A high order accurate and provably stable fully discrete continuous Galerkin framework on summation-by-parts form for advection-diffusion equationsWe present a high-order accurate fully discrete numerical scheme for solving Initial Boundary Value Problems (IBVPs) within the Continuous Galerkin (CG)-based Finite Element framework. Both the…Mrityunjoy Mandal, Jan Nordström, Arnaud G Malan·Jan 8, 2026SaveLearn
A Virtual Heat Flux Method for Simple and Accurate Neumann Thermal Boundary Imposition in the Material Point MethodIn the Material Point Method (MPM), accurately imposing Neumann-type thermal boundary conditions, particularly convective heat flux boundaries, remains a significant challenge due to the inherent…Jidu Yu, Jidong Zhao·Jan 8, 2026SaveLearn
Mixed-mode loading of a straight crack with surface strain-gradient elasticityThis work models brittle fracture using a linearized surface-substrate theory in which the crack faces possess surface stresses derived from a surface strain-gradient elastic energy. The model…C. Rodriguez, A. Zemlyanova·Jan 8, 2026SaveLearn
A Non-Reciprocal Elliptic Spectral Solution of the Right-Angle Penetrable Wedge Transmission Problem for =2We consider the two-dimensional time-harmonic transmission problem for an impedance-matched ( = 1) right-angle penetrable wedge at refractive index ratio = 2, in the integrable…Jonas Matuzas·Jan 7, 2026SaveLearn
Boxed UC plane partitions and the two-site generalized phase modelThis study investigates the connection between boxed UC plane partitions and the two-site generalized phase model. By introducing two maps, we investigate the representation of two-side generalized…Shengyu Zhang, Jinzhou Liu, Zhaowen Yan·Jan 7, 2026SaveLearn
Incremental equations in curvature-dependent surface elasticityWe develop a general incremental framework for hyperelastic solids whose surfaces exhibit both stretch-dependent and curvature-dependent elastic behavior. Building upon a variational formulation of…Xiang Yu, Michal Šmejkal, Martin Horák·Jan 7, 2026SaveLearn
Egorov-Type Semiclassical Limits for Open Quantum Systems with a Bi-Lindblad StructureThis paper develops a bridge between bi-Hamiltonian structures of Poisson--Lie type, contact Hamiltonian dynamics, and the Gorini--Kossakowski--Sudarshan--Lindblad (GKSL) formalism for open quantum…Leonardo Colombo, Asier López-Gordón·Jan 6, 2026SaveLearn
Boundary operators in the Brownian loop soupWe obtain infinitely many boundary operators in the Brownian loop soup in the subcritical phase by analyzing the conformal block expansion of the two-point function that computes the probability of…Federico Camia, Rongvoram Nivesvivat·Jan 6, 2026SaveLearn
Broadband quasistatic passive cloaking: bounds and limitations in the near-field regimeWe consider here several aspects of the following challenging question: is it possible to use a passive cloak to make invisible a dielectric inclusion on a finite frequency interval in the…Maxence Cassier, Graeme W. Milton, Aaron Welters·Jan 5, 2026SaveLearn
Renormalisation for Reaction-Diffusion Systems with Non-Local InteractionsModels of reaction diffusion processes usually employ discrete lattice models with particles interacting at the same site, resulting in localized reactions in the continuum limit. Here, various…Chris D Greenman·Jan 5, 2026SaveLearn
Second-order superintegrable systems from semi-simple and nilpotent Frobenius structuresRecently, it was shown that a rich class of second-order (maximally) superintegrable systems has an underpinning Hesse-Frobenius structure, i.e.\ a Frobenius structure that is compatible with a…Andreas Vollmer·Jan 5, 2026SaveLearn
Optical dispersive shock waves of initial pulses in optical fibers with high-order dispersion and quintic nonlinearity effectsThis paper probes the dispersive shock waves (DSWs) theory in nonlinear optical systems through Whitham modulation theory for the high-order Chen-Lee-Liu (HOCLL) equation. We systematically derived…Hua-Ying Ren, Rui Guo, Jian-Wen Zhang·Jan 5, 2026SaveLearn
