Instabilities in threshold-diffusion equations with delay

The introduction of delays into ordinary or partial differential equation models is well known to facilitate the production of rich dynamics, ranging from periodic solutions through to spatio-temporal chaos. In this paper, we consider a class of scalar partial differential equations with a delayed threshold nonlinearity which admits exact solutions for equilibria, periodic orbits and travelling waves. Importantly, we show how the spectra of periodic and travelling wave solutions can be determined in terms of the zeros of a complex analytic function. Using this as a computational tool to determine stability, we show that delays can have very different effects on threshold systems with negative as opposed to positive feedback. Direct numerical simulations are used to confirm our bifurcation analysis, and to probe some of the rich behaviour possible for mixed feedback.     

铌酸锶钡薄膜的微结构与电光性能的研究

本文叙述了使用溶胶凝胶法在MgO(0 0 1)的衬底上制备铌酸锶钡薄膜的过程 ,膜层厚度可达 5 μm。通过X射线衍射、摇摆曲线、扫描、拉曼散射光谱等方法研究了薄膜的微结构性能 ,实验发现 ,铌酸锶钡薄膜具有了较好的 (0 0 1)方向的优先取向性能 ,并且随着薄膜厚度的增加 ,其晶体取向性也会随之不断改进。熔石英的透明衬底上生长的SBN薄膜具有较大的电致双折射效应 ,其有效电光系数能够高达 6 6 2× 10 -11m/V。     

Every rational surface is separably split

Partially supported by the NSF.     

Determination of platinum in ores by a combined fire assay—X-ray fluorescence method

A combined fire assay—x-ray fluorescence procedure for the determination of platinum in ores is described. Silver beads obtained by cupellation in the classical fire assay process are flattened to constant thickness before placement in the x-ray beam. A standard plot of platinum—silver intensity ratio versus platinum concentration is used to measure the platinum content of ore samples.     

Bumps, breathers, and waves in a neural network with spike frequency adaptation

We introduce a continuum model of neural tissue that includes the effects of spike frequency adaptation (SFA). The basic model is an integral equation for synaptic activity that depends upon nonlocal network connectivity, synaptic response, and the firing rate of a single neuron. We consider a phenomenological model of SFA via a simple state-dependent threshold firing rate function. As without SFA, Mexican-hat connectivity allows for the existence of spatially localized states (bumps). Importantly recent Evans function techniques are used to show that bumps may destabilize leading to the emergence of breathers and traveling waves. Moreover, a similar analysis for traveling pulses leads to the conditions necessary to observe a stable traveling breather. Simulations confirm our theoretical predictions and illustrate the rich behavior of this model.     

Oriented polymers from solution. II. Fibers and films of polyethylene/polypropylene blends

A version of the surface growth method by Zwijnenburg and Pennings is being used to produce blended fibers of polyethylene and polypropylene under conditions where polypropylene does not yield to this fiber growth technique but would grow films. The blended fiber contains intimately mixed crystalline regions of each pure component and combines thermal and mechanical properties of both. The growth method itself underlines the part played by adsorbed surface layers and entanglements within such layers which can involve the entanglement of chemically different species. This feature suggests a potentially new method for blend production.