Article
Mathematics, Applied
Hanzhang Hu, Yanping Chen
Summary: Two-grid algorithms based on two conservative and implicit finite element methods are studied for the two-dimensional nonlinear Schrodinger equation with wave operator. Both algorithms have three steps involving Newton iterations and error corrections. Optimal order L-p error estimations are conducted for error analysis of the algorithms without any time-step size conditions.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2021)
Article
Materials Science, Multidisciplinary
Pinki Kumari, R. K. Gupta, Sachin Kumar, K. S. Nisar
Summary: Abundant Jacobi elliptic type solutions with distinct physical structures of complex nonlinear conformable time-fractional modified Schrodinger equation are obtained using the generalized Jacobi elliptic function method. These solutions may be significant for the study of wave propagation, especially in the fields of nonlinear optics, biological sciences, and fluid dynamics.
RESULTS IN PHYSICS
(2022)
Article
Mathematics, Applied
Kailong Yang
Summary: This article investigates the multilinear distorted multiplier estimate associated with the Schrodinger operator H=-Delta+V in the framework of the corresponding distorted Fourier transform. The result extends existing bilinear estimates to multilinear cases and provides the estimate of Leibniz's law of integer-order derivations for the first time. Additionally, it obtains small data scattering for a kind of generalized mass-critical NLS with good potential in low dimensions d=1,2.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2022)
Article
Materials Science, Multidisciplinary
Asif Khan, Amir Ali, Shabir Ahmad, Sayed Saifullah, Kamsing Nonlaopon, Ali Akgul
Summary: In this article, the behaviour of the time fractional nonlinear Schrodinger equation under two different operators are investigated. Numerical and analytical solutions are obtained using the modified double Laplace transform. The error analysis shows that the system depends primarily on time, with small errors observed for small time values. The efficiency of the proposed scheme is verified with examples and further analyzed graphically and numerically.
RESULTS IN PHYSICS
(2022)
Article
Physics, Multidisciplinary
Mark J. Ablowitz, Joel B. Been, Lincoln D. Carr
Summary: This article presents a new class of integrable fractional nonlinear evolution equations that describe dispersive transport in fractional media. These equations can be constructed from nonlinear integrable equations using a widely generalizable mathematical process and have been applied to fractional extensions of the Korteweg-deVries and nonlinear Schrodinger equations.
PHYSICAL REVIEW LETTERS
(2022)
Article
Optics
Solve Selsto
Summary: In quantum physics, a method for calculating differential probabilities of unbound particles subject to a complex absorbing potential is presented, which uses projection onto single-particle scattering states to avoid calculating multiparticle scattering states. By resolving the dynamics of remaining particles, singly differential spectra from subsequent absorptions are obtained. The method is illustrated with numerical examples involving two-particle model-systems, showing how energy distributions of unbound particles can be determined on smaller numerical domains than the actual system extension.
Article
Optics
Sriganapathy Raghav, Barun Halder, Pradosh Basu, Utpal Roy
Summary: We provide an analytical model to achieve exponential localization of a Bose-Einstein condensate under a bichromatic optical lattice, known as Anderson localization. The degree of localization is investigated using the participation ratio, and the laser parameter domain for Anderson localization is identified. The exponential nature of the localization is proved, and the tunneling and revival phenomenon of Anderson-localized condensate are observed. The study also examines the dynamical and structural stability of the condensate during Anderson localization.
Article
Mathematics, Applied
Chu-Hee Cho, Youngwoo Koh, Jungjin Lee
Summary: This paper demonstrates that a local space-time estimate implies a global space-time estimate for dispersive operators. By considering a Littlewood-Paley type square function estimate and a generalization of Tao's epsilon removal lemma in mixed norms for dispersive operators in a time variable, the authors obtain sharp global space-time estimates with optimal regularity from previously known local ones.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2022)
Article
Mathematics, Applied
Gelson C. G. dos Santos, Sabado Saide Muhassua
Summary: This paper investigates the existence of solutions for a quasilinear Schrodinger problem with zero-mass, using the variational method and various mathematical tools for analysis.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2022)
Article
Mathematics, Interdisciplinary Applications
Asim Zafar, Muhammad Raheel, Muhammad Qasim Zafar, Kottakkaran Sooppy Nisar, Mohamed S. Osman, Roshan Noor Mohamed, Ashraf Elfasakhany
Summary: This paper explores solitary wave solutions for the perturbed nonlinear Schrodinger equation with six different nonlinearities utilizing the beta derivative. Various dark, bright, singular, and combined solutions are obtained through an efficient integration scheme. The simplicity, directness, and reliability of this method are highlighted in comparison to existing methods. Investigating the perturbed nonlinear Schrodinger equation in different nonlinear media using a novel derivative operator is the unique contribution of this study, which also includes numerical simulations of certain solutions.
FRACTAL AND FRACTIONAL
(2021)
Article
Mechanics
E. Heifetz, S. Zucker
Summary: In this study, we demonstrate that diffusion can be explained using a pressureless, compressible, and irrotational flow dynamics, where the effective force is determined by the divergence of the viscous stress tensor. This finding unifies the seemingly unrelated processes of mass and momentum transports.
