Article
Mathematics, Applied
Sun-Ho Choi, Hyowon Seo
Summary: In this paper, the asymptotic behavior of a macroscopic power grid system derived from energy conservation is studied. A sufficient condition for the existence of a special solution as well as the stability of the solution are provided.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
Article
Computer Science, Interdisciplinary Applications
S. Blanes, F. Casas, C. Gonzalez, M. Thalhammer
Summary: This paper explores the extension of modified potential operator splitting methods to specific classes of nonlinear evolution equations. Numerical experiments confirm the advantages of the proposed fourth-order modified operator splitting method over traditional splitting methods in dealing with Gross-Pitaevskii systems.
COMPUTER PHYSICS COMMUNICATIONS
(2024)
Article
Mathematics, Applied
Francois Mauger, Cristel Chandre, Mette B. Gaarde, Kenneth Lopata, Kenneth J. Schafer
Summary: This study revisits the equations of Kohn-Sham time-dependent density-functional theory (TDDFT) and demonstrates their derivation from a canonical Hamiltonian formalism. By using a geometric description, families of symplectic split-operator schemes are defined to accurately and efficiently simulate the time propagation for specific classes of DFT functionals. Numerical simulations are conducted to illustrate the approach, focusing on the far-from-equilibrium electronic dynamics of a one-dimensional carbon chain. The optimized 4th order scheme is found to provide a good compromise between numerical complexity and accuracy of the simulation.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
Article
Mathematics, Applied
Carlos A. Pires, David Docquier, Stephane Vannitsem
Summary: This study presents a general theory for computing information transfers in nonlinear stochastic systems driven by deterministic forcings and additive and/or multiplicative noises. It extends the Liang-Kleeman framework of causality inference to nonlinear cases based on information transfer across system variables. The study introduces an effective method called the 'Causal Sensitivity Method' (CSM) for computing the rates of Shannon entropy transfer between selected causal and consequential variables. The CSM method is robust, cheaper, and less data-demanding than traditional methods, and it opens new perspectives on real-world applications.
PHYSICA D-NONLINEAR PHENOMENA
(2024)
Article
Computer Science, Interdisciplinary Applications
Usman Riaz, E. Seegyoung Seol, Robert Hager, Mark S. Shephard
Summary: The accurate representation and effective discretization of a problem domain into a mesh are crucial for achieving high-quality simulation results and computational efficiency. This work presents recent developments in extending an automated tokamak modeling and meshing infrastructure to better support the near flux field following meshing requirements of the XGC Gyro-kinetic Code.
COMPUTER PHYSICS COMMUNICATIONS
(2024)
Article
Computer Science, Interdisciplinary Applications
A. Bagci, Gustavo A. Aucar
Summary: The electron repulsion integrals over Slater-type orbitals with non-integer principal quantum numbers are investigated in this study. These integrals are important in calculations of many-electron systems. New relationships free from hyper-geometric functions are derived to simplify the calculations. With the use of auxiliary functions and straightforward recurrence relationships, these integrals can be efficiently computed, providing initial conditions for the evaluation of expectation values and potentials.
COMPUTER PHYSICS COMMUNICATIONS
(2024)
Article
Mathematics, Applied
Ling An, Liming Ling, Xiaoen Zhang
Summary: In this paper, an integrable fractional derivative nonlinear Schrodinger equation is proposed and a reconstruction formula of the solution is obtained by constructing an appropriate Riemann-Hilbert problem. The explicit fractional N-soliton solution and the rigorous verification of the fractional one-soliton solution are presented.
PHYSICA D-NONLINEAR PHENOMENA
(2024)
Article
Computer Science, Interdisciplinary Applications
Christian Tantardini, Miroslav Ilias, Matteo Giantomassi, Alexander G. Kvashnin, Valeria Pershina, Xavier Gonze
Summary: Material discovery has been an active research field, and this study focuses on developing pseudopotentials for actinides and super-heavy elements. These pseudopotentials are crucial for accurate first-principles calculations and simulations.
COMPUTER PHYSICS COMMUNICATIONS
(2024)
Article
Computer Science, Interdisciplinary Applications
G. Heinrich, S. P. Jones, M. Kerner, V. Magerya, A. Olsson, J. Schlenk
Summary: We present a major update of the program pySECDEC, a toolbox for the evaluation of dimensionally regulated parameter integrals. The new version enables the evaluation of multi-loop integrals and amplitudes in a highly distributed and flexible way, optionally on GPUs, and runs up to an order of magnitude faster than the previous release. New integration procedures and functions for analyzing and introducing analytic regulators have been implemented.
COMPUTER PHYSICS COMMUNICATIONS
(2024)
Article
Mathematics, Applied
Gourav Mandal, Lakshmi Narayan Guin, Santabrata Chakravarty
Summary: The ecological framework investigates the dynamical complexity of a system influenced by prey refuge and alternative food sources for predators. This study provides a thorough investigation of the stability-instability phenomena, system parameters sensitivity, and the occurrence of bifurcations. The bubbling phenomenon, which indicates a change in the amplitudes of successive cycles, is observed in the current two-dimensional continuous system. The controlling system parameter for the bubbling phenomena is found to be the most sensitive. The prediction and identification of bifurcations in the dynamical system are crucial for theoretical and field researchers.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
Article
Computer Science, Interdisciplinary Applications
Dongming Li, James Kestyn, Eric Polizzi
Summary: This study introduces a practical and efficient approach to calculate the all-electron full potential band structure in real space using a finite element basis. Instead of the k-space method, this method solves the Kohn-Sham equation self-consistently within a larger finite system enclosing the unit-cell. Non-self-consistent calculations are then performed in the Brillouin zone to obtain the band structure results, which are found to be in excellent agreement with the pseudopotential k-space method. Furthermore, the study successfully observes the band bending of core electrons.
