Article
Computer Science, Interdisciplinary Applications
Aidan P. Thompson, H. Metin Aktulga, Richard Berger, Dan S. Bolintineanu, W. Michael Brown, Paul S. Crozier, Pieter J. in 't Veld, Axel Kohlmeyer, Stan G. Moore, Trung Dac Nguyen, Ray Shan, Mark J. Stevens, Julien Tranchida, Christian Trott, Steven J. Plimpton
Summary: LAMMPS, a classical molecular dynamics simulator released as an open source code in 2004, has gained popularity for its wide variety of particle interaction models, platform compatibility, and user control over simulation details. With contributions from numerous developers, it has grown from 50,000 lines of code to a million today, showcasing new capabilities like dynamic load balancing and quantum-accuracy machine learning interatomic potentials.
COMPUTER PHYSICS COMMUNICATIONS
(2022)
Article
Computer Science, Interdisciplinary Applications
Sifan Wang, Xinling Yu, Paris Perdikaris
Summary: This work investigates the Neural Tangent Kernel (NTK) of Physics-informed neural networks (PINNs) and demonstrates that it can converge to a deterministic kernel that remains constant during training under appropriate conditions. A novel gradient descent algorithm is proposed to adaptively calibrate the convergence rate of total training error using the eigenvalues of NTK. A series of numerical experiments are conducted to validate the theory and practical effectiveness of the proposed algorithms.
JOURNAL OF COMPUTATIONAL PHYSICS
(2022)
Article
Computer Science, Interdisciplinary Applications
Zherui Han, Xiaolong Yang, Wu Li, Tianli Feng, Xiulin Ruan
Summary: Four Phonon is a computational package for calculating four-phonon scattering rates in crystals, built within the ShengBTE framework. It features an adaptive energy broadening scheme and a separate Python script for calculating fourth-order interatomic force constants. The program design is straightforward, and example calculations are demonstrated in Si, BAs, and LiCoO2.
COMPUTER PHYSICS COMMUNICATIONS
(2022)
Article
Mathematics, Interdisciplinary Applications
Run-Fa Zhang, Ming-Chu Li, Jian-Yuan Gan, Qing Li, Zhong-Zhou Lan
Summary: In this work, new test functions are constructed by setting generalized activation functions in different artificial network models. The explicit solution of a generalized breaking soliton equation is solved using the bilinear neural network method. Rogue waves of the generalized breaking soliton equation are obtained using symbolic computing technology and displayed intuitively with the help of Maple software.
CHAOS SOLITONS & FRACTALS
(2022)
Article
Mathematics, Interdisciplinary Applications
Qin Zhou, Houria Triki, Jiakun Xu, Zhongliang Zeng, Wenjun Liu, Anjan Biswas
Summary: We investigated the transmission of localized waves through a dual-power law medium exhibiting various perturbations. A novel class of nonlinear waves and their chirping phenomena were reported. The study also revealed the influence of nonlinearity on the dynamical properties of the chirped structures.
CHAOS SOLITONS & FRACTALS
(2022)
Article
Physics, Applied
S. U. Mamatha, R. L. V. Renuka Devi, N. Ameer Ahammad, Nehad Ali Shah, B. Madhusudhan Rao, C. S. K. Raju, M. Ijaz Khan, Kamel Guedri
Summary: This study analyzes the flow of a two-dimensional incompressible magneto-hydrodynamic fluid on a linear stretching sheet in the presence of suction or injection and convective boundary conditions. The flow governing equations are solved using a scaling group transformation method and shooting technique. The computational results are validated and the effects of different parameters on friction and mass transfer rate are investigated.
INTERNATIONAL JOURNAL OF MODERN PHYSICS B
(2023)
Article
Mathematics, Applied
Si-Jia Chen, Xing Lu
Summary: Based on the test function method, this paper presents the necessary and sufficient conditions for deriving lump solutions to special types of (3+1)-dimensional nonlinear evolution equations. Two approaches to construct lump multi-kink solutions are proposed. The existence of lump solutions and lump-multi-kink solutions is illustrated with examples. These methods are of significance for studying the existence of lump solutions and mixed solutions.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2022)
Article
Mathematics, Interdisciplinary Applications
Qiang Lai, Cong Lai, Hui Zhang, Chunbiao Li
Summary: This paper presents a novel neuron model by coupling a memristor to obtain a memristive neuron model. The study shows that memristor can enhance the chaos complexity of the discrete neuron, resulting in hyperchaos. Additionally, a new encryption scheme for image encryption is proposed, which exhibits excellent security characteristics.
