Slow and Fast Variables in Non-autonomous Difference Equations

In this paper we present an existence and smoothness result for center-like invariant manifolds of non-autonomous difference equations with slow and fast state-space variables. This result can be seen as a first step to obtain Fenichel's geometric theory for difference equations. Hereby, our basic tool is an abstract integral manifold theorem.     

Integral manifolds under explicit variable time-step discretization

We study the behavior of the “full hierarchy” of integral manifolds, i.e. in particular those of stable, center-stable, center, center-unstable and unstable type, for nonautonomous ordinary differential equations in Banach spaces under explicit one-step discretization with varying step-sizes. Our main results on C ^m ? 1-closeness under such discretizations are formulated in a quantitative fashion and turn out to be an easy consequence of a general theorem on the existence of invariant fiber bundles within the “calculus on time scales”.     

Bifurcation and invariant manifolds of the logistic competition model

In this paper, we study a new logistic competition model. We will investigate stability and bifurcation of the model. In particular, we compute the invariant manifolds, including the important centre manifolds, and study their bifurcation. Saddle-node and period-doubling bifurcation route to chaos are exhibited via numerical simulations.     

Semi-symmetric Lorentzian hypersurfaces in Lorentzian space forms

In the present paper, we shall investigate and classify Lorentzian hypersurfaces in Lorentzian space forms satisfying some curvature conditions. We shall focus especially on semi-symmetric Lorentzian hypersurfaces. Those of constant curvature and those so-called “good” are explicitly described and classified. We shall also classify Einstein–Lorentzian hypersurfaces.     

FGM with REDx: chemically reactive dimensionality extension

We propose a new approach to improve the accuracy of flamelet-generated manifolds (FGMs) method by extending the manifolds with additional chemically reactive degrees of freedom. Following the ideas of intrinsic low-dimensional manifold, the dimensionality of the FGM is increased by performing a local time-scale analysis of the chemical source term. A few slow characteristic directions of the reaction kinetics are used to extend the FGM, while the remaining reaction groups, characterised by fast time-scales, are assumed in steady state. The introduced method for FGM REactive Dimensionality extension is abbreviated as FGM-REDx. It is tested in one-dimensional simulations reproducing an expansion of burnt gases in an aero-engine stator. This process is characterised by a rapid change of enthalpy and pressure, altering, among others, the chemistry of pollutants CO and NO. The primary focus was on the assessment of the FGM's capability to predict the pollutants emissions. The rates of physical/thermodynamic perturbations turned out to be severe enough for the chemical species composition to go off the flamelet. The FGM extended with one additional chemically reactive dimension has been generated and successfully applied to the test cases, yielding a high accuracy gain over the standard FGM.     

Resonances on Some Geometrically Finite Hyperbolic Manifolds

Abstract

We first prove the meromorphic extension to ? for the resolvent of the Laplacian on a class of geometrically finite hyperbolic manifolds with infinite volume and we give a polynomial bound on the number of resonances. This class notably contains the quotients Γ\ ⁿ⁺¹ with rational nonmaximal rank cusps previously studied by Froese-Hislop-Perry.     

硅量子点的形状及其弯曲表面效应

硅量子点的弯曲表面引起系统的对称性破缺, 致使某些表面键合在能带的带隙中形成局域电子态.计算结果表明:硅量子点的表面曲率不同形成的表面键合结合能和电子态分布明显不同. 例如, Si–O–Si桥键在曲率较大的表面键合能够在带隙中形成局域能级, 而在硅量子点曲率较小的近平台表面上键合不会形成任何局域态, 但此时的键合结合能较低. 用弯曲表面效应(CS)可以解释较小硅量子点的光致荧光光谱的红移现象. CS效应揭示了纳米物理中又一奇妙的特性. 实验证实, CS效应在带隙中形成的局域能级可以激活硅量子点发光. 关键词： 硅量子点 弯曲表面效应 表面键合 局域能级     

Surface tension curvature correction for fluid–vapour interface by thermodynamics of curved boundary layers

Thermodynamics of curved boundary layers is used to study surface properties of Lennard–Jones fluids and an equation is obtained for the surface tension of the spherical interfaces. The work of cavity formation inside a fluid is utilised to calculate the surface tension. The scaled particle theory (SPT) equation of Pierotti and Stillinger are properly modified. The calculations by the modified Stillinger equation predicts the surface tension in any radius of curvature and the results are in good agreement with the experimental data. But for Pierotti equation, due to low sensitivity to temperature, good agreement obtained only at low temperatures.