Article
Quantum Science & Technology
Vladimir Vargas-Calderon, Herbert Vinck-Posada, Fabio A. Gonzalez
Summary: This study applies the Feynman-Kitaev formalism to a spin chain described by the transverse-field Ising model. Neural quantum states (NQSs), represented by variational wave functions parameterized by artificial neural networks, are used to find the ground state of the system. The research focuses on evaluating the expressivity and trainability of NQSs in the context of the Feynman-Kitaev formalism. The results show that NQSs can accurately approximate the true ground state of the system, but reaching the correct values for the variational parameters becomes more difficult as the number of time steps increases.
QUANTUM INFORMATION PROCESSING
(2023)
Article
Mathematics, Applied
Anmin Mao, Shuai Mo
Summary: This article studies the nonlocal Schrodinger problem with general nonlinearities and the semiclassical ground state solutions of Nehari-Pohoaey type. By making assumptions on the potential V, improved existence results are obtained, along with the analysis of the concentration behavior of the ground state solutions in the limit case. These results extend previous related research.
ADVANCES IN NONLINEAR ANALYSIS
(2022)
Article
Environmental Sciences
Zhanat Karashbayeva, Julien Berger, Helcio R. B. Orlande, Bolatbek Rysbaiuly
Summary: In this study, the ground diffusivity was indirectly measured by solving an inverse problem. The conjugate gradient method with adjoint problem formulation was used to obtain stable and effective results, which were consistent with literature values.
Article
Mathematics, Applied
Xiaotao Qian
Summary: This paper investigates a nonlocal problem and proves the existence of a ground state sign-changing solution with energy strictly larger than the ground state energy. The asymptotic behavior of the solution as the parameter approaches zero is also discussed.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2021)
Article
Mathematics, Applied
Rakesh Arora, Alessio Fiscella, Tuhina Mukherjee, Patrick Winkert
Summary: In this paper, we study quasilinear elliptic equations driven by the double phase operator and involving a Choquard term. We prove the existence of ground state solutions using the Hardy-Littlewood-Sobolev inequality, the Nehari manifold, and variational tools under different assumptions on the data.
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
(2023)
Article
Mathematics, Applied
Andre M. McDonald, Michael A. van Wyk, Guanrong Chen
Summary: We propose a direct solution to the stochastic inverse eigenvalue problem by utilizing Markov state disaggregation to construct a stochastic transition matrix with the desired eigenspectrum. Unlike existing solutions that are limited to real-valued eigenspectra, our novel solution directly constructs matrices with complex-valued eigenspectra by combining a new disaggregation technique with a technique from a previous solution. This generalization allows for successful modeling of physical systems from a larger family. Additionally, our solution constructs the matrix in a finite number of iterations without numerical approximation, as demonstrated through the derivation of a set of 4x4 stochastic matrices with the same prescribed complex-valued eigenspectrum indexed by a real parameter.
LINEAR ALGEBRA AND ITS APPLICATIONS
(2023)
Article
Mathematics, Applied
Xiaotao Qian, Wen Chao
Summary: In this paper, we investigate a nonlocal problem in R-N and prove the existence of ground state solutions under certain assumptions on f(x) when the parameter A is large enough. Additionally, we analyze the concentration behaviors of these solutions as the parameter lambda approaches infinity.
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
(2021)
Article
Computer Science, Interdisciplinary Applications
Nicola Bianchessi, Angel Corberan, Isaac Plana, Miguel Reula, Jose M. Sanchis
Summary: This article discusses the Profitable Close-Enough Arc Routing Problem (PCEARP), an extension of the Close-Enough ARP (CEARP). A formulation for this new problem and some valid inequalities are presented, and a polyhedral study of its feasible solutions is conducted. A heuristic and a branch-and-cut procedure are proposed for solving the PCEARP, and their performance has been tested on several sets of instances with different characteristics.
COMPUTERS & OPERATIONS RESEARCH
(2022)
Article
Thermodynamics
Cheng-Hung Huang, Kai-Jyun He
Summary: This study estimated the unknown spatially dependent surface heat flux for a three-dimensional steady-state inverse heat conduction-convection conjugated problem (IHCCCP). The conjugate gradient method (CGM) was used for optimization, enabling correction and estimation of a large number of unknowns in each iteration to yield accurate estimates. Experimental verification and analysis of measurement errors were conducted. The accuracy of the estimated heat flux decreases as the plate thickness increases due to the ill-posed nature of the inverse problem.
CASE STUDIES IN THERMAL ENGINEERING
(2022)
News Item
Physics, Multidisciplinary
Dalziel J. Wilson
Summary: Scientists have achieved the cooling of levitated nanoparticles to the motional ground state in two dimensions, which could pave the way for a new generation of macroscopic quantum experiments.
Article
Mathematics, Applied
Er-Wei Xu, Hong-Rui Sun
Summary: This paper deals with a nonlocal problem involving combined critical nonlinearities. The problem is posed in a domain Omega which is a bounded C-1,C-1 domain with Lipschitz boundary in R-N, and the equation involves a fractional Laplacian operator (-Delta)(s). The paper establishes the existence of a ground state solution for the problem under certain conditions on the parameters.
ELECTRONIC JOURNAL OF QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS
(2023)
Article
Chemistry, Multidisciplinary
Yuri Katagiri, Yamato Tsuchida, Yutaka Matsuo, Michito Yoshizawa
Summary: An efficient micellar capsule was designed and prepared to uptake molecules of different sizes, even forming ternary core-shell structures.
JOURNAL OF THE AMERICAN CHEMICAL SOCIETY
(2021)
Article
Chemistry, Multidisciplinary
Guoliang Liu, Ziqi Yang, Mi Zhou, Yuxiang Wang, Daqiang Yuan, Dan Zhao
Summary: The study introduces a heterogeneous postassembly modification (PAM) method to synthesize a zirconium metal-organic cage decorated with acrylate functional groups. The modification process is carried out efficiently under mild conditions, confirmed by analysis techniques, and demonstrates potential applications.
CHEMICAL COMMUNICATIONS
(2021)
Article
Mathematics, Applied
Mihai Bucataru, Liviu Marin
Summary: In this study, we investigate the acceleration of two iterative algorithms for accurate reconstruction of missing temperature and normal heat flux on an inaccessible boundary. The convergence of each algorithm is analyzed by considering the properties of the corresponding operator and determining the optimal value of the relaxation parameter. Numerical experiments confirm the effectiveness of the algorithms in reducing CPU time.
NUMERICAL ALGORITHMS
(2023)
Article
Mathematics, Applied
Darko Volkov, Yulong Jiang
Summary: This paper presents a Lipschitz stability result for a crack inverse problem in half space, focusing on the unknown geometry and location of the crack. By assuming certain conditions on the geometry, it is shown that the inverse problem is uniquely solvable, highlighting the stability of reconstructing the crack plane despite the unknown forcing term.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2021)
