84 citations · 409 across the 24 of their papers we have counts for
24 papers
Biases in Inverse Ising Estimates of Near-Critical Behaviour
Maximilian Benedikt Kloucek, Thomas Machon, Shogo Kajimura +3
Inverse Ising inference allows pairwise interactions of complex binary systems to be reconstructed from empirical correlations. Typical estimators used for this inference, such as…
Poisson structures on sets of Maurer-Cartan elements
Thomas Machon
Given a differential graded Lie algebra (dgla) L satisfying certain conditions, we construct Poisson structures on the gauge orbits of its set of Maurer-Cartan (MC) elements, terme…
Anti-Holomorphic Modes in Vortex Lattices
Brook J Hocking, Thomas Machon
A continuum theory of linearized Helmholtz-Kirchoff point vortex dynamics about a steadily rotating lattice state is developed by two separate methods: firstly by a direct procedur…
Uniaxial versus Biaxial Pathways in One-Dimensional Cholesteric Liquid Crystals
Yucen Han, James Dalby, Benjamin MGD Carter +2
Cholesteric liquid crystals exhibit great morphological richness of static metastable states. Understanding the transitions between such states is key for the development of switch…
Some Morse-type inequalities for symplectic manifolds
Thomas Machon
Morse-type inequalities are given for the symplectic versions of the Bott-Chern and Aeppli cohomology groups defined by Tseng and Yau.
The Topological Origin of the Peierls-Nabarro Barrier
Brook J. Hocking, Helen S. Ansell, Randall D. Kamien +1
Crystals and other condensed matter systems described by density waves often exhibit dislocations. Here we show, by considering the topology of the ground state manifolds (GSMs) of…
Stability of highly-twisted Skyrmions from contact topology
Yichen Hu, Thomas Machon
We describe a topological protection mechanism for highly-twisted two-dimensional Skyrmions in systems with Dyloshinskii-Moriya (DM) coupling, where non-zero DM energy density (dub…
A Poisson bracket on the space of Poisson structures
Thomas Machon
Let be a smooth closed orientable manifold and the space of Poisson structures on . We construct a Poisson bracket on depending on a choice…
Good Fibrations: Packing Rules for Diabolic Domains
Randall D. Kamien, Thomas Machon
We describe a theory of packing hyperboloid 'diabolic' domains in bend-free textures of liquid crystals. The domains sew together continuously, providing a menagerie of bend-free t…
The Godbillon-Vey Invariant as Topological Vorticity Compression and Obstruction to Steady Flow in Ideal Fluids
Thomas Machon
If the vorticity field of an ideal fluid is tangent to a foliation, additional conservation laws arise. For a class of zero-helicity vorticity fields the Godbillon-Vey (GV) invaria…
The Godbillon-Vey Invariant as a Restricted Casimir of Three-dimensional Ideal Fluids
Thomas Machon
We show the Godbillon-Vey invariant arises as a `restricted Casimir' invariant for three-dimensional ideal fluids associated to a foliation. We compare to a finite-dimensional syst…
A Björling Representation for Jacobi Fields on Minimal Surfaces and Soap Film Instabilities
Gareth P. Alexander, Thomas Machon
We develop a general framework for the description of instabilities on soap films using the Björling representation of minimal surfaces. The construction is naturally geometric and…
Inverse Ising inference, hyperuniformity and absorbing states in the Manna model
Thomas Machon
Using inverse Ising inference we show that the absorbing states of the one-dimensional Manna model can be described by an equilibrium model with an emergent interaction displaying…
Aspects of Defect Topology in Smectic Liquid Crystals
Thomas Machon, Hillel Aharoni, Yichen Hu +1
We study the topology of smectic defects in two and three dimensions. We give a topological classification of smectic point defects and disclination lines in three dimensions. In a…
Woven Nematic Defects, Skyrmions and the Abelian Sandpile Model
Thomas Machon, Gareth P. Alexander
We show that a fixed set of woven defect lines in a nematic liquid crystal supports a set of non-singular topological states which can be mapped on to recurrent stable configuratio…
Contact Topology and the Structure and Dynamics of Cholesterics
Thomas Machon
Using tools and concepts from contact topology we show that non-vanishing twist implies conservation of the layer structure in cholesteric liquid crystals. This leads to a number o…
Composite Dislocations in Smectic Liquid Crystals
Hillel Aharoni, Thomas Machon, Randall D. Kamien
Smectic liquid crystals are charcterized by layers that have a preferred uniform spacing and vanishing curvature in their ground state. Dislocations in the smectics play an importa…
Global Defect Topology in Nematic Liquid Crystals
Thomas Machon, Gareth P. Alexander
We give the global homotopy classification of nematic textures for a general domain with weak anchoring boundary conditions and arbitrary defect set in terms of twisted cohomology,…
Instabilities and Solitons in Minimal Strips
Thomas Machon, Gareth P. Alexander, Raymond E. Goldstein +1
We show that highly twisted minimal strips can undergo a non-singular transition, unlike the singular transitions seen in the Möbius strip and the catenoid. If the strip is non-ori…
Umbilic Lines in Orientational Order
Thomas Machon, Gareth P. Alexander
Three-dimensional orientational order in systems whose ground states possess non-zero, chiral gradients typically exhibits line-like structures or defects: lines in cholesteric…
The Geometry of the Cholesteric Phase
Daniel A. Beller, Thomas Machon, Simon Čopar +4
We propose a construction of a cholesteric pitch axis for an arbitrary nematic director field as an eigenvalue problem. Our definition leads to a Frenet-Serret description of an or…
Knotted Defects in Nematic Liquid Crystals
Thomas Machon, Gareth P. Alexander
We show that the number of distinct topological states associated to a given knotted defect, , in a nematic liquid crystal is equal to the determinant of the link . We give a…
Knotted Nematics
Thomas Machon, Gareth P. Alexander
Knotted line defects in continuous fields entrain a complex arrangement of the material sur- rounding them. Recent experimental realisations in optics, fluids and nematic liquid cr…
Nematics, Knots and Non-orientable Surfaces
Thomas Machon, Gareth P. Alexander
Knots and knotted fields enrich physical phenomena ranging from DNA and molecular chemistry to the vortices of fluid flows and textures of ordered media. Liquid crystals provide an…