is particularly attractive in this regard because SiC is itself a useful semiconductor and, by suitable manipulation of the growth conditions, epitaxial films can be produced that exhibit all the transport properties of ideal, two-dimensional graphene desired for device applications. Nevertheless, there is little or no understanding of the actual kinetics of growth, which is likely to be required for future process control. As a step in this direction, we propose a local heat release mechanism to explain finger-like structures observed when graphene is grown by step flow decomposition of SiC(0001). Using a continuum equation of motion for the shape evolution of a moving step, a linear stability analysis predicts whether a shape perturbation of a straight moving step grows or decays as a function of growth temperature, the background pressure of Si maintained during growth, and the effectiveness of an inert buffer gas to retard the escape of Si atoms from the crystal surface. The theory gives semi-quantitative agreement with experiment for the characteristic separation between fingers observed when graphene is grown in a low-pressure induction furnace or under ultrahigh vacuum conditions.

cond-mat.mtrl-sci↗

arXiv2009

Step bunching of vicinal 6H-SiC{0001} surfaces

We use kinetic Monte Carlo simulations to understand growth- and etching-induced step bunching of 6H-SiC{0001} vicinal surfaces oriented towards [1-100] and [11-20]. By taking account of the different rates of surface diffusion on three inequivalent terraces, we reproduce the experimentally observed tendency for single bilayer height steps to bunch into half unit cell height steps. By taking account of the different mobilities of steps with different structures, we reproduce the experimentally observed tendency for adjacent pairs of half unit cell height steps to bunch into full unit cell height steps. A prediction of our simulations is that growth-induced and etching-induced step bunching lead to different surface terminations for the exposed terraces when full unit cell height steps are present.

cond-mat.mtrl-sci↗

arXiv2000

Convective instability on a crystal surface

The distinction between absolute and convective instabilities is well known in the context of hydrodynamics and plasma physics. In this Letter, we examine an epitaxial crystal growth model from this point of view and show that a strain-induced step bunching instability can be convective. Using analytic stability theory and numerical simulations, we study the response of the crystal surface to an inhomogeneous deposition flux that launches impulsive and time-periodic perturbations to a uniform array of steps. The results suggest a new approach to morphological patterning.

cond-mat.mtrl-sci↗

arXiv1999

Epitaxial Growth Kinetics with Interacting Coherent Islands

The Stranski-Krastanov growth kinetics of undislocated (coherent) 3-dimensional islands is studied with a self-consistent mean field rate theory that takes account of elastic interactions between the islands. The latter are presumed to facilitate the detachment of atoms from the islands with a consequent decrease in their average size. Semi-quantitative agreement with experiment is found for the time evolution of the total island density and the mean island size. When combined with scaling ideas, these results provide a natural way to understand the often-observed initial increase and subsequent decrease in the width of the coherent island size distribution.

cond-mat.stat-mech↗