🔢 Category

math-ph

2548 papers

Mathematical physics sits at the fascinating intersection where abstract equations meet the fundamental laws of our universe. This field uses rigorous mathematical tools to model everything from the behavior of subatomic particles to the curvature of spacetime, turning complex theories into testable predictions. It is the language through which physicists describe reality, bridging the gap between pure mathematics and physical observation.

On Gist.Science, we process every new preprint published in this category on arXiv to make these dense studies accessible to everyone. Whether you are a specialist or a curious reader, you will find both plain-language overviews and detailed technical summaries for each paper. Below are the latest mathematical physics papers from arXiv, curated to help you explore the cutting edge of theoretical science.

🔢 mathematics

Equation of Motion for Open Thermodynamic Systems and Its Dynamical Equivalence with Mechanical and Electrical Systems

This paper derives an explicit equation of motion for open thermodynamic systems directly from the first law of thermodynamics, demonstrating their dynamical equivalence to driven damped harmonic oscillators and RLC circuits, and establishing a unified Lagrangian framework that reveals a common structural foundation across thermodynamic, mechanical, and electrical systems.

E Aydiner2026-09-09
🔢 mathematics

GridapGeosciences.jl: A Julia finite element package for partial differential equations on general manifolds

This paper introduces GridapGeosciences.jl, a parallel Julia package built on the Gridap library for solving partial differential equations on general manifolds, demonstrating its capabilities through intrinsic formulations of scalar transport, thermal shallow water, and Boussinesq equations on a cubed sphere.

Tamara A. Tambyah, Alberto F. Martín, David Lee, Santiago Badia2026-09-09
⚛️ high-energy theory

Bogomol'nyi equations for Kruglov strings

This paper constructs Bogomol'nyi equations for Abelian gauge-Higgs vortices within Kruglov nonlinear electrodynamics by deriving first-order equations via the stressless method, analyzing the resulting constitutive maps to establish admissibility conditions for various exponents, and demonstrating that the BPS string tension remains purely topological and independent of the nonlinear parameters.

I. Praseyto, U. Ubaydillah, H. S. Ramadhan2026-09-09
🔢 mathematics

A finite-strain logarithmic viscoelastic model for Antarctic ice shelves based on an additive split

This paper presents a finite-strain logarithmic viscoelastic model for Antarctic ice shelves that employs an additive split of Hencky strain rates to integrate Glen's flow law with isotropic elasticity, demonstrating through finite-element simulations how viscoelasticity and front morphology govern tension near the ice shelf terminus.

Maxime Nutte, Sebastian Skatulla, Carlo Sansour2026-09-09
🔢 mathematics

Arithmetic triangular structures in the transfer-matrix of finite Kronig-Penney models

This paper provides a rigorous analytical derivation of closed-form expressions for the transfer matrix of finite Kronig-Penney models with Dirac delta potentials by expressing the Nth power of the unit-cell matrix in terms of Chebyshev polynomials of the second kind, thereby revealing a novel structural correspondence between quantum scattering processes, discrete convolutions, and hypercomplex combinatorial structures.

Lidia Aceto, Pietro Antonio Grassi, Helmuth Robert Malonek2026-09-09
🔢 mathematics

The phase coordinates transformation in Moyal noncommutative framework 2-dimensional harmonic oscillator and Painlevé second equation

This paper introduces new phase coordinate transformations within the Moyal noncommutative framework that incorporate space-space and space-momentum noncommutativity to construct deformed, superintegrable two-dimensional harmonic oscillators and derive the Painlevé second equation, thereby revealing additional symmetries and generating Yablonskii-Vorobev polynomials.

Irfan Mahmood2026-09-09
🔢 mathematics

Full Characterisation of the Polarisation Primary Beam of the GRAO 32-m Telescope

This paper presents a comprehensive electromagnetic simulation-based characterisation of the direction-dependent polarisation primary beam of the GRAO 32-m telescope at 5.0 and 6.7 GHz, quantifying key parameters such as beam widths, efficiencies, squint, and instrumental leakage to establish a quantitative baseline for high-fidelity polarimetric calibration.

Theophilus Ansah-Narh, Nia Imara, Benedicta Woode, Joseph Bremang Tandoh, Emmanuel Proven Adzri, Diana Klutse, Evaristus (…)2026-09-09
🌀 nonlinear sciences

Reduction Based Dynamical Systems Analysis of Nonlinear Wave Equations: A Review

This review presents a reduction-based methodological framework that connects nonlinear wave equations to reduced dynamical systems to analyze invariant phase-space structures, stability, and waveform correspondence across diverse physical models, while identifying current methodological gaps and emphasizing physical admissibility and predictive relevance over the mere generation of formal solutions.

Naresh Saha, Arnob Ray2026-09-09