CHAOS SOLITONS & FRACTALS
(2022)
Article
Mathematics, Interdisciplinary Applications
Xi-Hu Wu, Yi-Tian Gao, Xin Yu, Cui-Cui Ding, Liu-Qing Li
Summary: In this paper, a Lakshmanan-Porsezian-Daniel equation describing the nonlinear spin excitations in a (1+1)-dimensional isotropic biquadratic Heisenberg ferromagnetic spin chain is investigated. The semirational solutions of the equation are discussed, including degenerate soliton solutions, interaction solutions among solitons and degenerate solitons, and bound state solutions among a set of degenerate solitons.
CHAOS SOLITONS & FRACTALS
(2022)
Article
Mathematics, Applied
Changjin Xu, Dan Mu, Zixin Liu, Yicheng Pang, Maoxin Liao, Chaouki Aouiti
Summary: Delay has a significant impact on the dynamics of neural networks, making it a hot topic in mathematics and engineering. This paper presents a new fractional-order 4D neural network model with two different time delays based on previous research. The existence, uniqueness, and boundedness of the solution are analyzed using contraction mapping principle and the construction of an adaptive function. The stability and emergence of Hopf bifurcation are explored using the stability and bifurcation theory of fractional-order dynamical system. Novel stability criteria and bifurcation conditions are established for different delay cases. The impact of delay on stabilizing neural networks and controlling the emergence of Hopf bifurcation is thoroughly investigated, and Matlab simulations confirm the scientific validity of the derived conclusions.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2023)
Article
Mathematics, Interdisciplinary Applications
Huizi Cui, Lingge Zhou, Yan Li, Bingyi Kang
Summary: This paper introduces a method based on belief entropy to measure the complexity of physiological signals in biological systems. The method has better accuracy and applicability compared to existing entropy algorithms.
CHAOS SOLITONS & FRACTALS
(2022)
Article
Mathematics, Interdisciplinary Applications
Bo Li, Houjun Liang, Lian Shi, Qizhi He
Summary: This paper discusses the complex dynamics of the Kopel model with nonsymmetric response. The research shows that the fixed point of the nonsymmetric model may undergo various bifurcations under specific parameter combinations. The research also reveals that the effects from rivals can lead to more complex dynamics compared to self-adjustment.
CHAOS SOLITONS & FRACTALS
(2022)
Article
Physics, Applied
R. Naveen Kumar, Fehmi Gamaoun, Amal Abdulrahman, Jasgurpreet Singh Chohan, R. J. Punith Gowda
Summary: This research focuses on the heat transport analysis of three-dimensional unsteady flow of non-Newtonian nanofluid. A comparison between water-based ternary hybrid nanofluid and ZnO-SAE50Nanolubricant is made using two different models. The results show that ZnO-SAE50Nanolubricant exhibits the highest heat transport when the radiation parameter increases.
INTERNATIONAL JOURNAL OF MODERN PHYSICS B
(2022)
Article
Mathematics, Applied
Wen-Xiu Ma
Summary: This study proposes a nonlocal real reverse-spacetime integrable hierarchies of PT symmetric matrix AKNS equations, achieved through nonlocal symmetry reductions on the potential matrix, to determine generalized Jost solutions. By applying the Sokhotski-Plemelj formula, the associated Riemann-Hilbert problems are transformed into integral equations of Gelfand-Levitan-Marchenko type. The Riemann-Hilbert problems corresponding to the reflectionless case are explicitly solved, presenting soliton solutions for the resulting nonlocal real reverse-spacetime integrable PT-symmetric matrix AKNS equations.
PHYSICA D-NONLINEAR PHENOMENA
(2022)
Article
Mathematics, Interdisciplinary Applications
Xuejun Li, Jun Mou, Santo Banerjee, Zhisen Wang, Yinghong Cao
Summary: This paper proposes a high-security image cryptosystem based on a fractional-order hyperchaotic detuned laser system (FHDLS), an improved shuffling algorithm, and a DNA mutation diffusion algorithm. The experimental results demonstrate that the proposed system performs well in encryption and can effectively resist various attacks.
