On the fast-time oscillatory instabilities of Liñán's diffusion-flame regime

Fast-time instability for diffusion flames, with Lewis numbers set equal for fuel and oxidizer but greater than unity, is numerically analysed by the activation energy asymptotics and Evans function method. The time and length scales being chosen to be those of the inner reactive–diffusive layer, the problem corresponds to the instability problem for the Liñán's diffusion-flame regime. The instability is primarily oscillatory and emerges prior to reaching the turning point of the characteristic C-curve, usually known as the Liñán's extinction condition. A critical Lewis number, L _c , is also found, across which the instability changes its qualitative character. Below L _c , the instability possesses primarily a pulsating nature in that the two real branches of the dispersion relation existing for small wave numbers merge at a finite wave number, from which a pair of complex conjugate branches bifurcate. The maximum growth rate is found at the zero wave number. For Lewis numbers greater than L _c , the eigensolution branch for small reactant leakages is found to be purely complex with the maximum growth rate found at a finite wave number, thereby exhibiting a travelling nature. As the reactant-leakage parameter is further increased, the instability characteristics turns into a pulsating type, similar to that for 1 < L < L _c . The switching between different instability characters is found to correspond to the Bogdanov-Takens bifurcation.     

The rheology of bread dough made from four commercial flours

 A selection of four commercial flours has been subjected to extensive rheological measurements as part of a comprehensive program of wheat improvement. The results have been used to determine which of the many types of rheological measurements provide significant discrimination between various types of modern baker's flours (including biscuit flours) and to procure data suitable for use in mathematical models describing the dough rheology. The rheological measurements undertaken include oscillatory shear at low amplitude, steady shear at a low shear rate, stress relaxation and extensional viscosity testing. Although oscillatory shear data show minor differences between these flours, the other tests show significant variations and these provide very good discrimination between the different flour types in comparison with conventional dough testing (e.g. by the extensograph). The current dough rheological measurements provide further insight into molecular structure. In the future, mathematical (constitutive) models are expected to provide a means of predicting processing and baking behaviour of bread dough. Received: 27 June 2001 Accepted: 28 August 2001     

Rheology as a tool for the analysis of the dispersion of carbon filler in polymers

The aim of this work is to validate the use of dynamic oscillatory measurements in the melt to characterize the dispersion of a filler in a matrix after melt blending. Polyethylene oxide (PEO) is used as a polymeric matrix. Active carbon is used as a filler at a constant filler volume content of 26.4%. The melt viscosity of the polymeric matrix is varied by melt blending of two miscible POE and polyethylene glycol (PEG) species having very different molecular weight distributions. This enables to obtain various matrix viscosities and in turn various states of dispersion of the filler that were characterized by optical microscopy and image analysis. Dynamic mechanical measurements in the melt in the terminal zone show a large increase of the moduli associated to the presence of the filler. Comparison with the results of optical microscopy shows that this increase is clearly related to the dispersion. The interparticle distance is likely to be the leading parameter rather than the number of particles. Characterization of the amount of bound polymer shows that the amount of bound polymer is nearly independent of the matrix composition. Futhermore, the composition of the bound layer reflects the matrix composition though PEO is slightly preferentially bound on the active carbon.     

Effect of pH and added electrolyte on the thermal-induced transitions of egg yolk

Thermally-induced transitions of egg yolk were studied using Differential Scanning Calorimetry (DSC) and temperature-controlled Small Amplitude Oscillatory Shear (SAOS). The influence of composition (pH and electrolyte content and type) was analysed. The results obtained under DSC measurements suggest a continuous evolution in protein denaturation that depends on pH and salt content. Cure experiments performed using SAOS show dramatic increases in viscoelasticity functions. Protein gelation is affected by the pH, ionic strength and salt type. SAOS was also used to obtain the mechanical spectra of egg yolk dispersions and gels as a function of composition. The microstructures of gels were also evaluated by Scanning Electron Microscopy (SEM). SEM results reveal an increase in microstructure homogeneity and a decrease in the size of aggregates at lowered pH. The influence of pH and ionic strength on linear viscoelastic properties and microstructure may be explained in terms of the model for the formation of gel networks of globular proteins. However, the characteristic structure of native yolk must also be considered.This paper was presented at the first Annual European Rheology Conference (AERC) held in Guimarães, Portugal, September 11-13, 2003.     

