Article
Mathematics, Applied
F. Abdolabadi, A. Zakeri, A. Amiraslani
Summary: In this paper, a split-step Fourier pseudo-spectral method is proposed for solving the space fractional coupled nonlinear Schrodinger equations. The method splits the equations into two subproblems, with one of them being linear. The solution for the nonlinear subproblem is computed exactly, and the Riesz space fractional derivative is approximated using a Fourier pseudo-spectral method. The stability, convergence, discrete charge, and multi-symplectic preserving properties of the proposed method are investigated, and it is extended for solving two-dimensional problems. Numerical experiments are conducted to validate the theoretical analysis and demonstrate the efficiency of the proposed scheme.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2023)
Article
Mathematics, Applied
Vaibhav Mehandiratta, Mani Mehra, Guenter Leugering
Summary: In this paper, the numerical approximation of fractional initial and boundary value problems using Haar wavelets is proposed. Unlike existing methods, which approximate the fractional derivative of the function using the Haar basis, this approach approximates the function and its classical derivatives using Haar basis functions. Error bounds in the approximation of fractional integrals and derivatives are derived, and the proposed method is shown to be efficient through numerical experiments.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2021)
Article
Computer Science, Theory & Methods
Lan-Lan Huang, Guo-Cheng Wu, Dumitru Baleanu, Hong-Yong Wang
Summary: This study investigates linear fractional difference equations with respect to interval-valued functions, introduces w-monotonicity, provides discrete Leibniz integral laws, and obtains exact solutions of two linear equations through Picard's iteration. The solutions are given in discrete Mittag-Leffler functions with and without delay, respectively, compared to deterministic initial problems. This paper provides a novel tool to understand fractional uncertainty problems on discrete time domains.
FUZZY SETS AND SYSTEMS
(2021)
Article
Optics
Da-Sheng Mou, Chao-Qing Dai
Summary: By modifying the discrete Riccati equation mapping method using the conformable fractional derivative, rich vector exact solutions for the coupled discrete conformable fractional nonlinear Schro center dot dinger equations are obtained, including vector bright solitons, vector dark solitons, and vector trigonometric function solutions. The parameter range for these solutions is provided, and the effects of parameters related to group velocity and fractional derivatives on wave amplitude modulation are investigated.
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
Computer Science, Information Systems
R. Beigmohamadi, A. Khastan, J. J. Nieto, R. Rodriguez-Lopez
Summary: In this study, the basis of the theory of discrete fuzzy fractional calculus is established and applied to the area of fuzzy fractional difference equations. The basic composition rules of fuzzy fractional difference and sum operators are provided. Moreover, the results are applied to solve a fuzzy fractional initial value problem.
INFORMATION SCIENCES
(2022)
Article
Computer Science, Interdisciplinary Applications
Anastassiya Semenova, Sergey A. Dyachenko, Alexander O. Korotkevich, Pavel M. Lushnikov
Summary: This study provides a systematic comparison of two numerical methods for solving the NLSE: the standard second order split-step (SS2) method and the Hamiltonian integration method (HIM). In most simulations, HIM shows smaller numerical errors compared to SS2, and it allows for larger time steps while maintaining numerical stability.
JOURNAL OF COMPUTATIONAL PHYSICS
(2021)
Article
Mathematics, Interdisciplinary Applications
Arran Fernandez, Hafiz Muhammad Fahad
Summary: We conducted a formal study on weighted fractional calculus and its extension, comparing it with classical Riemann-Liouville fractional calculus, proving fundamental properties and solving ordinary differential equations in specific cases.
FRACTAL AND FRACTIONAL
(2022)
Article
Mathematics, Applied
Alexander Ostermann, Fangyan Yao
Summary: In this paper, we propose and analyze a fully discrete low-regularity integrator for the one-dimensional cubic nonlinear Schrodinger equation on the torus. The scheme is explicit and implemented using the fast Fourier transform with a complexity of O(N log N) operations per time step. Numerical examples demonstrate the convergence behavior of the proposed scheme.
JOURNAL OF SCIENTIFIC COMPUTING
(2022)
Article
Mathematics, Interdisciplinary Applications
Ming Zhong, Zhenya Yan
Summary: In this paper, the Fourier neural operator (FNO) is extended to discover the mapping between two infinite-dimensional function spaces, and applied to the soliton solutions of fractional integrable nonlinear wave equations. The FNO exhibits powerful approximation capability and the performance is influenced by certain factors.
CHAOS SOLITONS & FRACTALS
(2022)
Article
Mathematics, Applied
Muhammad Naeem, Ahmed A. Khammash, Ibrahim Mahariq, Ghaylen Laouini, Jeevan Kafle
Summary: The paper introduces an algorithm using Laplace transform to calculate approximate solutions for fuzzy fractional-order nonlinear equal width equations, demonstrating its utility and capability. The fuzzy iterative transform method is found to be effective in accurately and precisely studying the behavior of suggested problems.
