Tootfinder

A kernel-free boundary integral method for elliptic interface problems on surfaces
Pengsong Yin, Wenjun YIng, Yulin Zhang, Han Zhou
https://arxiv.org/abs/2508.16061 https://

A kernel-free boundary integral method for elliptic interface problems on surfaces
This work presents a generalized boundary integral method for elliptic equations on surfaces, encompassing both boundary value and interface problems. The method is kernel-free, implying that the explicit analytical expression of the kernel function is not required when solving the boundary integral equations. The numerical integration of single- and double-layer potentials or volume integrals at the boundary is replaced by interpolation of the solution to an equivalent interface problem, which…

Well-posedness of the compressible boundary layer equations with analytic initial data
Ya-Guang Wang, Yi-Lei Zhao
https://arxiv.org/abs/2507.18247 https://…

Well-posedness of the compressible boundary layer equations with analytic initial data
We study the well-posedness of the compressible boundary layer equations with data being analytic in the tangential variable of the boundary. The compressible boundary layer equations, a nonlinear coupled system of degenerate parabolic equations and an elliptic equation, describe the behavior of thermal layer and viscous layer in the small viscosity and heat conductivity limit, for the two-dimensional compressible viscous flow with heat conduction with nonslip and zero heat flux boundary condit…

Hybrid Boundary Physics-Informed Neural Networks for Solving Navier-Stokes Equations with Complex Boundary
Chuyu Zhou, ianyu Li, Chenxi Lan, Rongyu Du, Guoguo Xin, Pengyu Nan, Hangzhou Yang, Guoqing Wang, Xun Liu, Wei Li
https://arxiv.org/abs/2507.17535

Hybrid Boundary Physics-Informed Neural Networks for Solving Navier-Stokes Equations with Complex Boundary
Physics-informed neural networks (PINN) have achieved notable success in solving partial differential equations (PDE), yet solving the Navier-Stokes equations (NSE) with complex boundary conditions remains a challenging task. In this paper, we introduce a novel Hybrid Boundary PINN (HB-PINN) method that combines a pretrained network for efficient initialization with a boundary-constrained mechanism. The HB-PINN method features a primary network focused on inner domain points and a distance metr…

Instruction Boundary: Quantifying Biases in LLM Reasoning under Various Coverage
Zipeng Ling, Yuehao Tang, Chen Huang, Shuliang Liu, Gaoyang Jiang, Shenghong Fu, Junqi Yang, Yao Wan, Jiawan Zhang, Kejia Huang, Xuming Hu
https://arxiv.org/abs/2509.20278

Instruction Boundary: Quantifying Biases in LLM Reasoning under Various Coverage
Large-language-model (LLM) reasoning has long been regarded as a powerful tool for problem solving across domains, providing non-experts with valuable advice. However, their limitations - especially those stemming from prompt design - remain underexplored. Because users may supply biased or incomplete prompts - often unintentionally - LLMs can be misled, undermining reliability and creating risks. We refer to this vulnerability as the Instruction Boundary. To investigate the phenomenon, we dist…

On the Boundary of the Robust Admissible Set in State and Input Constrained Nonlinear Systems
Franz Ru{\ss}wurm, Jean L\'evine, Stefan Streif
https://arxiv.org/abs/2509.18825

On the Boundary of the Robust Admissible Set in State and Input Constrained Nonlinear Systems
In this paper, we consider nonlinear control systems subject to bounded disturbances and to both state and input constraints. We introduce the definition of robust admissible set - the set of all initial states from which the state and input constraints can be satisfied for all times against all admissible disturbances. We focus on its boundary that can be decomposed into the usable part on the state constraint boundary and the barrier, interior to the state constraints. We show that, at the in…

Discrete conformal structures on surfaces with boundary (III) -- Deformation
Xu Xu, Chao Zheng
https://arxiv.org/abs/2507.18495 https://arxiv.org/pdf/2507.…

Discrete conformal structures on surfaces with boundary (III) -- Deformation
The present work constitutes the third installment in a series of investigations devoted to discrete conformal structures on surfaces with boundary. In our preceding works \cite{X-Z DCS1, X-Z DCS2}, we established, respectively, a classification of these discrete conformal structures and results on their rigidity and existence. Building on this foundation, the present work focuses on the deformation theory of discrete conformal structures on surfaces with boundary. Specifically, we introduce th…

(Non-)Conserved Currents and Cosmological Correlators
Charlotte Sleight, Massimo Taronna
https://arxiv.org/abs/2509.18888 https://arxiv.org/pdf/2509.18888

Ribbonness on boundary surface-link
Akio Kawauchi
https://arxiv.org/abs/2507.18154 https://arxiv.org/pdf/2507.18154…

Ribbonness on boundary surface-link
It is shown that a boundary surface-link in the 4-sphere is a ribbon surface-link if the surface-knot obtained from it by surgery along a pairwise nontrivial 1-handle system is a ribbon surface-link. As a corollary, the surface-knot obtained from the anti-parallel surface-link of a non-ribbon surface-knot by surgery along a nontrivial fusion 1-handle is a non-ribbon surface-knot. This result answers Cochran's conjecture on non-ribbon sphere-knots in the affirmative.

Well-posed geometric boundary data in General Relativity, III: conformal-volume boundary data
Zhongshan An, Michael T. Anderson
https://arxiv.org/abs/2507.15567

Well-posed geometric boundary data in General Relativity, III: conformal-volume boundary data
In this third work in a series, we prove the local-in-time well-posedness of the IBVP for the vacuum Einstein equations in general relativity with twisted DIrichlet boundary conditions on a finite timelike boundary. The boundary conditions consist of specification of the pointwise conformal class of the boundary metric, together with a scalar density involving a combination of the volume form of the bulk metric restricted to the boundary together with the volume form of the boundary metric itse…

Plasma Position Constrained Free-Boundary MHD Equilibrium in Tokamaks using pyIPREQ
Udaya Maurya, Amit K. Singh, Suman Aich, Jagabandhu Kumar, Rohit Kumar, Daniel Raju
https://arxiv.org/abs/2507.18324 …

Plasma Position Constrained Free-Boundary MHD Equilibrium in Tokamaks using pyIPREQ
A free-boundary, axisymmetric magnetohydrodynamic (MHD) equilibrium code, pyIPREQ, has been developed for Tokamak plasmas using finite difference and Green's function approach. The code builds upon the foundational frameworks of the PEST and IPREQ codes, introducing several enhancements and new capabilities. Notably, pyIPREQ supports the specification of limiter boundaries and enables the computation of key physical quantities. The code has also been extended to compute equilibria constrained b…

Weak in the boundary: How weak SPT phases spoil anomaly matching
Daniel Sheinbaum, Omar Antol\'in Camarena
https://arxiv.org/abs/2507.17179 https://arx…

Weak in the boundary: How weak SPT phases spoil anomaly matching
We show how weak symmetry protected topological (SPT) phases on systems with a boundary are not in 1-to-1 correspondence with weak SPT phases on fully periodic systems, breaking the standard anomaly inflow interpretation of SPT phases. We further discuss the implications for the crystalline equivalence principle (CEP).

Edge states at the boundary of graphene-like and Lieb lattices
I. V. Kozlov, Yu. A. Kolesnichenko
https://arxiv.org/abs/2507.17612 https://arxiv.org/pdf/25…

Edge states at the boundary of graphene-like and Lieb lattices
Properties of the boundary of two conductors in a quantizing magnetic field are studied: with conventional Dirac charge carriers and so-called pseudospin-1 fermions, which are realized in graphene-like and Lieb lattices respectively. It is shown that edge states arise that relate the properties of conductors to the trivial and nontrivial Berry phase. These edge states lead to the appearance of a characteristic series of root features in the density of states.

