MATH Research Publications
https://soar.wichita.edu/handle/10057/120
2023-01-30T03:16:39ZDevelopment of a neutrino detector capable of operating in space
https://soar.wichita.edu/handle/10057/24914
Development of a neutrino detector capable of operating in space
Solomey, Nickolas
The ?SOL experiment to operate a neutrino detector close to the Sun is building a small test detector to orbit the Earth to test the concept in space. This detector concept is to provide a new way to detect neutrinos unshielded in space. A double peak delayed coincidence on Gallium nuclei that have a large cross section for solar neutrino interactions emitting a conversion electron and converting the nuclei into an excited state of Germanium, which decays with a well-known energy and half-life. This unique signature permits operation of the detector volume mostly unshielded in space with a high single particle counting rate from gamma and cosmic ray events. The test detector concept which has been studied in the lab and is planned for a year of operations orbiting Earth which is scheduled for launch in late 2024. It will be surrounded by an active veto and shielding will be operated in a polar orbit around the Earth to validate the detector concept and study detailed background spectrums that can fake the double peak delayed coincidence timing and energy signature from random galactic cosmic or gamma rays. The success of this new technology development will permit the design of a larger spacecraft with a mission to fly close to the Sun and is of importance to the primary science mission of the Heliophysics division of NASA Space Science Mission Directorate, which is to better understand the Sun by measuring details of our Sun’s fusion core.
Preprint version available from arXiv. Click on the DOI to access the publisher's version of this article.
2023-02-01T00:00:00ZStrong local nondeterminism and exact modulus of continuity for isotropic Gaussian random fields on compact two-point homogeneous spaces
https://soar.wichita.edu/handle/10057/24893
Strong local nondeterminism and exact modulus of continuity for isotropic Gaussian random fields on compact two-point homogeneous spaces
Lu, Tianshi; Ma, Chunsheng; Xiao, Yimin
This paper is concerned with sample path properties of real-valued isotropic Gaussian fields on compact two-point homogeneous spaces. In particular, we establish the property of strong local nondeterminism of an isotropic Gaussian field and then exploit this result to establish an exact uniform modulus of continuity for its sample paths.
Preprint version available from arXiv. Click on the DOI to access the publisher's version of this article.
2023-01-03T00:00:00ZManifolds with $4\frac{1}{2}$-Positive Curvature Operator of the Second Kind
https://soar.wichita.edu/handle/10057/24866
Manifolds with $4\frac{1}{2}$-Positive Curvature Operator of the Second Kind
Li, Xiaolong
We show that a closed four-manifold with $4\frac{1}{2}$-positive curvature operator of the second kind is diffeomorphic to a spherical space form. The curvature assumption is sharp as both ${\mathbb{CP}\mathbb{}}^2$and ${\mathbb {S}}^3 \times {\mathbb {S}}^1$have $4\frac{1}{2}$-nonnegative curvature operator of the second kind. In higher dimensions $n\ge 5$, we show that closed Riemannian manifolds with $4\frac{1}{2}$-positive curvature operator of the second kind are homeomorphic to spherical space forms. These results are proved by showing that $4\frac{1}{2}$-positive curvature operator of the second kind implies both positive isotropic curvature and positive Ricci curvature. Rigidity results for $4\frac{1}{2}$-nonnegative curvature operator of the second kind are also obtained.
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2022-08-04T00:00:00ZAn adaptive multiresolution ultra-weak discontinuous Galerkin method for nonlinear Schrödinger equations
https://soar.wichita.edu/handle/10057/24859
An adaptive multiresolution ultra-weak discontinuous Galerkin method for nonlinear Schrödinger equations
Tao, Zhanjing; Huang, Juntao; Liu, Yuan; Guo, Wei; Cheng, Yingda
This paper develops a high-order adaptive scheme for solving nonlinear Schrödinger equations. The solutions to such equations often exhibit solitary wave and local structures, which make adaptivity essential in improving the simulation efficiency. Our scheme uses the ultra-weak discontinuous Galerkin (DG) formulation and belongs to the framework of adaptive multiresolution schemes. Various numerical experiments are presented to demonstrate the excellent capability of capturing the soliton waves and the blow-up phenomenon.
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2021-01-25T00:00:00Z