Theoretical and numerical research of wire array Z-pinch and dynamic hohlraum at IAPCM

Dense Z-pinch plasmas are powerful and energy-efficient laboratory sources of X-rays,and show the possibility to drive inertial confinement fusion(ICF).Recent advances in wire-array Z-pinch and Z-pinch dynamic hohlraum(ZPDH)researches at the Institute of Applied Physics and Computational Mathematics are presented in this paper.Models are setup to study different physical processes.A full circuit model(FCM)was used to study the coupling between Z-pinch implosion and generator discharge.A mass injection model with azimuthal modulation was setup to simulate the wire-array plasma initiation,and the two-dimensional MHD code MARED was developed to investigate the Z-pinch implosion,MRT instability,stagnation and radiation.Implosions of nested and quasi-spherical wire arrays were also investigated theoretically and numerically.Key processes of ZPDH,such as the arrayefoam interaction,formation of the hohlraum radiation,as well as the following capsule ablation and implosion,were analyzed with different radiation magneto-hydrodynamics(RMHD)codes.An integrated 2D RMHD simulation of dynamic hohlraum driven capsule implosion provides us the physical insights of wire-array plasma acceleration,shock generation and propagation,hohlraum formation,radiation ablation,and fuel compression.

The relative importance of competition to contagion:evidence from the digital currency market

How does the valuation change of an industry leader influence its competitors?Does it induce a competitive effect or a contagion effect?What are the driving forces of such influences?We attempted to answer these questions within digital currency markets.We found that both close and distant competitors against an industry leader experience high competitive effects,while moderate competitors experience high contagion effects.Next,we empirically demonstrated how this Ushaped pattern reduces to a linear relationship depending on the industry concentration.Lastly,we identified eight distinct information categories from a social media platform of the industry leader and compared the influence of the eight information categories on the industry leader’s competitors.Our analysis suggests that the relative importance of the competitive effect to the contagion effect in the industry depends on the category of the information.

Quadratic Finite Volume Element Schemes over Triangular Meshes for a Nonlinear Time-Fractional Rayleigh-Stokes Problem

In this article,we study a 2D nonlinear time-fractional Rayleigh-Stokes problem,which has an anomalous subdiffusion term,on triangular meshes by quadratic finite volume element schemes.Time-fractional derivative,defined by Caputo fractional derivative,is discretized through L2−1σformula,and a two step scheme is used to approximate the time first-order derivative at time tn−α/2,where the nonlinear term is approximated by using a matching linearized difference scheme.A family of quadratic finite volume element schemes with two parameters are proposed for the spatial discretization,where the range of values for two parameters areβ1∈(0,1/2),β2∈(0,2/3).For testing the precision of numerical algorithms,we calculate some numerical examples which have known exact solution or unknown exact solution by several kinds of quadratic finite volume element schemes,and contrast with the results of an existing quadratic finite element scheme by drawing diversified comparison plots and showing the detailed data of L2 error results and convergence orders.Numerical results indicate that,L2 error estimate of one scheme with parameters β_(1)=(3−√3)/6,β2=(6+√3−√21+6√3)/9 is O(h^(3)+△t^(2)),and L^(2) error estimates of other schemes are O(h^(2)+△t^(2)),where h and △t denote the spatial and temporal discretization parameters,respectively.

An Interpolation-Free Cell-Centered Finite Volume Scheme for 3D Anisotropic Convection-Diffusion Equations on Arbitrary Polyhedral Meshes

Most existing cell-centered finite volume schemes need to introduce auxiliary unknowns in order to maintain the second-order accuracy when the mesh is distorted or the problem is discontinuous,so interpolation algorithms of auxiliary unknowns are required.Interpolation algorithms are not only difficult to construct,but also bring extra computation.In this paper,an interpolation-free cell-centered finite volume scheme is proposed for the heterogeneous and anisotropic convectiondiffusion problems on arbitrary polyhedral meshes.We propose a new interpolationfree discretization method for diffusion term,and two new second-order upwind algorithms for convection term.Most interestingly,the scheme can be adapted to any mesh topology and can handle any discontinuity strictly.Numerical experiments show that this new scheme is robust,possesses a small stencil,and has approximately secondorder accuracy for both diffusion-dominated and convection-dominated problems.

A Vertex-Centered and Positivity-Preserving Finite Volume Scheme for Two-Dimensional Three-Temperature Radiation Diffusion Equations on General Polygonal Meshes

Two-dimensional three-temperature(2-D 3-T)radiation diffusion equa-tions are widely used to approximately describe the evolution of radiation energy within a multimaterial system and explain the exchange of energy among electrons,ions and photons.In this paper,we suggest a new positivity-preserving finite volume scheme for 2-D 3-T radiation diffusion equations on general polygonal meshes.The vertex unknowns are treated as primary ones for which the finite volume equations are constructed.The edgemidpoint and cell-centered unknowns are used as auxiliary ones and interpolated by the primary unknowns,which makes the final scheme a pure vertex-centered one.By comparison,most existing positivity-preserving finite volume schemes are cell-centered and based on the convex decomposition of the co-normal.Here,the conormal decomposition is not convex in general,leading to a fixed stencil of the flux approximation and avoiding a certain search algo-rithm on complex grids.Moreover,the new scheme effectively alleviates the nu-merical heat-barrier issue suffered by most existing cell-centered or hybrid schemes in solving strongly nonlinear radiation diffusion equations.Numerical experiments demonstrate the second-order accuracy and the positivity of the solution on various distorted grids.For the problem without analytic solution,the contours of the nu-merical solutions obtained by our scheme on distorted meshes accord with those on smooth quadrilateral meshes.