Article
Mathematics, Interdisciplinary Applications
Alberto Bueno-Guerrero
Summary: In this paper, we propose a model-free axiomatic formulation for option pricing theory and establish a connection between the discounted zero-coupon bond price and the wave function, similar to axiomatic quantum mechanics. By linking the theory to term structure models through the Hamiltonian operator, we demonstrate the consistency between its associated Schrödinger equation and the [25] model. We also identify the quantum mechanical equivalent of the standard risk-neutral option pricing formula and apply a time-dependent perturbation theory to derive an approximate closed-form expression for call option pricing under the [26] model with a small local volatility perturbation.
CHAOS SOLITONS & FRACTALS
(2022)
Article
Quantum Science & Technology
Shi Jin, Xiantao Li, Nana Liu
Summary: This paper discusses the solution of the time-dependent Schrodinger equation in the semi-classical regime, considering the multiple-scale behavior and the impact of a small parameter. Quantum analogues of pseudo-spectral methods on classical computers are explored, and estimates on the gate counts are obtained. It is found that the number of required qubits scales logarithmically, and when physical observables are the desired outcomes, the gate complexity is reduced.
Article
Physics, Multidisciplinary
Axel Schulze-Halberg
Summary: This article presents a method for constructing solvable cases of generalized linear Dunkl-Schrodinger equations through suitable point transformations, and discusses the quantum-mechanical framework related to these equations and analyzes the special case of a position-dependent mass scenario.
Article
Physics, Multidisciplinary
Georgi Gary Rozenman, Wolfgang P. Schleich, Lev Shemer, Ady Arie
Summary: In this study, we theoretically investigate and experimentally observe the evolution of periodic wave trains using surface gravity water wave packets. For low steepness waves, the waves form a Talbot carpet in the linear regime. By increasing the wave steepness and the corresponding nonlinear response, the waves follow the Akhmediev breather solution, resulting in the disappearance of higher frequency periodic patterns at the fractional Talbot distance.
PHYSICAL REVIEW LETTERS
(2022)
Article
Education, Scientific Disciplines
Siu A. Chin
AMERICAN JOURNAL OF PHYSICS
(2015)
Article
Mathematics, Applied
Siu A. Chin
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS
(2016)
Article
Physics, Fluids & Plasmas
Siu A. Chin
Article
Physics, Multidisciplinary
Siu A. Chin, Omar A. Ashour, Stanko N. Nikolic, Milivoj R. Belic
Article
Engineering, Mechanical
Stanko N. Nikolic, Najdan B. Aleksic, Omar A. Ashour, Milivoj R. Belic, Siu A. Chin
NONLINEAR DYNAMICS
(2017)
Article
Engineering, Mechanical
Stanko N. Nikolic, Omar A. Ashour, Najdan B. Aleksic, Milivoj R. Belic, Siu A. Chin
NONLINEAR DYNAMICS
(2019)
Article
Engineering, Mechanical
Stanko N. Nikolic, Omar A. Ashour, Najdan B. Aleksic, Yiqi Zhang, Milivoj R. Belic, Siu A. Chin
NONLINEAR DYNAMICS
(2019)
Article
Education, Scientific Disciplines
Siu A. Chin, John Massey
AMERICAN JOURNAL OF PHYSICS
(2019)
Article
Education, Scientific Disciplines
Siu A. Chin
AMERICAN JOURNAL OF PHYSICS
(2020)
Article
History & Philosophy Of Science
Siu A. Chin
Summary: The ongoing feud between Robert Hooke and Isaac Newton revolves around whether Newton should have acknowledged Hooke's influence on his graphical method of constructing planet orbits. This controversy has intensified in recent decades with claims that Hooke may have accomplished what Newton did not. Modern understanding of Newton's graphical method as a symplectic integrator may help determine the credibility of these claims.
HISTORIA MATHEMATICA
(2022)
Article
Computer Science, Interdisciplinary Applications
Siu A. Chin, Durward Cator
Summary: This work provides a Lie operator derivation of various Boris solvers by studying trajectory errors in a constant magnetic field. It reveals two distinct ways to eliminate these errors and achieve accurate particle trajectory on the cyclotron orbit. The study also highlights the misconception in distinguishing between different Boris solvers and demonstrates the mathematical equivalence between Buneman's cycloid fitting scheme and Boris' on-orbit solver.
JOURNAL OF COMPUTATIONAL PHYSICS
(2022)
Article
Chemistry, Physical
Siu A. Chin
Summary: This paper derives the discrete form of the short-time propagator through simple algebraic operations, proving its universality and optimization method.
JOURNAL OF CHEMICAL PHYSICS
(2023)
Article
Physics, Fluids & Plasmas
Siu A. Chin
Summary: By using the Lorentz force law instead of Hamilton's equation, two basic algorithms for solving trajectories in a magnetic field similar to the velocity Verlet and position Verlet symplectic integrators can be derived, which require modification of the time step to achieve exact trajectory on the gyrocircle.
