Tootfinder

Coherent motions to predict Lagrangian trajectories
Ali R Khojasteh, Dominique Heitz
https://arxiv.org/abs/2508.21191 https://arxiv.org/pdf/2508.21191

Coherent motions to predict Lagrangian trajectories
Accurate prediction of Lagrangian trajectories in turbulent flow remains challenging due to limited temporal information in transport functions. This paper shows that even with sparse temporal observations, there might be enough information from surrounding coherent motions, sharing the same dynamics, to provide highly probable trajectories. The proposed coherent predictor is derived from the concept of Lagrangian coherent structures (LCSs), which are advective transport barriers that govern th…

Shifted Lagrangian thickenings of shifted Poisson derived schemes
Nikola Tomi\'c
https://arxiv.org/abs/2506.23348 https://arxiv.o…

Shifted Lagrangian thickenings of shifted Poisson derived schemes
We prove that the space of shifted Poisson structures on a derived scheme $X$ locally of finite presentation is equivalent to the space of shifted Lagrangian thickenings out $X$, solving a conjecture in shifted Poisson geometry. As a corollary, we show that for $M$ a compact oriented $d$-dimensional manifold and an $n$-shifted Poisson structure on $X$, the mapping stack $\mathrm{Map}(M,X)$ has an $(n-d)$-shifted Poisson structure. It extends a known theorem for shifted symplectic structures to …

Anomalous Couplings from the Electroweak Chiral Lagrangian for Off-Shell Higgs in $gg\to Z_L Z_L$
Gerhard Buchalla, Florian Pandler
https://arxiv.org/abs/2507.23658 https://

Anomalous Couplings from the Electroweak Chiral Lagrangian for Off-Shell Higgs in $gg\to Z_L Z_L$
We investigate the production of (longitudinal) $Z$-boson pairs in gluon fusion as a probe of anomalous Higgs couplings. Of particular interest is the kinematic region of large center-of-mass energy, where the Higgs-boson is highly off-shell. We employ the electroweak chiral Lagrangian with a light Higgs, which is the most natural effective field theory (EFT) for this process. We demonstrate this by a detailed analysis of the leading and next-to-leading EFT contributions to the amplitude, at le…

One-Loop Nonlinear Matter Power Spectrum from Unified Lagrangian Perturbation Theory: Fast Computation and Comparison with Emulators
Naonori Sugiyama
https://arxiv.org/abs/2508.21275

One-Loop Nonlinear Matter Power Spectrum from Unified Lagrangian Perturbation Theory: Fast Computation and Comparison with Emulators
We present a fast and accurate formulation for computing the nonlinear matter power spectrum at one-loop order based on Unified Lagrangian Perturbation Theory (ULPT). ULPT decomposes the density field into the Jacobian deviation, capturing intrinsic nonlinear growth, and the displacement-mapping factor, accounting for large-scale distortions due to bulk flows. This structural separation leads to a natural division of the power spectrum into a source term and a displacement-mapping factor, ensur…

EL-AGHF: Extended Lagrangian Affine Geometric Heat Flow
Sangmin Kim, Hae-Won Park
https://arxiv.org/abs/2505.24751 https://arxiv.org/…

EL-AGHF: Extended Lagrangian Affine Geometric Heat Flow
We propose a constrained Affine Geometric Heat Flow (AGHF) method that evolves so as to suppress the dynamics gaps associated with inadmissible control directions. AGHF provides a unified framework applicable to a wide range of motion planning problems, including both holonomic and non-holonomic systems. However, to generate admissible trajectories, it requires assigning infinite penalties to inadmissible control directions. This design choice, while theoretically valid, often leads to high com…

Augmented Lagrangian methods for infeasible convex optimization problems and diverging proximal-point algorithms
Roland Andrews, Justin Carpentier, Adrien Taylor
https://arxiv.org/abs/2506.22428

Augmented Lagrangian methods for infeasible convex optimization problems and diverging proximal-point algorithms
This work investigates the convergence behavior of augmented Lagrangian methods (ALMs) when applied to convex optimization problems that may be infeasible. ALMs are a popular class of algorithms for solving constrained optimization problems. We establish progressively stronger convergence results, ranging from basic sequence convergence to precise convergence rates, under a hierarchy of assumptions. In particular, we demonstrate that, under mild assumptions, the sequences of iterates generated …

Wess-Zumino-Witten Interactions of Axions: Three-Flavor
Yang Bai, Ting-Kuo Chen, Jia Liu, Xiaolin Ma
https://arxiv.org/abs/2505.24822 https://

Wess-Zumino-Witten Interactions of Axions: Three-Flavor
We present a complete Lagrangian describing axion interactions with pseudoscalar and (axial-)vector mesons within the three light-flavor quark framework. This formulation incorporates both the standard chiral Lagrangian and the full Wess-Zumino-Witten (WZW) term. By including instanton effects associated with the anomalous $U(1)_A$ symmetry, we demonstrate that physical observables remain invariant under arbitrary chiral phase rotations of the quark fields. This comprehensive Lagrangian provide…

Replaced article(s) found for cs.CV. https://arxiv.org/list/cs.CV/new
[4/4]:
- Fully Differentiable Lagrangian Convolutional Neural Network for Physics-Informed Precipitation N...
Peter Pavl\'ik, Martin V\'yboh, Anna Bou Ezzeddine, Viera Rozinajov\'a

Tightness of Chekanov's bound on displacement energy for some Lagrangian knots
David Keren Yaar
https://arxiv.org/abs/2507.21282 https://arxiv.org/pdf/…

Tightness of Chekanov's bound on displacement energy for some Lagrangian knots
By a classical theorem of Chekanov, the displacement energy, $e$, of a Lagrangian submanifold is bounded from below by the minimal area of pseudo-holomorphic disks with boundary on the Lagrangian, $\hbar$. We compute $e$ and $\hbar$ for displaceable Chekanov tori in $\mathbb{C}P^n$, and for an infinite family of exotic tori in $\mathbb{C}^3$ constructed by Brendel. In these families, $e=\hbar$. We compare continuity properties of $e$ and $\hbar$ on the space of Lagrangians. This provides an e…

Lagrangian Finite-Time Fluctuation Relation in isotropic turbulence
Hanxun Yao, Tamer A. Zaki, Charles Meneveau
https://arxiv.org/abs/2506.23336 https://…

Lagrangian Finite-Time Fluctuation Relation in isotropic turbulence
The entropy generation rate in turbulence can be defined using the energy cascade rate as described in the scale-integrated Kolmogorov-Hill equation at a specified length scale. The fluctuation relation (FR) from non-equilibrium thermodynamics, which predicts exponential behaviour of the ratio of probability densities for positive and negative entropy production rates, was confirmed in prior work \citep{yao2023entropy}, but under certain limiting assumptions. We here examine the applicability o…

Constrained Dynamics on Eccentric Conic Orbits: Dirac-Bergmann and Hamilton-Jacobi Approaches
Alejandro G. Andarcia-Caballero, Jaime Manuel-Cabrera, Luis G. Romero-Hern\'andez, Jorge M. Paulin-Fuentes
https://arxiv.org/abs/2507.23271

Constrained Dynamics on Eccentric Conic Orbits: Dirac-Bergmann and Hamilton-Jacobi Approaches
In this work, we investigate a Lagrangian model describing a particle constrained to move along non-degenerate conic sections, parameterized by the orbital eccentricity \( e \). In the non-relativistic regime, we apply the Dirac--Bergmann algorithm to identify a set of four second-class constraints, compute the corresponding Dirac brackets, and isolate the true physical degrees of freedom. This procedure yields a unified Hamiltonian treatment of circular (\( e = 0 \)), elliptical (\( 0 < e < 1 …

Macroscopic fluctuation theory from a Lagrangian viewpoint and the Schr\"odinger problem
L. Bertini, D. Gabrielli, G. Jona-Lasinio
https://arxiv.org/abs/2506.22085

Macroscopic fluctuation theory from a Lagrangian viewpoint and the Schrödinger problem
We formulate the Schrödinger problem for interacting particle systems in the hydrodynamical regime thus extending the standard setting of independent particles. This involves the large deviations rate function for the empirical measure which is in fact a richer observable than the hydrodynamic observables density and current. In the case in which the constraints are the initial and final density, we characterize the optimal measure for the Schrödinger problem. We also introduce versions of th…

Existence and spectral stability analysis of viscous-dispersive shock profiles for isentropic compressible fluids of Korteweg type
R. Folino, C. Lattanzio, R. G. Plaza
https://arxiv.org/abs/2507.00374

Existence and spectral stability analysis of viscous-dispersive shock profiles for isentropic compressible fluids of Korteweg type
The system describing the dynamics of a compressible isentropic fluid exhibiting viscosity and internal capillarity in one space dimension and in Lagrangian coordinates, is considered. It is assumed that the viscosity and the capillarity coefficients are nonlinear smooth, positive functions of the specific volume, making the system the most general case possible. It is shown, under very general circumstances, that the system admits traveling wave solutions connecting two constant states and tra…