JOURNAL OF FUNCTION SPACES
(2021)
Article
Mathematics, Applied
Ridvan Cem Demirkol
Summary: In this paper, a novel class of magnetic curves, called pseudo-solitonic magnetic curves, is introduced by considering their connection with the nonlinear heat system/nonlinear Schrodinger equation and moving space curves in the Minkowski 3-space. A very special class of soliton surfaces, named pseudo-solitonic magnetic surfaces, is also constructed by considering the effects of pseudo-solitonic magnetic flows in the Minkowski 3-space. These curves and surfaces are not only rich in geometric and physical features but also can be constructed using a simple geometric procedure compared to other models.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Engineering, Multidisciplinary
Saima Rashid, Yu-Ming Chu, Jagdev Singh, Devendra Kumar
Summary: This paper evaluates the potential improvement of classification results using discrete proportional fractional operators, focusing on novel versions of Polya-Szego and CebyseV type inequalities. The generalizations discussed have utility in finite difference equations and statistical analysis, with consequences including general forms of Polya-Szego and CebyseV variants. The paper also serves as a discrete analogue of integral inequalities and expands on discrete variants for nabla (h) over cap -fractional sums.
ALEXANDRIA ENGINEERING JOURNAL
(2021)
Article
Mathematics, Applied
Shanshan Wang
Summary: This paper constructs split-step quintic B-spline collocation (SS5BC) methods for nonlinear Schrodinger equations in various dimensions. The proposed methods are verified to be convergent and efficient through numerical tests and comparisons. Furthermore, the SS5BC scheme is also successfully applied to compute Bose-Einstein condensates.
Article
Physics, Fluids & Plasmas
Mario I. Molina
Summary: The study focused on linear and nonlinear modes of a one-dimensional nonlinear electrical lattice with a fractional discrete Laplacian. Long-range intersite coupling was induced by the fractional discrete Laplacian. In the linear regime, plane waves spectrum and mean-square displacement were computed in closed form, showing ballistic behavior at long times. In the nonlinear regime, the number of generated discrete solitons decreased as the fractional exponent decreased.
Article
Quantum Science & Technology
Logan E. Hillberry, Matthew T. Jones, David L. Vargas, Patrick Ra, Nicole Yunger Halpern, Ning Bao, Simone Notarnicola, Simone Montangero, Lincoln D. Carr
Summary: Cellular automata are classical bits that interact and display diverse emergent behaviors; quantum cellular automata (QCA) can exhibit complexity by following 'Goldilocks rules' that balance activity and stasis. These rules generate robust dynamical features, network structure, and persistent entropy fluctuations.
QUANTUM SCIENCE AND TECHNOLOGY
(2021)
Article
Education, Scientific Disciplines
Abraham Asfaw, Alexandre Blais, Kenneth R. Brown, Jonathan Candelaria, Christopher Cantwell, Lincoln D. Carr, Joshua Combes, Dripto M. Debroy, John M. Donohue, Sophia E. Economou, Emily Edwards, Michael F. J. Fox, Steven M. Girvin, Alan Ho, Hilary M. Hurst, Zubin Jacob, Blake R. Johnson, Ezekiel Johnston-Halperin, Robert Joynt, Eliot Kapit, Judith Klein-Seetharaman, Martin Laforest, H. J. Lewandowski, Theresa W. Lynn, Corey Rae H. McRae, Celia Merzbacher, Spyridon Michalakis, Prineha Narang, William D. Oliver, Jens Palsberg, David P. Pappas, Michael G. Raymer, David J. Reilly, Mark Saffman, Thomas A. Searles, Jeffrey H. Shapiro, Chandralekha Singh
Summary: The paper provides a roadmap for constructing a quantum engineering education program to meet the workforce needs of the United States and international community. Through a workshop and drawing on best practices, the researchers make specific findings and recommendations, including the design of a first quantum engineering course accessible to all STEM students and the education and training methods for producing quantum-proficient engineers.
IEEE TRANSACTIONS ON EDUCATION
(2022)
Article
Physics, Multidisciplinary
Justin Q. Anderson, P. A. Praveen Janantha, Diego A. Alcala, Mingzhong Wu, Lincoln D. Carr
Summary: We report the experimental verification of cubic-quintic complex Ginzburg-Landau (CQCGL) physics in a single driven, damped system. Different types of complex dynamical behavior and pattern formation are observed, including periodic breathing, complex recurrence, spontaneous spatial shifting, and intermittency. These behaviors are observed in self-generated spin wave envelopes circulating within a dispersive, nonlinear yttrium iron garnet waveguide. The stable and long-lasting nature of these behaviors makes them promising for technological applications.
