Article
Astronomy & Astrophysics
Michele Levi, Jan Steinhoff
Summary: In this work, the spin-dependent conservative dynamics of inspiralling compact binaries at the fourth post-Newtonian order was completed, including the derivation of the next-to-next-to-leading order spin-squared interaction potential. The physical equations of motion of position and spin were derived from a direct variation of the action, along with the expressions of quadratic-in-spin Hamiltonians. Conserved integrals of motion were constructed to provide a consistency check for the validity of the result.
JOURNAL OF COSMOLOGY AND ASTROPARTICLE PHYSICS
(2021)
Article
Computer Science, Interdisciplinary Applications
Majid Haghi, Mohammad Ilati, Mehdi Dehghan
Summary: In this paper, a high-order compact scheme is proposed for solving two-dimensional nonlinear time-fractional fourth-order reaction-diffusion equations. The unique solvability of the numerical method is proved in detail, and the convergence of the proposed algorithm is proved using the energy method. Numerical examples are given to verify the theoretical analysis and efficiency of the developed scheme.
ENGINEERING WITH COMPUTERS
(2023)
Article
Astronomy & Astrophysics
Sebastian Murk
Summary: The existence of black holes is crucial for testing the consistency of general relativity and modified gravity theories. Only two types of dynamic solutions in spherical symmetry are compatible with the formation of an apparent horizon. Properties of f(R) and generic fourth-order gravity theories naturally fit both types of solutions. Observations of an apparent horizon alone may not be sufficient to distinguish between general relativity and modifications with up to fourth-order derivatives in the metric.
Article
Physics, Particles & Fields
Bofeng Wu, Chao-Guang Huang
Summary: By using the irreducible Cartesian tensors and the symmetric and trace-free formalism, the metric for the external gravitational field of a spatially compact stationary source is derived in the F(X, Y, Z) gravity theory. A new gauge condition is proposed to simplify the linearized gravitational field equations, and the stationary metric outside the source is obtained. The multipole expansion of the metric potential reveals the Yukawa-like corrections of F(X, Y, Z) gravity to General Relativity, characterized by two characteristic lengths and additional sets of mass-type source multipole moments.
JOURNAL OF HIGH ENERGY PHYSICS
(2023)
Article
Astronomy & Astrophysics
Miguel A. Garcia-Aspeitia, A. Hernandez-Almada, Juan Magana, V Motta
Summary: This passage presents an exhaustive analysis of unimodular gravity as a potential solution to the cosmological constant problem and current universe acceleration. By estimating the CC-like value and a new parameter z(ini), the analysis gets numbers close to the reionization epoch. Joint analysis of various observational data shows consistent results with estimations from Planck and Supernovae measurements.
PHYSICS OF THE DARK UNIVERSE
(2021)
Article
Mathematics, Applied
Deepti Kaur, R. K. Mohanty
Summary: The aim of this study is to develop a compact difference method for approximating fourth-order parabolic PDEs with Dirichlet and Neumann boundary conditions involving half-step points. The proposed method converges quaternary and quadratically in space and time, respectively. The imbedding technique is applied to approximate lower-order derivative terms using the governing differential equation to deduce the high-order method. The method is able to simulate the complex and intriguing long time dynamics of the good Boussinesq equation.
NUMERICAL ALGORITHMS
(2023)
Article
Engineering, Multidisciplinary
Rachel Gordon, Eli Turkel, Dan Gordon
Summary: A compact fourth-order scheme was developed for the three-dimensional elastic wave equation in frequency space, using the first-order velocity-stress formulation. The numerical implementation for homogeneous media showed significant improvements over the second-order scheme in both acoustic and elastic cases, with results comparing favorably to analytic solutions.
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
(2021)
Article
Mathematics, Applied
Reymundo Itza Balam, Miguel Uh Zapata
Summary: This paper presents a fourth-order compact immersed interface method to solve two-dimensional Poisson equations with discontinuous solutions on arbitrary domains divided by an interface. The new method is based on an implicit formulation obtained from generalized Taylor series expansions, and it is constructed from a few modifications to the central finite difference near the interface. Numerical experiments verify the feasibility and accuracy of the proposed method.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2022)
Article
Astronomy & Astrophysics
Luca Fabbri
Summary: We use the fourth-order differential theory of gravitation to address the issue of singularity avoidance, specifically studying the short-distance behavior in the case of black holes and the big bang.
