Article
Astronomy & Astrophysics
Adam Cieslik, Patryk Mach
Summary: The theory of Schwarzschild geodesics is revisited in this paper. Based on a result by Weierstrass and Biermann, a formula describing all non radial, timelike and null trajectories in terms of Weierstrass elliptic functions is derived. Remarkably, this single formula works for an entire geodesic trajectory, even when it passes through turning points. Using this formula, expressions for the proper and coordinate time along the geodesic are obtained.
CLASSICAL AND QUANTUM GRAVITY
(2022)
Article
Mathematics
Isra Al-Shbeil, Afis Saliu, Abbas Kareem Wanas, Adriana Catas
Summary: This paper deals with a specific class of functions called rational equivariant functions and investigates which elliptic zeta functions arising from integrals can yield rational equivariant functions. The paper aims to provide examples of rational equivariant functions and establishes a criterion to determine the rationality of equivariant functions derived from ratios of modular functions of low weight. Modular forms have important applications in number theory and various areas of mathematics and physics.
Article
Mathematics, Applied
Mykola Korenkov, Yurii Kharkevych
Summary: This paper presents a refined asymptotic approximation of the Jacobi theta functions and their logarithmic derivatives, and finds the asymptotics of the Nevanlinna characteristics of the indicated functions and arbitrary elliptic functions. An estimation of the type of the Weierstrass sigma functions is also provided.
Article
Mathematics
Magnus Aspenberg, Weiwei Cui
Summary: The study provides a comprehensive description of the possible Hausdorff dimensions of escaping sets for meromorphic functions with a finite number of singular values. It shows the existence of meromorphic functions with escaping sets of specific dimensions and demonstrates the uncountable existence of quasiconformally equivalent meromorphic functions with escaping sets of different Hausdorff dimensions.
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
(2021)
Article
Mathematics, Interdisciplinary Applications
Yong-Shun Liang
Summary: This paper investigates the approximation of functions with fractal dimension in continuous functions space. It analyzes the fractal dimension of linear combinations of continuous functions with different fractal dimensions, introduces fractal winding of continuous functions, and establishes a theorem about the approximation of continuous functions with non-integer fractal dimension using trigonometric polynomials. The conditions for continuous functions with fractal dimension one and two are also discussed.
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY
(2022)
Article
Mathematics, Applied
Xing Li, Da-jun Zhang
Summary: We propose a bilinear framework for elliptic soliton solutions composed of Lame-type plane wave factors. We derive tau functions in Hirota's form and present vertex operators that generate these tau functions. Bilinear identities are constructed and a calculation algorithm for residues and bilinear equations is formulated. We investigate these concepts in detail for the KdV equation and provide a brief overview for the KP hierarchy. Degenerations by the periods of elliptic functions are explored, leading to a bilinear framework associated with trigonometric/hyperbolic and rational functions. Reductions by dispersion relation are considered through the use of elliptic N-th roots of unity, resulting in tau functions, vertex operators, and bilinear equations of the KdV hierarchy and Boussinesq equation obtained from those of the KP hierarchy. We also propose two methods to calculate bilinear derivatives involving Lame-type plane wave factors, which demonstrate the quasi-gauge property of bilinear equations.
JOURNAL OF NONLINEAR SCIENCE
(2022)
Article
Physics, Multidisciplinary
Alvaro H. S. Salas, S. A. El-Tantawy, M. R. Alharthi
Summary: Novel analytical and numerical solutions for the (un)damped Helmholtz-Duffing equation are derived and applied to the study of nonlinear oscillations in various plasma models, showing excellent accuracy and consistency.
Article
Mathematics, Applied
David J. Unger
Summary: This study explores the basic properties of a newly defined yield criterion and applies it to plane stress, mode I, perfectly plastic crack problems. The study finds that the mathematics becomes more complicated when the yield criterion lies on or outside the von Mises yield condition in the principal stress plane. It is also found that the maximum normal stress is higher under the modified version of the generalized Tresca yield condition compared to the equivalent mode I crack problem under the von Mises yield condition.
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK
(2023)
Article
Physics, Multidisciplinary
Xing Li, Tomoyuki Takenawa
Summary: This paper investigates the dynamical system determined by a QRT map and proposes a method to construct the solution directly using the Weierstrass sigma function. The method simplifies the complicated steps in the normalization process.
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
(2022)
Article
Mathematics
Benjamin Olea, Francisco J. Palomo
Summary: We define null-projectively relation as every null geodesic of a Lorentzian metric is an unparametrized geodesic of a semi-Riemannian metric on the same manifold M, which includes conformally related metrics and projectively equivalent metrics. We characterize this relation through certain tensors and provide examples. When both metrics share parametrized null geodesics, they are said to be null-related. We show how to construct projectively equivalent metrics via a conformal transformation from null-related metrics, and vice versa, adapting the classical Levi-Civita theorem to the case of null-related metrics and proving some results under curvature conditions ensuring that two null-related metrics are affinely equivalent.
JOURNAL OF GEOMETRIC ANALYSIS
(2023)
Article
Mathematics, Interdisciplinary Applications
Isao Shoji, Masahiro Nozawa
Summary: This article discusses a geometric method for analyzing nonlinear oscillations. By transforming the differential equation into a system of first-order ordinary differential equations, the trajectory can be embedded as a curve in R-3, allowing for the investigation of the dynamic properties of nonlinear oscillations.
