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We propose two novel numerical schemes for approximate implementation of the dynamic programming~(DP) operation concerned with finite-horizon, optimal control of discrete-time systems with input-affine dynamics. The proposed algorithms…

Optimization and Control · Mathematics 2022-03-18 M. A. S. Kolarijani , P. Mohajerin Esfahani

We have presented some practical consequences on the molecular-dynamics simulations arising from the numerical algorithm published recently in paper Int. J. Mod. Phys. C 16, 413 (2005). The algorithm is not a finite-difference method and…

Exactly Solvable and Integrable Systems · Physics 2015-06-26 B. Brzostowski , M. R. Dudek , B. Grabiec , T. Nadzieja

Integrable two-dimensional models which possess an integral of motion cubic or quartic in velocities are governed by a single prepotential, which obeys a nonlinear partial differential equation. Taking into account the latter's invariance…

Mathematical Physics · Physics 2015-06-16 Anton Galajinsky , Olaf Lechtenfeld

Motility-induced phase separation (MIPS) is a purely non-equilibrium phenomenon in which self-propelled particles phase separate without any attractive interactions. One surprising feature of MIPS is the emergence of polar, nematic, and…

Soft Condensed Matter · Physics 2022-02-08 Chiu Fan Lee

Optimization-based robot control strategies often rely on first-order dynamics approximation methods, as in iLQR. Using second-order approximations of the dynamics is expensive due to the costly second-order partial derivatives of the…

Robotics · Computer Science 2022-08-16 Shubham Singh , Ryan P. Russell , Patrick M. Wensing

We present a coordinate-free approach for constructing approximate first integrals of generalized slow-fast Hamiltonian systems, based on the global averaging method on parameter-dependent phase spaces with $\mathbb{S}^1 -$symmetry.…

Dynamical Systems · Mathematics 2014-05-06 M. Avendaño-Camacho , J. A. Vallejo , Yu. Vorobiev

We develop a method to fit high-temperature Gibbs free energy data for the development of interatomic potentials for atomic systems. The approach is based on Hamiltonian thermodynamic integration, enabling the identification of suitable…

Materials Science · Physics 2026-03-04 Liangrui Wei , Yang Sun

We address nonautonomous initial boundary value problems for decoupled linear first-order one-dimensional hyperbolic systems, investigating the phenomenon of finite time stabilization. We establish sufficient and necessary conditions…

Analysis of PDEs · Mathematics 2025-12-10 Irina Kmit , Natalya Lyul'ko

We develop an algorithm for the computation of general Fourier integral operators associated with canonical graphs. The algorithm is based on dyadic parabolic decomposition using wave packets and enables the discrete approximate evaluation…

Numerical Analysis · Mathematics 2015-05-27 Maarten V. de Hoop , Gunther Uhlmann , Andras Vasy , Herwig Wendt

Here we present an efficient method for finding and using a nonlocal symmetry admitted by a rational second order ordinary differential equation (rational 2ODE) in order to find a Liouvillian first integral (belonging to a vast class of…

Chaotic Dynamics · Physics 2025-12-11 I. Deme , L. G. S. Duarte , L. A. C. P. da Mota

The single-step explicit time integration methods have long been valuable for solving large-scale nonlinear structural dynamic problems, classified into single-solve and multi-sub-step approaches. However, no existing explicit single-solve…

Numerical Analysis · Mathematics 2025-11-25 Liu Yaokun , Li Jinze , Yu Kaiping

We present a novel approach to system identification (SI) using deep learning techniques. Focusing on parametric system identification (PSI), we use a supervised learning approach for estimating the parameters of discrete and…

Systems and Control · Electrical Eng. & Systems 2023-06-21 Connor James Stephens , Emmanuel Blazquez

Here we present an algorithm to find elementary first integrals of rational second order ordinary differential equations (SOODEs). In \cite{PS2}, we have presented the first algorithmic way to deal with SOODEs, introducing the basis for the…

Mathematical Physics · Physics 2008-10-02 J. Avellar , L. G. S. Duarte , S. E. S. Duarte , L. A. C. P. da Mota

A variety of complex biological, natural and man-made systems exhibit non-Markovian dynamics that can be modeled through fractional order differential equations, yet, we lack sample comlexity aware system identification strategies. Towards…

Systems and Control · Electrical Eng. & Systems 2025-06-23 Xiaole Zhang , Vijay Gupta , Paul Bogdan

We propose two novel unbiased estimators of the integral $\int_{[0,1]^{s}}f(u) du$ for a function $f$, which depend on a smoothness parameter $r\in\mathbb{N}$. The first estimator integrates exactly the polynomials of degrees $p<r$ and…

Computation · Statistics 2023-06-12 Nicolas Chopin , Mathieu Gerber

We prove a priori estimates and, as sequel, existence of Euclidean Gibbs states for quantum lattice systems. For this purpose we develop a new analytical approach, the main tools of which are: first, a characterization of the Gibbs states…

Probability · Mathematics 2007-05-23 Sergio Albeverio , Yuri G. Kondratiev , Tatiana Pasurek , Michael Röckner

We consider the general problem of estimating an unknown control parameter of an open quantum system. We establish a direct relation between the evolution of both system and environment and the precision with which the parameter can be…

Quantum Physics · Physics 2016-02-10 Katarzyna Macieszczak , Madalin Guta , Igor Lesanovsky , Juan P. Garrahan

A Hamiltonian with two degrees of freedom is said to be superintegrable if it admits three functionally independent integrals of the motion. This property has been extensively studied in the case of two-dimensional spaces of constant…

Mathematical Physics · Physics 2007-05-23 E. G. Kalnins , J. M. Kress , P. Winternitz

We present a midpoint policy iteration algorithm to solve linear quadratic optimal control problems in both model-based and model-free settings. The algorithm is a variation of Newton's method, and we show that in the model-based setting it…

Optimization and Control · Mathematics 2022-02-16 Benjamin Gravell , Iman Shames , Tyler Summers

A fast algorithm (linear in the degrees of freedom) for the solution of linear variable-coefficient rational-order fractional integral and differential equations is described. The approach is related to the ultraspherical method for…

Numerical Analysis · Mathematics 2017-12-04 Nicholas Hale , Sheehan Olver