Delay-independent stability of homogeneous systems

A class of nonlinear systems with homogeneous right-hand sides and time-varying delay is studied. It is assumed that the trivial solution of a system is asymptotically stable when delay is equal to zero. By the usage of the Lyapunov direct method and the Razumikhin approach, it is proved that the asymptotic stability of the zero solution of the system is preserved for an arbitrary continuous nonnegative and bounded delay. The conditions of stability of time-delay systems by homogeneous approximation are obtained. Furthermore, it is shown that the presented approaches permit to derive delay-independent stability conditions for some types of nonlinear systems with distributed delay. Two examples of nonlinear oscillatory systems are given to demonstrate the effectiveness of our results.     

Homogenization for nonlinear PDEs in general domains with oscillatory Neumann boundary data

In this article we investigate averaging properties of fully nonlinear PDEs in bounded domains with oscillatory Neumann boundary data. The oscillation is periodic and is present both in the operator and in the Neumann data. Our main result states that, when the domain does not have flat boundary parts and when the homogenized operator is rotation invariant, the solutions uniformly converge to the homogenized solution solving a Neumann boundary problem. Furthermore we show that the homogenized Neumann data is continuous with respect to the normal direction of the boundary. Our result is the nonlinear version of the classical result in [3] for divergence-form operators with co-normal boundary data. The main ingredients in our analysis are the estimate on the oscillation on the solutions in half-spaces (Theorem 3.1), and the estimate on the mode of convergence of the solutions as the normal of the half-space varies over irrational directions (Theorem 4.1).     

An operator van der Corput estimate arising from oscillatory Riemann–Hilbert problems

We study an operator analogue of the classical problem of finding the rate of decay of an oscillatory integral on the real line. This particular problem arose in the analysis of oscillatory Riemann–Hilbert problems associated with partial differential equations in the Ablowitz–Kaup–Newell–Segur hierarchy, but is interesting in its own right as a question in harmonic analysis and oscillatory integrals. As was the case in earlier work of the first author [9], the approach is general and purely real-variable. The resulting estimates we achieve are strongly uniform as a function of the phase and can simultaneously accommodate phases with low regularity (as low as C^1,α$C^{1,\alpha }$), local singularities, and essentially arbitrary sets of stationary points that degenerate to finite or infinite order.     

Interlacing properties of roots of certain biorthogonal polynomials

In this paper we consider the biorthogonal polynomials with respect to the measure e^-x4-y2+2τxydxdy, and show that their roots interlace. The proof involves showing total nonnegativity of matrices related to Jacobi type matrices.     

非理想性对B-Z反应体系时间自组织的影响

从理论和实验上研究了非理想性对B Z反应体系时间自组织行为的影响 ,重点考察了加入惰性电解质对B Z反应体系振荡周期的影响 ,按照Oregonator模型 ,通过小寄生参数法动力学理论分析表明 ,非理想性对B Z反应体系振荡周期的影响体现在振荡周期与铈离子的活度系数成反比 ,而且惰性电解质的加入使得振荡周期进一步加长 .通过一系列实验观测 ,原则上得到了与理论分析一致的结论     

<Emphasis Type="Italic">L</Emphasis><Superscript><Emphasis Type="Italic">p</Emphasis></Superscript> estimates of rough maximal functions along surfaces with applications

In this paper, we study the L^p mapping properties of certain class of maximal oscillatory singular integral operators. We prove a general theorem for a class of maximal functions along surfaces. As a consequence of such theorem, we establish the L^p boundedness of various maximal oscillatory singular integrals provided that their kernels belong to the natural space Llog L(S^n-1). Moreover, we highlight some additional results concerning operators with kernels in certain block spaces. The results in this paper substantially improve previously known results.