Variational hydrodynamics of the classical Yukawa one-component plasma
Daniels Krimans, Hanno K\"ahlert
https://arxiv.org/abs/2506.23006 https://

Variational hydrodynamics of the classical Yukawa one-component plasma
We consider a recently developed variational approach to the hydrodynamics of strongly coupled plasmas [D. Krimans and S. Putterman, Phys. Fluids 36, 037131 (2024)] and extend it to the Yukawa one-component plasma. This approach generalizes the ordinary hydrodynamic equations to finite length scales by explicitly including terms that depend on the pair distribution function. After discussing the form of the Lagrangian, we derive equations of motion and explicit formulas for the momentum and ene…

Instantons and topological order in two-leg electron ladders: A universality class
S. -R. Eric Yang, Hyun Cheol Lee, Hoang-Anh Le, In-Hwan Lee
https://arxiv.org/abs/2505.24130

Instantons and topological order in two-leg electron ladders: A universality class
Our numerical study of the disordered Hubbard model with nearest-neighbor hopping shows that a two-leg electron ladder has a finite topological entanglement entropy in the regime where the density of states exhibits an exponentially decaying gap. The value of the topological entanglement entropy suggests that two-leg ladders belong to the same universality class as graphene zigzag nanoribbons, despite several structural differences. A Shankar-Witten-type bosonization Lagrangian with disorder ca…

Fast Methods For Multisite Charge Transfer Processes II: Analytic Nuclear Gradients and Nonadiabatic Dynamics For cCASSCF(1,M) and cCASSCF(2M-1,M) Wavefunctions
Tian Qiu, Joseph E. Subotnik
https://arxiv.org/abs/2508.21139

Fast Methods For Multisite Charge Transfer Processes II: Analytic Nuclear Gradients and Nonadiabatic Dynamics For cCASSCF(1,M) and cCASSCF(2M-1,M) Wavefunctions
We derive and implement analytic nuclear gradients and derivative couplings for a constrained Complete Active Space Self-Consistent Field with a small active space designed to model electron or hole transfer. Using a Lagrangian formalism, we are able to differentiate both the CASSCF energy and the constraint (which is required for globally smooth surfaces), and the resulting efficient algorithm can be immediately applied to nonadiabatic dynamics simulations of charge transfer processes. Here, w…

Boundedness of some fibered K-trivial varieties
Philip Engel, Stefano Filipazzi, Fran\c{c}ois Greer, Mirko Mauri, Roberto Svaldi
https://arxiv.org/abs/2507.00973

Boundedness of some fibered K-trivial varieties
We prove that irreducible Calabi-Yau varieties of a fixed dimension, admitting a fibration by abelian varieties or primitive symplectic varieties of a fixed analytic deformation class, are birationally bounded. We prove that there are only finitely many deformation classes of primitive symplectic varieties of a fixed dimension, admitting a Lagrangian fibration. We also show that fibered Calabi-Yau 3-folds are bounded. Conditional on the generalized abundance or hyperkähler SYZ conjecture, our …

The Chiral Limit of Fully Nonlinear Minimal Massive Gravity
Massimo Porrati, Xilin Sheng
https://arxiv.org/abs/2507.22762 https://arxiv.org/pdf/2507.22762

The Chiral Limit of Fully Nonlinear Minimal Massive Gravity
We study 3D Anti de Sitter Minimal Massive Gravity near the chiral limit where one of the boundary Brown-Henneaux central charges vanishes and two modes become null. We go beyond the known free-theory analysis to prove that these modes decouple completely also in the full MMG Lagrangian and field equations. We also use the full action to ascertain if the interacting theory becomes infinitely strongly coupled in the chiral limit. We show that this is not the case at tree level but that a strong …

An Efficient Alternating Minimization Algorithm for Computing Quantum Rate-Distortion Function
Lingyi Chen, Deheng Yuan, Wenyi Zhang, Hao Wu, Huihui Wu
https://arxiv.org/abs/2507.19920

An Efficient Alternating Minimization Algorithm for Computing Quantum Rate-Distortion Function
We consider the computation of the entanglement-assisted quantum rate-distortion function, which plays a central role in quantum information theory. We propose an efficient alternating minimization algorithm based on the Lagrangian analysis. Instead of fixing the multiplier corresponding to the distortion constraint, we update the multiplier in each iteration. Hence the algorithm solves the original problem itself, rather than the Lagrangian relaxation of it. Moreover, all the other variables a…

Configurations of Lagrangian spheres in $K3$ surfaces
Juan Mu\~noz-Ech\'aniz
https://arxiv.org/abs/2507.15039 https://arxiv.org/pdf/2507.15039

Configurations of Lagrangian spheres in $K3$ surfaces
We study Dehn--Seidel twists on configurations of Lagrangian spheres in symplectic $K3$ surfaces, using tools from Seiberg--Witten theory. In the case of $ADE$ configurations of Lagrangian spheres, we prove that a naturally associated representation of the generalised Braid group in the symplectic mapping class group is always faithful after abelianising, in a suitable sense. More generally, we prove that squared Dehn--Seidel twists on homologically-distinct Lagrangian spheres are algebraically…

Conditionally adaptive augmented Lagrangian method for physics-informed learning of forward and inverse problems using artificial neural networks
Qifeng Hu, Shamsulhaq Basir, Inanc Senocak
https://arxiv.org/abs/2508.15695

Conditionally adaptive augmented Lagrangian method for physics-informed learning of forward and inverse problems using artificial neural networks
We present several advances to the physics and equality constrained artificial neural networks (PECANN) framework that substantially improve its capability to learn solutions of canonical partial differential equations (PDEs). First, we generalize the augmented Lagrangian method (ALM) to support multiple independent penalty parameters, enabling simultaneous enforcement of heterogeneous constraints. Second, we reformulate pointwise constraint enforcement and Lagrange multipliers as expectations …

On Lagrangian barriers and applications of Non-Squeezing
Alejandro Vicente
https://arxiv.org/abs/2507.20222 https://arxiv.org/pdf/2507.20222

On Lagrangian barriers and applications of Non-Squeezing
In this note we show the existence of Lagrangian barriers in a certain class of domains in $\mathbb{R}^{2n}$, including dual Lagrangian products and some ``sufficiently" round domains. Many of these results come as applications of the Non-Squeezing Theorem. We also give a new interesting application of the Non-Squeezing Theorem and the Symplectic Camel Theorem.

McGehee blowup for Lagrangian systems and instability of equilibria
J. M. Burgos
https://arxiv.org/abs/2506.19135 https://arxiv.org/p…

McGehee blowup for Lagrangian systems and instability of equilibria
We prove that total instability is a generic phenomenon in the real analytic class of electromagnetic Lagrangian systems under a weak magnetism hypothesis. The main object in the proof is an adaptation of the McGehee blowup for these systems. Together with this result, new criteria for total instability are introduced for both generic and non-generic cases.

Convexity and the degenerate special Lagrangian equation
Vasanth Pidaparthy, Yanir A. Rubinstein
https://arxiv.org/abs/2507.17018 https://arxiv.org/pdf/250…

Convexity and the degenerate special Lagrangian equation
In 2015 Rubinstein--Solomon introduced the degenerate special Lagrangian equation (DSL) that governs geodesics in the space of positive Lagrangians, showed that subsolutions in the top branch of DSL are convex in space, and raised the question of whether they should be convex in space-time and whether subsolutions in the second branch possess any convexity properties. In 2019, Darvas--Rubinstein gave a partial answer to the first problem by showing subsolutions in the top branch must be bi-conv…

Proximal aiming in weak KAM theory with nonsmooth Lagrangian
Yurii Averboukh
https://arxiv.org/abs/2506.21373 https://arxiv.org/pdf/2…

Proximal aiming in weak KAM theory with nonsmooth Lagrangian
This work extends weak KAM theory to the case of a nonsmooth Lagrangian satisfying a superlinear growth condition. Using the solution of a weak KAM equation that is a stationary Hamilton-Jacobi equation and the proximal aiming method, we construct a family of discontinuous feedback strategies that are nearly optimal for every time interval. This result leads to an analogue of the weak KAM theorem. Additionally, as in classical weak KAM theory, we demonstrate that the effective Hamiltonian (Mañ…

TURB-Smoke. A database of Lagrangian pollutants emitted from point-sources and dispersed in turbulent flows
Luca Biferale, Fabio Bonaccorso, Niccol\`o Cocciaglia, Robin A. Heinonen, Lorenzo Piro
https://arxiv.org/abs/2507.22749