Emergent statistical mechanics in holographic random tensor networks
Shozab Qasim, Jens Eisert, Alexander Jahn
https://arxiv.org/abs/2508.16570 https://arx…

Emergent statistical mechanics in holographic random tensor networks
Recent years have enjoyed substantial progress in capturing properties of complex quantum systems by means of random tensor networks (RTNs), which form ensembles of quantum states that depend only on the tensor network geometry and bond dimensions. Of particular interest are RTNs on hyperbolic geometries, with local tensors typically chosen from the unitary Haar measure, that model critical boundary states of holographic bulk-boundary dualities. In this work, we elevate static pictures of ensem…

Using the Immersed Penalized Boundary Method with Splines to Solve PDE's on Curved Domains in 3D
Aussie Greene, Larry L. Schumaker
https://arxiv.org/abs/2508.16060 https://

Using the Immersed Penalized Boundary Method with Splines to Solve PDE's on Curved Domains in 3D
Second-order elliptic boundary-value problems defined on curved domains in 2D and 3D arise frequently in practice. A lot of work has gone into developing numerical methods for solving such problems. One of the newest and most promising methods is the $\textit{immersed penalized boundary method}$ (IPBM) introduced in [Schumaker, L. L., Solving elliptic PDE's on domains with curved boundaries with an immersed penalized boundary method, J. Sci. Comp. ${\bf 80(3)}$ (2019), 1369--1394]. For a compre…

Characterization of boundary layers on isothermal and adiabatic curved surfaces of a supersonic turbine cascade
Gabriel Y. R. Hamada, Hugo F. S. Lui, William R. Wolf, Carlos Junqueira-Junior
https://arxiv.org/abs/2509.17745

Characterization of boundary layers on isothermal and adiabatic curved surfaces of a supersonic turbine cascade
The effects of adiabatic and isothermal boundary conditions are investigated on the shock-boundary layer interactions (SBLIs) in a supersonic turbine cascade. Special attention is given to the characterization of the incoming boundary layers over the convex and concave walls of the blade and their impact in the SBLIs. Large eddy simulations (LES) are performed for an inlet Mach number of $\mathbf{M_\infty = 2.0}$ and Reynolds number based on the axial chord $\mathbf{Re = 200\,000}$. For the iso…

On the uniqueness of the discrete Calderon problem on multi-dimensional lattices
Maolin Deng, Bangti Jin
https://arxiv.org/abs/2509.18203 https://arxiv.org…

Boundary Feller-Dynkin processes associated with Laguerre processes and Pickrell diffusions
Alexander I. Bufetov, Yosuke Kawamoto
https://arxiv.org/abs/2509.17045 https://

Boundary Feller-Dynkin processes associated with Laguerre processes and Pickrell diffusions
In this paper, we construct a Feller-Dynkin boundary process by applying the method of intertwiners to the coherent family, introduced in our previous work, of Laguerre processes with a fixed parameter. The corresponding boundary process is computed explicitly, and it turns out to be a deterministic dynamical system. Since the Pickrell diffusions that leave the Pickrell measure invariant are coherent with respect to the same projective system, we also obtain the stochastic boundary process asso…

$H^s_x$ regularity of solutions to the stationary Boltzmann equation with the incoming boundary condition
Daisuke Kawagoe
https://arxiv.org/abs/2507.18211 https://

$H^s_x$ regularity of solutions to the stationary Boltzmann equation with the incoming boundary condition
We consider the stationary Boltzmann equation with the cross section of the form $B(|v - \tilde{v}, θ|) = B_0 |v - \tilde{v}|^γ\cos θ\sin θ$ for $-3 < γ\leq 1$ in a bounded convex domain under the incoming boundary condition. In this article, we shall show the existence of a solution in a weighted $L^\infty$ space with fractional Sobolev regularity without assuming the positivity of the Gaussian curvature on the boundary. For boundary data sufficiently smooth and close …

Closed-Form and Boundary Expressions for Task-Success Probability in Status-Driven Systems
Jianpeng Qi, Chao Liu, Rui Wang, Junyu Dong, Yanwei Yu
https://arxiv.org/abs/2507.17195

Closed-Form and Boundary Expressions for Task-Success Probability in Status-Driven Systems
Timely and efficient dissemination of server status is critical in compute-first networking systems, where user tasks arrive dynamically and computing resources are limited and stochastic. In such systems, the access point plays a key role in forwarding tasks to a server based on its latest received server status. However, modeling the task-success probability suffering the factors of stochastic arrivals, limited server capacity, and bidirectional link delays. Therefore, we introduce a unified …

The exact relation between the entanglement entropies of the $XY$ and quantum Ising chains with free and fixed boundary conditions
Tianhao He, Xintian Wu
https://arxiv.org/abs/2509.16880

The exact relation between the entanglement entropies of the $XY$ and quantum Ising chains with free and fixed boundary conditions
The entanglement entropies of $XY$ chains and quantum Ising chains (QICs) with fixed boundary conditions are studied here. Three kinds of boundary conditions (BCs) are considered: fixed up--up or down--down (the spins at both ends are aligned in the same direction), fixed up--down or down--up (the spins at the two ends are aligned in opposite directions), and fixed--free (the spin at one end is aligned, and the other end is free). It is shown that i) the entanglement entropy of an $XY$ chain wi…

A note on the boundary dynamics of holomorphic iterated function systems
Argyrios Christodoulou
https://arxiv.org/abs/2507.16358 https://

A note on the boundary dynamics of holomorphic iterated function systems
We consider the boundary dynamics of iterated function systems of holomorphic self-maps of the unit disc. Our main result provides a sufficient condition which guarantees that the dynamical behaviour of a left iterated function system in the interior of the unit disc can be extended to the boundary. This generalises an extension of the classical Denjoy--Wolff Theorem, due to Bourdon, Matache and Shapiro, to the setting of iterated function systems. To do so we modify estimates for the Hardy nor…

Matrix-Free Evaluation of High-Order Shifted Boundary Finite Element Operators
Micha{\l} Wichrowski
https://arxiv.org/abs/2507.17053 https://arxiv.org/pdf/…

Matrix-Free Evaluation of High-Order Shifted Boundary Finite Element Operators
This paper presents a matrix-free approach for implementing the shifted boundary method (SBM) in finite element analysis. The SBM is a versatile technique for solving partial differential equations on complex geometries by shifting boundary conditions to nearby surrogate boundaries. We focus on the efficient evaluation of shifted boundary operators using precomputed data and tensor-product structures. The proposed method avoids the explicit assembly of global matrices, achieving a computational…

null2: Boundary-Dissolving Bodies and Architecture towards Digital Nature
Yoichi Ochiai
https://arxiv.org/abs/2509.18498 https://arxiv.org/pdf/2509.18498…

The Plateau's Problem for intrinsic graphs in the Heisenberg Group
Roberto Monti, Giacomo Vianello
https://arxiv.org/abs/2507.17714 https://arxiv.org/p…

The Plateau's Problem for intrinsic graphs in the Heisenberg Group
Using a geometric construction, we solve Plateau's Problem in the Heisenberg group $\mathbb{H}^{1}$ for intrinsic graphs defined on a convex domain $D$, under a smallness condition either on the boundary $\partial D$ or on the Lipschitz boundary datum $φ: \partial D \to \mathbb{R}$. The proof relies on a calibration argument. We then apply these techniques to establish a new regularity result for $H$-perimeter minimizers.

