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Ab initio Monte Carlo simulations have been performed to determine the equilibrium properties of liquid lithium and lithium clusters at different temperatures. First-principles density-functional methods were employed to calculate the…
An inverse problem to identify unknown coefficients of a partial differential equation by a single interior measurement is considered. The equation considered in this paper is a strongly elliptic second order scalar equation which can have…
A Monte Carlo sampling of diagrammatic corrections to the non-crossing approximation is shown to provide numerically exact estimates of the long-time dynamics and steady state properties of nonequilibrium quantum impurity models. This…
Classical results from Sturm-Liouville theory state that the number of unstable eigenvalues of a scalar, second-order linear operator is equal to the number of associated conjugate points. Recent work has extended these results to a much…
Eigenvalue analysis is a well-established tool for stability analysis of dynamical systems. However, there are situations where eigenvalues miss some important features of physical models. For example, in models of incompressible fluid…
Understanding the equation of state (EOS) of pure neutron matter is necessary for interpreting multimessenger observations of neutron stars. Reliable data analyses of these observations require well-quantified uncertainties for the EOS…
Thermoacoustic instabilities are one of the most challenging problems faced by gas turbine and rocket motor manufacturers. The key instability mechanism is described by the {\it Rayleigh criterion}. The Rayleigh criterion does not directly…
This Dissertation presents results of a thorough study of ultracold bosonic and fermionic gases in three-dimensional and quasi-one-dimensional systems. Although the analyses are carried out within various theoretical frameworks…
Understanding the real time dynamics of quantum systems without quasiparticles constitutes an important yet challenging problem. We study the superfluid-insulator quantum-critical point of bosons on a two-dimensional lattice, a system whose…
The issue of how epistemic uncertainties affect the outcome of Monte Carlo simulation is discussed by means of a concrete use case: the simulation of the longitudinal energy deposition profile of low energy protons. A variety of…
We show how Monte Carlo approach can be used to study the double scaling limit in matrix models. As an example, we study a solvable hermitian one-matrix model with the double-well potential, which has been identified recently as a dual…
High statistical precision is critical for Monte Carlo (MC) samples in high energy physics and is degraded by negatively weighted events. This paper investigates a procedure to learn the relationship between the negative and positive weight…
This paper considers the problem of robust stability for a class of uncertain nonlinear quantum systems subject to unknown perturbations in the system Hamiltonian. The nominal system is a linear quantum system defined by a linear vector of…
We consider a class of density-driven flow problems. We are particularly interested in the problem of the salinization of coastal aquifers. We consider the Henry saltwater intrusion problem with uncertain porosity, permeability, and…
Monte Carlo methods are used to study the phase transition in ammonium chloride from the orientationally ordered $\delta$ phase to the orientationally disordered $\gamma$ phase. An effective pair potential is used to model the interaction…
In this paper we propose a new method to detect and classify coexisting solutions in nonlinear systems. We focus on mechanical and structural systems where we usually avoid multistability for safety and reliability. We want to be sure that…
This paper considers the problem of robust stability for a class of uncertain nonlinear quantum systems subject to unknown perturbations in the system Hamiltonian. The case of a nominal linear quantum system is considered with non-quadratic…
We study metastability and nucleation in a kinetic two-dimensional Ising model which is driven out of equilibrium by a small random perturbation of the usual dynamics at temperature T. We show that, at a mesoscopic/cluster level, a…
Contemporary scientific studies often rely on the understanding of complex quantum systems via computer simulation. This paper initiates the statistical study of quantum simulation and proposes a Monte Carlo method for estimating…
The hardcore-Bose-Hubbard model with random chemical potential is investigated using quantum Monte Carlo simulation. We consider two cases of random distribution of the chemical potential: a uniformly random distribution and a correlated…