TURB-Smoke. A database of Lagrangian pollutants emitted from point-sources and dispersed in turbulent flows
Identifying the location and characteristics of pollution sources in turbulent flows is challenging, especially for environmental monitoring and emergency response, due to sparse, stochastic, and infrequent cue detection. Even in idealized settings, accurately modeling these phenomena remains highly complex, with realistic representations typically achievable only through experimental or simulation-based data. We introduce TURB-Smoke, a cutting-edge numerical dataset designed for investigating …

Chaoticus: a parallel approach to the computation of chaos indicators
Javier Jim\'enez-L\'opez, Jos\'e S\'aez-Landete, Victor J. Garc\'ia-Garrido
https://arxiv.org/abs/2507.00622

Chaoticus: a parallel approach to the computation of chaos indicators
In this paper we present Chaoticus, a Python-based package for the GPU-accelerated integration of ODE systems and the computation of chaos indicators, including SALI, GALI, Lagrangian Descriptors based indicators and the Lyapunov exponent spectrum. By leveraging GPU parallelization, our package significantly reduces the computation times by several orders of magnitude compared to CPU-based approaches. This significant reduction in computing time facilitates the generation of extensive datasets,…

Gromov-Witten invariants of log Calabi-Yau 3-folds are holomorphic lagrangian correspondences
Brett Parker
https://arxiv.org/abs/2506.20092 https://…

Gromov-Witten invariants of log Calabi-Yau 3-folds are holomorphic lagrangian correspondences
We introduce a holomorphic version of Weinstein's symplectic category, in which objects are holomorphic symplectic manifolds, and morphisms are holomorphic lagrangian correspondences. We then extend this category to log schemes, and prove that Gromov-Witten invariants of log Calabi-Yau 3-folds are naturally encoded as holomorphic lagrangian correspondences. Gromov-Witten invariants and Donaldson-Thomas invariants are then conjecturally related by a natural unitary lagrangian correspondence.

Production of the $ X(3872)$ state via the $B^0 \to K^{\ast 0} X(3872)$ decay
Luciano M. Abreu
https://arxiv.org/abs/2508.21223 https://arxiv.org/pdf/2508.…

Production of the $ X(3872)$ state via the $B^0 \to K^{\ast 0} X(3872)$ decay
In this work the production of the state $X(3872)$ is estimated via the reaction $B^0 \to K^{\ast 0} X(3872)$ through triangle mechanisms described by the sequence $B^0 \to D_s^{(*)+} (\to K^{\ast 0} D^{(*)+} ) \ D^{(*)-} \to K^{\ast 0} \ ( D^{(*)+} D^{(*)-} ) \to K^{\ast 0} X(3872) $. The molecular configuration $(D\bar D^* - c.c. )$ of the $X(3872)$ is considered. By means of the effective Lagrangian approach, the branching ratio $\mathcal{B}(B^0 \to K^{\ast 0} X(3872))$ is calculated as a fu…

A Unified Lagrangian Framework for Galaxy Clustering: Consistent Modeling of Bias, Redshift-Space Distortions, and Reconstruction
Naonori Sugiyama
https://arxiv.org/abs/2508.17331

A Unified Lagrangian Framework for Galaxy Clustering: Consistent Modeling of Bias, Redshift-Space Distortions, and Reconstruction
We present \emph{Unified Lagrangian Perturbation Theory} (ULPT), a perturbative framework for consistently modeling galaxy density fluctuations across real space, redshift space, and post-reconstruction fields. Unlike existing approaches that treat these cases separately, ULPT provides a single theoretical structure that incorporates the three essential coordinate mappings: the Lagrangian-to-Eulerian transformation, the real-to-redshift mapping induced by peculiar velocities, and the remapping …

Structure Preserving Finite Volume Schemes on Voronoi Grids: Curl Involution, Asymptotic Limit and Thermodynamics
Walter Boscheri, Firas Dhaouadi
https://arxiv.org/abs/2507.21351

Structure Preserving Finite Volume Schemes on Voronoi Grids: Curl Involution, Asymptotic Limit and Thermodynamics
We propose a new curl-free and thermodynamically compatible finite volume scheme on Voronoi grids to solve compressible heat conducting flows written in first-order hyperbolic form. The approach is based on the definition of compatible discrete curl-grad operators, exploiting the triangular nature of the dual mesh. We design a cell solver reminiscent of the nodal solvers used in Lagrangian schemes to discretize the evolution equation for the thermal impulse vector, and we demonstrate that the r…

Lagrangian Simulation Volume-Based Contour Tree Simplification
Domantas Dilys, Hamish Carr, Steven Boeing
https://arxiv.org/abs/2508.14339 https://arxiv.or…

Lagrangian Simulation Volume-Based Contour Tree Simplification
Many scientific and engineering problems are modelled by simulating scalar fields defined either on space-filling meshes (Eulerian) or as particles (Lagrangian). For analysis and visualization, topological primitives such as contour trees can be used, but these often need simplification to filter out small-scale features. For parcel-based convective cloud simulations, simplification of the contour tree requires a volumetric measure rather than persistence. Unlike for cubic meshes, volume cannot…

Some Lagrangian quiver Grassmannians for the equioriented cycle
Matteo Micheli
https://arxiv.org/abs/2507.15841 https://arxiv.org/pdf…

Some Lagrangian quiver Grassmannians for the equioriented cycle
The goal of this paper is to better understand a family of linear degenerations of the classical Lagrangian Grassmannians $Λ(2n)$. It is the special case for $k=n$ of the varieties $X(k,2n)^{sp}$, introduced in previous joint work with Evgeny Feigin, Martina Lanini and Alexander Pütz. These varieties are obtained as isotropic subvarieties of a family of quiver Grassmannians $X(n,2n)$, and are acted on by a linear degeneration of the algebraic group $Sp_{2n}$. We prove a conjecture proposed in…

Consistent quantum treatments of non-convex kinetic energies
C. Koliofoti, M. A. Javed, R. -P. Riwar
https://arxiv.org/abs/2507.21993 https://arxiv.org/pdf…

Consistent quantum treatments of non-convex kinetic energies
The task of finding a consistent relationship between a quantum Hamiltonian and a classical Lagrangian is of utmost importance for basic, but ubiquitous techniques like canonical quantization and path integrals. Nonconvex kinetic energies (which appear, e.g., in Wilczek and Shapere's classical time crystal, or nonlinear capacitors) pose a fundamental problem: the Legendre transformation is ill-defined, and the more general Legendre-Fenchel transformation removes nonconvexity essentially by defi…

Shadow excited state molecular dynamics with the \DeltaSCF method
O. Jonathan Fajen (Department of Chemistry and PULSE Institute, Stanford University, SLAC National Accelerator Laboratory, Theoretical Division, Los Alamos National Laboratory), Oscar Gr\r{a}n\"as (Division of Materials Theory, Department of Physics and Astronomy, Uppsala University), Todd J. Mart\'inez (Department of Chemistry and PULSE Institute, Stanford University, SLAC National Accelerator Laboratory), Ande…

Shadow excited state molecular dynamics with the \DeltaSCF method
We present an extension of the shadow extended Lagrangian Born-Oppenheimer molecular dynamics (XL-BOMD) method to excited state molecular dynamics (ESMD) in the context of \DeltaSCF Kohn-Sham density functional theory, with demonstrations performed using self-consistent charge density functional tight binding (SCC-DFTB) theory. In this shadow ESMD approach, the approximate iterative solution to the exact potential in conventional ESMD is replaced by an exact single-step solution to an approxima…

Nodal Tangles
Joel Schmitz
https://arxiv.org/abs/2506.23754 https://arxiv.org/pdf/2506.23754

Nodal Tangles
We study piecewise linear knot diagrams in the base of almost toric fibrations of symplectic four-manifolds. These diagrams translate to deformations of the almost toric fibration. We give several applications to symplectic topology, among them a proof of a conjecture by Symington, the calculation of the displacement energy for many fibres of toric moment maps, and an elementary recipe for building and distinguishing Lagrangian torus knots.

