Research
Research
Research
Research
2,115+ open-access research outputs.
In 1978, A. C. Newell [SIAM J. Appl. Math. 35(4) (1978) 650-664] proposed an exactly solvable model called Newell equation, which simulates the investigation of significant interaction mechanism betwe…
We study a class of quantum dynamical maps for d-level systems that interpolate between positive, Schwarz, and completely positive evolutions. Our approach is based on a geometric analysis of the para…
We study the ODE/IM correspondence between the linear problem associated with the supersymmetric affine Toda field equation for the twisted affine Lie superalgebra $C(2)^{(2)} = \mathfrak{osp}(2|2)^{(…
We analyze the Schwarz inequality and its generalizations, as well as inequalities resulting from the Jensen inequality. They are used in quantum theory to derive the Heisenberg-Robertson (HR) and Sch…
F-theory compactifications with a nontrivial Mordell-Weil group realize abelian gauge symmetry through rational sections, but their consistency is ultimately a statement about the quantum effective ac…
We study the deformation of the classical Szeg\H{o} curve $\gamma_0$ given by $\gamma_t = \{ z\in\mathbb{C}: |z\, e^{1-z}| = e^{-t}, |z|\leq 1\}$, $t\geq 0$ from three different viewpoints: an electro…
The electrochromic response of Ni-deficient NiO is governed by vacancy-mediated electronic processes that can be strongly influenced by dopant chemistry and lattice deformation. Using density function…
When three-dimensional bodies contain thin features, non-trivial topology, or scan-derived surfaces, volumetric meshing can become the dominant bottleneck in simulation workflows. We replace this step…
In this work, we continue the investigation of correlation numbers in $\mathcal{N}=1$ super Minimal Liouville Gravity (SMLG), with physical fields in the Ramond sector. Building upon our previous cons…
We show that to every small and decaying solution of the linearized constraint equations about Minkowski spacetime, one can add a quadratically small correction to obtain a solution of the full constr…
We present a new way to construct analytical solutions for flow in complex microfluidic channel networks, as well as planar disordered media. Using a combination of Schwarz-Christoffel maps and segmen…
A foundational result in constructive quantum field theory is the construction of the free bosonic quantum field theory in four-dimensional Euclidean spacetime and the proof that it satisfies the Glim…
In this paper we introduce a new model for the quantum-mechanical system of the hydrogen atom. We start with a four-dimensional Lorentzian quadratic space $(V,q)$ and let $C \subset V$ be the corres…
We demonstrate that the diagonal curvature in second-order Jahn-Teller theory (SOJTT) can be negative, invalidating its foundational positivity assumption. Using a frozen-phonon many-body expansion, w…
In this paper I argue against Carcassi, Calderon, and Aidala's recent claim that the Hilbert spaces are unphysical and should be replaced with the Schwartz spaces in quantum mechanics, since Hilbert s…
Rational design of interface passivators for perovskite solar cells is hindered by the entanglement of intrinsic molecular efficacy with extrinsic platform-dependent performance - a confounding factor…
The charge, bonding, and optical properties of the calcium-doped boron cluster B$_7$Ca$_2$ have been systematically investigated using density functional theory calculations. Extensive global basin-ho…
We reformulate and generalize the equilibrium hyperforce sum rule, a generalization of the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy, by employing the Schwartz space and its dual. We show …
In this dissertation, we study various aspects of type IIB string theory compactified on freely acting orbifolds. We focus particularly on asymmetric orbifolds, which are examples of non-geometric str…
We investigate analytically and numerically the dynamics of a two-dimensional superflow governed by the Gross-Pitaevskii equation passing over finite-size rectangular obstacles: an impenetrable wall a…
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