相关论文: Solving the Flowgraphs Case with Eclectic

Turbulent and vortical flows are ubiquitous and their characterization is crucial for the understanding of several natural and industrial processes. Among different techniques to study spatio-temporal flow fields, complex networks represent…

Bifurcation phenomena in nonlinear dynamical systems often lead to multiple coexisting stable solutions, particularly in the presence of symmetry breaking. Deterministic machine learning models are unable to capture this multiplicity,…

In this paper, I discuss the challenges in porting hydrodynamic codes to futuristic exascale HPC systems. In particular, we describe the computational complexities of finite difference method, pseudo-spectral method, and Fast Fourier…

Many physical systems of interest involve the close interaction of a flow in a domain with complex, time-varying boundaries. Treatment of boundaries of this nature is cumbersome due to the difficulty in explicitly tracking boundaries that…

There exist rotationally symmetric translating solutions to mean curvature flow that can be written as a graph over Euclidean space. This result is well-known. Its proof uses the symmetry and techniques from partial differential equations.…

The flow equation approach is a robust framework applicable to a broad class of singular SPDEs, including those with fractional Laplacians, throughout the entire subcritical regime. Inspired by Wilson's renormalization group, this method…

We present a complete categorical axiomatization of a wide class of dataflow programs. This gives a three-dimensional diagrammatic language for workflows, more expressive than the directed acyclic graphs generally used for this purpose.…

Deep learning provides a versatile suite of methods for extracting structured information from complex datasets, enabling deeper understanding of underlying fluid dynamic phenomena. The field of turbulence modeling, in particular, benefits…

Complex algebraic calculations can be performed by reconstructing analytic results from numerical evaluations over finite fields. We describe FiniteFlow, a framework for defining and executing numerical algorithms over finite fields and…

We introduce Lagrange2D, a Mathematica package for analysis and characterization of complex fluid flows using Lagrangian transport metrics. Lagrange2D includes built-in functions for integrating ensembles of trajectories subject to…

A traffic flow is one of the main transportation issues in nowadays industrialized agglomerations. Configuration of traffic lights is among the key aspects in traffic flow management. This paper proposes an evolutionary optimization tool…

The paper presents a solution of the Hello World! An Instructive Case for the Transformation Tool Contest using the VIATRA2 model transformation tool.

We introduce Lagrangian Flow Networks (LFlows) for modeling fluid densities and velocities continuously in space and time. By construction, the proposed LFlows satisfy the continuity equation, a PDE describing mass conservation in its…

Understanding the flow of complex media is relevant for a wide range of research fields and industrial applications. Several numerical approaches exist by which approximate solutions can be determined for the Stokes equations that describe…

We explore the oscillatory behavior observed in inversion methods applied to large-scale text-to-image diffusion models, with a focus on the "Flux" model. By employing a fixed-point-inspired iterative approach to invert real-world images,…

A machine learning method to predict steady external fluid flows using elliptic input features is introduced. Using data from as few as one high-fidelity simulation, the proposed method produces models generalizable under changes to…

The isentropic vortex problem is frequently solved to test the accuracy of numerical methods and verify corresponding code. Unfortunately, its existing solution was derived in the relativistic magnetohydrodynamics by numerically solving an…

In this paper, we consider a numerical method to solve scattering problems with multi-periodic layers with different periodicities. The main tool applied in this paper is the Bloch transform. With this method, the problem is written into an…

Some work in progress is announced, on the use of algebraic geometry, mostly concerning elliptic curve theory, to model turbulence. Attention is given to flows across the scales, on some convenient model space, and some current trials are…

We use the vorticity transportation equation as the start point--with the help of stream function for two-dimensional planar incompressible flows--to obtain exact solutions that characterize evolution and dynamics of the flows. These…