Cosmology with Distinct Functions $f$ of the Non-metricity Scalar $Q$ : A Dynamical System Approach
Promila Biswas, Subhajit Pal, Ritabrata Biswas, Satyajit Pal
https://arxiv.org/abs/2506.21646

Cosmology with Distinct Functions $f$ of the Non-metricity Scalar $Q$ : A Dynamical System Approach
Symmetric teleparallel gravity is one among the general relativistic trinity which deals with the non-metricity scalar $Q$. In the Einstein Hilbert action, a function of $Q$ is chosen to be the main contributory part of the Lagrangian and a modified theory of gravity is constructed. In literature, different structures of the function of $Q$ are found which sustain several astrophysical observations like Big Bang nucleosynthesis, late-time cosmic acceleration etc. Autonomous systems for each suc…

Deterministic diffusion models for Lagrangian turbulence: robustness and encoding of extreme events
Tianyi Li, Flavio Tuteri, Michele Buzzicotti, Fabio Bonaccorso, Luca Biferale
https://arxiv.org/abs/2507.19103

Deterministic diffusion models for Lagrangian turbulence: robustness and encoding of extreme events
Modeling Lagrangian turbulence remains a fundamental challenge due to its multiscale, intermittent, and non-Gaussian nature. Recent advances in data-driven diffusion models have enabled the generation of realistic Lagrangian velocity trajectories that accurately reproduce statistical properties across scales and capture rare extreme events. This study investigates three key aspects of diffusion-based modeling for Lagrangian turbulence. First, we assess architectural robustness by comparing a U-…

Polarization Probes of New Physics in Lepton-Flavor-Violating Hyperon Production from $e^- N \to \tau^- Y$ Scattering
Xin-Shuai Yan, Zhen-Qing Hu, Qin Chang, Ya-Dong Yang
https://arxiv.org/abs/2506.23804

Polarization Probes of New Physics in Lepton-Flavor-Violating Hyperon Production from $e^- N \to τ^- Y$ Scattering
While charged lepton-flavor-violating tau decays to strange mesons provide powerful probes of the underlying $τ\to\ell d \bar{s}$ transition, the corresponding decay modes involving hyperons are kinematically forbidden. To address this gap, we propose the quasi-elastic scattering processes $e^- N \to τ^- Y$. Within a general low-energy effective Lagrangian, we perform a comprehensive analysis of the final-state polarizations of both the $τ$ lepton and the hyperon $Y$, systematically addressi…

Covariant phase space and $L_\infty$ algebras
Vin\'icius Bernardes, Theodore Erler, Atakan Hilmi F{\i}rat
https://arxiv.org/abs/2506.20706 https://

Covariant phase space and $L_\infty$ algebras
We propose a symplectic structure for the phase space of a generic Lagrangian field theory expressed in the framework of $L_\infty$ algebras. The symplectic structure does not require explicit knowledge of the derivative content of the Lagrangian, and therefore is applicable to nonlocal models, such as string field theory, where traditional constructions are difficult to apply. We test our proposal in a number of examples ranging from general relativity to $p$-adic string theory.

Special Lagrangian sections and stability conditions on threefolds
Jacopo Stoppa
https://arxiv.org/abs/2508.17709 https://arxiv.org/pdf/2508.17709

Special Lagrangian sections and stability conditions on threefolds
We study a class of Lagrangian submanifolds, given by sections of a special Lagrangian fibration, contained in certain almost Calabi-Yau threefolds (mirrors of polarised toric threefolds satisfying suitable assumptions). We show that, for a Lagrangian section $L$ in this class, the shift $L[2]$ defines an object in the heart of a natural Bridgeland stability condition on the relevant Fukaya-Seidel category, and that if $L[2]$ is semistable with respect to this stability condition, then it is is…

Pre-Lagrangian tori transverse to an Anosov flow
Francesco Ruscelli
https://arxiv.org/abs/2508.17396 https://arxiv.org/pdf/2508.17396

Pre-Lagrangian tori transverse to an Anosov flow
An Anosov flow on a smooth three-manifold \( M \) gives rise to a Liouville structure on \( \mathbb{R} \times M \) by a construction of Mitsumatsu. In a recent paper, Cieliebak, Lazarev, Massoni and Moreno ask whether an embedded torus \( Σ\subseteq M \) transverse to an Anosov flow gives rise to a Lagrangian in \( \mathbb{R} \times M \). We show that the answer to this question is in general negative by finding a topological obstruction related to the foliations induced on the torus by the we…

Orthogonality conditions for convex regression
Sheng Dai, Timo Kuosmanen, Xun Zhou
https://arxiv.org/abs/2506.21110 https://arxiv.org…

Orthogonality conditions for convex regression
Econometric identification generally relies on orthogonality conditions, which usually state that the random error term is uncorrelated with the explanatory variables. In convex regression, the orthogonality conditions for identification are unknown. Applying Lagrangian duality theory, we establish the sample orthogonality conditions for convex regression, including additive and multiplicative formulations of the regression model, with and without monotonicity and homogeneity constraints. We th…

Replaced article(s) found for cs.ET. https://arxiv.org/list/cs.ET/new
[1/1]:
- Lagrangian neural networks for nonholonomic mechanics
Viviana Alejandra Diaz, Leandro Martin Salomone, Marcela Zuccalli

Eight-Dimensional Symplectic Nilpotent Lie Groups with Lagrangian Normal Subgroups: A Complete Classification
T. A\"it Aissa, M. W. Mansouri
https://arxiv.org/abs/2508.16978

Eight-Dimensional Symplectic Nilpotent Lie Groups with Lagrangian Normal Subgroups: A Complete Classification
We investigate symplectic nilpotent Lie groups with Lagrangian normal subgroups. We show that there exists a bijection between the isomorphism classes of nilpotent Lie groups with Lagrangian normal subgroups and the isomorphism classes of geodesically complete, flat, nilpotent Lie groups with Lagrangian extension cohomology class. Finally, we provide a complete classification of eight-dimensional symplectic nilpotent Lie groups with Lagrangian normal subgroups, identifying exactly ninety-five s…

Unsteady solutions of the spray flamelet equations
Felipe Huenchuguala, Francisco Rivadeneira, Arne Scholtissek, Christian Hasse, Eva Gutheil, Hernan Olguin
https://arxiv.org/abs/2506.23389

Unsteady solutions of the spray flamelet equations
Solutions of the spray flamelet equations reported in the literature during the last decade have been limited to very specific situations presenting steady evaporation profiles only. In contrast, intrinsically unsteady interactions between the liquid and gas phases have received little attention so far. In this work, the spray flamelet equations are closed by means of a Lagrangian description of the liquid phase in mixture fraction space, which allows solving them for unsteady situations. The r…

A local sign decomposition for symplectic self-dual Galois representations of rank two
Ashay Burungale, Shinichi Kobayashi, Kentaro Nakamura, Kazuto Ota
https://arxiv.org/abs/2508.17776

A local sign decomposition for symplectic self-dual Galois representations of rank two
We prove the existence of a new structure on the first Galois cohomology of generic families of symplectic self-dual $p$-adic representations of $G_{\mathbb{Q}_p}$ of rank two (a local sign decomposition): a functorial decomposition into free rank one Lagrangian submodules which encodes the $p$-adic variation of Bloch--Kato subgroups via completed epsilon constants, mirroring a symplectic structure. The local sign decomposition has diverse local as well as global arithmetic consequences. This…

Cutting Slack: Quantum Optimization with Slack-Free Methods for Combinatorial Benchmarks
Monit Sharma, Hoong Chuin Lau
https://arxiv.org/abs/2507.12159 htt…

Cutting Slack: Quantum Optimization with Slack-Free Methods for Combinatorial Benchmarks
Constraint handling remains a key bottleneck in quantum combinatorial optimization. While slack-variable-based encodings are straightforward, they significantly increase qubit counts and circuit depth, challenging the scalability of quantum solvers. In this work, we investigate a suite of Lagrangian-based optimization techniques including dual ascent, bundle methods, cutting plane approaches, and augmented Lagrangian formulations for solving constrained combinatorial problems on quantum simulat…

Neural inference of fluid-structure interactions from sparse off-body measurements
Rui Tang, Ke Zhou, Jifu Tan, Samuel J. Grauer
https://arxiv.org/abs/2506.23480

Neural inference of fluid-structure interactions from sparse off-body measurements
We report a novel physics-informed neural framework for reconstructing unsteady fluid-structure interactions (FSI) from sparse, single-phase observations of the flow. Our approach combines modal surface models with coordinate neural representations of the fluid and solid dynamics, constrained by the fluid's governing equations and an interface condition. Using only off-body Lagrangian particle tracks and a moving-wall boundary condition, the method infers both flow fields and structural motion.…

Asymptotic behavior at infinity and existence of solutions to the Lagrangian mean curvature flow equation in $\mathbb R^{n 1}_-$
Jiguang Bao, Zixiao Liu
https://arxiv.org/abs/2507.16129

Asymptotic behavior at infinity and existence of solutions to the Lagrangian mean curvature flow equation in $\mathbb R^{n+1}_-$
This paper investigates the asymptotic behavior at infinity of ancient solutions to the Lagrangian mean curvature flow equation. Under conditions that admit Liouville type rigidity theorems, we prove that every classical solution converges exponentially to a quadratic polynomial of form $τt+\frac{1}{2}x'Ax+bx+c$ at infinity, with an explicitly derived convergence rate. Furthermore, we investigate Dirichlet type problems with prescribed asymptotic behavior, featuring two key innovations: applic…

BSM: Extended Scalar Sectors
Tania Robens, Rui Santos
https://arxiv.org/abs/2507.21910 https://arxiv.org/pdf/2507.21910

BSM: Extended Scalar Sectors
In particle physics the world is described by a function, the Lagrangian. Each of its sectors characterizes the interactions between the particles of the Standard Model (SM). The addition of hypothetical new particles is done by including new terms in the Lagrangian. The scalar or Higgs sector of the SM is built with only one scalar complex field and it is extended by including new spin zero fields. This can help to solve questions that cannot be answered by the SM alone, like introducing dark …

Parameterized Lagrangian Floer homotopy
Kenneth Blakey, Ciprian Mircea Bonciocat
https://arxiv.org/abs/2506.20122 https://arxiv.org/p…

Parameterized Lagrangian Floer homotopy
We construct the Lagrangian Floer homotopy type, in the exact setting, as a spectrum parameterized over the moduli space of Maslov data. Our primary motivation for this construction is to provide stronger lower bounds for (possibly degenerate) Lagrangian intersections in plumbings of cotangent bundles.

