In this paper, a high-order oscillation-free (OF) discontinuous Galerkin (DG) scheme is presented for one-dimensional compressible multi-material flows. For describing the dynamics of fluid mixture, we couple a conservative equation related to the volume-fraction model with the Euler equations. For controlling the oscillations, some damping terms are added into the weak formulation of the system to automatically adjust the high-order terms. There are not any parameters which need to be adjusted artificially in the new damping terms, and the difficulties in solving discontinuous solutions and complexities of designing limiters can be avoided. Our scheme can be applied to the simulation of compressible multi-material flows efficiently with the essentially non-oscillatory property. Moreover, our scheme can be extended to the one with any high order as long as the order of basis functions is increased. In this paper, we only study the third-order OFDG scheme with the basis functions up to the quadratic polynomial. Some examples are tested to demonstrate the third-order accuracy and essentially non-oscillatory property of our scheme.
In this paper, considering the effect of light on phytoplankton, we develop a nonlocal reaction-diffusion-advection model to study the effects of environmental toxicants on phytoplankton in a polluted water column. We first establish the existence and uniqueness of positive solutions to the system and then, by the eigenvalue theory, we investigate the stability of the semi-trivial steady state. Finally, we establish a priori estimate of the steady state of system, and prove the existence of positive steady states under certain conditions by using fixed point index theory.
This article introduces a new generalized inverse weak, namely, m-MPD inverse and discusses its related properties. Several different representations of the weak m-MPD inverse are listed, including Hartwig-Spindelböck decomposition forms. Next, the solution of a new equation corresponding to the weak m-MPD inverse is explored. Besides, the perturbation formula for the weak m-MPD inverse is derived.
Observation-driven integer-valued autoregressive models are wide-ly used for modeling count time series exhibiting dynamic dependence,yet their performance critically depends on the way that thinning probabilities are linked to past observations.Most existing specifications rely on the logit link and may respond excessively to large counts.In this paper,we introduce a class of new observation-driven integer-valued autoregressive models using logarithmic and soft-clipping links that attenuate the influence of large obser-vations.The proposed framework allows for stochastic covariates.Estima-tion is carried out using conditional maximum likelihood and conditional least squares methods.Simulation studies and two real data applications are used to illustrate the proposed models.
In this work,a homogeneous two-phase flow model in two-dimen-sional space is proposed for systems without a sharp interface between phases.The model allows the two phases to coexist within the same domain with distinct pressures,while their local proportions are represented by volume fractions.Within an arbitrary Lagrangian-Eulerian(ALE)framework,a two-dimensional Riemann solver is developed to construct the numerical scheme with novel formulations for numerical fluxes and nodal velocities,ensuring consistency on moving control volumes.Furthermore,a new moving-mesh strategy is designed,in which the evolution of the volume fraction is obtained directly from the geometric motion of the mesh and mass conservation,thereby avoiding solving the non-conservative convective equation with source terms.This enables the incorporation of physical drag models and finite relaxation co-efficients,allowing the gradual equilibration of velocity and pressure between the two phases to be calculated.Based on the volume-fraction formulation,a discrete representation of the pressure work term is derived.Finally,a series of numerical experiments are presented to demonstrate the accuracy,stability,and physical consistency of the proposed model and numerical scheme.
