Article
Chemistry, Physical
Simen Kvaal
Summary: Three fully variational formulations of the complete-active space coupled-cluster (CASCC) method are derived, which allows the approximation of model vectors by smooth manifolds to overcome the scaling issue. Matrix-product states are considered, and the variational formulation not only enables favorable scaling multireference coupled-cluster calculations, but also systematic correction of tailored coupled-cluster calculation and quantum chemical density-matrix renormalization group methods. The extension of the formulations to the time-domain and derivations of abstract evolution equations are also discussed.
JOURNAL OF CHEMICAL PHYSICS
(2023)
Article
Mechanics
Yuan Shen, Bo Tian, Chong-Dong Cheng, Tian-Yu Zhou
Summary: In this paper, a (3 + 1)-dimensional generalized Konopelchenko-Dubrovsky-Kaup-Kupershmidt system in fluid mechanics is studied. The bilinear form of the system is determined using the Hirota method. Nth-order Pfaffian solutions are obtained using the Pfaffian technique and the bilinear form, where N is a positive integer. Based on these solutions, various phenomena such as elastic interaction, fission, and fusion between solitary waves and breathers are presented.
Article
Mathematics, Interdisciplinary Applications
Lu Tang
Summary: This paper studies the dynamical behavior and dispersive optical solitons in birefringent fibers with coupled Schrodinger-Hirota equation. By applying traveling wave transformations and the theory of planar dynamical system, a range of solutions with different waveforms are obtained. The single traveling wave solutions for the coupled nonlinear Schrodinger-Hirota equation are classified using the complete discriminant system method and symbolic computation, improving upon existing conditions and proposing a new method for constructing dispersive optical solitons.
CHAOS SOLITONS & FRACTALS
(2022)
Article
Engineering, Multidisciplinary
Zhenhao Guo, Hehua Ju, Kaimeng Wang
Summary: In this article, an innovative joint-space explicit dynamics symbolic computation model is proposed for closed-chain mechanisms, with reduced complexity in both symbolic and numerical aspects. The model is developed based on a previous work on the explicit dynamics model of tree-chain. By decoupling the closed-chain mechanism problem into a tree-chain problem using simplified system dynamics, the kinematic constraint equation and constraint force equation of the closed-chain are derived based on Axis-Invariant, simplifying the establishment and solution process. The correctness and universality of the proposed method are verified through comparison with common closed-chain mechanisms using ADAMS software.
APPLIED MATHEMATICAL MODELLING
(2023)
Article
Mathematics, Applied
Takeshi Torii
Summary: The paper presents another proof of the dual equivalence between the infinity-category of monoidal infinity-categories with left adjoint oplax monoidal functors and that with right adjoint lax monoidal functors by constructing a perfect pairing between them.
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
(2023)
Review
Physics, Nuclear
Chongji Jiang, Junchen Pei
Summary: In this work, we investigate the behavior of a pairing Hamiltonian with four particles at finite temperatures using both a quantum simulator and a superconducting quantum computer. We employ the variational quantum deflation to obtain the excited states and apply error-mitigation methods to improve the noisy results. By simulating thermal excitation states using the same variational circuit as at zero temperature, we find that the quantum computing results closely match the exact solutions at high temperatures. Additionally, we observe a smooth superfluid-normal phase transition as expected in finite systems.
Article
Engineering, Chemical
Fei Zhao, Ignacio E. Grossmann, Salvador Garcia-Munoz, Stephen D. Stamatis
Summary: Design space definition is crucial in pharmaceutical research and development. This article proposes a novel solution strategy to explicitly describe the design space without recourse decisions. The proposed algorithm efficiently aggregates constraints, creates surrogate models, expands boundary points, and transforms the model using symbolic computation. The efficiency of the algorithm is demonstrated through two case studies.
