Tootfinder

A non-iterative domain decomposition time integrator for linear wave equations
Tim Buchholz, Marlis Hochbruck
https://arxiv.org/abs/2507.19379 https://arxi…

A non-iterative domain decomposition time integrator for linear wave equations
We propose and analyze a non-iterative domain decomposition integrator for the linear acoustic wave equation. The core idea is to combine an implicit Crank-Nicolson step on spatial subdomains with a local prediction step at the subdomain interfaces. This enables parallelization across space while advancing sequentially in time, without requiring iterations at each time step. The method is similar to the methods from Blum, Lisky and Rannacher (1992) or Dawson and Dupont (1992), which have been d…

Real-time analog circuit for auto-correlative weak-value amplification in the time domain
Jing-Hui Huang, Guang-Jun Wang, Xiang-Yun Hu
https://arxiv.org/abs/2507.18180 https://

Real-time analog circuit for auto-correlative weak-value amplification in the time domain
The auto-correlative weak-value amplification (AWVA) technique demonstrates distinct advantages over standard weak-value amplification (SWVA) for quantum parameter estimation. To achieve enhanced precision in real-time parameter estimation, the AWVA requires additional resources compared to SWVA, namely real-time multiplication and integrator modules. We implemented a real-time analog circuit for AWVA using an AD835 multiplier and an NE5532 operational amplifier for the integrator. The circuit …

Physics Of Eclipsing Binaries. VIII. Multiple systems
Miroslav Bro\v{z}, Kyle E. Conroy, Andrej Pr\v{s}a
https://arxiv.org/abs/2506.20866 https://

Physics Of Eclipsing Binaries. VIII. Multiple systems
Multiple stellar systems are common especially among O and B stars. In order to accurately describe their dynamics, interactions among components must be accounted for. In this work, we describe the new dynamical model in Phoebe, which could be used just for this purpose. The n-body model is based on the Reboundx numerical integrator and accounts for mutual perturbations, oblateness, relativistic effects, or light-time effects. The initial conditions can be set up as hierarchical or two-pairs g…

An adaptive symplectic integrator for gravitational dynamics
Keqi Ye, Zizhe Cai, Mingji Wang, Kun Yang, Xiaodong Liu
https://arxiv.org/abs/2507.14881 https…

An adaptive symplectic integrator for gravitational dynamics
This paper presents an adaptive symplectic integrator, SQQ-PTQ, developed on the basis of the fixed-step symplectic integrator SQQ. To mitigate the Runge phenomenon, SQQ-PTQ employs Chebyshev interpolation for approximating the action, enhancing both the precision and stability of the interpolation. In addition, to reduce the computational cost of evaluating interpolation functions, SQQ-PTQ introduces a projection method that improves the efficiency of these computations. A key feature of SQQ-P…

On the stability of the low-rank projector-splitting integrator for hyperbolic and parabolic equations
Shiheng Zhang, Jingwei Hu
https://arxiv.org/abs/2507.15192

On the stability of the low-rank projector-splitting integrator for hyperbolic and parabolic equations
We study the stability of a class of dynamical low-rank methods--the projector-splitting integrator (PSI)--applied to linear hyperbolic and parabolic equations. Using a von Neumann-type analysis, we investigate the stability of such low-rank time integrator coupled with standard spatial discretizations, including upwind and central finite difference schemes, under two commonly used formulations: discretize-then-project (DtP) and project-then-discretize (PtD). For hyperbolic equations, we show t…

Fast evaluation of Feynman integrals for Monte Carlo generators
Pau Petit Ros\`as, William J. Torres Bobadilla
https://arxiv.org/abs/2507.12548 https://

Fast evaluation of Feynman integrals for Monte Carlo generators
Building on the idea of numerically integrating differential equations satisfied by Feynman integrals, we propose a novel strategy for handling branch cuts within a numerical framework. We develop an integrator capable of evaluating a basis of integrals in both double and quadruple precision, achieving significantly reduced computational times compared to existing tools. We demonstrate the performance of our integrator by evaluating one- and two-loop five-point Feynman integrals with up to nine…

