Related papers: Adaptive Hagen-Poiseuille flows on graphs

Based on the recently developed picture of an electronic ideal relativistic fluid at the Dirac point, we present an analytical model for the conductivity in graphene that is able to describe the linear dependence on the carrier density and…

A modified Reynolds equation governing the steady flow of a fluid with low Reynolds number through a curvilinear, narrow tube, with its derivation from Stokes equations through asymptotic methods is presented. The channel considered may…

We find steady channel flows that are locally optimal for transferring heat from fixed-temperature walls, under the constraint of a fixed rate of viscous dissipation (enstrophy = $Pe^2$), also the power needed to pump the fluid through the…

Network remodeling, or adaptation, in the presence of periodically driven forcings has hereto remained largely unexplored, despite the fact that a broad class of biological transport networks, e.g. animal vasculature, depends on periodic…

We develop a method to calculate the persistent currents and their spatial distribution (and transport properties) on graphs made of quasi-1D diffusive wires. They are directly related to the field derivatives of the determinant of a matrix…

Robust heteroclinic networks are invariant sets that can appear as attractors in symmetrically coupled or otherwise constrained dynamical systems. These networks may have a very complicated structure that is poorly understood and determined…

We study topology optimization governed by the incompressible Navier-Stokes flows using a phase field model. Novel stabilized semi-implicit schemes for the gradient flows of Allen-Cahn and Cahn-Hilliard types are proposed for solving the…

Graph-based models require aggregating information in the graph from neighbourhoods of different sizes. In particular, when the data exhibit varying levels of smoothness on the graph, a multi-scale approach is required to capture the…

Spectral graph convolutional neural networks (CNNs) require approximation to the convolution to alleviate the computational complexity, resulting in performance loss. This paper proposes the topology adaptive graph convolutional network…

We present an analytically solvable random graph model in which the connections between the nodes can evolve in time, adiabatically slowly compared to the dynamics of the nodes. We apply the formalism to finite connectivity attractor neural…

Over the last few years, we have witnessed the availability of an increasing data generated from non-Euclidean domains, which are usually represented as graphs with complex relationships, and Graph Neural Networks (GNN) have gained a high…

An adaptive sampling approach for efficient detection of bifurcation boundaries in parametrized fluid flow problems is presented herein. The study extends the machine-learning approach of Silvester~(J. Comput. Phys., 553 (2026), 114743),…

Electron transport in two-dimensional conducting materials such as graphene, with dominant electron-electron interaction, exhibits unusual vortex flow that leads to a nonlocal current-field relation (negative resistance), distinct from the…

In this work, we derive a new model for immiscible two-layer gas-liquid stratified flows in pipes with general cross sections. The bottom layer is occupied by an incompressible fluid in liquid phase with hydrodynamics based on a hydrostatic…

We have measured the nonlinear rheological response of a model transient network over a large range of steady shear rates. The system is built up from an oil in water droplet microemulsion into which a telechelic polymer is incorporated.…

We propose a new reduced model for gravity-driven free-surface flows of shallow elastic fluids. It is obtained by an asymptotic expansion of the upper-convected Maxwell model for elastic fluids. The viscosity is assumed small (of order…

The asymptotic derivation of a new family of one-dimensional, weakly nonlinear and weakly dispersive equations that model the flow of an ideal fluid in an elastic vessel is presented. Dissipative effects due to the viscous nature of the…

Network routing approaches are widely used to study the evolution in time of self-adapting systems. However, few advances have been made for problems where adaptation is governed by time-dependent inputs. In this work we study a dynamical…

For Gagen-Poiseuille flow, we show that exponential instability (to extremely small, axially symmetric disturbances represented by Galerkin's approximation) is possible only if there exists bi-periodic variability of the disturbances along…

Message passing is the core operation in graph neural networks, where each node updates its embeddings by aggregating information from its neighbors. However, in deep architectures, this process often leads to diminished expressiveness. A…