Fourth- and Higher-Order Semi-Lagrangian Finite Volume Methods for the Two-dimensional Advection Equation on Arbitrarily Complex Domains
Yunxia Sun, Kaiyi Liang, Yuke Zhu, Zhi Lin, Qinghai Zhang
https://arxiv.org/abs/2506.15142

Fourth- and Higher-Order Semi-Lagrangian Finite Volume Methods for the Two-dimensional Advection Equation on Arbitrarily Complex Domains
To numerically solve the two-dimensional advection equation, we propose a family of fourth- and higher-order semi-Lagrangian finite volume (SLFV) methods that feature (1) fourth-, sixth-, and eighth-order convergence rates, (2) applicability to both regular and irregular domains with arbitrarily complex topology and geometry, (3) ease of handling both zero and nonzero source terms, and (4) the same algorithmic steps for both periodic and incoming penetration conditions. Test results confirm the…

Dynamics on Bi-Lagrangian Structures and Cherry maps
Bertuel Tangue Ndawa
https://arxiv.org/abs/2508.12350 https://arxiv.org/pdf/2508.12350

Dynamics on Bi-Lagrangian Structures and Cherry maps
We consider a bi-Lagrangian structure $(ω,\mathcal{F}_{1},\mathcal{F}_{2})$ on a manifold $M$, that is, $(M,ω,\mathcal{F}_{1},\mathcal{F}_{2})$ is a bi-Lagrangian manifold. We prolong bi-Lagrangian structures on $M$, and lift a dynamic on its tangent and cotangent bundles in different ways. In some cases, we show that the lifted structures are affine. In the case of the 2-dimensional torus, we find that an extension of the same dynamic on pairs of so-called Cherry vector fields induces a conj…

Lagrangian-based Equilibrium Propagation: generalisation to arbitrary boundary conditions & equivalence with Hamiltonian Echo Learning
Guillaume Pourcel, Debabrota Basu, Maxence Ernoult, Aditya Gilra
https://arxiv.org/abs/2506.06248

Lagrangian-based Equilibrium Propagation: generalisation to arbitrary boundary conditions & equivalence with Hamiltonian Echo Learning
Equilibrium Propagation (EP) is a learning algorithm for training Energy-based Models (EBMs) on static inputs which leverages the variational description of their fixed points. Extending EP to time-varying inputs is a challenging problem, as the variational description must apply to the entire system trajectory rather than just fixed points, and careful consideration of boundary conditions becomes essential. In this work, we present Generalized Lagrangian Equilibrium Propagation (GLEP), which e…

The trace of field equations for higher-derivative gravity and an equality associating the Lagrangian density with a divergence term
Jun-Jin Peng, Hua Li
https://arxiv.org/abs/2508.13549

The trace of field equations for higher-derivative gravity and an equality associating the Lagrangian density with a divergence term
We figure out the explicit expression for the trace of the field equations associated to higher derivative theories of gravity endowed with Lagrangians depending upon the metric and its Riemann tensor, together with arbitrary order covariant derivatives of the Riemann tensor. Then an equality linking the Lagrangian density with the divergence of a vector field is proposed under a constraint on the Lagrangian density. As a significant application, we further obtain an equality to establish the r…

Proper Orthogonal Decomposition-based Model-Order Reduction for Smoothed Particle Hydrodynamics Simulation
Lidong Fang, Zilong Song, Kirk Fraser, Faisal Habib, Christopher Drummond, Huaxiong Huang
https://arxiv.org/abs/2507.19825

Proper Orthogonal Decomposition-based Model-Order Reduction for Smoothed Particle Hydrodynamics Simulation
In this paper, we present a projection-based model-order reduction (MOR) technique for smoothed particle hydrodynamics (SPH) simulations, which is a mesh-free approach within the Lagrangian framework. Our approach utilizes the proper orthogonal decomposition (POD) technique to generate a subspace basis for the reduction process. The main objective of this study is to conduct an initial exploration of the feasibility of employing POD-based MOR (POD-MOR) in SPH simulations and to quantify the a…

The Augmented Mixing Method: Computing High-Accuracy Primal-Dual Solutions to Large-Scale SDPs via Column Updates
Daniel Brosch, Jan Schwiddessen, Angelika Wiegele
https://arxiv.org/abs/2507.20386

The Augmented Mixing Method: Computing High-Accuracy Primal-Dual Solutions to Large-Scale SDPs via Column Updates
The Burer-Monteiro factorization has become a powerful tool for solving large-scale semidefinite programs (SDPs), enabling recently developed low-rank solvers to tackle problems previously beyond reach. However, existing methods are typically designed to prioritize scalability over solution accuracy. We introduce the Augmented Mixing Method, a new algorithm that combines the Burer-Monteiro factorization with an inexact augmented Lagrangian framework and a block coordinate descent scheme. Our me…

Augmented Lagrangian methods produce cutting-edge magnetic coils for stellarator fusion reactors
Pedro F. Gil, Alan A. Kaptanoglu, Eve V. Stenson
https://arxiv.org/abs/2507.12681 …

Augmented Lagrangian methods produce cutting-edge magnetic coils for stellarator fusion reactors
Finding feasible coils for stellarator fusion devices is a crux of realizing this concept for future power plants. The coils must reproduce the physics properties of the target plasma while satisfying myriad engineering constraints. Current efforts struggle to navigate the highly nonconvex optimization landscape and result in suboptimal stellarator coils, and/or they end up spending considerable resources scanning the continuous parameter space. In this work, we present an augmented Lagrangian …

A Multidimensional Birkhoff Theorem for Recurrent Lagrangian Submanifolds by a Tonelli Hamiltonian
Skander Charfi
https://arxiv.org/abs/2507.14561 https://…

A Multidimensional Birkhoff Theorem for Recurrent Lagrangian Submanifolds by a Tonelli Hamiltonian
Consider a closed manifold $M$ and a time-periodic Tonelli Hamiltonian $H : \mathbb{R}/\mathbb{Z} \times T^*M \to \mathbb{R}$ with flow $ϕ_H$. Let $\mathcal{L} \subset T^*M$ be a Lagrangian submanifold Hamiltonianly isotopic to the zero section. We prove that if $ϕ_H^n(\mathcal{L})$ admits convergent subsequences in both positive and negative times, in the Hausdorff topology and with control on the Liouville primitives, to two Lagrangian submanifolds, then $\mathcal{L}$ is a graph over the ze…

Eulerian-Lagrangian scaling of the Lyapunov exponent in homogeneous turbulence
Jin Ge, Joran Rolland, John Christos Vassilicos
https://arxiv.org/abs/2507.19972 https://

Eulerian-Lagrangian scaling of the Lyapunov exponent in homogeneous turbulence
We present a heuristic derivation of the maximal Lyapunov exponent $γ$ of homogeneous turbulence which yields two new relations, a sweeping relation and the scaling of the uncertainty field's integral length $L_Δ$. These relations and the maximal Lyapunov exponent's scaling that they imply are confirmed by periodic turbulence simulations. As the Reynolds number $Re_\lammbda$ increases, $L_Δ$ and $γ^{-1}$ decrease towards values smaller than the Kolmogorov length and time scales.

