arXiv subjects

James Chapman

Publications and source records attributed to James Chapman.

28 records · Page 2Linked to original sources

arXiv2021

A Physically-informed Graph-based Order Parameter for the Universal Characterization of Atomic Structures

A new graph-based order parameter is introduced for the characterization of atomistic structures. The order parameter is universal to any material/chemical system, and is transferable to all structural geometries. Three sets of data are used to validate both the generalizability and accuracy of the algorithm: (1) liquid lithium configurations spanning up to 300 GPa, (2) condensed phases of carbon along with nanotubes and buckyballs at ambient and high temperature, and (3) a diverse set of aluminum configurations including surfaces, compressed and expanded lattices, point defects, grain boundaries, liquids, nanoparticles, all at non-zero temperatures. The aluminum configurations are also compared to existing characterization methods for both speed and accuracy. Our order parameter uniquely classifies every configuration and outperforms all crystalline order parameters studied here, opening the door for its use in a multitude of complex application spaces that can require fine configurational characterization of materials.

cond-mat.mtrl-sci↗

arXiv2020

On the Determinant Problem for the Relativistic Boltzmann Equation

This article considers a long-outstanding open question regarding the Jacobian determinant for the relativistic Boltzmann equation in the center-of-momentum coordinates. For the Newtonian Boltzmann equation, the center-of-momentum coordinates have played a large role in the study of the Newtonian non-cutoff Boltzmann equation, in particular, we mention the widely used cancellation lemma by Alexandre et al. (Arch. Ration. Mech. Anal. 152(4):327-355, 2000). In this article we calculate specifically the very complicated Jacobian determinant, in ten variables, for the relativistic collision map from the momentum $p$ to the post-collisional momentum $p'$; specifically we calculate the determinant for $p\mapsto u = θp'+\left(1-θ\right)p$ for $θ\in [0,1]$. Afterwards we give an upper-bound for this determinant that has no singularity in both $p$ and $q$ variables. Next we give an example where we prove that the Jacobian goes to zero in a specific pointwise limit. We further explain the results of our numerical study which shows that the Jacobian determinant has a very large number of distinct points at which it is machine zero. This generalizes the work of Glassey-Strauss (Transport Theory Statist. Phys. 20(1):55-68, 1991) and Guo-Strain (Comm. Math. Phys. 310(3):649-673, 2012). These conclusions make it difficult to envision a direct relativistic analog of the Newtonian cancellation lemma in the center-of-momentum coordinates.

math.AP↗

arXiv2016

Machine learning force fields: Construction, validation, and outlook

Force fields developed with machine learning methods in tandem with quantum mechanics are beginning to find merit, given their (i) low cost, (ii) accuracy, and (iii) versatility. Recently, we proposed one such approach, wherein, the vectorial force on an atom is computed directly from its environment. Here, we discuss the multi-step workflow required for their construction, which begins with generating diverse reference atomic environments and force data, choosing a numerical representation for the atomic environments, down selecting a representative training set, and lastly the learning method itself, for the case of Al. The constructed force field is then validated by simulating complex materials phenomena such as surface melting and stress-strain behavior - that truly go beyond the realm of $ab\ initio$ methods both in length and time scales. To make such force fields truly versatile an attempt to estimate the uncertainty in force predictions is put forth, allowing one to identify areas of poor performance and paving the way for their continual improvement.

cond-mat.mtrl-sci↗

arXiv2016

A study of adatom ripening on an Al (111) surface with machine learning force fields

Surface phenomena are increasingly becoming important in exploring nanoscale materials growth and characterization. Consequently, the need for atomistic based simulations is increasing. Nevertheless, relying entirely on quantum mechanical methods limits the length and time scales one can consider, resulting in an ever increasing dependence on alternative machine learning based force fields. Recently, we proposed a machine learning approach, known as AGNI, that allows fast and accurate atomic force predictions given the atom's neighborhood environment. Here, we make use of such force fields to study and characterize the nanoscale diffusion and growth processes occurring on an Al (111) surface. In particular we focus on the adatom ripening phenomena, confirming past experimental findings, wherein a low and high temperature growth regime were observed, using entirely molecular dynamics simulations.

cond-mat.mtrl-sci↗

arXiv2015

Superconductivity in potassium-doped metallic polymorphs of MoS2

Superconducting layered transition metal dichalcogenides (TMDs) stand out among other superconductors due to the tunable nature of the superconducting transition, coexistence with other collective electronic excitations (charge density waves) and strong intrinsic spin-orbit coupling. Molybdenum disulphide (MoS2) is the most studied representative of this family of materials, especially since the recent demonstration of the possibility to tune its critical temperature, Tc, by electric-field doping. However, just one of its polymorphs, band-insulator 2H-MoS2, has so far been explored for its potential to host superconductivity. We have investigated the possibility to induce superconductivity in metallic polytypes, 1T- and 1T'-MoS2, by potassium (K) intercalation. We demonstrate that at doping levels significantly higher than that required to induce superconductivity in 2H-MoS2, both 1T and 1T' phases become superconducting, with Tc = 2.8 and 4.6K, respectively. Unusually, K intercalation in this case is responsible both for the structural and superconducting phase transitions. By adding new members to the family of superconducting TMDs our findings open the way to further manipulate and enhance the electronic properties of these technologically important materials.