Article
Astronomy & Astrophysics
Damiano Anselmi
Summary: In this study, inflationary perturbation spectra and the quantity r + 8n(T) were computed to the next-to-next-to-leading log order in quantum gravity with solely virtual particles. The spectra are functions of inflationary running coupling and satisfy cosmic renormalization group flow equations. Tensor fluctuations receive contributions from the spin-2 fakeon chi(mu nu), while the scalar spectrum's dependence on chi(mu nu) starts from alpha(2) corrections. The theoretical predictions have errors ranging from alpha(4) to alpha(3), and nontrivial issues regarding the fakeon projection at higher orders are discussed.
JOURNAL OF COSMOLOGY AND ASTROPARTICLE PHYSICS
(2021)
Article
Mathematics, Applied
Hanen Boujlida, Kaouther Ismail, Khaled Omrani
Summary: This study investigates a high-order accuracy finite difference scheme for solving the one-dimensional extended Fisher-Kolmogorov (EFK) equation. A new compact difference scheme is proposed and the a priori estimates and unique solvability are discussed using the discrete energy method. The unconditional stability and convergence of the difference solution are proved. Numerical experiments demonstrate the accuracy and efficiency of the proposed technique.
APPLIED NUMERICAL MATHEMATICS
(2024)
Article
Astronomy & Astrophysics
Marcello Miranda, Daniele Vernieri, Salvatore Capozziello, Francisco S. N. Lobo
Summary: This article presents a method to solve the problem of the initial singularity in the Big Bang by using bouncing solutions. By incorporating extended theories of gravity and an order reduction technique, the study aims to find solutions that closely resemble General Relativity.
Article
Mathematics, Applied
Fenghua Tong, Xinlong Feng, Zhilin Li
Summary: A fourth order finite difference method combined with an integrating factor strategy is proposed for solving steady convection and diffusion partial differential equations with variable coefficients in both 2D and 3D using uniform Cartesian grids. The integrating factor strategy and finite difference method provide an efficient way to handle large convection coefficients. Numerical examples demonstrate the convergence order and comparison of the two fourth order methods.
APPLIED MATHEMATICS LETTERS
(2021)
Article
Physics, Particles & Fields
Kourosh Nozari, Sara Saghafi, Fateme Aliyan
Summary: This paper studies the motion of electrically neutral and charged particles around a regular spherically symmetric MOG dark compact object to explore their related ISCO and energy flux. Furthermore, the accretion of perfect fluid onto the regular spherically symmetric MOG dark compact object is investigated. The results show that the MOG parameter increases the ISCO radius of test particles while decreasing the corresponding energy flux. In addition, the energy density and the radial component of the four-velocity of the infalling fluid decrease near the central source as the MOG parameter increases.
EUROPEAN PHYSICAL JOURNAL C
(2023)
Article
Computer Science, Interdisciplinary Applications
Jia Yin
Summary: This paper presents an approach to deal with the dynamics of the Dirac equation by introducing the time-ordering technique for time-dependent Hamiltonians, limiting the influence of time-dependence to certain steps. By only amending steps involving potentials, the scheme remains efficient, accurate, and easy to implement, as demonstrated in numerical examples in 1D and 2D.
JOURNAL OF COMPUTATIONAL PHYSICS
(2021)
Article
Astronomy & Astrophysics
M. Abdelwahab, S. Carloni, P. K. S. Dunsby
CLASSICAL AND QUANTUM GRAVITY
(2008)
Article
Astronomy & Astrophysics
Amare Abebe, Mohamed Abdelwahab, Alvaro de la Cruz-Dombriz, Peter K. S. Dunsby
CLASSICAL AND QUANTUM GRAVITY
(2012)
Article
Engineering, Multidisciplinary
Mohammed M. Ali, Mohammed M. Abu Shquier, Afag Slah Eldeen, Mohamed E. Zidan, Ra'ed M. Al-Khatib
INTERNATIONAL JOURNAL OF COMPUTING SCIENCE AND MATHEMATICS
(2020)