NEW JOURNAL OF PHYSICS
(2022)
Article
Optics
Zachary C. Coleman, Lincoln D. Carr
Summary: We obtained the exact analytical solution for a continuously driven qutrit in different configurations, and calculated the linear susceptibility in each system. We identified regimes of transient gain without inversion and identified parameter values for specific effects such as superluminal, vanishing, and negative group velocity for the probe field.
JOURNAL OF PHYSICS B-ATOMIC MOLECULAR AND OPTICAL 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
Physics, Multidisciplinary
Mark J. Ablowitz, Joel B. Been, Lincoln D. Carr
Summary: The inverse scattering transform allows explicit construction of solutions to many physically significant nonlinear wave equations, and can be extended to fractional nonlinear evolution equations characterized by anomalous dispersion. Using symmetries present in the linear scattering problem, these equations can be connected with a scalar family of nonlinear evolution equations, of which fractional mKdV, fsineG, and fsinhG are special cases.
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
(2022)
Article
Multidisciplinary Sciences
Eric B. Jones, Logan E. Hillberry, Matthew T. Jones, Mina Fasihi, Pedram Roushan, Zhang Jiang, Alan Ho, Charles Neill, Eric Ostby, Peter Graf, Eliot Kapit, Lincoln D. Carr
Summary: This study demonstrates the implementation of Quantum Cellular Automata (QCA) on a digital quantum processor, simulating a one-dimensional Goldilocks rule on chains of superconducting qubits. The results show the formation of small-world mutual information networks and provide measurements of population dynamics and complex network measures. These findings contribute to the understanding of complexity in quantum systems.
NATURE COMMUNICATIONS
(2022)
Article
Education & Educational Research
Nathan Crossette, Lincoln D. Carr, Bethany R. Wilcox
Summary: Social network analysis (SNA) was used to quantitatively study student collaboration in three courses during the COVID-19 pandemic. Results varied widely between the courses, with strong correlations between centrality measures and performance in the remote course at the Colorado School of Mines, weaker correlations in the two hybrid courses at the University of Colorado Boulder, and nearly no correlations in one of the courses. The study also investigated the effect of missing nodes on correlations and found that the measured correlations were not spurious.
PHYSICAL REVIEW PHYSICS EDUCATION RESEARCH
(2023)
Article
Materials Science, Multidisciplinary
Arya Dhar, Daniel Jaschke, Lincoln D. Carr
Summary: The bilinear-biquadratic model is a promising candidate for studying spin-1 systems and designing quantum simulators based on its underlying Hamiltonian. It contains various phases, including the valuable and exotic Haldane phase. We investigate the Kibble-Zurek physics of linear quenches into the Haldane phase and propose ideal quench protocols to minimize defects in the final state.
Article
Mathematics, Interdisciplinary Applications
Bhuvanesh Sundar, Mattia Walschaers, Valentina Parigi, Lincoln D. Carr
Summary: The study focuses on investigating the ground states of spin models defined on networks and their responses to network attacks, quantifying complexity and responses through calculating distributions of network measures. The emergent networks in the ground state do not meet the usual criteria for complexity, with attacks rescaling properties by a constant factor. The findings suggest that complex spin networks are not more robust to attacks than non-complex spin networks, contrary to classical networks.
JOURNAL OF PHYSICS-COMPLEXITY
(2021)
Article
Quantum Science & Technology
Yuri Alexeev, Dave Bacon, Kenneth R. Brown, Robert Calderbank, Lincoln D. Carr, Frederic T. Chong, Brian DeMarco, Dirk Englund, Edward Farhi, Bill Fefferman, Alexey Gorshkov, Andrew Houck, Jungsang Kim, Shelby Kimmel, Michael Lange, Seth Lloyd, Mikhail D. Lukin, Dmitri Maslov, Peter Maunz, Christopher Monroe, John Preskill, Martin Roetteler, Martin J. Savage, Jeff Thompson
Summary: The development of quantum computers and the discovery of scientific applications should be considered together by co-designing full-stack quantum computer systems and applications to accelerate their development. In the next 2-10 years, quantum computers for science face significant challenges and opportunities.
Article
Physics, Multidisciplinary
Tinggui Chen, Baizhan Xia, Dejie Yu, Chuanxing Bi
Summary: This study proposes a gradient phononic crystal structure for enhanced acoustic sensing. By breaking the symmetry of the PC structure, topologically protected edge states are introduced, resulting in topological acoustic rainbow trapping. The robustness and enhancement properties are verified numerically and experimentally.