Article
Physics, Multidisciplinary
Xin-Yi Gao, Yong-Jiang Guo, Wen-Rui Shan
Summary: This study focuses on the extended coupled (2+1)-dimensional Burgers system and employs scaling transformation, Bell polynomials, Hirota operators, and symbolic computation to derive two hetero-Ba?cklund transformations. The research also constructs two sets of bilinear forms with one-and two-soliton solutions, which are reliant on coefficients in the original system.
CHINESE JOURNAL OF PHYSICS
(2021)
Article
Chemistry, Multidisciplinary
Xiaojing Cong, Wenwen Ren, Jody Pacalon, Rui Xu, Lun Xu, Xuewen Li, Claire A. de March, Hiroaki Matsunami, Hongmeng Yu, Yiqun Yu, Jerome Golebiowski
Summary: This study investigated how the amino-acid sequences of olfactory receptors (ORs) encode diversified responses to various ligands. Using a proteochemometric model, the researchers were able to predict OR responses to odorants and discover new OR-ligand pairs. This approach will contribute to the mapping of OR-odorant interactions and the identification of orphan receptors.
ACS CENTRAL SCIENCE
(2022)
Article
Engineering, Mechanical
Jian-Guo Liu, Wen-Hui Zhu
Summary: Multiple rogue wave solutions of a generalized (3 + 1)-dimensional variable-coefficient nonlinear wave equation are obtained based on direct variable transformation, including first-order, two-order, and three-order rogue wave solutions. The dynamic behaviors of these solutions are illustrated using 3D plots. It is demonstrated that the approach used in this study does not rely on the Hirota bilinear form, and can handle variable-coefficient integrable equations, leading to interaction solutions between rogue wave and periodic wave as well as abundant breather wave solutions.
NONLINEAR DYNAMICS
(2021)
Article
Computer Science, Artificial Intelligence
Michael Hayes
Summary: Lcapy is an open-source Python package for symbolically solving linear circuits, offering multiple analysis methods and features. It can model various types of circuits and provide different representations for equations and output results.
PEERJ COMPUTER SCIENCE
(2022)
Article
Multidisciplinary Sciences
Daiki Nishioka, Takashi Tsuchiya, Wataru Namiki, Makoto Takayanagi, Masataka Imura, Yasuo Koide, Tohru Higuchi, Kazuya Terabe
Summary: Physical reservoir computing has gained attention for reducing computational resources, but reported reservoirs have lacked sufficient computing capacity and have been difficult to apply practically. The Li+ electrolyte-based ion-gating reservoir described here offers high performance and can achieve optimal computational capacity in an edge-of-chaos state.
Article
Mathematics, Interdisciplinary Applications
Lingfei Li, Yingying Xie
Summary: This work focuses on finding multi-order rogue wave solutions for the generalized (3+1)-dimensional Kadomtsev-Petviashvili equation, deriving them analytically through its bilinear form and symbolic computation. First, second and third order rogue waves are systematically analyzed, and numerical simulations are used to investigate their dynamical features. Additionally, a circular structure among the obtained rogue waves is explored.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Engineering, Electrical & Electronic
Michiel Haemers, Clara-Mihaela Ionescu, Kurt Stockman, Stijn Derammelaere
Summary: This study introduces a novel co-design optimization method for complex systems, specifically applied to the design of hardware architecture and control configurations in an active car suspension setup. The co-design approach simultaneously determines optimal actuator and sensor placement, control architecture, and controller tuning parameters. The results showcase a Pareto front illustrating the trade-off between maximum performance and total implementation cost, with validation conducted through measurements of the physical active car suspension setup.
Article
Mathematics
Natanael Karjanto, Husty Serviana Husain
Summary: This article introduces and explains the use of the computer algebra system wxMaxima in tertiary level Calculus teaching and learning, highlighting the importance of incorporating technology to enhance students' understanding of Calculus concepts. The article aims to stimulate further discussion among mathematics educators, software users, symbolic computation experts, and software developers by discussing both the strengths and limitations of the software.
