Results 151 to 160 of about 10,613 (298)
Numerical Solution of a Nonlinear Eigenvalue Problem
Indagationes Mathematicae (Proceedings), 1965 No abstract.
openaire +3 more sources
International Journal for Numerical and Analytical Methods in Geomechanics, EarlyView.ABSTRACT Numerical simulation of hydraulic fracturing remains challenging due to the strong coupling between geomechanics and fluid flow when modelling multiple physical mechanisms of rock deformation, fracture evolution and fluid leak‐off. This study develops a coupled hydraulic fracture propagation framework that combines the extended finite element ...
Ran Tao, Juliana Y. Leung, Samer Adeeb
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International Journal for Numerical and Analytical Methods in Geomechanics, EarlyView.ABSTRACT An efficient semi‐analytical approach based on the Fourier–Bessel series (FBS) system of vector functions and the stiffness matrix method is proposed to study the dynamic response of axially loaded piles embedded in transversely isotropic (TI) layered soil.
Quoc Kinh Tran +5 more
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Nordgren PINNs to VQE: Advancing Hydraulic Fracturing Simulations in Shale Reservoirs
International Journal for Numerical and Analytical Methods in Geomechanics, EarlyView.ABSTRACT This study advances hydraulic fracturing simulations in shale reservoirs using two computational paradigms, Physics‐Informed Neural Networks (PINNs) and the Variational Quantum Eigensolver (VQE). PINNs were employed to solve Nordgren's equation, which governs fracture width evolution, by embedding physical laws into the neural network ...
Dennis Delali Kwesi Wayo +7 more
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Subcritical perturbations of resonant linear problems with sign-changing potential
Electronic Journal of Differential Equations, 2005 We establish existence and multiplicity theorems for a Dirichlet boundary-value problem at resonance. This problem is a nonlinear subcritical perturbation of a linear eigenvalue problem studied by Cuesta, and includes a sign-changing potential. We obtain
Teodora-Liliana Dinu
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Evaluating anisotropy‐based Monin–Obukhov similarity theory over canopies and complex terrain
Quarterly Journal of the Royal Meteorological Society, EarlyView.This study shows that an anisotropy‐based generalization of Monin–Obukhov surface‐layer scaling (SC23) applies readily across a wide range of atmospheric conditions with variable terrain, canopies, and land‐cover complexity. This work focuses on the scaling of velocity variances for 7 years at the 47 sites in the National Ecological Observation Network
Tyler S. Waterman +3 more
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Existence of solutions for an eigenvalue problem with weight
Electronic Journal of Differential Equations, 2010 In this work we study the existence of solutions for the nonlinear eigenvalue problem with p-biharmonic $ Delta_p^2 u =lambda m(x)|u|^{p-2}u$ in a smooth bounded domain under Neumann boundary conditions.
Abdel Rachid El Amrouss +2 more
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New views of some invariants associated with the Cartesian 2D velocity gradient tensor
Quarterly Journal of the Royal Meteorological Society, EarlyView.Vorticity and divergence of horizontal flow are fundamental quantities in meteorology; both are linear functions of the four elements of the 2D velocity gradient tensor and both are formally unchanged under coordinate rotation. We explore four quadratic functions of the elements that are geometrically invariant in this sense, finding some novel ...
I. Roulstone, S. A. Clough, A. A. White
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Optimal Homogeneous ℒp$$ {\boldsymbol{\mathcal{L}}}_{\boldsymbol{p}} $$‐Gain Controller
International Journal of Robust and Nonlinear Control, EarlyView.ABSTRACT Nonlinear ℋ∞$$ {\mathscr{H}}_{\infty } $$‐controllers are designed for arbitrarily weighted, continuous homogeneous systems with a focus on systems affine in the control input. Based on the homogeneous ℒp$$ {\mathcal{L}}_p $$‐norm, the input–output behavior is quantified in terms of the homogeneous ℒp$$ {\mathcal{L}}_p $$‐gain as a ...
Daipeng Zhang +3 more
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Properties of the first eigenvalue of a model for non Newtonian fluids
Electronic Journal of Differential Equations, 2010 We consider a nonlinear Stokes problem on a bounded domain. We prove the existence of the first eigenvalue which is given by a minimization formula. Some properties such as strict monotony and the Fredholm alternative are established.
Omar Chakrone +2 more
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