Implementation of a particle-in-cell method for the energy solver in 3D spherical geodynamic modeling

The thermal evolution of the Earth’s interior and its dynamic effects are the focus of Earth sciences.However,the commonly adopted grid-based temperature solver is usually prone to numerical oscillations,especially in the presence of sharp thermal gradients,such as when modeling subducting slabs and rising plumes.This phenomenon prohibits the correct representation of thermal evolution and may cause incorrect implications of geodynamic processes.After examining several approaches for removing these numerical oscillations,we show that the Lagrangian method provides an ideal way to solve this problem.In this study,we propose a particle-in-cell method as a strategy for improving the solution to the energy equation and demonstrate its effectiveness in both one-dimensional and three-dimensional thermal problems,as well as in a global spherical simulation with data assimilation.We have implemented this method in the open-source finite-element code CitcomS,which features a spherical coordinate system,distributed memory parallel computing,and data assimilation algorithms.

Three-dimensional magnetotelluric modeling in the spherical and Cartesian coordinate systems:A comparative study

With the increase in the coverage area of magnetotelluric data,three-dimensional magnetotelluric modeling in spherical coordinates and its differences with respect to traditional Cartesian modeling have gradually attracted attention.To fully understand the influence of the Earth’s curvature and map projection deformations on Cartesian modeling,qualitative and quantitative analyses based on realistic three-dimensional models need to be examined.Combined with five representative map projections,a type of model conversion method that transforms the original spherical electrical conductivity model to Cartesian coordinates is described in this study.The apparent resistivity differences between the spherical western United States electrical conductivity model and the corresponding five Cartesian models are then compared.The results show that the cylindrical equal distance map projection has the smallest error.A meridian convergence correction resulting from the deformation of the map projection is introduced to rotate the Cartesian impedance tensor from grid north to geographic north,which reduces differences from the spherical results.On the basis of the magnetotelluric field data,the applicability of the Cartesian coordinate system to western and contiguous United States models is quantitatively evaluated.Precise interpretations of the contiguous United States model were found to require spherical coordinates.

Numerical Modeling of a Spherical Buoy Moored by a Cable in Three Dimensions

Floating facilities have been studied based on the static analysis of mooring cables over the past decades. To analyze the floating system of a spherical buoy moored by a cable with a higher accuracy than before, the dynamics of the cables are considered in the construction of the numerical modeling. The cable modeling is established based on a new element frame through which the hydrodynamic loads are expressed efficiently. The accuracy of the cable modeling is verified with an experiment that is conducted by a catenary chain moving in a water tank. In addition, the modeling of a spherical buoy is established with respect to a spherical coordinate in three dimensions, which can suffers the gravity, the variable buoyancy and Froude-Krylov loads. Finally, the numerical modeling for the system of a spherical buoy moored by a cable is established, and a virtual simulation is proceeded with the X- and Y-directional linear waves and the X-directional current. The comparison with the commercial simulation code Proteus DS indicates that the system is accurately analyzed by the numerical modeling. The tensions within the cable, the motions of the system, and the relationship between the motions and waves are illustrated according to the defined sea state. The dynamics of the cables should be considered in analyzing the floating system of a spherical buoy moored by a cable.

Analysis of Error Caused by Replacing Spherical Shell with an Elastic Plate Model in Studying Bending Deformation of the Lithosphere

To study the bending deformation of the lithosphere, the simplification of replacing a spherical shell by a plate model is usually made. Based on the differential equations for the bending of plates and shallow spherical shells, an expression for the error caused by such a simplification is derived in this paper. The effect of model sizes on the error is discussed. It is proved that if we replace the shallow spherical shell by a plate model to solve the bending deformation of lithospheric plate, a large error will be caused. In contrast, if we use a plate on an elastic foundation instead, an approximate solution closer to that of spherical shell can be obtained. In such a way, the error can be reduced effectively and the actual geological condition can be modeled more closely.

Establishment of European Regional Ionosphere Model Based on Spherical Harmonic Functions

In order to study the temporal and spatial variation characteristics of the regional ionosphere and the modeling accuracy,the experiment is based on the spherical harmonic function model,using the GPS,Glonass,and Galileo dual-frequency observation data from the 305th-334th day of the European CORS network in 2019 to establish a global ionospheric model.By analyzing and evaluating the accuracy of the global ionospheric puncture points,VTEC,and comparing code products,the test results showed that the GPS system has the most dense puncture electricity distribution,the Glonass system is the second,and the Galileo system is the weakest.The values of ionospheric VTEC calculated by GPS,Glonass and Galileo are slightly different,but in terms of trends,they are the same as those of ESA,JPL and UPC.GPS data has the highest accuracy in global ionospheric modeling.GPS,Glonass and Galileo have the same trend,but Glonass data is unstable and fluctuates greatly.

