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The aim of this work is to study homogeneous stable solutions to the thin (or fractional) one -phase free boundary problem. The problem of classifying stable (or minimal) homogeneous solutions in dimensions n >= 3 is completely open. In this context, axial ...
We study the statistical mechanics and the equilibrium dynamics of a system of classical Heisenberg spins with frustrated interactions on a d -dimensional simple hypercubic lattice, in the limit of infinite dimensionality d -> infinity . In the analysis we ...
This work introduces a reduced order modeling (ROM) framework for the solution of parameterized second-order linear elliptic partial differential equations formulated on unfitted geometries. The goal is to construct efficient projection-based ROMs, which r ...
In this paper, we set the mathematical foundations of the Dynamical Low Rank Approximation (DLRA) method for high-dimensional stochastic differential equations. DLRA aims at approximating the solution as a linear combination of a small number of basis vect ...
Modern solid-state devices were made possible by the discovery of semiconductor heterostructures. Heterostructures offer the ability to fabricate low-dimensional nanostructures such as quantum dots which can restrain carriers in all three-directions. Quant ...
This thesis is a study of the global well-posedness of the Cauchy problems for half-wave maps from the Minkowski space of dimension n+1 to the 2-dimensional sphere and the hyperbolic plane. The work is mainly based on the results from Krieger-Sire 17' in ...
The field of computational topology has developed many powerful tools to describe the shape of data, offering an alternative point of view from classical statistics. This results in a variety of complex structures that are not always directly amenable for ...
Machine learning frameworks based on correlations of interatomic positions begin with a discretized description of the density of other atoms in the neighborhood of each atom in the system. Symmetry considerations support the use of spherical harmonics to ...
The conjugate heat transfer in mixtures of a fluid and single granular clusters is studied in this paper using a novel lattice Boltzmann method (LBM) programmed for parallel computation on the graphics processing unit (GPU). The LBM is validated for heat c ...
The use of model-based numerical simulations of wave propagation in rooms for engineering applications requires that acoustic conditions for multiple parameters are evaluated iteratively, which is computationally expensive. We present a reduced basis metho ...