Boundary pointwise regularity for the divergence form elliptic boundary problem on uniform domain
Tianyu Guan, Lihe Wang, Chunqin Zhou
https://arxiv.org/abs/2509.17690 https://

Boundary pointwise regularity for the divergence form elliptic boundary problem on uniform domain
In this paper, we study the boundary pointwise regularity for the divergence form elliptic boundary problem. In generality, it is not convenient to define weak solutions for nonzero boundary data on domain with the rough boundary, e.g. uniform domain. However, in this paper, we introduce a definition of weak solutions for the boundary problem on uniform domain. What is interesting is that this definition can be considered to analysis the regularity of weak solutions. In particular, by establish…

On Kinodynamic Global Planning in a Simplicial Complex Environment: A Mixed Integer Approach
Otobong Jerome, Alexandr Klimchik, Alexander Maloletov, Geesara Kulathunga
https://arxiv.org/abs/2508.16511 …

On Kinodynamic Global Planning in a Simplicial Complex Environment: A Mixed Integer Approach
This work casts the kinodynamic planning problem for car-like vehicles as an optimization task to compute a minimum-time trajectory and its associated velocity profile, subject to boundary conditions on velocity, acceleration, and steering. The approach simultaneously optimizes both the spatial path and the sequence of acceleration and steering controls, ensuring continuous motion from a specified initial position and velocity to a target end position and velocity.The method analyzes the admiss…

Edge densities of drawings of graphs with one forbidden cell
Benedikt Hahn, Torsten Ueckerdt, Birgit Vogtenhuber
https://arxiv.org/abs/2508.16368 https://a…

Edge densities of drawings of graphs with one forbidden cell
A connected topological drawing of a graph divides the plane into a number of cells. The type of a cell $c$ is the cyclic sequence of crossings and vertices along the boundary walk of $c$. For example, all triangular cells with three incident crossings and no incident vertex share the same cell type. When a non-homotopic drawing of an $n$-vertex multigraph $G$ does not contain any such cells, Ackerman and Tardos [JCTA 2007] proved that $G$ has at most $8n-20$ edges, while Kaufmann, Klemz, Knorr…

A Comprehensive Review of Agricultural Parcel and Boundary Delineation from Remote Sensing Images: Recent Progress and Future Perspectives
Juepeng Zheng, Zi Ye, Yibin Wen, Jianxi Huang, Zhiwei Zhang, Qingmei Li, Qiong Hu, Baodong Xu, Lingyuan Zhao, Haohuan Fu
https://arxiv.org/abs/2508.14558

A Comprehensive Review of Agricultural Parcel and Boundary Delineation from Remote Sensing Images: Recent Progress and Future Perspectives
Powered by advances in multiple remote sensing sensors, the production of high spatial resolution images provides great potential to achieve cost-efficient and high-accuracy agricultural inventory and analysis in an automated way. Lots of studies that aim at providing an inventory of the level of each agricultural parcel have generated many methods for Agricultural Parcel and Boundary Delineation (APBD). This review covers APBD methods for detecting and delineating agricultural parcels and syst…

Filtrations and asymptotic geometry of non-Archimedean norms on section rings
R\'emi Reboulet
https://arxiv.org/abs/2508.16322 https://arxiv.org/pdf/25…

Filtrations and asymptotic geometry of non-Archimedean norms on section rings
This article is concerned with the metric study of a construction of Gérardin of the action of the boundary at infinity of the space of norms on a non-Archimedean vector space, and its generalisation to graded algebras. Namely, given (X,L) a polarised variety over an arbitrary non-Archimedean field, we show that there is a jointly d_1-contracting action of the space of filtrations of the section ring R(X,L) on the space of graded norms on R(X,L). This naturally yields non-Archimedean geodesic …

A boundary characterization of Turaev-Viro TQFTs
Max-Niklas Steffen, Christoph Schweigert
https://arxiv.org/abs/2508.13759 https://arxiv.org/pdf/2508.13759…

A boundary characterization of Turaev-Viro TQFTs
We consider three-dimensional topological field theories on manifolds with boundary defects and identify explicit boundary locality conditions. These conditions imply a state sum construction of the given TQFT. As a consistency check, we prove that Turaev-Viro state sum models obey the boundary locality conditions. Recent progress (arXiv:2410.18049v1) in the description of defects in Dijkgraaf-Witten theories enables us to show that these theories likewise satisfy boundary locality. This direct…

Localized five-dimensional rotating brane-world black hole Analytically Connected to an to an AdS$_5$ boundary
Milko Estrada, Francisco Tello-Ortiz
https://arxiv.org/abs/2509.18435

Bulk/boundary quotients of Gaussian multiplicative chaos measures II: Tail profile of bulk Gaussian multiplicative chaos measures in the exact scale-invariant case
Yichao Huang, Youtao Liu
https://arxiv.org/abs/2509.17363

Bulk/boundary quotients of Gaussian multiplicative chaos measures II: Tail profile of bulk Gaussian multiplicative chaos measures in the exact scale-invariant case
This is the second part of a series of papers where we consider questions related to the tail profile of the bulk/boundary quotients of Gaussian multiplicative chaos measures appearing in boundary Liouville conformal field theory. In this part, we study of the right tail profile of a Gaussian multiplicative chaos measure with uniform singularity on the boundary, especially in the case of an exact scale-invariant kernel for the underlying log-correlated Gaussian field. This extends previous resu…

Local Connectivity of Right-angled Coxeter group boundaries
Michael Mihalik, Kim Ruane, Steve Tschantz
https://arxiv.org/abs/2507.17574 https://arxiv.org/p…

Local Connectivity of Right-angled Coxeter group boundaries
We provide conditions on the defining graph of a right-angled Coxeter group presentation that guarantees the boundary of any CAT(0) space on which the group acts geometrically will be locally connected. This is a revised version of a published paper where we streamline some of the proofs and add figures.

Physics-informed, boundary-constrained Gaussian process regression for the reconstruction of fluid flow fields
Adrian Padilla-Segarra, Pascal Noble, Olivier Roustant, \'Eric Savin
https://arxiv.org/abs/2507.17582

Physics-informed, boundary-constrained Gaussian process regression for the reconstruction of fluid flow fields
Gaussian process regression techniques have been used in fluid mechanics for the reconstruction of flow fields from a reduction-of-dimension perspective. A main ingredient in this setting is the construction of adapted covariance functions, or kernels, to obtain such estimates. In this paper, we derive physics-informed kernels for simulating two-dimensional velocity fields of an incompressible (divergence-free) flow around aerodynamic profiles. These kernels allow to define Gaussian process pri…

Constant mean curvature Radial graphs over domains of $\mathbb{S}^n$
Fl\'avio Cruz, Jos\'e T. Cruz, Jocel Oliveira
https://arxiv.org/abs/2507.18496 https://

Constant mean curvature Radial graphs over domains of $\mathbb{S}^n$
We establish the existence of hypersurfaces with constant mean curvature and a prescribed boundary in Euclidean space, represented as radial graphs over domains of the unit sphere. Under the assumptions that the mean curvature of the domain's boundary is positive and that a subsolution exists for the associated Dirichlet problem, we extend Serrin's classical result to include the case of positive constant mean curvature.

Nanoscale Strain Evolution and Grain Boundary-Mediated Defect Sink Behavior in Irradiated SiC: Insights from N-PED and DFT
Nabil Daghbouj, Ahmed. T. AlMotasem, Jan. Ducho\v{n}b, Bingsheng. Li, Mohamed. Bensalem, Frans. Munnik, Xin Ou, Anna. Mackov\'a, William. J. Weber, Tomas. Polcara
https://arxiv.org/abs/2509.18895

Quantum Properties of Non-Dirichlet Boundary Conditions in Gravity
Patrick Draper, Manthos Karydas, Hao Zhang
https://arxiv.org/abs/2509.16190 https://arxi…

Quantum Properties of Non-Dirichlet Boundary Conditions in Gravity
The Euclidean path integral for gravity is enriched by the addition of boundaries, which provide useful probes of thermodynamic properties. Common boundary conditions include Dirichlet conditions on the boundary induced metric; microcanonical conditions, which refers to fixing some components of the Brown-York boundary stress tensor; and conformal conditions, in which the conformal structure of the induced metric and the trace of the extrinsic curvature are fixed. Boundaries also present intere…

Replaced article(s) found for astro-ph.SR. https://arxiv.org/list/astro-ph.SR/new
[1/1]:
- High-resolution Observation of Mini-Filament Eruptions Near Coronal Hole Boundary and Their Respo...
Nengyi Huang, Haimin Wang

Regularity of the free boundary in an unstable parabolic problem
Mark Allen, Gilles Bokolo-Tamba
https://arxiv.org/abs/2508.15997 https://arxiv.org/pdf/250…

Regularity of the free boundary in an unstable parabolic problem
We study the free boundary in an unstable parabolic problem arising from a model in combustion. We consider the physical situation in which the heat advances and prove that the free boundary is a $C^{1,α/2}$ hypersurface.