Article
Physics, Fluids & Plasmas
Siu A. Chin
Article
Physics, Fluids & Plasmas
Siu A. Chin, Omar A. Ashour, Stanko N. Nikolic, Milivoj R. Belic
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
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
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
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
Computer Science, Interdisciplinary Applications
Andrzej Daniluk
Summary: RHEED_DIFF_2D is an open-source software for qualitative numerical simulations of RHEED oscillation intensity changes with layer deposition, used for interpreting heteroepitaxial structures under different scattering crystal potential models.
COMPUTER PHYSICS COMMUNICATIONS
(2024)
Article
Computer Science, Interdisciplinary Applications
Niklas Kuehl, Hendrik Fischer, Michael Hinze, Thomas Rung
Summary: The article presents a strategy and algorithm for simulation-accompanying, incremental Singular Value Decomposition (SVD) for time-evolving, spatially parallel discrete data sets. The proposed method improves computational efficiency by introducing a bunch matrix, resulting in higher accuracy and practical applicability.
COMPUTER PHYSICS COMMUNICATIONS
(2024)
Article
Computer Science, Interdisciplinary Applications
Jose M. Rodriguez-Borbon, Xian Wang, Adrian P. Dieguez, Khaled Z. Ibrahim, Bryan M. Wong
Summary: This paper presents an open-source software package called TRAVOLTA for massively parallelized quantum optimal control calculations on GPUs. The TRAVOLTA package is an improvement on the previous NIC-CAGE algorithm and incorporates algorithmic improvements for faster convergence. Three different variants of GPU parallelization are examined to evaluate their performance in constructing optimal control fields in various quantum systems. The benchmarks show that the GPU-enhanced TRAVOLTA code produces the same results as previous CPU-based algorithms but with a speedup of more than ten times. The GPU enhancements and algorithmic improvements allow large quantum optimal control calculations to be efficiently executed on modern multi-core computational hardware.
COMPUTER PHYSICS COMMUNICATIONS
(2024)
Article
Computer Science, Interdisciplinary Applications
Weijie Hua
Summary: This work introduces a program called MCNOX for computing and analyzing ultrafast nonlinear X-ray spectra. It is designed for cutting-edge applications in photochemistry/photophysics enabled by X-ray free-electron lasers and high harmonic generation light sources. The program can calculate steady-state X-ray absorption spectroscopy and three types of ultrafast nonlinear X-ray spectra, and it is capable of identifying major electronic transitions and providing physical and chemical insights from complex signals.
COMPUTER PHYSICS COMMUNICATIONS
(2024)
Article
Computer Science, Interdisciplinary Applications
Leandro Benatto, Omar Mesquita, Lucimara S. Roman, Rodrigo B. Capaz, Graziani Candiotto, Marlus Koehler
Summary: Photoluminescence Quenching Simulator (PLQ-Sim) is a user-friendly software for studying the dynamics of photoexcited states at the interface between organic semiconductors. It provides important information on organic photovoltaic and photothermal devices and calculates transfer rates and quenching efficiency.
COMPUTER PHYSICS COMMUNICATIONS
(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
R. Kleiber, M. Borchardt, R. Hatzky, A. Koenies, H. Leyh, A. Mishchenko, J. Riemann, C. Slaby, J. M. Garcia-Regana, E. Sanchez, M. Cole
Summary: This paper describes the current state of the EUTERPE code, focusing on the implemented models and their numerical implementation. The code is capable of solving the multi-species electromagnetic gyrokinetic equations in a three-dimensional domain. It utilizes noise reduction techniques and grid resolution transformation for efficient computation. Additionally, various hybrid models are implemented for comparison and the study of plasma-particle interactions. The code is parallelized for high scalability on multiple CPUs.
COMPUTER PHYSICS COMMUNICATIONS
(2024)
Article
Computer Science, Interdisciplinary Applications
Pengliang Yang
Summary: This paper presents an open source software called SMIwiz, which combines seismic modelling, reverse time migration, and full waveform inversion into a unified computer implementation. SMIwiz supports both 2D and 3D simulations and provides various computational recipes for efficient calculation. Its independent processing and batchwise job scheduling ensure scalability, and its viability is demonstrated through applications on benchmark models.
COMPUTER PHYSICS COMMUNICATIONS
(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
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
Computer Science, Interdisciplinary Applications
Siegfried Kaidisch, Thomas U. Hilger, Andreas Krassnigg, Wolfgang Lucha
Summary: Motivated by a use case in theoretical hadron physics, this paper revisits an application of a pole-sum fit to dressing functions of a confined quark propagator. Specifically, it investigates approaches to determine the number and positions of singularities closest to the origin for a function known numerically on a specific grid on the positive real axis. Comparing the efficiency of standard techniques to a pure artificial-neural-network approach and a combination of both, it finds that the combined approach is more efficient. This approach can be applied to similar situations where the positions of poles need to be estimated quickly and reliably from real-axis information alone.
COMPUTER PHYSICS COMMUNICATIONS
(2024)