Results 51 to 60 of about 856 (206)

Variational system identification of the partial differential equations governing microstructure evolution in materials: Inference over sparse and spatially unrelated data

, 2021
Pattern formation is a widely observed phenomenon in diverse fields including materials physics, developmental biology and ecology, among many others.
Huan, X., Wang, Z., Garikipati, K.
core   +1 more source

Subspace Acceleration for Efficient Nonlinear Water Wave Simulation

International Journal for Numerical Methods in Fluids, EarlyView.
We introduce an exponentially weighted subspace acceleration technique to reduce GMRES iterations for solving the Poisson equation with time‐dependent coefficients in nonlinear, dispersive free‐surface flows governed by the incompressible Navier‐Stokes equations. The method significantly reduces memory requirements and computational complexity compared
Rasmus Kleist Hørlyck Sørensen, Margherita Guido, Allan Peter Engsig‐Karup, Daniel Kressner   +3 more
wiley   +1 more source

Several Proofs of Coerciveness of First-Order System Least-Squares Methods for General Second-Order Elliptic PDEs

, 2022
In this paper, we present proofs of the coerciveness of first-order system least-squares methods for general (possibly indefinite) second-order linear elliptic PDEs under a minimal uniqueness assumption. For general linear second-order elliptic PDEs, the
Zhang, Shun
core  

Introduction: big data and partial differential equations [PDF]

, 2017
Partial differential equations (PDEs) are expressions involving an unknown function in many independent variables and their partial derivatives up to a certain order. Since PDEs express continuous change, they have long been used to formulate a myriad of
CAROLA-BIBIANE SCHÖNLIEB, Sch�nlieb, Carola-Bibiane, YVES VAN GENNIP, van Gennip, Yves, Schönlieb, Carola-Bibiane   +4 more
core   +1 more source

Closing the Loop in Precision Oncology: A Digital Twin‐Driven Paradigm for Dynamic Decision‐Making

iMetaMed, EarlyView.
This review introduces the Closed‐Loop Intelligent Oncology System (CIOS), a five‐layer framework integrating digital twins and AI to enable adaptive, data‐driven cancer treatment. By synthesizing advances in multimodal perception, mechanistic simulation, and safe reinforcement learning, CIOS charts a roadmap toward dynamic, personalized oncology ...
Junye Zhu, Mengqi Yang, Chenxi Ouyang, Lin Zhang   +3 more
wiley   +1 more source

New Drain Spacing Formulas Using the Variational Iteration Method

Irrigation and Drainage, EarlyView.
ABSTRACT In this study, the drain spacing is computed using the variational iteration method (VIM) to the linearized Boussinesq equation. By applying at most two iterations of the VIM method under three different initial condition scenarios, three equations for drain spacing calculation were derived. These equations predict values of drain spacing that
George Kargas, Leonidas Mindrinos, Paraskevi Londra   +2 more
wiley   +1 more source

Comparison Between Respiratory‐Triggered and Free‐Breathing Signal Acquisition Methods for Single‐Voxel Phosphorus Magnetic Resonance Spectroscopy of the Liver on a Clinical System

Journal of Magnetic Resonance Imaging, EarlyView.
ABSTRACT Background The optimal protocol for clinical liver 31P‐magnetic resonance spectroscopy (MRS) remains unclear. Single‐voxel 31P‐MRS using image‐selected in vivo spectroscopy (ISIS) employs respiratory‐triggering (RT) or free‐breathing (FB) acquisition.
Kumi Ozaki, Jihun Kwon, Marc Van Cauteren, Yasutomo Katsumata, Yukichi Tanahashi, Satoshi Goshima   +5 more
wiley   +1 more source

Uniqueness for Neumann Problems for Nonlinear Elliptic Equations With Lower Order Terms

Mathematische Nachrichten, EarlyView.
ABSTRACT In this paper, we prove uniqueness results for weak solutions to a class of Neumann problems, whose prototype is λ(1+u2)(p−2)/2u−div((1+|∇u|2)(p−2)/2∇u)−div(c(x)(1+|u|2)(τ+1)/2)+b(x)(1+|∇u|2)(σ+1)/2=finΩ(1+|∇u|2)(p−2)/2∇u+c(x)(1+|u|2)(τ+1)/2)·n̲=0on∂Ω,$$\begin{equation*} {\begin{cases} {}\lambda {(1+ u^2)}^{(p-2)/2}u-{\operatorname{div}}({(1+|\
Maria Francesca Betta, Olivier Guibé, Anna Mercaldo, Maria Rosaria Posteraro   +3 more
wiley   +1 more source

Modelling cell movement and chemotaxis pseudopod based feedback

, 2011
A computational framework is presented for the simulation of eukaryotic cell migration and chemotaxis. An empirical pattern formation model, based on a system of non-linear reaction-diffusion equations, is approximated on an evolving cell boundary using ...
Neilson, Matthew Paterson, Mackenzie, J.A., Webb, Steven, Mackenzie, John, R. H. Insall, J. A. Mackenzie, M. P. Neilson, S. D. Webb, Insall, Robert H., Webb, S.D., Neilson, M.P., Insall, R.H.   +11 more
core   +1 more source

The Combined Effects of Variable Viscosity and Thermal Conductivity of An Unsteady Casson Fluid Flow Along a Vertical Porous Channel With Convective Cooling Walls, Using the Bivariate Spectral Local Linearization Method

Mathematical Methods in the Applied Sciences, EarlyView.
ABSTRACT This study examines the combined impact of different thermal conductivity and viscosity on unsteady non‐Newtonian Casson fluid flow of incompressible, electrical conductivity in a porous vertical channel with convective cooling walls, uniform magnetic field, and constant pressure gradient.
A. S. Adeyemo, Precious Sibanda, S. P. Goqo   +2 more
wiley   +1 more source