Dynamical properties of oscillating, viscous, transonic accretion disks around black holes
Sanjit Debnath, Indranil Chattopadhyay, Raj Kishor Joshi, Philippe Laurent, Priyesh Kumar Tripathi, M. Saleem Khan
https://arxiv.org/abs/2509.19934

Dynamical properties of oscillating, viscous, transonic accretion disks around black holes
We investigate the time evolution of sub-Keplerian transonic accretion flow onto a non-rotating black hole using axisymmetric viscous hydrodynamic simulations. We simulate the accretion flow using boundary values from semi-analytical analysis and set up three different models. Two of the models do not predict accretion shocks from the semi-analytic analysis, while one of them does. We also consider radiative cooling along with viscosity in the simulation. Our two-dimensional simulation deviated…

Crank-rocker optical fiber mode scrambler prototype for the GMT-Consortium Large Earth Finder (G-CLEF)
Matthew C. H. Leung, Colby Jurgenson, Andrew Szentgyorgyi, William Podgorski, Mark Mueller, Yahel Sofer Rimalt, Joseph Zajac, Cem Onyuksel, Daniel Durusky, Peter Doherty
https://arxiv.org/abs/2509.18306

Thin-film boundary-layer diffusion of non-equilibrium flow to kinetically limited reactive surfaces via Damk\"ohler thermochemistry tables
Jeffrey D. Engerer, Lincoln N. Collins
https://arxiv.org/abs/2509.15427

Thin-film boundary-layer diffusion of non-equilibrium flow to kinetically limited reactive surfaces via Damköhler thermochemistry tables
Traditional ablation thermochemistry tables for atmospheric entry are derived from boundary-layer element diffusion assuming homogeneous and heterogeneous thermochemical equilibrium at the vehicle surface. Prior techniques for finite-rate surface reactions predominantly embed specific heterogeneous reaction models within the homogeneous equilibrium solution procedures and tables. This paper disseminates a boundary-layer integral solution for wall-gas free oxygen coupled to finite-rate surface k…

Reduction theory for Fuchsian groups with cusps
Adam Abrams, Svetlana Katok, Ilie Ugarcovici
https://arxiv.org/abs/2507.16958 https://arxiv.org/pdf/2507.16…

Reduction theory for Fuchsian groups with cusps
We study a family of Bowen-Series-like maps associated to any finitely generated Fuchsian group of the first kind with at least one cusp. These maps act on the boundary of the hyperbolic plane in a piecewise manner by generators of the group. We show that the two-dimensional natural extension (reduction map) of the boundary map has a domain of bijectivity and global attractor with a finite rectangular structure, confirming a conjecture of Don Zagier. Our work is based on the construction of a s…

Structures of group-15 elemental solids from an effective boundary theory
Ashland Knowles, R. Ganesh
https://arxiv.org/abs/2509.18267 https://arxiv.org/pdf…

Structures of group-15 elemental solids from an effective boundary theory
We present an effective description for the crystal structures of pnictogen elemental solids. In these materials, each atom contains three valence electrons in $p$ orbitals. They are shared between neighbouring atoms to form valence bonds. We propose a trivalent network model on the simple cubic lattice. As a generalization of a dimer model, we impose a constraint that three dimers must touch every site. We argue that intra-orbital Coulomb repulsion prohibits the formation of two adjacent, para…

Revisiting boundary-driven method for transport: Finite-size effects and the role of system-bath coupling
Mariel Kempa, Markus Kraft, Sourav Nandy, Jacek Herbrych, Jiaozi Wang, Jochen Gemmer, Robin Steinigeweg
https://arxiv.org/abs/2507.16528

Revisiting boundary-driven method for transport: Finite-size effects and the role of system-bath coupling
Understanding transport in interacting quantum many-body systems is a central challenge in condensed matter and statistical physics. Numerical studies typically rely on two main approaches: Dynamics of linear-response functions in closed systems and Markovian dynamics governed by master equations for boundary-driven open systems. While the equivalence of their dynamical behavior has been explored in recent studies, a systematic comparison of the transport coefficients obtained from these two cl…

Blow-up problem for porous medium equation with absorption under nonlinear nonlocal boundary condition
Alexander Gladkov
https://arxiv.org/abs/2507.17310 https://

Blow-up problem for porous medium equation with absorption under nonlinear nonlocal boundary condition
In this paper we consider initial boundary value problem for porous medium equation with absorption under nonlinear nonlocal boundary condition and nonnegative initial datum. We prove local existence, comparison principle, global existence and blow-up of solutions.

Solving time-fractional diffusion equations with Robin boundary conditions via fractional Hamiltonian boundary value methods
Qian Luo, Aiguo Xiao, Xiaoqiang Yan, Jingmin Xia
https://arxiv.org/abs/2509.17793

Solving time-fractional diffusion equations with Robin boundary conditions via fractional Hamiltonian boundary value methods
In this paper, we propose a novel numerical scheme for solving time-fractional reaction-diffusion problems with Robin boundary conditions, where the time derivative is in the Caputo sense of order $α\in(0,1)$. The existence and uniqueness of the solution is proved. Our proposed method is based on the spectral collocation method in space and Fractional Hamiltonian boundary value methods in time. For the considered spectral collocation method, the basis functions used are not the standard polyno…

Extremal Steklov-Neumann Eigenvalues
Chiu-Yen Kao, Braxton Osting, Chee Han Tan, Robert Viator
https://arxiv.org/abs/2509.15975 https://arxiv.org/pdf/2509.…

Extremal Steklov-Neumann Eigenvalues
Let $Ω$ be a bounded open planar domain with smooth connected boundary, $Γ$, that has been partitioned into two disjoint components, $Γ= Γ_S \sqcup Γ_N$. We consider the Steklov-Neumann eigenproblem on $Ω$, where a harmonic function is sought that satisfies the Steklov boundary condition on $Γ_S$ and the Neumann boundary condition on $Γ_N$. We pose the extremal eigenvalue problems (EEPs) of minimizing/maximizing the $k$-th non-trivial Steklov-Neumann eigenvalue among boundary partitions…

Quantum-enhanced parameter estimation in continuously monitored boundary time crystals
Eoin O'Connor, Victor Montenegro, Francesco Albarelli, Matteo G. A. Paris, Abolfazl Bayat, Marco G. Genoni
https://arxiv.org/abs/2508.15448

Quantum-enhanced parameter estimation in continuously monitored boundary time crystals
We investigate quantum-enhanced parameter estimation in boundary time crystals (BTCs) via continuous monitoring. By analytically deriving the global quantum Fisher information rate, we show that in the time-crystal phase the ultimate precision exhibits a cubic scaling with the system size, $f_{\mathrm{global}}\sim N^3$, surpassing both the sensitivity at the critical point and the standard quantum limit (SQL). We then numerically demonstrate that this bound can be attained already at finite $N$…

Vacuum Energy and Topological Mass from a Constant Magnetic Field and Boundary Conditions in Coupled Scalar Field Theories
A. J. D. Farias Junior, Andrea Erdas, Herondy F. Santana Mota
https://arxiv.org/abs/2508.15121

Vacuum Energy and Topological Mass from a Constant Magnetic Field and Boundary Conditions in Coupled Scalar Field Theories
We investigate the combined effects of a uniform magnetic field and boundary conditions on vacuum energy and topological mass generation in a coupled scalar field theory. The system consists of a real scalar field, subject to Dirichlet boundary conditions, interacting via self- and cross-couplings with a gauge-coupled complex scalar field obeying mixed boundary conditions between two perfectly reflecting parallel plates. The magnetic field induces Landau quantization, leading to novel contribut…

Exponential Spectral Scaling: Robust and Efficient Stellarator Boundary Optimization via Mode-Dependent Scaling
Byoungchan Jang, Rory Conlin, Matt Landreman
https://arxiv.org/abs/2509.16320

Exponential Spectral Scaling: Robust and Efficient Stellarator Boundary Optimization via Mode-Dependent Scaling
Stellarator boundary optimization faces a fundamental numerical challenge: the extreme disparity between low- and high-mode amplitudes creates an optimization landscape in which direct full-spectrum approaches typically converge to poor local minima. Traditionally, this challenge has been addressed through a computationally expensive, multi-step Fourier continuation, in which low Fourier modes are optimized first, followed by the gradual incorporation of higher modes. We present Exponential Spe…

