Direct discontinuous Galerkin method for nonlinear reaction–diffusion systems in pattern formation

Nonlinear reaction–diffusion systems are often employed in mathematical modeling for pattern formation. Most of the work to date has been concerned within one-dimensional or rectangular domains. However, it is recognised that in most applications multidimensional complex geometrical domains are typically more important. In this paper we solve reaction–diffusion systems by combining direct discontinuous Galerkin (DDG) finite element methods with implicit integration factor (IIF) time integration method, on triangular meshes. This allows us solve the nonlinear algebraic systems on an element-by-element bases with significant gains in computational time. Numerical solutions of two reaction–diffusion systems, the well-studied Schnakenberg model and chloride–iodide–malonic acid (CIMA) reactive model, are presented to demonstrate effects of various domain geometries on the resulting biological patterns. Our numerical results are in good agreement with other numerical and analytical results, and with experimental results.     

The Fourier-finite-element method with Nitsche mortaring

^** Email: bernd.heinrich{at}mathematik.tu-chemnitz.de The paper deals with a combination of the Fourier-finite-elementmethod with the Nitsche-finite-element method (as a mortar method).The approach is applied to the Dirichlet problem for the Poissonequation in 3D axisymmetric domains with non-axisymmetric data.The approximating Fourier method yields a splitting of the 3Dproblem into 2D problems on the meridian plane of the givendomain. For solving these 2D problems, the Nitsche-finite-elementmethod with non-matching meshes is applied. Some important propertiesof the approximation scheme are derived and the rate of convergencein an H¹-like norm as well as in the L₂-norm is estimated fora regular solution. Finally, some numerical results are presented.     

Convergence and superconvergence analysis of a new quadratic Hermite-type triangular element on anisotropic meshes

A new quadratic Hermite-type triangular finite element is conceived to solve a class of two-dimensional second-order elliptic boundary value problems. Its error estimates on anisotropic meshes are developed. Furthermore, we verify that some conditions set to the meshes contribute to the proof of its superconvergence properties, which can improve the approximation results. Numerical examples are given to confirm our theoretical analysis.     

Mechanically Robust Electrospun Hydrogel Scaffolds Crosslinked via Supramolecular Interactions

One of the major challenges in the processing of hydrogels based on poly(ethylene glycol) (PEG) is to create mechanically robust electrospun hydrogel scaffolds without chemical crosslinking postprocessing. In this study, this is achieved by the introduction of physical crosslinks in the form of supramolecular hydrogen bonding ureido‐pyrimidinone (UPy) moieties, resulting in chain‐extended UPy‐PEG polymers (CE‐UPy‐PEG) that can be electrospun from organic solvent. The resultant fibrous meshes are swollen in contact with water and form mechanically stable, elastic hydrogels, while the fibrous morphology remains intact. Mixing up to 30 wt% gelatin with these CE‐UPy‐PEG polymers introduce bioactivity into these scaffolds, without affecting the mechanical properties. Manipulating the electrospinning parameters results in meshes with either small or large fiber diameters, i.e., 0.63 ± 0.36 and 2.14 ± 0.63 µm, respectively. In that order, these meshes provide support for renal epithelial monolayer formation or a niche for the culture of cardiac progenitor cells.     

一类基于ENO插值的守恒重映算法

在大变形流体力学问题的数值模拟中,常常会涉及到计算网格的重分.基于不同网格的物理量传递便是所谓的重映技术.基于ENO插值的思想,发展了一类适用于任意网格的ENO守恒重映算法,并给出了数值结果.     

A tuneable 600 GHz bandpass-filter with large free-spectral-range

Considering recent ozon problems in the upper atmosphere the measuring technique in the spectral range of about some hundred GHz gains in importance increasingly. Ozon concentration is measured by high sensitive radiometers consisting of several quasioptical components. A tunable bandpass filter represents a versatile component in such a test assembly. The bandpass filter is realized as interferometer and can be adapted to its respective application by individual tuning of its coupling links. Metallic meshes of different aperture size are used for injection and feedback of the electromagnetic wave. A stepper motor control serves for the integration in an automatic measurement setup. The construction principles of the interferometer are summarized. An analysis of the component by means of plane wave theory is extended to a theory of diffraction. Finally the theoretical approach is verified on an application as single-sideband filter comparing the measured results with the computed values of the simulation.     

反应流体的移动网格动理学格式

在移动网格上构造一种反应流的动理学格式.首先利用BGK模型推导含化学反应的流体力学方程组,并利用其积分形式构造移动网格上离散格式,再利用自适应移动网格方法得到网格速度,最后利用时间精确的动理学数值方法构造数值通量,得到移动网格单元上新的物理量.一维与二维的数值实验表明这种格式同时具有高精度、高分辨率的特点.