Integrability enabled computations relating to the fixed trace Laguerre ensembleStudies of density matrices for random quantum states lead naturally to the fixed trace Laguerre ensemble in random matrix theory. Previous studies have uncovered explicit rational function formulas…Peter J. Forrester, Shinsuke M. Nishigaki·Jan 5, 2026SaveLearn
Vogel universality and beyondFor simple Lie algebras we construct characteristic identities for split (polarized) Casimir operators in representations T Yn and T Yn', where T -- defining (minimal…A. P. Isaev·Jan 4, 2026SaveLearn
A Globally Convergent Variational Framework for Mode Number Detection via Spectral Cutting CurvesAutomatically determining the number of intrinsic mode functions (IMFs) and their center frequencies in Variational Mode Decomposition (VMD) remains an open mathematical challenge. Existing methods…Chenjie Zhong, Zhipeng Li, Shangzhi Xu et al.·Jan 4, 2026SaveLearn
Exact Solvability via the KP Hierarchy for β=L2 Random Matrix EnsemblesRandom matrix ensembles with Dyson index β=L2 describe systems of M charge-L particles interacting logarithmically in the presence of an external potential, yet exact formulas for their…Christopher D. Sinclair·Jan 3, 2026SaveLearn
The Ground State Energy of a Mean-Field Fermi Gas in Two DimensionsWe rigorously establish a formula for the correlation energy of a two-dimensional Fermi gas in the mean-field regime for potentials whose Fourier transform V satisfies $V(·) | ·…Gregorio Casadei, Sascha Lill·Jan 2, 2026SaveLearn
On the computation of the dyadic Green's functions of Maxwell's equations in layered mediaIn this paper, two formulations for the computation of the dyadic Green's functions of Maxwell's equations in layered media are presented in details. The first formulation derived using TE/TM…Heng Yuan, Wenzhong Zhang, Bo Wang·Jan 2, 2026SaveLearn
Noncommutative spaces as quantized constrained Hamiltonian systemsWe investigate the strong-field limit of a charged particle in an electromagnetic field as a toy model for general covariant systems, establishing a novel connection between constrained Hamiltonian…Andreas Sykora·Jan 2, 2026SaveLearn
The Lagrangian and symplectic structures of the Kuramoto oscillator modelDespite being under intense scrutiny for 50 years, the Kuramoto oscillator model has remained a quintessential representative of non-equilibrium phase transitions. One of the reasons for its enduring…Sherwin Kouchekian, Razvan Teodorescu·Dec 31, 2025SaveLearn
Bilinear tau forms of quantum Painlevé equations and C2/Z2 blowup relations in SUSY gauge theoriesWe derive bilinear tau forms of the canonically quantized Painlevé equations, thereby relating them to those previously obtained from the C2/Z2 blowup relations for the…Giulio Bonelli, Anton Shchechkin, Alessandro Tanzini·Dec 31, 2025SaveLearn
Numerical study of solitary waves in Dirac--Klein--Gordon systemWe use numerics to construct solitary waves φω(x) e-iω t in Dirac--Klein--Gordon (in one and three spatial dimensions) and study the dependence of energy and charge of…Andrew Comech, Julien Ricaud, Marco Roque·Dec 31, 2025SaveLearn
Geometric approaches to Lie bialgebras, their classification, and applicationsThis PhD Thesis consists of two parts. The first part focuses on novel algebraic and geometric approaches to the classification problem of coboundary Lie bialgebras up to Lie algebra automorphisms.…Daniel Wysocki·Dec 31, 2025SaveLearn
Products of random Hermitian matrices and brickwork Hurwitz numbers. Products of normal matricesWe consider products of n random Hermitian matrices which generalize the one-matrix model and show its relation to Hurwitz numbers which count ramified coverings of certain type. Namely, these…Ch. Li, A. Yu. Orlov·Dec 31, 2025SaveLearn
Collective behaviors of an electron gas in the mean-field regimeIn this paper, we study the momentum distribution of an electron gas in a 3-dimensional torus. The goal is to compute the occupation number of Fourier modes for some trial state obtained through…Dong Hao Ou Yang·Dec 31, 2025SaveLearn