Investigation Of Analysis Models And Probabilistic Design Methods For Durability Of Marine Concrete Structures

Black holes are extreme compact celestial objects predicted by general relativity.Studying black holes is a crucial step in deepening our understanding of gravitational theory and exploring the universe.However,black holes possess an event horizon from which not even light can escape.Therefore,to investigate black holes,we can only rely on the celestial dynamics characteristics around black holes and the high-energy radiation from accreting material.In astrodynamics,there exists a peculiar nonlinear phenomenon—chaotic motion,indicating that system evolution is extremely sensitive to initial conditions.This physical behavior holds potential guiding value in explaining certain astronomical observations and astrophysical models.It is worth emphasizing that numerical simulations of chaotic motion in celestial bodies require the use of high-precision,high-stability numerical integration algorithms.To address this,a groundbreaking approach has been pioneered,constructing six-dimensional and ten-dimensional strictly energy-conserving algorithms with second-order numerical accuracy based on the discretization format of the canonical equations of Hamiltonian systems.These algorithms were then applied respectively to the particle orbital dynamics in black hole spacetime with an additional magnetic field and the orbital dynamics of spinning binary black holes,exploring the corresponding chaotic orbital characteristics.In the former study,it was found that the chaotic behavior of charged particles is not solely determined by a single parameter but rather by the combined effects of particle energy,magnetic field strength,particle angular momentum,and black hole spin.Among these,the first two parameters promote chaotic effects in charged particle dynamics,while the latter two parameters can suppress the occurrence of chaotic phenomena.The chaotic motion of charged particles near black holes may provide reasonable speculation for accretion disk evolution and jet formation.In the spinning binary black hole model,it was discovered that increasing the initial eccentricity of the orbit or decreasing the distance between the binary black holes can induce chaotic orbits of black holes.Such chaotic orbits hold significant importance in studying the evolution of binary black hole systems and gravitational wave radiation.Observational images of black holes stem from the radiation of accreting matter,serving as a powerful tool for studying the intrinsic properties of black holes and the surrounding high-energy environment.Since the Event Horizon Telescope Collaboration released the first black hole image,research on black hole image characteristics has rapidly gained momentum.On the theoretical level,studies of black hole images mainly focus on the features presented under different accretion environments,such as photon rings,black hole shadow morphology,and spot positions.Utilizing relativistic ray-tracing algorithms,numerical simulations have been conducted to obtain the images of modified gravitational Schwarzschild black holes within the scalar-tensor-vector theory framework under various accretion backgrounds,including static spherically symmetric accretion flows,infalling spherically symmetric accretion flows,and equatorial accretion disks.The study has found that the gravitational coupling parameter promotes the size of the black hole photon ring.When the black hole is surrounded by a spherically symmetric accretion flow,the photon ring and shadow silhouette of the black hole always overlap,with their sizes unaffected by changes in the accretion material’s motion.However,the acceleration of the accretion material can significantly affect the brightness of the image,especially the brightness of the photon ring,due to the Doppler effect.In optically and geometrically thin equatorial accretion disk models,using photon orbit numbers,the light rays emitted from the accretion disk are divided into direct emission,lensing ring emission,and photon ring emission.Numerical simulations were conducted to obtain the image of modified gravitational Schwarzschild black holes surrounded by an equatorial accretion disk with different radiation spectra.In this scenario,the observable profile of the black hole shadow no longer overlaps with the photon ring but gradually decreases depending on the extent of the accretion disk radiation region extending toward the black hole event horizon.This indicates that unlike the photon ring,the black hole shadow is influenced by the radiation details of the accretion disk.To study black hole properties through observed shadows,it is necessary to establish a connection between the shadow radius and the photon ring size,obtain geometric parameters of the photon ring through the shadow,and then identify the black hole and test gravitational theory.In the inclined accretion disk model,black hole images also exhibit noteworthy features.Using relativistic ray-tracing algorithms,numerical simulations have been conducted to obtain images of non-rotating scalar hairy black holes at 230 GHz within the Horndeski modified gravity theory.The study has found that introducing the scalar hair parameter enlarged the photon ring and inner shadow of the image but significantly suppressed image brightness.Additionally,it was observed that changes in the viewing angle and accretion disk inclination affect the morphology of the inner shadow and the brightness of image spots.These two parameters are degenerate due to spacetime spherical symmetry,and their combined effect on image features can be described using an equivalent viewing angle.Specifically,when the equivalent viewing angle is negative,the image appears inverted.Furthermore,the study has indicated that changes in the viewing azimuth angle can result in noticeable rotations of image spots and the position of the inner shadow.This suggests that information about accretion disk precession can be encoded in the details of the black hole image,making it feasible to infer accretion details from changes in observed image features obtained through continuous observations.When scalar hairy black holes are surrounded simultaneously by inclined accretion disks and equatorial accretion disks,the accretion environment exhibits a significant obscuring effect on the black hole’s inner shadow.This indicates that extra caution is required when using the inner shadow to test gravitational theories.