Considering contact forces during the formation of planetesimals by gravitational collapse: mutual orbits, spin states, and shapes
Jackson T. Barnes, Stephen R. Schwartz, Seth A. Jacobson
https://arxiv.org/abs/2507.16739

Considering contact forces during the formation of planetesimals by gravitational collapse: mutual orbits, spin states, and shapes
In this work, we apply a soft-sphere discrete element method (SSDEM) within the PKDGRAV N-body integrator to investigate the formation of planetesimal systems through the gravitational collapse of clouds of super-particles. Previously published numerical models have demonstrated that the gravitational collapse of pebble clouds is an efficient pathway to produce binary planetesimal systems. However, such investigations were limited by their use of a perfect-merger and inflated-radii super-partic…

Projected integral control of impedance passive nonlinear systems
Nicolas Vanspranghe (CRAN), Pietro Lorenzetti (CRAN), Lassi Paunonen (TUT), George Weiss (TAU)
https://arxiv.org/abs/2506.14267

Projected integral control of impedance passive nonlinear systems
We propose an abstract framework for solving the constrained set-point tracking problem for impedance passive infinite-dimensional nonlinear systems. The class of systems considered is governed by monotone differential inclusions and allows us to exploit the theory of contraction semigroups. To account for possible operational constraints, e.g., bounds on the input, we replace a classical integral controller with a projected integral controller. This guarantees that the integrator state remains…

InflationEasy: A C Lattice Code for Inflation
Angelo Caravano
https://arxiv.org/abs/2506.11797 https://arxiv.org/pdf/2506.11797

InflationEasy: A C++ Lattice Code for Inflation
InflationEasy is the first lattice code specifically developed for cosmological inflation. It simulates the nonlinear dynamics of a scalar field on a three-dimensional lattice in an expanding FLRW universe, using finite-difference spatial derivatives and a staggered leapfrog integrator for time evolution. Based in part on the well-known LATTICEEASY, it incorporates several improvements tailored to inflationary applications. Among other features, InflationEasy implements a nonperturbative $δN$ …

The Within-Orbit Adaptive Leapfrog No-U-Turn Sampler
Nawaf Bou-Rabee, Bob Carpenter, Tore Selland Kleppe, Sifan Liu
https://arxiv.org/abs/2506.18746 https:…

The Within-Orbit Adaptive Leapfrog No-U-Turn Sampler
Locally adapting parameters within Markov chain Monte Carlo methods while preserving reversibility is notoriously difficult. The success of the No-U-Turn Sampler (NUTS) largely stems from its clever local adaptation of the integration time in Hamiltonian Monte Carlo via a geometric U-turn condition. However, posterior distributions frequently exhibit multi-scale geometries with extreme variations in scale, making it necessary to also adapt the leapfrog integrator's step size locally and dynamic…

Continuous-Time Output Feedback Adaptive Control for Stabilization and Tracking with Experimental Results
Mohammad Mirtaba, Ankit Goel
https://arxiv.org/abs/2506.08042

Continuous-Time Output Feedback Adaptive Control for Stabilization and Tracking with Experimental Results
This paper presents a continuous-time output feedback adaptive control technique for stabilization and tracking control problems. The adaptive controller is motivated by the classical discrete-time retrospective cost adaptive control algorithm. The particle swarm optimization framework automates the adaptive algorithm's hyper-parameter tuning. The proposed controller is numerically validated in the tracking problems of a double integrator and a bicopter system and is experimentally validated in…

Splitting-based randomised dynamical low-rank approximations for stiff matrix differential equations
Zi Wu, Yong-Liang Zhao
https://arxiv.org/abs/2506.15259

Splitting-based randomised dynamical low-rank approximations for stiff matrix differential equations
In the fields of control theory and machine learning, the dynamic low-rank approximation for large-scale matrices has received substantial attention. Considering the large-scale semilinear stiff matrix differential equations, we propose a dynamic numerical integrator for obtaining low-rank approximations of solutions. We first decompose the differential equation into a stiff linear component and a nonstiff nonlinear term, then employ an exponential integrator along with a dynamic low-rank appro…

