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The defect of valued field extensions is a major obstacle in open problems in resolution of singularities and in the model theory of valued fields, whenever positive characteristic is involved. We continue the detailed study of defect…
A continuum field theory approach is presented for modeling elastic and plastic deformation, free surfaces and multiple crystal orientations in non-equilibrium processing phenomena. Many basic properties of the model are calculated…
Purpose: Field monitoring measures field perturbations, which can be accounted for during image reconstructions. In certain field monitoring environments, significant phase deviations can arise far from isocenter due to the finite extent of…
I report on some work in progress on the dynamics of extended objects in field theories after a rapid phase transition, as is relevant in the early Universe. An analytic technique, originally introduced to approximate the dynamics of…
Scalar field dark matter offers an interesting alternative to the traditional WIMP dark matter picture. Astrophysical and cosmological simulations are useful to constraining the mass of the dark matter particle in this model. This is…
In the present thesis, a computational framework for the analysis of the deformation and damage phenomena occurring at the micro-scale of polycrystalline materials is presented. Micro-mechanics studies are commonly performed using the…
At a fixed lattice spacing, as determined by say m_\rho, adding additional fermion flavors to a dynamical simulation produces rougher gauge field configurations at the lattice scale. For domain wall fermions, these rough configurations lead…
We formulate a model for a point defect embedded in a homogeneous multilattice crystal with an empirical interatomic potential interaction. Under a natural, phonon stability assumption we quantify the decay of the long-range elastic fields…
Point defects affect material properties by altering electronic states and modifying local bonding environments. However, high-throughput first-principles simulations of point defects are costly due to large simulation cells and complex…
The present paper aims at developing a theory of computation of crystalline defects at finite temperature. In a one-dimensional setting we introduce Gibbs distributions corresponding to such defects and rigorously establish their asymptotic…
This paper is concerned with the Boundary Element simulation of elastic domains that contain thin inclusions that have elastic material properties, which are different to the domain. With thin inclusions we mean inclusions with extreme…
Atomistic-continuum multiscale modelling is becoming an increasingly popular tool for simulating the behaviour of materials due to its computational efficiency and reliable accuracy. In the case of ferromagnetic materials, the atomistic…
Zero- and two-dimensional crystal defects form in open statistical ensembles, such as the grand canonical, that are usually inaccessible with conventional simulation techniques. This longstanding challenge is overcome with a new Hamiltonian…
Point defects such as interstitials, vacancies, and impurities in otherwise perfect crystals induce complex displacement fields that are of long-range nature. In the present paper we study numerically the response of a two-dimensional…
The mechanical properties of crystalline materials can be substantially modified under confinement. Such modified macroscopic properties are usually governed by the altered microstructures and internal stress fields. Here, we use a parallel…
Amorphous interfacial complexions have been shown to restrict grain growth and improve damage tolerance in nanocrystalline alloys, with increased chemical complexity stabilizing the complexions themselves. Here, we investigate local…
Scientists use imaging to identify objects of interest and infer properties of these objects. The locations of these objects are often measured with error, which when ignored leads to biased parameter estimates and inflated variance.…
To simulate a macroscopic system from a simulation cell, a direct summation of the elastic fields produced by periodic images can be used. If the cell contains a non-zero elastic dipole component, the sum is known to be conditionally…
Experimentally obtained X-ray diffraction (XRD) patterns can be difficult to solve, precluding the full characterization of materials, pharmaceuticals, and geological compounds. Herein, we propose a method based upon a multi-objective…
The failure of heterogeneous materials with microstructures is a complex process of damage nucleation, growth and localisation. This process spans multiple length scales and is challenging to simulate numerically due to its high…