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In this paper, the impact behaviour of composite laminates is investigated, and their potential for ballistic protection assessed, as a function of the reinforcing materials and structures for three representative fibre-reinforced epoxy…
We developed a micromagnetic method for modeling magnetic systems with periodic boundary conditions along an arbitrary number of dimensions. The main feature is an adaptation of the Ewald summation technique for evaluation of long-range…
Machine learning models for functional materials design require precise and informative representations of material systems. Common representations encode atomic composition and bonding but often do not include local coordination…
Entanglement generated by Ising model has been studied for several authors in order to understand the relation between it and magnetic properties of materials, principally using one or two dimensional models for two or more particles. In…
We introduce a family of conformal invariants associated to a smooth metric measure space which generalize the relationship between the Yamabe constant and the best constant for the Sobolev inequality to the best constants for…
A conjecture is made as to how to quantize topological M theory. We study a Hamiltonian decomposition of Hitchin's 7-dimensional action and propose a formulation for it in terms of 13 first class constraints. The theory has 2 degrees of…
We present a conformally invariant generalized form of the free particle action by connecting the wave and particle aspects through gravity. Conformal invariance breaking is introduced by choosing a particular configurat$ of dynamical…
We construct two distinct yet related M-theory models that provide suitable frameworks for the study of knot invariants. We then focus on the four-dimensional gauge theory that follows from appropriately compactifying one of these M-theory…
The current state of the art for analytical and computational modelling of deformation in nonlinear electroelastic and magnetoelastic membranes is reviewed. A general framework and a list of methods to model large deformation and associated…
A regularization procedure developed in [1] for the integral curvature invariants on manifolds with conical singularities is generalized to the case of squashed cones. In general, the squashed conical singularities do not have rotational…
In this article, a novel explicit approach for designing complex thin-walled structures based on the Moving Morphable Component (MMC) method is proposed, which provides a unified framework to systematically address various design issues,…
A non-negative integer invariant, estimating from below the number of geometrically different critical points of a smooth function $f$ defined in the 2-disk, $f:\mathbb{B}^{2}\rightarrow\mathbb{R}$, is considered. (We denote it by…
We suggest two metrics for assessing the quality of atomistic configurations of disordered materials, both of which are based on quantifying the orientational distribution of neighbours around each atom in the configuration. The first…
Recent developments in imaging techniques and correlation algorithms enable measurement of strain fields on a deforming material at high spatial and temporal resolution. In such cases, the computation of the stress field from the known…
A two-dimensional quantum mechanical system consisting of a particle coupled to two magnetic impurities of different strengths, in a harmonic potential, is considered. Topological boundary conditions at impurity locations imply that the…
The problem of the linear microtearing mode in a slab magnetised plasma, and its connection to kinetic reconnecting modes, is addressed. Electrons are described using a novel hybrid fluid-kinetic model that captures electron heating, ions…
This PhD thesis conducts a focused study of strongly correlated materials with localized electron orbitals. We have studied two real materials (LuNiO$_3$ and VO$_2$) and one model system, i.e., the Anderson impurity model. The thesis is…
We consider lattice implementation of the recently proposed gauge invariant definition of the monopole charge. Because of the lattice discretization the algorithm gives rise to specific lattice artifacts and an effective Ising model. The…
Magnetic structures, which play a central role in determining their physical properties, are known for only very limited compounds. Traditional theoretical approaches to predicting magnetic structures predominantly rely on first-principles…
The material characterization of ultra-thin solid sheets, including two-dimensional materials like graphene, is often performed through indentation tests on a flake suspended over a hole in a substrate. While this `suspended indentation' is…