Riemann
No mentions found
This entity hasn't been tracked yet, or Iris is still building its knowledge base.
Related Articles from SNS
amerta: A Python Library for Idealized 1D Saint--Venant Dam-Break Simulation
arXiv:2605.31011v1 Announce Type: new Abstract: The Saint-Venant shallow water equations (SWE) govern depth-integrated free-surface flows arising in dam-break inundation, flood routing, tsunami runup, and estuarine tidal dynamics. Closed-form analytical solutions exist only for highly idealized Riemann configurations, making rigorously verified numerical solvers essential. This work presents amerta, an open-source Python library that solves the one-dimensional frictionless Saint-Venant...
Efficient Numerical Modeling of Near-Field Diffraction in ORIS-Assisted Free-Space Optical Links
Announce Type: new Abstract: This paper investigates near-field propagation in optical reconfigurable intelligent surface (ORIS)-assisted free-space optical (FSO) communication systems. Unlike conventional far-field scenarios, near-field propagation involves complex diffraction effects that hinder tractable closed-form analysis. To address this issue, a numerical framework for evaluating the optical field distribution of ORIS-assisted FSO links is proposed.
Universal Theory of Decaying Turbulence
Announce Type: replace-cross Abstract: We derive an exact solution of the loop equation for freely decaying incompressible turbulence in arbitrary spatial dimension $d>1$. Using the Mandelstam identity in the loop dynamics, we prove that the nonlinear advection term reduces to a pure derivative and drops out of the momentum-loop equation. As a result, the momentum-loop equation becomes purely diffusive, admitting an exact geometric solution as a random walk on a circle. Despite this distinct...
Numerical Study of Dissipative Weak Solutions for the Euler Equations of Gas Dynamics
arXiv:2601.17452v3 Announce Type: replace Abstract: We study dissipative weak (DW) solutions of the Euler equations of gas dynamics using the first-, second-, third-, fifth-, seventh-, and ninth-order local characteristic decomposition-based central-upwind (LCDCU), low-dissipation central-upwind (LDCU), and viscous finite volume (VFV) methods, whose higher-order extensions are obtained via the framework of the alternative weighted essentially non-oscillatory (A-WENO) schemes. These methods...
A golden age of maths is dawning and mathematicians are freaking out
I am attempting to solve a mathematical conundrum that has stumped many of humanity’s greatest thinkers. I have zero mathematical training, apart from a distant undergraduate physics degree, which should put my odds of success at slim to none. But I also have a trick up my sleeve – a kind of mathematical genie that can conjure arcane secrets seemingly out of thin air.
The Saddle Point of Everything
arXiv:2605.30386v1 Announce Type: new Abstract: The harmonic oscillator is the universal Hamiltonian of stable equilibrium. Its counterpart, the inverted harmonic oscillator (IHO), is the Hamiltonian of unstable equilibrium: the saddle point of physical systems. It appears across disciplines, from condensed matter, quantum optics, and quantum chemistry to the Standard Model Higgs instability and quantum field theory near gravitational horizons.
A One-Dimensional Discrete Boltzmann Method for Multidimensional Compressible Flows
arXiv:2603.01546v2 Announce Type: replace Abstract: A simple and efficient one-dimensional discrete Boltzmann method is developed for compressible flows with tunable specific heat ratios by incorporating extra degrees of freedom. To guarantee Galilean invariance in numerical simulations, a discrete velocity set is constructed with high spatial symmetry. Furthermore, an operator-splitting scheme is proposed to extend the one-dimensional kinetic formulation to simulations of one-, two-, and...
Geometric Solution of Turbulence as Diffusion in Loop Space
Announce Type: replace Abstract: Strongly nonlinear dynamics, from fluid turbulence to quantum chromodynamics, have long constituted some of the most challenging problems in theoretical physics. This review describes a unified theoretical framework, the loop space calculus, which offers an analytical approach to these problems. The central idea is a shift in perspective from pointwise fields to integrated loop observables, a transformation that recasts the governing nonlinear equations into...
Scientists finally complete Schrödinger’s 100-year-old color theory
Scientists finally complete Schrödinger’s 100-year-old color theory - Date: - June 7, 2026 - Source: - Los Alamos National Laboratory - Summary: - Researchers have finally resolved a key problem in a 100-year-old theory of color, showing that the qualities we perceive in colors are intrinsic to the mathematics of color space itself. The discovery sharpens our understanding of human vision and could lead to more precise color technologies and visualizations. - Share: A century old idea from...