Results 31 to 40 of about 281 (113)
On Compressible Fluid Flows of Forchheimer‐Type in Rotating Heterogeneous Porous Media
Mathematical Methods in the Applied Sciences, Volume 49, Issue 13, Page 15010-15055, 15 September 2026.ABSTRACT We study the dynamics of compressible fluids in rotating heterogeneous porous media. The fluid flow is of Forchheimer‐type and is subject to a mixed mass and volumetric flux boundary condition. The governing equations are reduced to a nonlinear partial differential equation for the pseudo‐pressure.
Emine Celik, Luan Hoang, Thinh Kieu
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On the Existence of Solutions of Dynamic Equations on Time Scales in Banach Spaces
Mathematical Methods in the Applied Sciences, Volume 49, Issue 13, Page 15358-15384, 15 September 2026.ABSTRACT In this paper we address the question of solvability of dynamic equations on time scales in Banach spaces. In particular, our main theorem extends the result for classical differential equations in Banach spaces of Banaś and Goebel established in [5], to an arbitrary time scale.
Dušan Oberta
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Model Predictive Control of Gas Networks Based on Port‐Hamiltonian Formulations
Proceedings in Applied Mathematics and Mechanics, Volume 26, Issue 3, September 2026.ABSTRACT To efficiently compute optimal compressor actions in gas networks, we investigate port‐Hamiltonian models consisting of linear and a nonlinear model assumptions. The control actions are derived via adjoint‐based gradients that incorporate the constraints of the underlying optimization problem. We then present results from the implementation of
Andres Ortegón‐Villacorte +1 more
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International Journal for Numerical Methods in Engineering, Volume 127, Issue 15, 15 August 2026.ABSTRACT Fluid‐filled phase‐field fracture simulations require robust, scalable solvers that can handle strongly nonlinear, non‐smooth mechanics and tightly coupled flow on locally refined meshes. In this work, we develop an adaptive finite element framework for quasi‐static, fluid‐filled phase‐field fractures that combines semi‐smooth Newton methods ...
Leon M. Kolditz +3 more
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Thermo‐Mechanical Topology Optimization: An Immersed FEM Level‐Set‐Based Approach
International Journal for Numerical Methods in Engineering, Volume 127, Issue 15, 15 August 2026.ABSTRACT This paper proposes a multi‐physics framework for topology optimization using an immersed level set‐finite element model. The work extends the capabilities of a recently developed immersed level‐set method to thermo‐mechanical problems, including coupling and material‐dependent properties.
Farzad Tatar +3 more
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Advanced Science, Volume 13, Issue 44, 7 August 2026.Thermal runaway propagation can transform a single‐cell failure into a system‐level hazard in lithium‐ion battery packs. This review clarifies how heat transfer, gas venting, combustion, and configuration govern cell‐to‐cell failure, and links measurable metrics, pathway‐oriented suppression materials, and experimental/modeling tools to guide safer ...
Jinrong Su +15 more
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Biotechnology and Bioengineering, Volume 123, Issue 8, Page 2139-2152, August 2026.ABSTRACT Oxygen supply is a critical parameter in 3D cell cultivation using bioreactors. Since bioreactor designs often prioritise practical constraints, understanding the oxygen supply dynamics of the media is crucial for achieving either uniform or spatially controlled oxygen delivery.
Franziska Alt +4 more
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Invariant Measure and Universality of the 2D Yang–Mills Langevin Dynamic
Communications on Pure and Applied Mathematics, Volume 79, Issue 8, Page 1973-2102, August 2026.ABSTRACT We prove that the Yang–Mills (YM) measure for the trivial principal bundle over the two‐dimensional torus, with any connected, compact structure group, is invariant for the associated renormalised Langevin dynamic. Our argument relies on a combination of regularity structures, lattice gauge‐fixing and Bourgain's method for invariant measures ...
Ilya Chevyrev, Hao Shen
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Physics Constraint‐Guided Neural Network for Solving Partial Differential Equations
Engineering Reports, Volume 8, Issue 8, August 2026.A Physics Constraint‐Guided Network (PCGN) is proposed to solve partial differential equations by integrating physical encoding, adaptive residual balancing, and constraint projection. The framework enables stable constraint propagation, improves physical consistency, and achieves higher accuracy and robustness compared with existing neural network ...
Zhihui Hou, Yaxu Peng
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Nordgren PINNs to VQE: Advancing Hydraulic Fracturing Simulations in Shale Reservoirs
International Journal for Numerical and Analytical Methods in Geomechanics, Volume 50, Issue 12, Page 4863-4878, 25 August 2026.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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