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Consensus-based optimization (CBO) is a versatile multi-particle optimization method for performing nonconvex and nonsmooth global optimizations in high dimensions. Proofs of global convergence in probability have been achieved for a broad…
The aim of this paper is to propose a novel methodology to deal with micro-structural boundary conditions for the analysis of granular materials. The response of the granular assembly is modelled through the discrete element method (DEM),…
The electronic structure, when restricted to the d-band approximation, is a computational model that is both efficient and useful for describing transition metals. In the absence of considering delocalized sp-states, this approximation…
In this paper, we propose a certified reduced basis (RB) method for quasilinear elliptic problems together with its application to nonlinear magnetostatics equations, where the later model permanent magnet synchronous motors (PMSM). The…
Pressure Poisson equation (PPE) reformulations of the incompressible Navier-Stokes equations (NSE) replace the incompressibility constraint by a Poisson equation for the pressure and a suitable choice of boundary conditions. This yields a…
In recent years, there has been a growing interest in flatband systems which exhibit macroscopic degeneracies. These systems offer a valuable mathematical framework for the extreme sensitivity to perturbations and interactions. This…
We discuss in details a modified variational matrix-product-state algorithm for periodic boundary conditions, based on a recent work by P. Pippan, S.R. White and H.G. Everts, Phys. Rev. B 81, 081103(R) (2010), which enables one to study…
A class of truncated tight-binding Hermitian and non-Hermitian lattices with commensurate energy levels, showing periodic reconstruction of the wave packet, is presented. Examples include exact Bloch oscillations on a finite lattice,…
Most real-world datasets consist of a natural hierarchy between classes or an inherent label structure that is either already available or can be constructed cheaply. However, most existing representation learning methods ignore this…
Stochastic contraction analysis is a recently developed tool for studying the global stability properties of nonlinear stochastic systems, based on a differential analysis of convergence in an appropriate metric. To date, stochastic…
We show that imposition of non-periodic, in place of periodic, boundary conditions (BC) can alter stability of modes in the Method of characteristics (MoC) employing certain ordinary-differential equation (ODE) numerical solvers. Thus,…
Realistic indoor or outdoor image synthesis is a core challenge in computer vision and graphics. The learning-based approach is easy to use but lacks physical consistency, while traditional Physically Based Rendering (PBR) offers high…
Restricted Boltzmann Machines (RBMs) are typically trained using finite-length Gibbs chains under a fixed sampling temperature. This practice implicitly assumes that the stochastic regime remains valid as the energy landscape evolves during…
Topological phases of matter give rise to exotic physics that can be leveraged for next generation quantum computation and spintronic devices. Thus, the search for topological phases and the quantum states that they exhibit have become the…
Classical electromagnetic boundary conditions (EMBCs) fail to describe quantum interface phenomena at nanoscale. Here, we construct the interface model with a transition layer describing the electromagnetic field inhomogeneity across the…
This paper proposes a novel robust model predictive control (RMPC) method for the stabilization of constrained systems subject to additive disturbance (AD) and multiplicative disturbance (MD). Concentric containers are introduced to…
Understanding the behavior of biomolecules such as proteins requires understanding the critical influence of the surrounding fluid (solvent) environment--water with mobile salt ions such as sodium. Unfortunately, for many studies, fully…
Tight-binding (TB) molecular dynamics (MD) has emerged as a powerful method for investigating the atomic-scale structure of materials --- in particular the interplay between structural and electronic properties --- bridging the gap between…
Astrophysical simulations of convection frequently impose different thermal boundary conditions at the top and the bottom of the domain in an effort to more accurately model natural systems. In this work, we study Rayleigh-Benard convection…
This thesis develops exact analytical tools to study strongly correlated stochastic systems, with a focus on extreme value statistics, gap statistics, and full counting statistics in multi-particle processes. A central contribution is the…