Least Energy Solutions for Cooperative and Competitive Schr\"odinger Systems with Neumann Boundary Conditions
Simone Mauro, Delia Schiera, Hugo Tavares
https://arxiv.org/abs/2509.18835

Least Energy Solutions for Cooperative and Competitive Schrödinger Systems with Neumann Boundary Conditions
We study the following gradient elliptic system with Neumann boundary conditions \begin{equation*} -Δu + λ_1 u = u^3 + βuv^2, \ -Δv + λ_2 v = v^3 + βu^2 v \ \text{in } Ω,\qquad \frac{\partial u}{\partial ν} = \frac{\partial v}{\partial ν} = 0 \ \text{on } \partial Ω, \end{equation*} where $Ω\subset \mathbb{R}^N $ is a bounded $ C^2$ domain with $ N \leq 4 $, and $ ν$ denotes the outward unit normal on the boundary. We investigate the existence of non-constant least energy solutions …

Into the Void: Understanding Online Health Information in Low-Web Data Languages
Hellina Hailu Nigatu, Nuredin Ali Abdelkadir, Fiker Tewelde, Stevie Chancellor, Daricia Wilkinson
https://arxiv.org/abs/2509.20245

Into the Void: Understanding Online Health Information in Low-Web Data Languages
Data voids--areas of the internet where reliable information is scarce or absent--pose significant challenges to online health information seeking, particularly for users operating in low-web data languages. These voids are increasingly encountered not on traditional search engines alone, but on social media platforms, which have gradually morphed into informal search engines for millions of people. In this paper, we introduce the phenomenon of data horizons: a critical boundary where algorithm…

Stability and Bifurcation Analysis of Two-term Fractional Difference Equation
Janardhan Chevala, Sachin Bhalekar
https://arxiv.org/abs/2509.18746 https://a…

Bicolored bosonic solvable lattice models
Talia Blum
https://arxiv.org/abs/2509.16468 https://arxiv.org/pdf/2509.16468

Bicolored bosonic solvable lattice models
Recent papers in solvable lattice models emphasize models where states can be visualized as colored paths through the lattice. We define a bosonic model in which there are two types of colors, one whose paths move down and to the right, the other whose paths move down and to the left. Depending on their boundary data, systems may have no states, exactly one state, or many states. We prove that these cases depend on a criterion involving two permutations extracted from the boundary data and thei…

Normal stable degenerations of Noether-Horikawa surfaces
Hiroto Akaike, Makoto Enokizono, Masafumi Hattori, Yuki Koto
https://arxiv.org/abs/2507.17633 https://

Normal stable degenerations of Noether-Horikawa surfaces
We classify all normal stable Horikawa surfaces with only $\mathbb{Q}$-Gorenstein smoothable log canonical singularities. Furthermore, we provide a criterion for their global $\mathbb{Q}$-Gorenstein smoothability and describe the boundary strata of the moduli space of $\mathbb{Q}$-Gorenstein smoothable normal stable Horikawa surfaces.

Symmetries of the periodic Fredkin chain
Andrei G. Pronko
https://arxiv.org/abs/2507.18291 https://arxiv.org/pdf/2507.18291

Symmetries of the periodic Fredkin chain
Fredkin chain is a spin-$1/2$ model with interaction of three nearest neighbors. In the case of periodic boundary conditions the ground state is degenerated and can be described in terms of equivalence classes of the Dyck paths. We introduce two operators commuting with the Hamiltonian, which play the roles of lowering and raising operators when acting at the ground states. These operators generate the $B$- or $C$-type Lie algebras, depending on whether the number of sites $N$ is odd or even, r…

Families of Morse functions for manifolds with boundary
Maciej Borodzik, Weronika Buczy\'nska
https://arxiv.org/abs/2507.15847 https://arxiv.org/pdf/25…

Families of Morse functions for manifolds with boundary
We study 1-parameter families of Morse functions for manifolds with boundary. We list all degeneracies that may occur in generic 1-parameter families.

Spontaneous excitation of a centripetally accelerated atom coupled to electromagnetic vacuum fluctuations near a reflecting boundary
Yan Peng, Jiawei Hu, Hongwei Yu
https://arxiv.org/abs/2509.16488

Spontaneous excitation of a centripetally accelerated atom coupled to electromagnetic vacuum fluctuations near a reflecting boundary
We investigate the rate of change of the mean atomic energy for centripetally accelerated atoms interacting with electromagnetic vacuum fluctuations near a reflecting boundary, using the Dalibard-Dupont-Roc-Cohen-Tannoudji formalism. The distinct contributions from vacuum fluctuations and radiation reaction are analyzed separately. Our results reveal that, when the centripetal acceleration significantly exceeds the characteristic acceleration set by the atomic transition frequency, vacuum fluct…

A Comparison of LES Inlet Boundary Conditions for Supersonic Jet Flows
Diego F. Abreu, Carlos Junqueira-Junior, Eron T. V. Dauricio, Jo\~ao Luiz F. Azevedo
https://arxiv.org/abs/2509.17732

A Comparison of LES Inlet Boundary Conditions for Supersonic Jet Flows
The present work evaluates the effects of three inflow boundary conditions on large-eddy simulations of supersonic jet flows. The three inlet flow configurations considered are an inviscid profile, a stationary turbulent profile extracted from a RANS calculation, and a time-dependent tripped turbulent profile. The study applies the nodal discontinuous Galerkin spatial discretization to perform the supersonic jet flow simulations. Initially, a mesh and polynomial resolution study is performed to…

The periodicity of three-dimensional oscillatory reconnection
Luiz A. C. A. Schiavo, Gert J. J. Botha, James A. McLaughlin
https://arxiv.org/abs/2509.19603 https://

The periodicity of three-dimensional oscillatory reconnection
Oscillatory reconnection is a dynamic, magnetic relaxation mechanism in which a perturbed null point reverts back to equilibrium via time-dependent reconnection. In this paper, we investigate the long-term periodic signal generated by a three-dimensional (3D) magnetic null point, when it is perturbed by a non-periodic driver, for a variety of driving amplitudes. We solve the 3D nonlinear magnetohydrodynamic (MHD) equations using a bespoke numerical boundary condition (a sponge region) that damp…

Notes from the bulk
Erica Bertolini
https://arxiv.org/abs/2507.16744 https://arxiv.org/pdf/2507.16744

Notes from the bulk
The scope of this Ph.D thesis is to study the effects of the presence of a boundary from a Quantum Field Theoretical perspective, searching for new physics and explanations of observed phenomena. In particular, thanks to the formal QFT setting, the issue of the existence of local, accelerated, edge modes in Hall systems is analyzed and understood in terms of the bulk-to-boundary approach as related to a curved background in topological QFTs with boundary. Within this formalism the induced metri…

Boundary effect on asymptotic behaviour of solution to the hyperbolic-parabolic chemotaxis system
Nangao Zhang
https://arxiv.org/abs/2509.19828 https://arx…

Boundary effect on asymptotic behaviour of solution to the hyperbolic-parabolic chemotaxis system
This paper is concerned with the global existence and stability of solution to the quasi linear hyperbolic-parabolic chemotaxis system on the half-line,which was proposed in[1] to primarily describe the formation of coherent vascular networks observed invitro experiment. Under two diffrent boundary conditions,we first establish the existence and uniqueness of the solution of the asymptotic state equation (the so-called nonlinear diffusion wave),and then prove that the solution of the orig…

Numerical solution of the time fractional nonlinear Fisher-KPP diffusion-reaction equation using the local domain boundary element method
Theodore V. Gortsas
https://arxiv.org/abs/2508.16241

Numerical solution of the time fractional nonlinear Fisher-KPP diffusion-reaction equation using the local domain boundary element method
The Fisher-KPP partial differential equation has been employed in science to model various biological, chemical, and thermal phenomena. Time fractional extensions of Fisher's equation have also appeared in the literature, aiming to model systems with memory. The solution of the time fractional Fisher-KPP equation is challenging due to the interplay between the nonlinearity and the nonlocality imposed by the fractional derivatives. An accurate method that for the solution of time fractional diff…

Submanifolds with boundary in sub-Riemannian Heisenberg Groups
Marco Di Marco, Davide Vittone
https://arxiv.org/abs/2508.15634 https://arxiv.org/pdf/2508.1…

Submanifolds with boundary in sub-Riemannian Heisenberg Groups
We discuss the notion of submanifolds with boundary with intrinsic $C^1$ regularity in sub-Riemannian Heisenberg groups and we provide some examples. Eventually, we present a Stokes' Theorem for such submanifolds involving the integration of Rumin's differential forms in Heisenberg groups.

