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Purpose: Field monitoring using field probes allows for accurate measurement of magnetic field perturbations, such as from eddy currents, during MRI scanning. However, errors may result when the spatial variation of the fields is not…
Polycrystalline materials undergoing coarsening can be represented as evolving networks of grain boundaries, whose statistical characteristics determine macroscopic materials properties. The process of formation of various statistical…
Reduced Bloch mode expansion is presented for fast periodic media band structure calculations. The expansion employs a natural basis composed of a selected reduced set of Bloch eigenfunctions. The reduced basis is selected within the…
A simple analytical model of intergranular normal stresses is proposed for a general elastic polycrystalline material with arbitrary shaped and randomly oriented grains under uniform loading. The model provides algebraic expressions for the…
An approach to the mechanical behaviour of textile composites at the scale of their constituting fibres, using an implicit finite element simulation code, is proposed in this chapter. The approach is based on efficient methods and…
We present an approach to deep estimation of discrete conditional probability distributions. Such models have several applications, including generative modeling of audio, image, and video data. Our approach combines two main techniques:…
Based on classical statistical mechanics, we calculate analytically the length extension and the fluctuations, under a pulling force, of a polymer modelled as a freely jointed chain with extensible bonds, the latter considered as harmonic…
Confinement can substantially alter the physicochemical properties of materials by breaking translational isotropy and rendering all physical properties position-dependent. Molecular dynamics (MD) simulations have proven instrumental in…
We study dendritic microstructure evolution using an adaptive grid, finite element method applied to a phase-field model. The computational complexity of our algorithm, per unit time, scales linearly with system size, rather than the…
Integral expressions are determined for the elastic displacement and stress fields due to stationary or moving dislocation loops in finite samples. These general expressions are valid for anisotropic media as well. Specifically for the…
The mathematical model of a real flexible elastic system with distributed and discrete parameters is considered. It is a partial differential equation with non-classical boundary conditions. Complexity of the boundary conditions results in…
Polymer models play the special role of elucidating the elementary features describing the physics of long molecules and become essential to interpret the measurements of their magnitudes. In this work the end-to-end distance of an…
In order to illustrate the adaptation of traditional continuum numerical techniques to the study of complex network systems, we use the equation-free framework to analyze a dynamically evolving multigraph. This approach is based on coupling…
Efficient modeling of dispersive materials via time-domain simulations of the Maxwell equations relies on the technique of auxiliary differential equations. In this approach, a material's frequency-dependent permittivity is represented via…
We introduce an accurate, self-contained and automatic atom based numerical algorithm to characterize grain distributions in two dimensional Phase Field Crystal simulations. Four input parameters must be set by the user and their effect is…
We study the distributional behavior of additive arithmetic functions evaluated at integers drawn from the harmonic distribution. Our main result shows that a broad family of such functions converges in law to conditioned Dickman-type…
Treatment of fields near domain boundaries is a long-standing problem in signal processing that has come into renewed focus following recent efforts in convolution-based multiscale coarse-graining and in machine-learned parameterizations…
In this work, we propose a novel formulation for the solution of partial differential equations using finite element methods on unfitted meshes. The proposed formulation relies on the discrete extension operator proposed in the aggregated…
We develop a method for constructing tolerance bounds for functional data with random warping variability. In particular, we define a generative, probabilistic model for the amplitude and phase components of such observations, which…
This paper presents an extension of the discrete element method using a phase-field formulation to incorporate grain shape and its evolution. The introduction of a phase variable enables an effective representation of grain geometry and…