Article
Ecology
Johannes Cairns, Alexandre Jousset, Lutz Becks, Teppo Hiltunen
Summary: Mutation supply can influence evolutionary and ecological dynamics by affecting population size and species interactions, particularly when population size is constrained by external conditions. Controlled experiments show that higher mutation supply enables faster adaptation to low-resource environments and anti-predatory defense mechanisms, leading to increased population size and better access to high-recurrence mutational targets.
Article
Computer Science, Interdisciplinary Applications
Ali C. Bekar, Erdogan Madenci
Summary: This study introduces an approach to identify significant terms in PDEs based on measured data using linear regression model, PDDO, and sparse linear regression learning algorithm. The solution is achieved through Douglas-Rachford algorithm with regularization, demonstrating effectiveness in handling challenging nonlinear PDEs.
JOURNAL OF COMPUTATIONAL PHYSICS
(2021)
Article
Mathematics, Applied
Davide Palitta
Summary: This study presents a novel solution strategy for addressing the discrete operator issues arising from the time-space discretization of evolutionary partial differential equations, efficiently solving problems with a large number of degrees of freedom while maintaining low storage demand.
JOURNAL OF SCIENTIFIC COMPUTING
(2021)
Article
Mathematics, Applied
S. S. Santra, S. Priyadharshini, V. Sadhasivam, J. Kavitha, U. Fernandez-Gamiz, S. Noeiaghdam, K. M. Khedher
Summary: This article investigates the oscillatory behavior of solutions to conformable elliptic partial differential equations of the Emden-Fowler type. By employing the Riccati method, new necessary conditions for the oscillation of all solutions are established. These findings build upon previous results for integer order equations and are further illustrated through an example.
Article
Mathematics
Antoine Hocquet
Summary: The study explores the Cauchy problem for a quasilinear equation with transport rough input, providing sufficient conditions for existence in any dimension and uniqueness in the case of divergence-free X. It focuses on one-dimensional scenario with slightly more regular coefficients, proving existence of a class of solutions satisfying a specific condition, and uniqueness by obtaining an L-infinity(L-1) estimate on the difference of two solutions. This is achieved by establishing a link with a backward dual equation and a (rough) iteration lemma akin to Moser.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2021)
Article
Physics, Multidisciplinary
Maximilian Gelbrecht, Niklas Boers, Juergen Kurths
Summary: By augmenting differential equations with artificial neural networks, it is possible to predict complex systems even with short and incomplete datasets. This approach is effective for high-dimensional chaotic systems and can forecast a horizon significantly longer than the training data length.
NEW JOURNAL OF PHYSICS
(2021)
Article
Mathematics, Applied
Ahmad Qazza, Rania Saadeh, Emad Salah
Summary: In this paper, we introduce a new technique, called the direct power series method, to solve various types of time-fractional partial differential equations and systems using the Caputo derivative. We present a simple algorithm to demonstrate the versatility of the method in solving different time-fractional partial problems. We also introduce a new theorem to explain the necessary substitutions in the proposed method and provide convergence analysis conditions. Furthermore, we discuss illustrative examples of time-fractional partial differential equations and systems to showcase the practicality and simplicity of the new approach.
Article
Mathematics, Applied
Xuehua Yang, Haixiang Zhang
Summary: This paper aims to prove the uniform l(1) optimal error estimate for solving time fractional partial differential equations with nonsmooth data using the L1 scheme. The convergence of the L1 scheme for both smooth and nonsmooth initial data has been studied, but it does not apply to the uniform l(1) long time convergence behavior.
APPLIED MATHEMATICS LETTERS
(2022)
Article
Computer Science, Artificial Intelligence
Somdatta Goswami, Katiana Kontolati, Michael D. D. Shields, George Em Karniadakis
Summary: This paper presents a transfer learning framework for task-specific learning based on Deep Operator Network (DeepONet), addressing conditional shifts in transfer learning scenarios such as nonlinear partial differential equations.