Blow-Up Results of Time Fractional Heat Equation With Nonlinear Neumann Boundary Conditions
Hind Ghazi Hameed, Burhan Selcuk, Maan A. Rasheed
https://arxiv.org/abs/2509.18927 ht…

Impact of 3D macro physics and nuclear physics on the p nuclei in O-C shell mergers
Joshua Issa, Falk Herwig, Pavel Denissenkov, Marco Pignatari
https://arxiv.org/abs/2507.16965

Impact of 3D macro physics and nuclear physics on the p nuclei in O-C shell mergers
O-C shell mergers in massive stars are a site for producing the p nuclei by the $γ$ process, but 1D stellar models rely on mixing length theory, which does not match the radial velocity profiles of 3D hydrodynamic simulations. We investigate how 3D macro physics informed mixing impacts the nucleosynthesis of p nuclei. We post-process the O-shell of the $M_\mathrm{ZAMS} = 15~\mathrm{M}_\odot$, $Z = 0.02$ model from the NuGrid stellar data set. Applying a downturn to velocities at the boundary a…

Scott-Vogelius element and iterated penalty method for inhomogeneous Dirichlet boundary conditions
Franziska Eickmann, Ridgway L. Scott, Tabea Tscherpel
https://arxiv.org/abs/2509.17899

Scott-Vogelius element and iterated penalty method for inhomogeneous Dirichlet boundary conditions
We present quasi-optimal a priori error estimates for general mixed finite element methods to approximate solutions of the Stokes problem subject to inhomogeneous Dirichlet boundary conditions. For the Scott-Vogelius element this yields pressure-robust a priori error estimates. Due to the exact divergence constraint, this requires a compatibility condition for the boundary data to hold. A key tool is a modified Fortin operator, capable of preserving this compatibility condition. Furthermore, we…

Random coverage of a manifold with boundary
Mathew D. Penrose, Xiaochuan Yang
https://arxiv.org/abs/2509.19278 https://arxiv.org/pdf/2509.19278

Singular-degenerate parabolic systems with the conormal boundary condition on the upper half space
Bekarys Bekmaganbetov, Hongjie Dong
https://arxiv.org/abs/2509.18418 https://

Singular-degenerate parabolic systems with the conormal boundary condition on the upper half space
We prove the well-posedness and regularity of solutions in mixed-norm weighted Sobolev spaces for a class of second-order parabolic and elliptic systems in divergence form in the half-space $\mathbb{R}^d_+ = \{x_d > 0\}$ subject to the conormal boundary condition. Our work extends results previously available for scalar equations to the case of systems of equations. The leading coefficients are the product of $x_d^α$ and bounded non-degenerate matrices, where $α\in (-1,\infty)$. The leading c…

Higher Structures on Boundary Conformal Manifolds: Higher Berry Phase and Boundary Conformal Field Theory
Yichul Choi, Hyunsoo Ha, Dongyeob Kim, Yuya Kusuki, Shuhei Ohyama, Shinsei Ryu
https://arxiv.org/abs/2507.12525

Higher Structures on Boundary Conformal Manifolds: Higher Berry Phase and Boundary Conformal Field Theory
We introduce the notion of higher Berry connection and curvature in the space of conformal boundary conditions in (1+1)d conformal field theories (CFT), related to each other by exactly marginal boundary deformations, forming a "boundary conformal manifold." Our definition builds upon previous works on tensor networks, such as matrix product states (MPS), where the triple inner product or multi-wavefunction overlap plays the key geometric role. On the one hand, our boundary conformal field theo…

Serrin-type problem in divergence form on Riemannian manifolds
M\'arcio Batista, M\'arcio Santos, Ant\^onio da Silva, Joyce Sindeaux
https://arxiv.org/abs/2507.17838 htt…

Serrin-type problem in divergence form on Riemannian manifolds
In this paper, we investigate an overdetermined boundary value problem of divergence type on bounded domains in Riemannian manifolds with non-negative Ricci curvature. Using integral identities and the $P$-function method, we derive geometric inequalities and rigidity results. Under natural conditions on the nonlinearity, we prove that equality implies the domain is isometric to a Euclidean ball, thereby extending classical symmetry results to the Riemannian setting.

Scalar induced gravitational waves in PV symmetric teleparallel gravity with non-minimally coupled boundary term
Fengge Zhang
https://arxiv.org/abs/2508.14584 https://

Scalar induced gravitational waves in PV symmetric teleparallel gravity with non-minimally coupled boundary term
The question of whether the parity violation occurs in gravitational interaction has recently attracted much attention. In this paper, we investigate the scalar induced gravitational waves (SIGWs) in symmetric teleparallel gravity incorporating a parity-violating (PV) term and a non-minimally coupled boundary term. The presence of this non-minimally coupled boundary term help to avoid the strong coupling problem inherent in PV symmetric teleparallel gravity, thereby enabling our study of the SI…

Immersed Boundary Projection Method for Navier Slip Boundaries
Takehiro Fujii, Takeshi Omori
https://arxiv.org/abs/2509.14713 https://arxiv.org/pdf/2509.14…

Immersed Boundary Projection Method for Navier Slip Boundaries
A formulation of the immersed boundary method for incompressible flow over bodies with surface slip described by the Navier boundary condition is presented. In the present method, the wall slip velocity and the boundary force are determined implicitly through a projection to satisfy the boundary conditions and the divergence-free condition of the velocity field as constraints. The present method is first-order accurate in space and fourth-order accurate in time, overcoming the difficulty of the…

Boundary H\"older gradient estimates for fully nonlinear degenerate or singular parabolic equations
Hyungsung Yun
https://arxiv.org/abs/2509.16613 https://

Boundary Hölder gradient estimates for fully nonlinear degenerate or singular parabolic equations
We study boundary regularity of viscosity solutions to fully nonlinear degenerate or singular parabolic equations. The gradient-dependent degeneracy or singularity, along with the time derivative, introduces significant challenges beyond the elliptic case. By combining compactness methods, barrier constructions, regularization techniques, and the boundary regularity of small perturbation solutions, we establish boundary Hölder gradient estimates that unify and extend previous results.

Second-order boundary estimates for solutions to a class of quasilinear elliptic equations
Giuseppe Spadaro, Domenico Vuono
https://arxiv.org/abs/2507.16402

Second-order boundary estimates for solutions to a class of quasilinear elliptic equations
We prove global second-order regularity for a class of quasilinear elliptic equations, both with homogeneous Dirichlet and Neumann boundary conditions. A condition on the integrability of the second fundamental form on the boundary of the domain is required. As a consequence, with the additional assumption that the source term has a sign, we obtain integrability properties of the inverse of the gradient of the solution. Assuming convexity of the domain, no boundary regularity is required.

Uniqueness in the Plateau problem near Quadratic cones
Vishnu Nandakumaran, G\'abor Sz\'ekelyhidi
https://arxiv.org/abs/2509.15503 https://arxiv.or…

Uniqueness in the Plateau problem near Quadratic cones
We consider minimal hypersurfaces inside the unit ball whose boundary on the sphere is a small perturbation of the link of a minimizing quadratic cone. We show that such minimal surfaces are uniquely determined by their boundary condition. In particular the solutions of the Plateau problem are unique for boundary conditions given by small perturbations of the link of a quadratic cone.