COMPUTER PHYSICS COMMUNICATIONS
(2024)
Article
Computer Science, Interdisciplinary Applications
Akihiro Koide, Sara Rabouli, Pierre Le Meur, Sylvain Tricot, Philippe Schieffer, Didier Sebilleau, Calogero R. Natoli
Summary: We present the MsSpec Atomic Scattering Amplitude Package (MASAP), which includes a computation program and a graphical interface for generating atomic scattering amplitude (ASA). The study investigates the applicability of plane wave (PW) and curved spherical wave (SW) scattering in describing electron propagation. The results show that the imaginary part of the optical potential enhances the elastic scattering in the forward direction but causes damping effects in other directions.
COMPUTER PHYSICS COMMUNICATIONS
(2024)
Article
Mathematics, Applied
Xavier Antoine, Jeremie Gaidamour, Emmanuel Lorin
Summary: This paper is interested in computing the ground state of nonlinear Schrodinger/Gross-Pitaevskii equations using gradient flow type methods. The authors derived and analyzed Fractional Normalized Gradient Flow methods, which involve fractional derivatives and generalize the well-known Normalized Gradient Flow method proposed by Bao and Du in 2004. Several experiments are proposed to illustrate the convergence properties of the developed algorithms.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
Article
Mathematics, Applied
Shangshuai Li, Da-jun Zhang
Summary: In this paper, the Cauchy matrix structure of the spin-1 Gross-Pitaevskii equations is investigated. A 2 x 2 matrix nonlinear Schrodinger equation is derived using the Cauchy matrix approach, serving as an unreduced model for the spin-1 BEC system with explicit solutions. Suitable constraints are provided to obtain reductions for the classical and nonlocal spin-1 GP equations and their solutions, including one-soliton solution, two-soliton solution, and double-pole solution.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
Article
Mathematics, Applied
Marco Cococcioni, Alessandro Cudazzo, Lorenzo Fiaschi, Massimo Pappalardo, Yaroslav D. Sergeyev
Summary: This work presents a new cutting plane method for lexicographic multi-objective integer linear programming. The method reformulates the problem into one with a single scalar objective function involving Grossone, and introduces a novel cutting plane named Gross-based Objective Function Cutting Plane. Furthermore, by combining different cutting planes, an algorithm called Gross-based Cutting Plane is proposed, which has been proven to find the optimal solution of the problem.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
Article
Mathematics, Applied
Yongjian Liu, Yasi Lu, Calogero Vetro
Summary: This paper introduces a new double phase elliptic inclusion problem (DPEI) involving a nonlinear and nonhomogeneous partial differential operator. It establishes the existence and extremality results to the elliptic inclusion problem and provides definitions for weak solutions, subsolutions, and supersolutions.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
Article
Computer Science, Interdisciplinary Applications
Leander Reascos, Fabio Carneiro, Andre Pereira, Nuno Filipe Castro, Ricardo Mendes Ribeiro
Summary: Density functional calculation of electronic structures of materials is a widely used technique in theoretical solid state physics. The berry suite of programs enhances this technique by ordering the eigenstates in analytic bands and calculating Berry connections, curvatures, and the second harmonic generation conductivity. It has been implemented for two dimensional materials and tested in hBN and InSe.
COMPUTER PHYSICS COMMUNICATIONS
(2024)
Article
Computer Science, Interdisciplinary Applications
Zhenglu Li, Gabriel Antonius, Yang-Hao Chan, Steven G. Louie
Summary: This article presents a workflow for practical calculations of electron-phonon coupling and includes the effect of many-electron correlations using GW perturbation theory. The workflow combines different software packages to enable accurate calculations at the level of quasiparticle band structures.
COMPUTER PHYSICS COMMUNICATIONS
(2024)
Article
Computer Science, Interdisciplinary Applications
Loric Torres, Annafederica Urbano, Catherine Colin, Sebastien Tanguy
Summary: Numerical simulations of Nucleate Boiling have gained increasing attention in recent years. Further studies are required on the modeling of heat flux near the contact line. This paper proposes a coupling methodology between a micro-region theoretical model and a larger scale DNS solver to investigate the quantitative effect of the micro-region on bubble growth in Nucleate Boiling.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Eran Treister, Rachel Yovel
Summary: In this work, the shifted Laplacian method is extended to the elastic Helmholtz equation, offering a novel approach for solving this challenging equation. The proposed method, combining the shifted Laplacian with linear elasticity approaches, shows a convergence rate independent of material properties, as demonstrated by local Fourier analysis and numerical evidence. Furthermore, the combination of the multigrid method with domain decomposition allows for efficient handling of large-scale problems, taking advantage of the strengths of both methods.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