Can Moons Exist around the Habitable-zone Planet K2-18b?
Shaan D. Patel, Billy Quarles, Manfred Cuntz, Nevin N. Weinberg
https://arxiv.org/abs/2507.11594 h…

Can Moons Exist around the Habitable-zone Planet K2-18b?
K2-18b closely orbits a nearby M3 dwarf within its habitable zone, where this planet could be either a super-Earth or a mini-Neptune. Recent studies using transit spectroscopy suggest that it is Hycean in nature, but this classification is currently controversial. We use the N-body integrator rebound and its extension library reboundx to investigate the possibility of exomoons around K2-18b. Due to tidal interactions that induce outward migration, we find that any moons would be extremely unlik…

Bi-Level optimization for parameter estimation of differential equations using interpolation
Siddharth Prabhu, Srinivas Rangarajan, Mayuresh Kothare
https://arxiv.org/abs/2506.00720

Bi-Level optimization for parameter estimation of differential equations using interpolation
Inverse problem or parameter estimation of ordinary differential equations is a process of obtaining the best parameters using experimental measurements of the states. Single (Multiple)-shooting is a type of sequential optimization method that minimizes the error in the measured and numerically integrated states. However, this requires computing sensitivities i.e. the derivatives of states with respect to the parameters over the numerical integrator, which can get computationally expensive. To …

On the convergence of N-body simulations of the Solar System
Hanno Rein, Garett Brown, Mei Kanda
https://arxiv.org/abs/2507.04987 https://

On the convergence of N-body simulations of the Solar System
Most direct N-body integrations of planetary systems use a symplectic integrator with a fixed timestep. A large timestep is desirable because simulations run fast. However, simulations yield unphysical results if the timestep is too large. Surprisingly, no systematic convergence study has been performed on long (Gyr) timescales. In this paper we present numerical experiments to determine the minimum timestep one has to use in long-term integrations of the Solar System in order to recover the sy…

Using BDF schemes in the temporal integration of POD-ROM methods
Bosco Garc\'ia-Archilla, Alicia Garc\'ia-Mascaraque, Julia Novo
https://arxiv.org/abs/2506.14543

Using BDF schemes in the temporal integration of POD-ROM methods
In this paper we consider the numerical approximation of a semilinear reaction-diffusion model problem (PDEs) by means of reduced order methods (ROMs) based on proper orthogonal decomposition (POD). We focus on the time integration of the fully discrete reduced order model. Most of the analysis in the literature has been carried out for the implicit Euler method as time integrator. We integrate in time the reduced order model with the BDF-q time stepping ($1\le q\le 5$) and prove optimal rate o…

A Spectral-Based Tuning Criterion for PI Controllers in IPDT Systems With Unified Tracking and Disturbance Rejection Performance
Dhamdhawach Horsuwan
https://arxiv.org/abs/2507.01197

A Spectral-Based Tuning Criterion for PI Controllers in IPDT Systems With Unified Tracking and Disturbance Rejection Performance
This paper proposes a spectral-based tuning method for proportional-integral (PI) controllers in integrating-plus-dead-time (IPDT) systems. The design objective is to achieve unified exponential decay for both reference tracking and disturbance rejection by minimizing the spectral abscissa of the closed-loop system. A second-order semi-discrete model accurately captures the integrator and delay dynamics while enabling efficient dominant pole extraction. These discrete-time poles are mapped to c…

Computing matrix $\varphi$-functions arising in exponential integrators
Awad H. Al-Mohy, Xiaobo Liu
https://arxiv.org/abs/2506.01193 https://

Computing matrix $φ$-functions arising in exponential integrators
A new scaling and recovering algorithm is proposed for simultaneously computing the matrix $φ$-functions that arise in exponential integrator methods for the numerical solution of certain first-order systems of ordinary differential equations (ODEs). The algorithm initially scales the input matrix down by a nonnegative integer power of two, then computes the $[m/m]$ diagonal Padé approximant to $φ_p$, where $p$ is the largest index of interest. The remaining $[m+p{-}j/m]$ Padé approximants …