Analysis of a new multispecies tumor growth model coupling 3D phase-fields with a 1D vascular network

In this work, we present and analyze a mathematical model for tumor growth incorporating ECM erosion, interstitial flow, and the effect of vascular flow and nutrient transport. The model is of phase-field or diffused-interface type in which multiple phases of cell species and other constituents are separated by smooth evolving interfaces. The model involves a mesoscale version of Darcy’s law to capture the flow mechanism in the tissue matrix. Modeling flow and transport processes in the vasculature supplying the healthy and cancerous tissue, one-dimensional (1D) equations are considered. Since the models governing the transport and flow processes are defined together with cell species models on a three-dimensional (3D) domain, we obtain a 3D–1D coupled model.     

基于平面通量展开的三维Pin by Pin输运SP3计算

基于Pin by Pin输运SP₃计算是下一代反应堆物理计算方法中一个重要的研究方向。节块法一般采用高阶通量和中子源展开以适应较大的节块尺寸，因此对于Pin by Pin计算来说效率偏低。由于反应堆堆芯不均匀性更多发生在径向，本文提出一种径向基于二维平面通量展开结合轴向常规节块法的综合方法进行三维Pin by Pin输运SP₃计算，其三个方向的节块耦合迭代均采用基于中子净流耦合的格式。通过IAEA 2D/3D基准问题和典型输运基准问题计算，验证该计算方法对于堆芯扩散计算和输运计算的正确性和可行性。     

A nonlinear model for marble sulphation including surface rugosity and mechanical damage

Here we propose and analyze a mathematical model that aims to describe the marble sulphation process occurring in a given material. The model accounts for rugosity as well as for damaging effects. This model is characterized by some technical difficulties that seem hard to overcome from a theoretical viewpoint. Therefore, we introduce some physically reasonable modifications in order to establish the existence of a suitable notion of solution on a given time interval. Numerical simulations are presented and discussed, also in view of further research.     

On a question of Thas on partial 3‐(qn + 1, q + 1, 1) designs

In this note, we answer a question of JA Thas about partial $3$‐ $\left(q^n+1,q+1,1\right)$ designs. We then extend this answer to a result about the embedding of certain partial $3$‐ $\left(q^2+1,q+1,1\right)$ designs into Möbius planes.     

Nonnegative solutions to reaction–diffusion system with cross-diffusion and nonstandard growth conditions

We establish the existence of nonnegative weak solutions to nonlinear reaction–diffusion system with cross-diffusion and nonstandard growth conditions subject to the homogeneous Neumann boundary conditions. We assume that the diffusion operators satisfy certain monotonicity condition and nonstandard growth conditions and prove that the existence of weak solutions using Galerkin's approximation technique.     

Weak solution of the merged mathematical equations of the polluted atmosphere

Considered as a geophysical fluid, the polluted atmosphere shares the shallow domain characteristics with other natural large-scale fluids such as seas and oceans. This means that its domain is excessively greater horizontally than in the vertical dimension, leading to the classic hydrostatic approximation of the Navier–Stokes equations. In the past there has been proved a convergence theorem for this model with respect to the ocean, without considering pollution effects. The novelty of this present work is to provide a generalization of their result translated to the atmosphere, extending the fluid velocity equations with an additional convection–diffusion equation representing pollutants in the atmosphere.     

Spectral estimates for saddle point matrices arising in weak constraint four‐dimensional variational data assimilation

We consider the large sparse symmetric linear systems of equations that arise in the solution of weak constraint four‐dimensional variational data assimilation, a method of high interest for numerical weather prediction. These systems can be written as saddle point systems with a 3 × 3 block structure but block eliminations can be performed to reduce them to saddle point systems with a 2 × 2 block structure, or further to symmetric positive definite systems. In this article, we analyse how sensitive the spectra of these matrices are to the number of observations of the underlying dynamical system. We also obtain bounds on the eigenvalues of the matrices. Numerical experiments are used to confirm the theoretical analysis and bounds.     

Symmetry analysis and optimal systems of generalized Chaplygin gas equations with a source term

The system of generalized Chaplygin gas equations with a coulomblike friction term has been investigated by using the famous Lie symmetry method. A direct and systematic algorithm based on the adjoint transformation and invariants of the admitted Lie algebras is then used to construct one- and two-dimensional optimal system of the Chaplygin gas equations. Inequivalent classes of group invariant solutions are then obtained using the one-dimensional optimal system. Further, the evolutionary behaviour of the weak discontinuity wave within the state characterized by one of the group invariant solutions is investigated in detail, and certain observations are noted in respect to their contrasting behaviour.     

基于SWT方法的钢绞线索微动疲劳特性分析

为得到钢绞线索丝间接触区的应力场分布并预测微动疲劳裂纹萌生位置和微动疲劳寿命，本文利用参数化方法建立了精细化的钢绞线拉索有限元模型，包括整索模型和不同层丝间接触区域的局部精细化子模型．分析了钢绞线索在两种交变荷载工况下的应力场变化情况，并基于多轴疲劳SWT(Smith-Watson-Topper)临界平面法进行了疲劳特性分析和疲劳寿命预测．主要结论如下：钢绞线索内接触区边缘处的微动幅值较大，中心处几乎没有相对滑动，微动疲劳的初始裂纹萌生点位于接触区域边缘；经不同区域子模型分析比较，在轴向循环荷载作用下，外层钢丝的接触区域比内层钢丝更易发生微动疲劳损伤；在横向位移循环荷载作用下，同层钢丝因位置角度不同而产生了较大的疲劳特性差异，且相比轴向循环拉伸，该工况下最不利单丝的微动疲劳寿命更低；与非接触区域相比，接触区的疲劳寿命大幅降低，微动现象对钢绞线索的抗疲劳性能有明显降低作用．