Article
Mathematics, Interdisciplinary Applications
Christopher Griffin
Summary: The replicator dynamics for zero-sum games emerge from a non-canonical bracket that combines elements of a Poisson Bracket and a Nambu Bracket. This bracket is parameterized by both the skew-symmetric payoff matrix and a mediating function, which plays a critical role in the dynamics. The mediating function also leads to the definition of a natural metric for phase flow conservation, showing potential implications for quantizing evolutionary games.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Computer Science, Interdisciplinary Applications
P. Cifani, M. Viviani, K. Modin
Summary: We propose an efficient and scalable numerical method for solving two-dimensional ideal fluid dynamics on the sphere. The method utilizes a tridiagonal splitting of the discrete spherical Laplacian and optimized numerical algorithms. For time-stepping, an isospectral integrator is adopted to preserve the geometric structure of Euler's equations. The algorithm achieves high computational performance by formulating the matrix Lie algebra basis through tridiagonal eigenvalue problems and implementing an efficient parallel computation.
JOURNAL OF COMPUTATIONAL PHYSICS
(2023)
Article
Multidisciplinary Sciences
Cristian Lazureanu
Summary: This paper presents a method for integrable deformations of a maximally superintegrable system by altering constants of motion to construct new systems. New maximally superintegrable systems are obtained using this method, along with deformations of arbitrary first-order autonomous differential equation systems.
Article
Computer Science, Interdisciplinary Applications
M. Casati, P. Lorenzoni, D. Valeri, R. Vitolo
Summary: We have implemented an algorithm for computing the Schouten bracket of weakly nonlocal Hamiltonian operators in three different computer algebra systems. This algorithm can handle almost all examples coming from the theory of (1+1)-integrable evolutionary PDEs.
COMPUTER PHYSICS COMMUNICATIONS
(2022)
Article
Computer Science, Interdisciplinary Applications
Anjiao Gu, Yang He, Yajuan Sun
Summary: This paper presents Particle-in-Cell algorithms for the Vlasov-Poisson system based on its Poisson bracket structure. The Poisson equation is solved using finite element methods, and splitting methods are utilized for discretization. Numerical experiments demonstrate the efficiency of the proposed methods.
JOURNAL OF COMPUTATIONAL PHYSICS
(2022)
Article
Mathematics, Applied
Alexander Polishchuk
Summary: This paper studies the Feigin-Odesskii brackets qn,1(C) associated with a normal elliptic curve C in Pn-1. It is shown that for odd n, the generators of the ideal of the secant variety of C can be seen as a Cremona transformation on Pn-1, generalizing the quadro-cubic Cremona transformation on P-4. Polynomial formulas for Cremona transformations associated with higher rank bundles on C are also found.
JOURNAL OF GEOMETRY AND PHYSICS
(2022)
Article
Mathematics, Applied
Alina Dobrogowska, Grzegorz Jakimowicz
Summary: This article presents a new perspective on the description of real finite-dimensional Lie algebras. The key component is a pair (F, v) consisting of a linear mapping F ∈ End(V) with an eigenvector v. This pair allows the construction of a Lie bracket on the dual space to a linear space V. The obtained Lie algebra is solvable and becomes nilpotent when F is nilpotent. The importance of these constructions is illustrated through examples and the geometric significance of the algebra invariants.
JOURNAL OF GEOMETRY AND PHYSICS
(2023)
Article
Meteorology & Atmospheric Sciences
Xingde Duan, Renjun Ma, Xiaolei Zhang
Summary: Tweedie's compound Poisson regression models are useful for modeling precipitation data, but they ignore the serial correlation between precipitation data. This study proposes using Autoregressive Integrated Moving Average models to accommodate the complex correlation structures of time series precipitation data.