cond-mat.supr-con↗

arXiv2015

Monads need not be endofunctors

We introduce a generalization of monads, called relative monads, allowing for underlying functors between different categories. Examples include finite-dimensional vector spaces, untyped and typed lambda-calculus syntax and indexed containers. We show that the Kleisli and Eilenberg-Moore constructions carry over to relative monads and are related to relative adjunctions. Under reasonable assumptions, relative monads are monoids in the functor category concerned and extend to monads, giving rise to a coreflection between relative monads and monads. Arrows are also an instance of relative monads.

cs.PL↗

arXiv2014

When is a container a comonad?

Abbott, Altenkirch, Ghani and others have taught us that many parameterized datatypes (set functors) can be usefully analyzed via container representations in terms of a set of shapes and a set of positions in each shape. This paper builds on the observation that datatypes often carry additional structure that containers alone do not account for. We introduce directed containers to capture the common situation where every position in a data-structure determines another data-structure, informally, the sub-data-structure rooted by that position. Some natural examples are non-empty lists and node-labelled trees, and data-structures with a designated position (zippers). While containers denote set functors via a fully-faithful functor, directed containers interpret fully-faithfully into comonads. But more is true: every comonad whose underlying functor is a container is represented by a directed container. In fact, directed containers are the same as containers that are comonads. We also describe some constructions of directed containers. We have formalized our development in the dependently typed programming language Agda.

cs.PL↗

arXiv2014

Toward Complete Statistics of Massive Binary Stars: Penultimate Results from the Cygnus OB2 Radial Velocity Survey

We analyze orbital solutions for 48 massive multiple-star systems in the Cygnus OB2 Association, 23 of which are newly presented here, to find that the observed distribution of orbital periods is approximately uniform in log P for P<45 d, but it is not scale-free. Inflections in the cumulative distribution near 6 d, 14, d, and 45 d, suggest key physical scales of ~0.2, ~0.4, and ~1 A.U. where yet-to-be-identified phenomena create distinct features. No single power law provides a statistically compelling prescription, but if features are ignored, a power law with exponent beta = -0.22 provides a crude approximation over P=1.4 -- 2000 d, as does a piece-wise linear function with a break near 45 d. The cumulative period distribution flattens at P > 45 d, even after correction for completeness, indicating either a lower binary fraction or a shift toward low-mass companions. A high degree of similarity (91% likelihood) between the Cyg OB2 period distribution and that of other surveys suggests that the binary properties at P<25 d are determined by local physics of disk/clump fragmentation and are relatively insensitive to environmental and evolutionary factors. Fully 30% of the unbiased parent sample is a binary with period P < 45 d. Completeness corrections imply a binary fraction near 55% for P < 5000 d. The observed distribution of mass ratios 0.2<q<1 is consistent with uniform, while the observed distribution of eccentricities 0.1<e<0.6 is consistent with uniform plus an excess of e ~ 0 systems. We identify six stars, all supergiants, that exhibit aperiodic velocity variations of ~30 km/s attributed to atmospheric fluctuations.

astro-ph.SR↗

arXiv2014

Normalization by Evaluation in the Delay Monad: A Case Study for Coinduction via Copatterns and Sized Types

In this paper, we present an Agda formalization of a normalizer for simply-typed lambda terms. The normalizer consists of two coinductively defined functions in the delay monad: One is a standard evaluator of lambda terms to closures, the other a type-directed reifier from values to eta-long beta-normal forms. Their composition, normalization-by-evaluation, is shown to be a total function a posteriori, using a standard logical-relations argument. The successful formalization serves as a proof-of-concept for coinductive programming and reasoning using sized types and copatterns, a new and presently experimental feature of Agda.

cs.LO↗

arXiv2012

Proceedings Fourth Workshop on Mathematically Structured Functional Programming

This volume contains the proceedings of the Fourth Workshop on Mathematically Structured Functional Programming (MSFP 2012), taking place on 25 March, 2012 in Tallinn, Estonia, as a satellite event of the European Joint Conferences on Theory and Practice of Software, ETAPS 2012. MSFP is devoted to the derivation of functionality from structure. It highlights concepts from algebra, semantics and type theory as they are increasingly reflected in programming practice, especially functional programming. The workshop consists of two invited presentations and eight contributed papers on a range of topics at that interface.

cs.LO↗