NATURE MACHINE INTELLIGENCE
(2022)
Article
Computer Science, Interdisciplinary Applications
Daniel A. Messenger, David M. Bortz
Summary: Sparse Identification of Nonlinear Dynamics (SINDy) has been extended to the weak formulation for partial differential equations (PDEs) to improve accuracy in model coefficient recovery and robustness in identifying PDEs in large noise regime. The implementation utilizes Fast Fourier Transform for efficient model identification and reveals a connection between noise robustness and spectra of test functions. Additionally, a learning algorithm for threshold in sequential thresholding least-squares (STLS) is introduced for model identification from large libraries.
JOURNAL OF COMPUTATIONAL PHYSICS
(2021)
Review
Mathematics, Applied
Duy Phan, Alexander Ostermann
Summary: This paper considers two types of second-order in time partial differential equations, namely semilinear wave equations and semilinear beam equations. To solve these equations with exponential integrators, an approach to efficiently compute the action of the matrix exponential and related matrix functions is presented. Various numerical simulations are provided to illustrate the effectiveness of this approach.
JOURNAL OF SCIENTIFIC COMPUTING
(2022)
Article
Mathematics
M. C. Carbinatto, K. P. Rybakowski
Summary: In this paper, a Conley index framework is introduced for partial differential equations with delay terms. The existence of special nonconstant full solutions for parametrized classes of such equations, which are close to PDEs without delays, is then proven. The proof utilizes a tubular Conley index continuation principle established in a previous work by Carbinatto and Rybakowski (2013) [1].
JOURNAL OF DIFFERENTIAL EQUATIONS
(2023)
Article
Mathematics
Diego Catalano Ferraioli, Tarcisio Castro Silva
Summary: This paper investigates third order equations describing spherical surfaces and pseudospherical surfaces. By classifying and providing examples of these equations, the problem of determining sequences of conservation laws in both cases is discussed.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2024)
Article
Mathematics
Mawia Osman, Yonghui Xia, Omer Abdalrhman Omer, Ahmed Hamoud
Summary: In this article, the fuzzy Adomian decomposition method and fuzzy modified Laplace decomposition method are presented to solve the fuzzy fractional Navier-Stokes equations. The fuzzy Elzaki transform and fuzzy Elzaki decomposition method are also investigated for solving fuzzy linear-nonlinear Schrodinger differential equations. Comparisons are made with other methods, and the proposed methods are found to be simpler and consistent with analytical and numerical results.
Article
Mathematics, Applied
Jizhao Huang, Danfeng Luo
Summary: In this article, the authors investigate conformable fractional stochastic differential equations with infinite delay using measures of noncompactness. They establish the existence of solutions for these equations by employing Monch fixed point theorem and measures of noncompactness. The controllability of the considered equations is then explored using Jensen inequality, Holder inequality, stochastic analysis techniques, and semigroup theory, with the support of a Monch fixed point theorem. The controllability of these equations with nonlocal conditions is also discussed, and the theoretical results are validated through an example.
Article
Mechanics
Xiaolin Wang, Silas Alben
Article
Mechanics
Xiaolin Wang, Silas Alben, Chenyang Li, Yin Lu Young
Article
Multidisciplinary Sciences
Xiaolin Wang, Silas Alben
PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
(2018)
Article
Physics, Fluids & Plasmas
Xiaolin Wang, Matthew T. Osborne, Silas Alben
Article
Engineering, Electrical & Electronic
Jonathan Kao, Xiaolin Wang, John Warren, Jie Xu, Daniel Attinger
JOURNAL OF MICROMECHANICS AND MICROENGINEERING
(2007)
Article
Thermodynamics
Xiaolin Wang, Daniel Attinger, Francisco Moraga
NANOSCALE AND MICROSCALE THERMOPHYSICAL ENGINEERING
(2006)