INTERNATIONAL JOURNAL OF CLIMATOLOGY
(2022)
Article
Computer Science, Interdisciplinary Applications
Igor Sokolov, Haomin Sun, Gabor Toth, Zhenguang Huang, Valeriy Tenishev, Lulu Zhao, Jozsef Kota, Ofer Cohen, Tamas I. Gombosi
Summary: In this paper, a finite volume scheme based on integral relation for Poisson brackets is proposed to solve the Liouville equation, which conserves the number of particles, maintains the total-variation-diminishing (TVD) property, and provides high-quality numerical results. The proposed scheme can be used to solve other types of kinetic equations, including the transport equations describing the acceleration and propagation of Solar Energetic Particles (SEPs), which is of practical importance due to radiation hazards. The scheme is demonstrated to be accurate and efficient, making it applicable to global simulation systems analyzing space weather.
JOURNAL OF COMPUTATIONAL PHYSICS
(2023)
Article
Mathematics
Omar Leon Sanchez, Rahim Moosa
Summary: Motivated by the Poisson Dixmier-Moeglin equivalence problem, this paper initiates a systematic study of commutative unitary rings equipped with a biderivation, exploring the geometry of the corresponding B-varieties. Foundational results regarding the extension of biderivations to localisations, algebraic extensions, and transcendental extensions are established. A base extension theory is achieved to address a deficiency in Poisson algebraic geometry, demonstrating that dominant B-morphisms have generic B-fibres. A bidifferential version of the Dixmier-Moeglin equivalence problem is articulated.
JOURNAL OF ALGEBRA
(2022)
Article
Mathematics
Velimir Jurdjevic
Summary: This paper defines a class of differentiable manifolds that include two distinct optimal problems - affine-quadratic and rolling problem, and shows remarkable connections between these problems through the associated Hamiltonians obtained by optimal control. It also demonstrates that each of these Hamiltonians is completely integrable in the sense of Liouville. Finally, the significance of these results for the theory of mechanical systems is demonstrated.
Article
Energy & Fuels
Chenyu Liu, Xuemin Zhang, Shengwei Mei, Zhao Zhen, Mengshuo Jia, Zheng Li, Haiyan Tang
Summary: This paper proposes a novel method for enhancing wind power forecasting using numerical weather prediction (NWP) based on rank ensemble and probabilistic fluctuation awareness. Experimental results demonstrate the superiority and robustness of the proposed method in reducing prediction errors compared to baseline models.
Article
Mathematics, Applied
Miguel A. Berbel, Marco Castrillon Lopez
Summary: A Poisson covariant formulation of the Hamilton equations is studied for a Hamiltonian system on a fiber bundle. When a Lie group G acts freely, properly, preserving the fibers of the bundle and the Hamiltonian density is G-invariant, the reduction of this formulation is examined to obtain an analogue of Poisson-Poincare reduction for field theories. This procedure is related to the Lagrange-Poincare reduction for field theories through a Legendre transformation. Finally, an application to a model of a charged strand evolving in an electric field is given.
JOURNAL OF GEOMETRY AND PHYSICS
(2023)
Article
Mathematics
Daria Holik, Marek Karas
Summary: This paper investigates the properties of the Poisson bracket of polynomials in n variables and proves that there are strict constraints on the homogeneous components of the polynomials when the degree of the Poisson bracket is small enough. It also establishes a relationship between the homogeneous components of a polynomial F with degrees deg F ???1 and deg F ???2, and presents some results on the divisibility of the homogeneous component of degree deg F ??? 1. Furthermore, a modification of a conjecture regarding the estimation of the degree of the Poisson bracket of two polynomials is proposed.
ANNALES POLONICI MATHEMATICI
(2022)
Article
Polymer Science
Dhanabhol Riowruangsanggoon, Apiwat Riddhabhaya, Nattisa Niyomtham, Irin Sirisoontorn
Summary: This study indicated that the shear bond strength is highest when ceramic brackets are bonded to glazed monolithic zirconia using non-woven polypropylene fiber adhesive. Metal brackets showed lower bond strength compared to ceramic brackets.