Lagrangian Translating Solitons and Special Lagrangians in $\mathbb{C}^m$ with Symmetries
Wei-Bo Su, Albert Wood
https://arxiv.org/abs/2507.01345 https://

Lagrangian Translating Solitons and Special Lagrangians in $\mathbb{C}^m$ with Symmetries
We construct novel families of exact immersed and embedded Lagrangian translating solitons and special Lagrangian submanifolds in $\mathbb{C}^m$ that are invariant under the action of various admissible compact subgroups $G \leq \text{SU}(m-1)$ with cohomogeneity-two. These examples are obtained via an Ansatz generalising a construction of Castro-Lerma in $\mathbb{C}^2$. We give explicit examples of admissible group actions, including a full classification for $G$ simple. We also describe novel…

A Hybrid Particle-Continuum Method for Simulating Fast Ice via Subgrid Iceberg Interaction
Carolin Mehlmann, Saskia Kahl
https://arxiv.org/abs/2507.20306 https://

A Hybrid Particle-Continuum Method for Simulating Fast Ice via Subgrid Iceberg Interaction
A significant fraction (4%-13%) of Antarctic sea ice remains stationary as landfast sea-ice ("fast ice"), typically anchored by grounded icebergs. Current global climate models do not represent fast-ice formation due to iceberg grounding, as iceberg-sea-ice interaction mostly occurs at subgrid scales. We propose a novel subgrid-scale coupling mechanism between Lagrangian iceberg particles and an Eulerian sea-ice continuum model. This hybrid particle-continuum approach integrates feedback from i…

Representations of the Chekanov-Eliashberg algebra from closed exact Lagrangians I
Baptiste Chantraine, Georgios Dimitroglou Rizell, Paolo Ghiggini
https://arxiv.org/abs/2508.20964

Representations of the Chekanov-Eliashberg algebra from closed exact Lagrangians I
This is the first of a series of two articles aiming at relating the compact Fukaya category of a Weinstein manifold to the derived category of finite dimensional representations of the Chekanov-Eliashberg differential graded algebra of the attaching spheres of the critical handles. In this first article we associate a finite dimensional representation $V_L$ to any compact exact Lagrangian submanifold $L$ and prove that for two any such Lagrangian submanifolds $L_0$ and $L_1$ the isomorphism $$…

An augmented Lagrangian method for strongly regular minimizers in a class of convex composite optimization problems
Chengjing Wang, Peipei Tang
https://arxiv.org/abs/2507.12040

An augmented Lagrangian method for strongly regular minimizers in a class of convex composite optimization problems
In this paper, we study a class of convex composite optimization problems. We begin by characterizing the equivalence between the primal/dual strong second-order sufficient condition and the dual/primal nondegeneracy condition. Building on this foundation, we derive a specific set of equivalent conditions for the perturbation analysis of the problem. Furthermore, we employ the augmented Lagrangian method (ALM) to solve the problem and provide theoretical guarantees for its performance. Specific…

Theories of the gravity gauge type in de Sitter space
Julian Lang, Yasha Neiman
https://arxiv.org/abs/2506.16707 https://arxiv.org/pd…

Theories of the gravity+gauge type in de Sitter space
We study theories of the "General Relativity + Yang-Mills" type in 4d spacetime with cosmological constant, focusing on formulations where the basic variables are connections and curvatures (but no metric). We present a new Lagrangian for GR coupled to Yang-Mills, which uses the same kind of variables for both sectors, and has a manifest double-copy structure. This Lagrangian comes in both non-chiral (real) and chiral (complex) versions. The chiral version makes it easy to isolate the self-dual…

Vacuum energy in effective field theory of general relativity
E. Epelbaum, J. Gegelia, Ulf-G. Mei{\ss}ner
https://arxiv.org/abs/2506.19182 https://

Vacuum energy in effective field theory of general relativity
It is shown to all orders of perturbation theory that in the effective field theory of general relativity the condition of vanishing of the vacuum energy leads to the same value of the cosmological constant, viewed as a parameter of the effective Lagrangian, as obtained by demanding the consistency of the effective field theory in Minkowski background. The resulting effective action is characterized by the cosmological constant term that vanishes exactly.

CSST Cosmological Emulator III: Hybrid Lagrangian Bias Expansion Emulation of Galaxy Clustering
Shuren Zhou, Zhao Chen, Yu Yu
https://arxiv.org/abs/2506.04671

CSST Cosmological Emulator III: Hybrid Lagrangian Bias Expansion Emulation of Galaxy Clustering
Galaxy clustering is an important probe in the upcoming China Space Station Telescope (CSST) survey to understand the structure growth and reveal the nature of the dark sector. However, it is a long-term challenge to model this biased tracer and connect the observable to the underlying physics. In this work, we present a hybrid Lagrangian bias expansion emulator, combining the Lagrangian bias expansion and the accurate dynamical evolution from $N$-body simulation, to predict the power spectrum …

Numerical approximation of effective diffusivities in homogenization of nondivergence-form equations with large drift by a Lagrangian method
Timo Sprekeler, Han Wu, Zhiwen Zhang
https://arxiv.org/abs/2506.14073

Numerical approximation of effective diffusivities in homogenization of nondivergence-form equations with large drift by a Lagrangian method
In this paper, we study numerical methods for the homogenization of linear second-order elliptic equations in nondivergence-form with periodic diffusion coefficients and large drift terms. Upon noting that the effective diffusion matrix can be characterized through the long-time variance of an associated diffusion process, we construct a Lagrangian numerical scheme based on a direct simulation of the underlying stochastic differential equation and utilizing the framework of modified equations, …

Exact Lagrangian fillability of 3-braid closures
James Hughes, Jiajie Ma
https://arxiv.org/abs/2507.16747 https://arxiv.org/pdf/2507.16747

Exact Lagrangian fillability of 3-braid closures
We determine when a Legendrian quasipositive 3-braid closure in standard contact $\mathbb{R}^3$ admits an orientable or non-orientable exact Lagrangian filling. Our main result provides evidence for the orientable fillability conjecture of Hayden and Sabloff, showing that a 3-braid closure is orientably exact Lagrangian fillable if and only if it is quasipositive and the HOMFLY bound on its maximum Thurston-Bennequin number is sharp. Of possible independent interest, we construct explicit Legen…

Hermitian K-theory of Lagrangian Grassmannians via reducible Gorenstein models
Tao Huang, Heng Xie
https://arxiv.org/abs/2508.07166 https://arxiv.org/pdf/2…

Hermitian K-theory of Lagrangian Grassmannians via reducible Gorenstein models
We construct a family of moduli spaces, called generalized Lagrangian flag schemes, that are reducible Gorenstein (hence singular), and that admit well-behaved pushforward and pullback operations in Hermitian $K$-theory. These schemes arise naturally in our computations. Using them, we prove that the Hermitian $K$-theory of a Lagrangian Grassmannian over a regular base splits as a direct sum of copies of the base's (Hermitian) $K$-theory, indexed by certain shifted Young diagrams. The isomorphi…

This https://arxiv.org/abs/2309.09432 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Entire solutions of two-convex Lagrangian mean curvature flows
Given an entire $C^2$ function $u$ on $\mathbb{R}^n$, we consider the graph of $D u$ as a Lagrangian submanifold of $\mathbb{R}^{2n}$, and deform it by the mean curvature flow in $\mathbb{R}^{2n}$. This leads to the special Lagrangian evolution equation, a fully nonlinear Hessian type PDE. We prove long-time existence and convergence results under a 2-positivity assumption of $(I+(D^2 u)^2)^{-1}D^2 u$. Such results were previously known only under the stronger assumption of positivity of $D^2 u…

The Legendrian Hopf Link has exactly two Lagrangian fillings
Bryce Thomson
https://arxiv.org/abs/2506.15111 https://arxiv.org/pdf/250…

The Legendrian Hopf Link has exactly two Lagrangian fillings
We prove that there are precisely two embedded exact Lagrangian fillings of the standard Legendrian Hopf link, up to compactly supported Hamiltonian isotopy. It was known that the standard Legendrian Hopf link admitted at least two such Lagrangian fillings: we show these are all. Specifically, we use a type of neck-stretching procedure to construct a pseudoholomorphic conic fibration that makes a given arbitrary exact Lagrangian filling fiber over a real curve, under a global pseudoholomorphic …

New Lagrangian framework for optimality conditions in optimal control of second order systems
Michael Konopik, Sigrid Leyendecker, Sofya Maslovskaya, Sina Ober-Bl\"obaum, Rodrigo T. Sato Mart\'in de Almagro
https://arxiv.org/abs/2507.06024

New Lagrangian framework for optimality conditions in optimal control of second order systems
It has been shown recently that optimal control problems with the dynamical constraint given by a second order system admit a regular Lagrangian formulation. This implies that the optimality conditions can be obtained in a new form based on the variational approach. In this paper we extend the first order necessary optimality conditions obtained previously to second order optimality conditions and discuss the role of the new Lagrangian.