Computation and analysis Computation and analysis of the geomagnetic field model in China and its adjacent area for 2003

Based on the geomagnetic data at 135 stations and 35 observatories in China in 2003, the Taylor polynomial model and the spherical cap harmonic model in China and its adjacent area for 2003 were established. In the model calculation, the truncation order of the model and the influences of the boundary restriction on the model calculation were carefully analyzed. The results show that the geomagnetic data used are precise and reliable, and the selection of the truncation order is reasonable. The Taylor polynomial model and the spherical cap harmonic model in China and its adjacent area established in this paper are consistent very well.

Internal co-seismic deformation and curvature effect based on an analytical approach

In this study, we present a new method to compute internal co-seismic deformations of a homoge- neous sphere, based on our previous approach （Dong et al. 2016）. In practical numerical computations, we consider a strike-slip point source as an example, and compute the vertical co-seismic displacement on different internal spherical surfaces （including the Earth surface）. Numerical results show that the internal co-seismic deformations are generally larger than that on the Earth surface; especially, the maximum co-seismic displacement appears around the seismic source. The co-seismic displacements are opposite in sign for the areas over and beneath the position of the seismic source. The results also indicate that the curvature effect of the internal deformation is pretty large, and larger than that on the Earth surface. The results indicate that the dislocation theory for a sphere is necessary in computing internal co-seismic deformations.

Ray-optics model for optical force and torque on a spherical metal-coated Janus microparticle

In this paper, we develop a theoretical method based on ray optics to calculate the optical force and torque on a metallo-dielectric Janus particle in an optical trap made from a tightly focused Gaussian beam. The Janus particle is a 2.8 μm diameter polystyrene sphere half-coated with gold thin film several nanometers in thickness. The calculation result shows that the focused beam will push the Janus particle away from the center of the trap,and the equilibrium position of the Janus particle, where the optical force and torque are both zero, is located in a circular orbit surrounding the laser beam axis. The theoretical results are in good agreement qualitatively and quantitatively with our experimental observation. As the ray-optics model is simple in principle, user friendly in formalism, and cost effective in terms of computation resources and time compared with other usual rigorous electromagnetics approaches, the developed theoretical method can become an invaluable tool for understanding and designing ways to control the mechanical motion of complicated microscopic particles in various optical tweezers.

DESIGNATION AND APPLICATION OF A SPHERICAL LONG-WAVE SPECTRAL MODEL

A two-level,quasi-geostrophic long-wave model based on spherical coordinates was developed with the explicit part belonging to a low-order model.However,it includes not only diabatic heating,Ekman fric- tion and mountain distribution,but also parameterized forcing effects of transfer properties of transient eddies. Experiment results showed that,due to the introduction of the parameterization of transfer properties of transient eddies,remarkable improvements on characters of low-order model had been obtained.In addition to its economization in calculation and conciseness in physics as in a low-order model,the long- wave model was shown to describe the energetics and angular momentum balance of the atmosphere much more reasonably,and to present the features of zonal mean westerlies and stationary waves much more correctly than the corresponding low-order model.This kind of long-wave model was therefore regarded as suitable for theoretical research and numerical modelling of some aspects of the general circulation of the atmosphere.

An engineering analysis of penetration of metal ball into fibre-reinforced composite targets

An engineering analysis of computing the penetration problem of a steel ball penetrating into fibre-reinforced composite targets is presented. Assume the metal ball is a rigid body, and the composite target is a transversely isotropic elasto-plastic material. In the analysis, a spherical cavity dilatation model is incorporated in the cylindrical cavity penetration method. Simulation results based on the modified model are in good agreement with the results for 3-D Kevlar woven （3DKW） composite anti-penetration experiments. Effects of the target material parameters and impact parameters on the penetration problem are also studied.

A one-way coupled atmospheric-hydrological modeling system with combination of high-resolution and ensemble precipitation forecasting

Coupled hydrological and atmospheric model- ing is an effective tool for providing advanced flood forecasting. However, the uncertainties in precipitation forecasts are still considerable. To address uncertainties, a one-way coupled atmospheric-hydrological modeling sys- tem, with a combination of high-resolution and ensemble precipitation forecasting, has been developed. It consists of three high-resolution single models and four sets of ensemble forecasts from the THORPEX Interactive Grande Global Ensemble database. The former provides higher forecasting accuracy, while the latter provides the range of forecasts. The combined precipitation forecasting was then implemented to drive the Chinese National Flood Forecasting System in the 2007 and 2008 Huai River flood hindcast analysis. The encouraging results demonstrated that the system can clearly give a set of forecasting hydrographs for a flood event and has a promising relative stability in discharge peaks and timing for warning purposes. It not only gives a deterministic prediction, but also generates probability forecasts. Even though the signal was not persistent until four days before the peak discharge was observed in the 2007 flood event, the visualization based on threshold exceedance provided clear and concise essential warning information at an early stage. Forecasters could better prepare for the possibility of a flood at an early stage, and then issue an actual warning if the signal strengthened. This process may provide decision support for civil protection authorities. In future studies, different weather forecasts will be assigned various weight coefficients to represent the covariance of predictors and the extremes of distributions.