CHAOS SOLITONS & FRACTALS
(2022)
Article
Thermodynamics
Y. Espinosa-Almeyda, R. Rodriguez-Ramos, H. Camacho-Montes, R. Guinovart-Diaz, F. J. Sabina
Summary: Effective properties of fiber-reinforced composites were analyzed using asymptotic homogenization method and Eisenstein-Rayleigh lattice sums, showing good agreements with available data in the literature. New easy-to-implement lattice sums were obtained, providing a set of tables with numerical values.
CONTINUUM MECHANICS AND THERMODYNAMICS
(2021)
Article
Mathematics, Applied
M. Smirnov
Summary: This paper considers the conformal mapping problem for the section of a channel filled with porous material under a rectangular dam, and uses the representation of Christoffel-Schwartz elliptic integral in terms of Weierstrass functions as a solution method. The calculation is based on the Taylor series for the sigma function, and a simple formula for a conformal mapping depending on four parameters and using the sigma function is obtained. Numerical experiments are conducted for a specific area, and the degeneration of the region is also considered, showing that the resulting formula has a limit that implements the solution of the limiting problem. A refined proof of Weierstrass recursive formula for the coefficients of the Taylor series of the sigma function is presented.
COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS
(2022)
Review
Engineering, Mechanical
Dan Zhao, Zhaqilao
Summary: The application of Weierstrass elliptic function solutions in the (2+1)-dimensional YTSF equation is investigated by using the traveling wave transformation and auxiliary equations. Through conversion formulas and selecting appropriate parameters, Weierstrass elliptic function solutions can be reduced to other types of elliptic function solutions and trigonometric function solutions.
NONLINEAR DYNAMICS
(2022)
Article
Physics, Multidisciplinary
Henri Roesch
Summary: The paper introduces a concept of Double Convexity that constrains the geometry of Marginally Outer Trapped Surfaces (MOTS) and aims to prove certain conditions regarding the Null Penrose Inequality. Furthermore, it identifies sufficient conditions for perturbations of quasi-round MOTS in Schwarzschild spacetime.
ANNALES HENRI POINCARE
(2021)
Article
Physics, Particles & Fields
M. Cariglia, A. Galajinsky, G. W. Gibbons, P. A. Horvathy
EUROPEAN PHYSICAL JOURNAL C
(2018)
Article
Astronomy & Astrophysics
P-M Zhang, M. Elbistan, G. W. Gibbons, P. A. Horvathy
GENERAL RELATIVITY AND GRAVITATION
(2018)
Article
Astronomy & Astrophysics
P. M. Zhang, M. Cariglia, M. Elbistan, G. W. Gibbons, P. A. Horvathy
Article
Astronomy & Astrophysics
Gary W. Gibbons, Marcus C. Werner
Article
Physics, Mathematical
Sumanto Chanda, G. W. Gibbons, Partha Guha, Paolo Maraner, Marcus C. Werner
JOURNAL OF MATHEMATICAL PHYSICS
(2019)
Article
Astronomy & Astrophysics
Krai Cheamsawat, Gary Gibbons, Toby Wiseman
CLASSICAL AND QUANTUM GRAVITY
(2020)
Article
Physics, Multidisciplinary
M. Cvetic, G. W. Gibbons, C. N. Pope, B. F. Whiting
PHYSICAL REVIEW LETTERS
(2020)
Article
Astronomy & Astrophysics
M. Elbistan, P. M. Zhang, G. W. Gibbons, P. A. Horvathy
Summary: This paper discusses the Lukash metric as a homogeneous gravitational wave approximating certain cosmological models, and presents the transcription to different coordinate systems. It also delves into the derivation of the 6-parameter isometry group and the global structure of spacetime, including the presence of a Killing horizon with distinct characteristics in different directions.
JOURNAL OF COSMOLOGY AND ASTROPARTICLE PHYSICS
(2021)
Article
Astronomy & Astrophysics
Gary W. Gibbons, Bernard S. Kay
Summary: This article discusses the naming issue of a formula representing the "square" of the Dirac operator in curved spacetime. The formula, g(mu nu)del(mu)del(nu) + m(2 )+ R/4, was originally discovered by Schrodinger in 1932 and later rediscovered by Lichnerowicz in 1962. However, the article overlooks the rediscovery of the formula by Asher Peres in 1963.
GENERAL RELATIVITY AND GRAVITATION
(2022)
Article
Astronomy & Astrophysics
M. Cvetic, G. W. Gibbons, C. N. Pope, B. F. Whiting
Summary: A problem in general relativity is the lack of viable theories for testing. This paper examines properties of a class of metrics that arise as solutions of ungauged supergravity, and evaluates their consistency using observational data. The study focuses on the massless, neutral, minimally coupled scalar wave equation and calculates the Love numbers of tidal perturbations and the harmonic coordinates for the background metric.
Article
Astronomy & Astrophysics
M. Elbistan, P-M Zhang, N. Dimakis, G. W. Gibbons, P. A. Horvathy
Article
Astronomy & Astrophysics
G. W. Gibbons, C. N. Pope, Sergey Solodukhin
Article
Astronomy & Astrophysics
M. Cvetic, G. W. Gibbons, H. Lu, C. N. Pope
Correction
Astronomy & Astrophysics
P. -M. Zhang, M. Cariglia, C. Duval, M. Elbistan, G. W. Gibbons, P. A. Horvathy
Article
Astronomy & Astrophysics
P. -M. Zhang, M. Cariglia, C. Duval, M. Elbistan, G. W. Gibbons, P. A. Horvathy