Determining the width of $D_{s0}^{*}(2317)$ by using $T_{c\bar{s}0}^{a}(2327)$ in a molecular frame
Zi-Li Yue, Quan-Yun Guo, Dian-Yong Chen, Elena Santopinto
https://arxiv.org/abs/2507.19641

Determining the width of $D_{s0}^{*}(2317)$ by using $T_{c\bar{s}0}^{a}(2327)$ in a molecular frame
Motivated by the recent observation of the open-charm tetraquark $T_{c\bar{s}0}^{a}(2327)$ by the LHCb Collaboration, as well as results from Lattice QCD calculations, we consider the $T_{c\bar{s}0}^{a}(2327)$ and the $D_{s0}^{*}(2317)$ as $DK$ molecular states, with $I(J^{P})$ equal to $1(0^{+})$ and $0(0^{+})$, respectively, and we investigate their strong decay behavior in an effective Lagrangian approach. Within the model parameter range, we can reproduce the $T_{c\bar{s}0}^{a}(2327)$ exper…

Exploring Dark Energy via Non-Minimal Coupling in $f(Q,L_m)$ Gravity with Gong-Zhang Parameterization
Yash B. Ingole, K. V. Somwanshi, S. R. Bhoyar, S. N. Bayaskar
https://arxiv.org/abs/2506.21083

Exploring Dark Energy via Non-Minimal Coupling in $f(Q,L_m)$ Gravity with Gong-Zhang Parameterization
In this study, we investigate the late-time accelerated expansion of the universe within the framework of non-minimally coupled $f(Q,L_m)$ gravity, where $Q$ is the non-metricity scalar and $L_m$ is the matter Lagrangian. We derive modified Friedmann equations in a flat FLRW background and employ the \textit{Gong-Zhang} parameterization for the DE equation of state (EoS), allowing an analytical form of the Hubble parameter $H(z)$. The model parameters are constrained using recent Cosmic Chronom…

Is memory all you need? Data-driven Mori-Zwanzig modeling of Lagrangian particle dynamics in turbulent flows
Xander de Wit, Alessandro Gabbana, Michael Woodward, Yen Ting Lin, Federico Toschi, Daniel Livescu
https://arxiv.org/abs/2507.16058

Is memory all you need? Data-driven Mori-Zwanzig modeling of Lagrangian particle dynamics in turbulent flows
The dynamics of Lagrangian particles in turbulence play a crucial role in mixing, transport, and dispersion processes in complex flows. Their trajectories exhibit highly non-trivial statistical behavior, motivating the development of surrogate models that can reproduce these trajectories without incurring the high computational cost of direct numerical simulations of the full Eulerian field. This task is particularly challenging because reduced-order models typically lack access to the full set…

A Semi-Lagrangian scheme on embedded manifolds using generalized local polynomial reproductions
Thomas Hangelbroek, Christian Rieger, Grady B. Wright
https://arxiv.org/abs/2508.10344

A Semi-Lagrangian scheme on embedded manifolds using generalized local polynomial reproductions
We analyze rates of uniform convergence for a class of high-order semi-Lagrangian schemes for first-order, time-dependent partial differential equations on embedded submanifolds of $\mathbb{R}^d$ (including advection equations on surfaces) by extending the error analysis of Falcone and Ferretti. A central requirement in our analysis is a remapping operator that achieves both high approximation orders and strong stability, a combination that is challenging to obtain and of independent interest. …

A distributed augmented Lagrangian decomposition algorithm for constrained optimization
Wenyou Guo, Ting Qu, Hainan Huang, Yafeng Wei
https://arxiv.org/abs/2508.04960 https://…

A distributed augmented Lagrangian decomposition algorithm for constrained optimization
Within the framework of the Augmented Lagrangian (AL), we introduce a novel distributed optimization method called Distributed Augmented Lagrangian Decomposition (DALD). We provide a rigorous convergence proof for the standard version of this method, which is designed to tackle general constrained optimization problems. To address the high iteration costs in early stages, we propose several accelerated variants of DALD that enhances efficiency without compromising theoretical guarantees, suppor…

On the Lagrangian and fermion mass of the unified $SU(2) \otimes SU(4)$ gauge field theory
Eckart Marsch, Yasuhito Narita
https://arxiv.org/abs/2508.15332 https://

On the Lagrangian and fermion mass of the unified $SU(2) \otimes SU(4)$ gauge field theory
{In the Standard Model of elementary particles the fermions are assumed to be intrinsically massless. Here we propose a new theoretical idea of fermion mass generation (other than by the Higgs mechanism) through the coupling with the vector gauge fields of the unified $SU(2) \otimes SU(4)$ gauge symmetry, especially with the $Z$ boson of the weak interaction that affects all elementary fermions. The resulting small masses are suggested to be proportional to the self-energy of the $Z$ field as d…

White dwarf structure in $f(R,T,L_m)$ gravity: beyond the Chandrasekhar mass limit
Edson Otoniel, Juan M. Z. Pretel, Cl\'esio E. Mota, C\'esar O. V. Flores, Victor B. T. Alves
https://arxiv.org/abs/2507.18745

White dwarf structure in $f(R,T,L_m)$ gravity: beyond the Chandrasekhar mass limit
In this work, we investigate the relativistic structure of white dwarfs (WDs) within the framework of modified gravity theory $f(R, T, L_m) = R + αT L_m$, which introduces a non-minimal coupling between matter and curvature. Using a realistic equation of state (EoS) that includes contributions from a relativistic degenerate electron gas and ionic lattice effects, we solve the modified Tolman-Oppenheimer-Volkoff (TOV) equations for two standard choices of the matter Lagrangian density: $L_m = p…

An adaptive dynamical low-rank optimizer for solving kinetic parameter identification inverse problems
Lena Baumann, Lukas Einkemmer, Christian Klingenberg, Jonas Kusch
https://arxiv.org/abs/2506.21405

An adaptive dynamical low-rank optimizer for solving kinetic parameter identification inverse problems
The numerical solution of parameter identification inverse problems for kinetic equations can exhibit high computational and memory costs. In this paper, we propose a dynamical low-rank scheme for the reconstruction of the scattering parameter in the radiative transfer equation from a number of macroscopic time-independent measurements. We first work through the PDE constrained optimization procedure in a continuous setting and derive the adjoint equations using a Lagrangian reformulation. For …

Lagrangian analysis of turbulent blood flow in the human left heart
Fabio Guglietta, Martino Andrea Scarpolini, Francesco Viola, Luca Biferale
https://arxiv.org/abs/2506.09708

Lagrangian analysis of turbulent blood flow in the human left heart
We present a Lagrangian analysis of turbulent blood flow in the human left heart using high-fidelity simulations based on a patient-specific anatomical model. Leveraging a fully coupled fluid-structure-electrophysiology interaction (FSEI) framework, we track the motion of Lagrangian (passive) tracers to investigate the multiscale statistical properties of velocity fluctuations over more than four decades. Our analysis reveals strong Lagrangian intermittency throughout the left heart, reflecting…

Probing Neutral Triple Gauge Couplings via $ZZ$ Production at $e^ e^-$ Colliders
John Ellis, Hong-Jian He, Rui-Qing Xiao, Shi-Ping Zeng
https://arxiv.org/abs/2506.21433

Probing Neutral Triple Gauge Couplings via $ZZ$ Production at $e^+e^-$ Colliders
Neutral triple gauge couplings (nTGCs) first arise from the dimension-8 operators of the Standard Model Effective Field Theory (SMEFT), rather than the dimension-4 SM Lagrangian and dimension-6 SMEFT operators, opening up a unique window for probing new physics at the dimension-8 level. In this work, we formulate the nTGC form factors of $ZZV^*$ ($V=Z,γ$) that are compatible with the spontaneous breaking of the SU(2)$\otimes$U(1) electroweak gauge symmetry and consistently match the dimension-…

More counterexamples to Lagrangian Poincar\'e recurrence in dimension four
Joel Schmitz
https://arxiv.org/abs/2507.13924 https://…

More counterexamples to Lagrangian Poincaré recurrence in dimension four
In earlier work, we constructed counterexamples to Lagrangian Poincaré recurrence for many toric symplectic four manifolds. Here we provide a few more examples extending the family of counterexamples to include all non-monotone toric symplectic four manifolds.

A semi-Lagrangian scheme for First-Order Mean Field Games based on monotone operators
Elisabetta Carlini, Valentina Coscetti
https://arxiv.org/abs/2506.10509

A semi-Lagrangian scheme for First-Order Mean Field Games based on monotone operators
We construct a semi-Lagrangian scheme for first-order, time-dependent, and non-local Mean Field Games. The convergence of the scheme to a weak solution of the system is analyzed by exploiting a key monotonicity property. To solve the resulting discrete problem, we implement a Learning Value Algorithm, prove its convergence, and propose an acceleration strategy based on a Policy iteration method. Finally, we present numerical experiments that validate the effectiveness of the proposed schemes an…

A Data-Driven Approach for Predicting Hydrodynamic Forces on Spherical Particles Using Volume Fraction Representations
Alexander Metelkin, Sam Jacob Jacob, Bernhard Vowinckel
https://arxiv.org/abs/2507.20767

A Data-Driven Approach for Predicting Hydrodynamic Forces on Spherical Particles Using Volume Fraction Representations
Particle-laden flows are simulated at various scales using numerical techniques that range from particle-resolved Direct Numerical Simulations (pr-DNS) for small-scale systems to Lagrange point-particle methods for laboratory-scale problems, and Euler-Euler approaches for larger-scale applications. Recent research has been particularly focused on the development of both physics-based and data-driven closures to enhance the accuracy of the Lagrangian point-particle approach by leveraging highly …