CHAOS SOLITONS & FRACTALS
(2022)
Article
Physics, Fluids & Plasmas
A. B. Zylstra, A. L. Kritcher, O. A. Hurricane, D. A. Callahan, J. E. Ralph, D. T. Casey, A. Pak, O. L. Landen, B. Bachmann, K. L. Baker, L. Berzak Hopkins, S. D. Bhandarkar, J. Biener, R. M. Bionta, N. W. Birge, T. Braun, T. M. Briggs, P. M. Celliers, H. Chen, C. Choate, D. S. Clark, L. Divol, T. Doppner, D. Fittinghoff, M. J. Edwards, M. Gatu Johnson, N. Gharibyan, S. Haan, K. D. Hahn, E. Hartouni, D. E. Hinkel, D. D. Ho, M. Hohenberger, J. P. Holder, H. Huang, N. Izumi, J. Jeet, O. Jones, S. M. Kerr, S. F. Khan, H. Geppert Kleinrath, V. Geppert Kleinrath, C. Kong, K. M. Lamb, S. Le Pape, N. C. Lemos, J. D. Lindl, B. J. MacGowan, A. J. Mackinnon, A. G. MacPhee, E. Marley, K. Meaney, M. Millot, A. S. Moore, K. Newman, J-M G. Di Nicola, A. Nikroo, R. Nora, P. K. Patel, N. G. Rice, M. S. Rubery, J. Sater, D. J. Schlossberg, S. M. Sepke, K. Sequoia, S. J. Shin, M. Stadermann, S. Stoupin, D. J. Strozzi, C. A. Thomas, R. Tommasini, C. Trosseille, E. R. Tubman, P. L. Volegov, C. R. Weber, C. Wild, D. T. Woods, S. T. Yang, C. Young
Summary: On August 8, 2021, an inertial fusion implosion on the National Ignition Facility achieved a fusion yield of over a megajoule and met Lawson's criterion for ignition. Experimental measurements show significant improvements in burn rate and hot-spot conditions, reaching unprecedented levels in inertial fusion research.
Article
Mathematics, Interdisciplinary Applications
Sina Etemad, Ibrahim Avci, Pushpendra Kumar, Dumitru Baleanu, Shahram Rezapour
Summary: In this paper, a new model of AH1N1/09 influenza virus is formulated based on the four classes of susceptible, exposed, infectious and recovered people. The model is investigated using fractal-fractional operators and power law type kernels. The existence of solution is studied using special mappings and the Leray-Schauder theorem. The stability criteria is explored and numerical solutions are approximated using the Adams-Bashforth scheme.
CHAOS SOLITONS & FRACTALS
(2022)
Article
Mathematics, Applied
Yunfei Liu, Zhaoye Qin, Fulei Chu
Summary: This article presents a coupled nonlinear modeling approach to investigate the nonlinear forced vibrations in composite cylindrical shells. By numerical simulations, the effects of external temperature change, magnetic potential, electric potential, and excitation amplitude on vibration response were evaluated.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2022)
Article
Mathematics, Interdisciplinary Applications
Kamal Shah, Muhammad Arfan, Aman Ullah, Qasem Al-Mdallal, Khursheed J. Ansari, Thabet Abdeljawad
Summary: This research work investigates the analysis of a general fractional order system under Atangana, Baleanu, and Caputo (ABC) fractional order derivative. The study focuses on existence theory, stability, and numerical analysis. The Krasnoselskii and Banach contraction theorems are used for the existence theory, and necessary results for Ulam Hyer's (UH) stability are developed using nonlinear analysis. The approximate solution is computed using the Adam's-Bashforth numerical technique, and three concrete examples with numerical and graphical interpretations are provided for validation.
CHAOS SOLITONS & FRACTALS
(2022)
Article
Mathematics, Applied
Fatemeh Parastesh, Mahtab Mehrabbeik, Karthikeyan Rajagopal, Sajad Jafari, Matjaz Perc
Summary: This study investigates the higher-order interactions among neurons and finds that second-order interactions can lead to synchronization under lower first-order coupling strengths. Additionally, the introduction of three-body interactions reduces the overall synchronization cost.