Replaced article(s) found for gr-qc. https://arxiv.org/list/gr-qc/new
[2/2]:
- Absolute entropy and the observer's no-boundary state
Andreas Blommaert, Jonah Kudler-Flam, Erez Y. Urbach

Finite element approximation of the stationary Navier-Stokes problem with non-smooth data
Mar\'ia Gabriela Armentano, Mauricio Mendiluce
https://arxiv.org/abs/2509.16461 htt…

Finite element approximation of the stationary Navier-Stokes problem with non-smooth data
The aim of this work is to analyze the finite element approximation of the stationary Navier-Stokes equations with non-smooth Dirichlet boundary data. The discrete approximation is obtained by considering the Navier-Stokes system with a regularized boundary solution. Based on the existence of the very weak solution for the Navier-Stokes system with L2 boundary data, and a suitable decomposition of this solution, we obtain a priori error estimates between the approximation of the Navier-Stokes s…

Stability of an elastodynamic system with localized internal damping and acoustic boundary conditions
Abdelkhalek Balehouane, Hicham Kasri, Rokia Kechkar
https://arxiv.org/abs/2507.16546

Stability of an elastodynamic system with localized internal damping and acoustic boundary conditions
In this paper, we prove a stability result for an elastodynamic system with acoustic boundary conditions and localized internal damping, defined in a bounded domain $Ω$ of $\mathbb{R}^3$. Here, the internal damping is only assumed to be locally distributed and satisfies suitable assumptions. The smooth boundary of $Ω$ is $Γ=Γ_0\cupΓ_1$ such that $\overline{Γ_0}\cap\overline{Γ_1}=\emptyset$. On $Γ_0$, we consider the homogeneous Dirichlet boundary condition, and on $Γ_1$ , we consider t…

JT gravity and deformed CFTs
Suchetan Das, Anirban Dinda
https://arxiv.org/abs/2507.17889 https://arxiv.org/pdf/2507.17889…

JT gravity and deformed CFTs
We propose alternative \textit{UV completion} of pure JT gravity as well as CFT coupled to JT gravity, via a class of \textit{deformed} 2D CFT. In AdS/CFT with a prescribed classical limit, pure JT gravity in \textit{one-sided} AdS$_{2}$ black hole is argued to be described by certain holographic deformed CFT on a strip. Equivalently, these deformed CFTs can be recast as CFTs on one-sided AdS$_{2}$ black hole with \textit{emergent conformal boundary condition on a stretched horizon}$-$providing…

Quantum Gravity and Inflation as an Open System: A New Paradigm
Alan Sebasti\'an Morales, Mauricio Bellini, Juan Ignacio Musmarra
https://arxiv.org/abs/2509.19507 https://…

Quantum Gravity and Inflation as an Open System: A New Paradigm
As part of our program to develop a general theory of relativity for open systems, we introduce a covariant theory that incorporates the effects of classical and quantum spacetime alterations in a new metric tensor that effectively includes these alterations, thereby generating a Riemannian manifold from a new varied action without boundary terms. We illustrate the theory by studying an inflationary model which incorporates the quantum feedback effects of spacetime on the dynamics of the inflat…

Asymmetric Kedem-Katchalsky boundary conditions for systems with spatial heterogeneities
Pablo \'Alvarez-Caudevilla, Cristina Br\"andle, Fermin Gonz\'alez-Pereiro
https://arxiv.org/abs/2507.18400

Asymmetric Kedem-Katchalsky boundary conditions for systems with spatial heterogeneities
This work investigates a model describing the interaction of two species in habiting separate but adjacent areas. These populations are governed by a system of equations that account for spatial variations in growth rates and the effects of crowding. A key feature is the presence of areas within each domain where resources are unlimited and crowding effects are absent. The species interact solely through a common bound ary interface, which is modeled by asymmetric Kedem-Katchalsky boundar…

Adaptive time-domain boundary element methods for the wave equation with Neumann boundary conditions
Alessandra Aimi, Giulia Di Credico, Heiko Gimperlein, Chiara Guardasoni
https://arxiv.org/abs/2508.12332

Adaptive time-domain boundary element methods for the wave equation with Neumann boundary conditions
This article investigates adaptive mesh refinement procedures for the time-domain wave equation with Neumann boundary conditions, formulated as an equivalent hypersingular boundary integral equation. Space-adaptive and time-adaptive versions of a space-time boundary element method are presented, based on a reliable a posteriori error estimate of residual type. Numerical experiments illustrate the performance of the proposed approach.

A fast direct solver for two-dimensional transmission problems of elastic waves
Yasuhiro Matsumoto, Taizo Maruyama
https://arxiv.org/abs/2509.19986 https://

A fast direct solver for two-dimensional transmission problems of elastic waves
This paper describes a fast direct boundary element method for elastodynamic transmission problems in two dimensions, which can be used for analyzing elastic wave scattering by an inclusion. This paper reports the development of an efficient solver based on a discretization method that is broadly applicable regardless of the inclusion shape. From the smoothness of the solutions of the Navier--Cauchy equation, it is reasonable that the displacement is approximated by the piecewise linear bases a…

On the simultaneous recovery of boundary impedance and internal conductivity
Jinchao Pan, Jijun Liu
https://arxiv.org/abs/2509.15878 https://arxiv.org/pdf/…

On the simultaneous recovery of boundary impedance and internal conductivity
Consider an inverse problem of the simultaneous recovery of boundary impedance and internal conductivity in the electrical impedance tomography (EIT) model using local internal measurement data, which is governed by a boundary value problem for an elliptic equation in divergence form with Robin boundary condition. We firstly express the solution to the forward problem by volume and surface potentials in terms of the Levi function. Then, for the inverse problem, we prove the uniqueness of the so…

Pattern formations of coupled PDEs with transparent boundary conditions in product-type ends and applications
Huaian Diao, Hongyu Liu, Qingle Meng, Li Wang
https://arxiv.org/abs/2507.14779

Pattern formations of coupled PDEs with transparent boundary conditions in product-type ends and applications
This paper studies pattern formations in coupled elliptic PDE systems governed by transparent boundary conditions. Such systems unify diverse areas, including inverse boundary problems (via a single passive/active boundary measurement), spectral geometry of transmission eigenfunctions, and geometric characterization of invisibility phenomena and inverse shape problems in wave scattering. We uncover and rigorously characterize a novel local pattern formation, establishing a sharp quantitative re…

$\textit{A Priori}$ Error Analysis for the $p$-Stokes Equations with Slip Boundary Conditions: A Discrete Leray Projection Framework
Alex Kaltenbach, J\"orn Wichmann
https://arxiv.org/abs/2507.15016

$\textit{A Priori}$ Error Analysis for the $p$-Stokes Equations with Slip Boundary Conditions: A Discrete Leray Projection Framework
We present an $\textit{a priori}$ error analysis for the kinematic pressure in a fully-discrete finite-differences/-elements discretization of the unsteady $p$-Stokes equations, modelling non-Newtonian fluids. This system is subject to both impermeability and perfect Navier slip boundary conditions, which are incorporated either weakly via Lagrange multipliers or strongly in the discrete velocity space. A central aspect of the $\textit{a priori}$ error analysis is the discrete Leray projection,…

The slender body free boundary problem
Laurel Ohm
https://arxiv.org/abs/2509.16800 https://arxiv.org/pdf/2509.16800…

The slender body free boundary problem
We consider the slender body free boundary problem describing the evolution of an inextensible, closed elastic filament immersed in a Stokes fluid in $\mathbb{R}^3$. The filament elasticity is governed by Euler-Bernoulli beam theory, and the coupling between this 1D elasticity law and the surrounding 3D fluid is governed by the slender body Neumann-to-Dirichlet (NtD) map, which treats the filament as a 3D object with constant cross-sectional radius $0<ε\ll1$. This map serves as a mathematical …

Sharp Boundary Growth Rate Estimate of the Singular Equation $-\Delta u=u^{-\gamma}$ in a Critical Cone
Leyun Wu, Chilin Zhang
https://arxiv.org/abs/2507.16319

