arXiv subjects

Thomas C. De Fraja

Publications and source records attributed to Thomas C. De Fraja.

4 recordsLinked to original sources

arXiv2026

Generalised Complex and Spinor Relations

Courant algebroid relations are used to define notions of relations between Dirac structures and spinors. It is shown under which circumstances a spinor relation gives a Courant algebroid relation and how it descends to a relation between Dirac structures. A converse to this result is proved: a T-duality relation induces a spinor relation that links the Dirac generating operators defining T-dual Courant algebroids, generalising the isomorphism of twisted cohomology associated with topological T-duality. We introduce the notion of relation between generalised complex structures and characterise their reduction. We also define relations between generalised Kähler structures, and rephrase them in terms of bi-Hermitian structures which induce T-duality relations between $\mathcal{N}=(2,2)$ supersymmetric sigma-models. We prove existence results for T-dual structures, and demonstrate compatibility of T-duality relations with Type II supergravity equations.

hep-th↗

arXiv2025

Courant Algebroid Relations, T-Dualities and Generalised Ricci Flow

The notion of Courant algebroid relation is used to introduce a definition of relation between divergence operators on Courant algebroids. By introducing invariant divergence operators, a notion of generalised T-duality between divergences is presented through an existence and uniqueness result for related divergence operators on T-dual pairs of exact Courant algebroids, which naturally incorporates the dilaton shift. When combined with the notion of generalised isometry, this establishes circumstances under which generalised Ricci tensors are related, proving that T-duality is compatible with generalised string background equations. This enables an analysis of the compatibility between T-duality and generalised Ricci flow, showing that the T-dual of a solution of generalised Ricci flow is also a solution of generalised Ricci flow. Our constructions are illustrated through many explicit examples.

hep-th↗

arXiv2024

T-Dualities and Courant Algebroid Relations

We develop a new approach to T-duality based on Courant algebroid relations which subsumes the usual T-duality as well as its various generalisations. Starting from a relational description for the reduction of exact Courant algebroids over foliated manifolds, we introduce a weakened notion of generalised isometries that captures the generalised geometry counterpart of Riemannian submersions when applied to transverse generalised metrics. This is used to construct T-dual backgrounds as generalised metrics on reduced Courant algebroids which are related by a generalised isometry. We prove an existence and uniqueness result for generalised isometric exact Courant algebroids coming from reductions. We demonstrate that our construction reproduces standard T-duality relations based on correspondence spaces. We also describe how it applies to generalised T-duality transformations of almost para-Hermitian manifolds.

math.DG↗

arXiv2022

An Efficient Moment Method for Modelling Nanoporous Evaporation

Thin-film-based nanoporous membrane technologies exploit evaporation to efficiently cool microscale and nanoscale electronic devices. At these scales, when domain sizes become comparable to the mean free path in the vapour, traditional macroscopic approaches such as the Navier-Stokes-Fourier (NSF) equations become less accurate, and the use of higher-order moment methods is called for. Two higher-order moment equations are considered; the linearised versions of the Grad 13 and Regularised 13 equations. These are applied to the problem of nanoporous evaporation, and results are compared to the NSF method and the method of direct simulation Monte Carlo (i.e. solutions to the Boltzmann equations). Linear and non-linear versions of the boundary conditions are examined, with the latter providing improved results, at little additional computational expense, compared to the linear form. The outcome is a simultaneously accurate and computationally efficient method, which can provide simulation-for-design capabilities at the nanoscale.

physics.flu-dyn↗