Strong Gravity Effects on $\mathcal{R}^2$-corrected Single Scalar Field Inflation and Compatibility with the ACT Data
V. K. Oikonomou
https://arxiv.org/abs/2508.17363 https://…

Strong Gravity Effects on $\mathcal{R}^2$-corrected Single Scalar Field Inflation and Compatibility with the ACT Data
In this work we introduce the rescaled $\mathcal{R}^2$-corrected minimally coupled scalar field theory, a theory that contains minimal quantum corrections of the single scalar field Lagrangian. We develop the theoretical framework in the string frame where the baryons geodesics are free fall geodesics and we do not treat the theory as a two scalar field theory in the Einstein frame. The theoretical framework can be reduced to a single scalar field theory framework by using a perturbative expans…

A Newton Augmented Lagrangian Method for Symmetric Cone Programming with Complexity Analysis
Rui-Jin Zhang, Ruoyu Diao, Xin-Wei Liu, Yu-Hong Dai
https://arxiv.org/abs/2506.04802

A Newton Augmented Lagrangian Method for Symmetric Cone Programming with Complexity Analysis
Symmetric cone programming incorporates a broad class of convex optimization problems, including linear programming, second-order cone programming, and semidefinite programming. Although the augmented Lagrangian method (ALM) is well-suited for large-scale scenarios, its subproblems are often not second-order continuously differentiable, preventing direct use of classical Newton methods. To address this issue, we observe that barrier functions from interior-point methods (IPMs) naturally serve a…

Augmented Lagrangian Solvers for Poroelasticity with Fracture Contact Mechanics
Marius Nevland, Inga Berre, Jakub Wiktor Both, Eirik Keilegavlen
https://arxiv.org/abs/2508.11508

Augmented Lagrangian Solvers for Poroelasticity with Fracture Contact Mechanics
In the subsurface, fractures and the surrounding porous rock can deform in interaction with fluid flow. Advanced mathematical models governing these coupled processes typically combine fluid flow, poroelasticity, and fracture contact mechanics, representing fractures as co-dimension one objects within the porous medium. The resulting system of equations is complex and highly nonlinear. As a result, convergence issues with nonlinear solvers are common, which hinders the practical implementation …

On the parametrised Whitehead torsion of families of nearby Lagrangian submanifolds
Sylvain Courte, Noah Porcelli
https://arxiv.org/abs/2506.06110 https://…

On the parametrised Whitehead torsion of families of nearby Lagrangian submanifolds
Motivated by the strong nearby Lagrangian conjecture, we constrain the parametrised Whitehead torsion of a family of closed exact Lagrangian submanifolds in a cotangent bundle. We prove the parametrised Whitehead torsion admits a factorisation through simpler maps, in particular implying it is trivial on $π_0$, $π_1$, and that its image is divisible by the Euler characteristic. We provide concrete implications for the Lagrangian monodromy question in the case of a high dimensional torus. Th…

Acceleration of Lagrangian Particles in Shell Models of Turbulence
Lorenzo Piro, Massimo Cencini, Roberto Benzi
https://arxiv.org/abs/2506.09633 https://…

Acceleration of Lagrangian Particles in Shell Models of Turbulence
Lagrangian acceleration has been investigated both experimentally and numerically in the past, and it has been shown to exhibit extreme fluctuations, which have been rationalized as events in which tracer particles get trapped into vortical structures such as vortex tubes or filaments. Here, we consider the statistics of acceleration within the multifractal framework, as in Biferale et al. Phys. Rev. Lett. 93 064502 (2004), and investigate the statistics of Lagrangian acceleration using shell m…

Confronting Rainbow-deformed $f(R)$ Gravity with the ACT Data
S. D. Odintsov, V. K. Oikonomou
https://arxiv.org/abs/2508.17358 https://arxiv.org/pdf/2508.1…

Confronting Rainbow-deformed $f(R)$ Gravity with the ACT Data
In this work we examine a theoretical scenario which combines two fundamental theoretical proposals for the early Universe and a possible evolution for the early post-inflationary epoch. Specifically, we assume that the early Universe contains gravity's rainbow effects on the spacetime and the inflationary Lagrangian contains $R^2$ corrections or $f(R)$ gravity corrections in general. In addition we assume that the era beyond the end of inflation until the reheating temperature is reached, is a…

Crosslisted article(s) found for math.OC. https://arxiv.org/list/math.OC/new
[1/1]:
- Conditionally adaptive augmented Lagrangian method for physics-informed learning of forward and i...
Qifeng Hu, Shamsulhaq Basir, Inanc Senocak

Role of $K^*_0(700)$ exchange in the $p \bar{p} \to \Lambda \bar{\Lambda}$ reaction
Hao-Nan Wang, Xing-Yi Ji, De-Min Li, Yue Ma, En Wang, Ju-Jun Xie
https://arxiv.org/abs/2508.16912

Role of $K^*_0(700)$ exchange in the $p \bar{p} \to Λ\barΛ$ reaction
Regarding the reaction $p \bar{p} \to Λ\barΛ$, we provide a dynamical explanation focusing on its total and differential cross section based on the effective Lagrangian approach. Incorporating the $t$-channel exchange of the $K^*_0(700)$ meson and $s$-channel contribution from the vector excited state, we can reproduce the current experimental data fairly well in a wide energy region. Compared to the conventional $K$ and $K^*$ mesons exchange, the $K^*_0(700)$ meson exchange plays a more esse…

Topological Entropy of Stationary Turbulent Flows
Ankan Biswas, Amal Manoharan, Ashwin Joy
https://arxiv.org/abs/2506.20973 https://a…

Topological Entropy of Stationary Turbulent Flows
Topological entropy serves as a viable candidate for quantifying mixing and complexity of a highly chaotic system. Particularly in turbulence, this is determined as the exponential stretching rate of a fluid material line that typically necessitates a Lagrangian description. We extend the recent work [A. Manoharan, S. Subramanian, and A. Joy, arXiv:2412.08996] to three dimensions, and present an exact Eulerian framework for the topological entropy in stationary turbulent flows that is devoid of…

Spontaneous breaking of global U(1) symmetry in an interacting Bose gas under rigid rotation
E. Siri, N. Sadooghi
https://arxiv.org/abs/2508.17055 https://…

Spontaneous breaking of global U(1) symmetry in an interacting Bose gas under rigid rotation
We investigate the impact of rigid rotation on the spontaneous breaking of U(1) symmetry in a Bose gas, which is described by a self-interacting complex scalar field Lagrangian. Rigid rotation is introduced through a specific metric that explicitly depends on the angular velocity $Ω$. We begin by determining the free propagator for this model at finite temperature $T$ and chemical potential $μ$. Using this propagator, we calculate the thermodynamic potential in terms of an energy dispersion r…

Lagrangian entropic lattice Boltzmann method for Courant-free supersonic compressible flow simulation
Woohyuk Noh, Changhoon Lee
https://arxiv.org/abs/2508.06911 https://…

Lagrangian entropic lattice Boltzmann method for Courant-free supersonic compressible flow simulation
This work presents the Lagrangian entropic lattice Boltzmann method (LELBM), a novel framework for supersonic lattice Boltzmann method that surpasses traditional restrictions on velocity, temperature, viscosity, and memory, resulting in stable and efficient Courant-free LBM formulation, while still maintaining explicit time stepping. A regularized central moment collision method coupled with a double-distribution function (DDF) that considers internal degrees of freedom enabled the precise cont…

A Lagrangian method for solving the spherical shallow water equations using power diagrams
Philip Caplan, Otis Milliken, Toby Pouler, Zeyi Tong, Col McDermott, Sam Millay
https://arxiv.org/abs/2508.08129

A Lagrangian method for solving the spherical shallow water equations using power diagrams
Numerical simulations of the air in the atmosphere and water in the oceans are essential for numerical weather prediction. The state-of-the-art for performing these fluid simulations relies on an Eulerian viewpoint, in which the fluid domain is discretized into a mesh, and the governing equations describe the fluid motion as it passes through each cell of the mesh. However, it is unclear whether a Lagrangian viewpoint, in which the fluid is discretized by a collection of particles, can outperfo…

The role of Lagrangian drift in the generation of surface waves by wind
L. R. Seitz, Mara A. Freilich, Nick Pizzo
https://arxiv.org/abs/2508.02580 https://…

The role of Lagrangian drift in the generation of surface waves by wind
A nonlinear stability analysis entirely in the Lagrangian frame is conducted, revealing the fundamental role of the wave-induced mean flow in modifying further wave growth and providing new insight into the classic problem of wave generation by wind. The prevailing theory, a critical-layer resonance mechanism proposed by Miles (1957), has seen numerous refinements; yet, the role of Lagrangian drift -- the velocity a fluid parcel actually experiences -- in wave growth was not understood. Our ana…