Sharp Boundary Growth Rate Estimate of the Singular Equation $-Δu=u^{-γ}$ in a Critical Cone
For $γ>0$, we study the sharp boundary growth rate estimate of solutions to the Dirichlet problem of the singular Lane-Emden-Fowler equation \begin{equation*} -Δu=u^{-γ} \end{equation*} in a critical $C^{1,1}$ epigraphical cone $Cone_Σ$. We show that the growth rate estimate exhibits fundamentally different behaviors in the following three cases: $1<γ<2$, $γ=2$, and $γ>2$. Moreover, we obtain the sharp growth rate estimate near the origin for $γ>1$. As a consequence, we show that wh…

Reconstruction of a potential parameter in time-fractional diffusion problems via a Kohn--Vogelius type functional: Theoretical aspects
Hamza Kahlaoui, Mourad Hrizi, Abdessamad Oulmelk, Xiangcheng Zheng, Ahmed Hendy
https://arxiv.org/abs/2509.19260

Reconstruction of a potential parameter in time-fractional diffusion problems via a Kohn--Vogelius type functional: Theoretical aspects
Of concern is the problem of reconstructing a space-dependent potential from boundary observations in the Caputo time-fractional diffusion equation, utilizing a stable and robust recovery method. We develop an algorithm to minimize the Kohn-Vogelius (KV) cost function, which measures the difference between the solutions of two excitations. The inverse potential problem is recast into an optimization problem, where the objective is to minimize a Kohn-Vogelius-type functional within a set of admi…

An FDM-sFEM scheme on time-space manifolds and its superconvergence analysis
Chengrun Jiang, Guozhi Dong, Hailong Guo, Zuoqiang Shi
https://arxiv.org/abs/2507.17378 https://

An FDM-sFEM scheme on time-space manifolds and its superconvergence analysis
We study superconvergent discretization of the Laplace-Beltrami operator on time-space product manifolds with Neumann temporal boundary values, which arise in the context of dynamic optimal transport on general surfaces. We propose a coupled scheme that combines finite difference methods in time with surface finite element methods in space. By establishing a new summation by parts formula and proving the supercloseness of the semi-discrete solution, we derive superconvergence results for the re…

Eyring-Kramers formula for the mean exit time of non-Gibbsian elliptic processes: the non characteristic boundary case
Dorian Le Peutrec (LMJL), Laurent Michel (IMB), Boris Nectoux (LMBP)
https://arxiv.org/abs/2509.17678

Eyring-Kramers formula for the mean exit time of non-Gibbsian elliptic processes: the non characteristic boundary case
In this work, we derive a new sharp asymptotic equivalent in the small temperature regime $h\to 0$ for the mean exit time from a bounded domain for the non-reversible process $dX\_t=b(X\_t)dt + \sqrt h \, dB\_t$ under a generic orthogonal decomposition of $b$ and when the boundary of $Ω$ is assumed to be \textit{non characteristic}. The main contribution of this work lies in the fact that we do not assume that the process $(X\_t,t\ge 0)$ is \textit{Gibbsian}. In this case, a new correction ter…

EigenWave: An Optimal O(N) Method for Computing Eigenvalues and Eigenvectors by Time-Filtering the Wave Equation
Daniel Appelo, Jeffrey W. Banks, William D. Henshaw, Ngan Le, Donald W. Schwendeman
https://arxiv.org/abs/2507.18282

EigenWave: An Optimal O(N) Method for Computing Eigenvalues and Eigenvectors by Time-Filtering the Wave Equation
An algorithm named EigenWave is described to compute eigenvalues and eigenvectors of elliptic boundary value problems. The algorithm, based on the recently developed WaveHoltz scheme, solves a related time-dependent wave equation as part of an iteration. At each iteration, the solution to the wave equation is filtered in time. As the iteration progresses, the filtered solution generally contains relatively larger and larger proportions of eigenmodes whose eigenvalues are near a chosen target fr…

Sharp Onofri trace inequality on the upper half space and quasi-linear Liouville equation with Neumann boundary
Jingbo Dou, Yazhou Han, Shuang Yuan, Yang Zhou
https://arxiv.org/abs/2509.17031

Sharp Onofri trace inequality on the upper half space and quasi-linear Liouville equation with Neumann boundary
In this paper, we establish a sharp Onofri trace inequality on the upper half space $\overline{\mathbb R_+^n} (n\geq 2)$ by considering the limiting case of Sobolev trace inequality and classify its extremal functions on a suitable weighted Sobolev space. For this aim, by the Serrin-Zou type identity and the Pohozaev type identity, we show the classification of the solutions for a quasi-linear Liouville equation with Neumann boundary which is closely related to the Euler-Lagrange equation of th…

Boundary vortices in the presence of a magnetic field
Khalida Awashra, Matthias Kurzke
https://arxiv.org/abs/2507.15412 https://arxiv…

Boundary vortices in the presence of a magnetic field
We study the behaviour of the magnetization vector field in a thin ferromagnetic film in the presence of an external in-plane constant magnetic field. We work on a specific thin-film regime where boundary vortices dominate the energy and show the Gamma-convergence at the second order of the micromagnetic energy to an energy term called the renormalized energy, representing the interaction energy between boundary vortices. We present a new approach to defining the renormalized energy and rigorou…

An Elliptic-Parabolic Free Boundary Problem with Discontinuous Data
Dennis Kriventsov, Mar\'ia Soria-Carro
https://arxiv.org/abs/2508.13299 https://arx…

An Elliptic-Parabolic Free Boundary Problem with Discontinuous Data
We consider an elliptic-parabolic free boundary problem that models the fluid flow through a partially saturated porous medium. The free boundary arises as the interface separating the saturated and unsaturated regions. Our main goal is to investigate, for the 1+1 dimensional model, how jump discontinuities on the boundary and initial data influence the regularity of both the solution and the free boundary. We show that if the data is merely bounded, then weak solutions are Lipschitz in space a…

Nonlocal Electrostatics and Boundary Charges in Continuum Limits of Two-Dimensional Materials
Shoham Sen, Yang Wang, Timothy Breitzman, Kaushik Dayal
https://arxiv.org/abs/2509.17744

Nonlocal Electrostatics and Boundary Charges in Continuum Limits of Two-Dimensional Materials
Two-dimensional (2D) electronic materials are of significant technological interest due to their exceptional properties and broad applicability in engineering. The transition from nanoscale physics, that dictates their stable configurations, to macroscopic engineering applications requires the use of multiscale methods to systematically capture their electronic properties at larger scales. A key challenge in coarse-graining is the rapid and near-periodic variation of the charge density, which e…

Superlinear gradient growth for 2D Euler equation without boundary
In-Jee Jeong, Yao Yao, Tao Zhou
https://arxiv.org/abs/2507.15739 https://

Superlinear gradient growth for 2D Euler equation without boundary
We consider the vorticity gradient growth of solutions to the two-dimensional Euler equations in domains without boundary, namely in the torus $\mathbb{T}^{2}$ and the whole plane $\mathbb{R}^{2}$. In the torus, whenever we have a steady state $ω^*$ that is orbitally stable up to a translation and has a saddle point, we construct ${\tildeω}_0 \in C^\infty(\mathbb{T}^2)$ that is arbitrarily close to $ω^*$ in $L^2$, such that superlinear growth of the vorticity gradient occurs for an open set …

The fully nonlinear Loewner-Nirenberg problem: Liouville theorems and counterexamples to local boundary estimates
Jonah A. J. Duncan, Luc Nguyen
https://arxiv.org/abs/2507.16383

The fully nonlinear Loewner-Nirenberg problem: Liouville theorems and counterexamples to local boundary estimates
In this paper we give a complete classification of positive viscosity solutions $w$ to conformally invariant equations of the form \begin{align}\label{ab}\tag{$*$} \begin{cases} f(λ(-A_w)) = \frac{1}{2}, \quad λ(-A_w)\inΓ& \text{in }\mathbb{R}_+^n \newline w = 0 & \text{on }\partial\mathbb{R}_+^n, \end{cases} \end{align} where $A_w$ is the Schouten tensor of the metric $g_w = w^{-2}|dx|^2$, $Γ\subset\mathbb{R}^n$ is a symmetric convex cone and $f$ is an associated de…