A CSP and tabulation-based adaptive chemistry model

We demonstrate the feasibility of a new strategy for the construction of an adaptive chemistry model that is based on an explicit integrator stabilized by an approximation of the Computational Singular Perturbation (CSP)-slow-manifold projector. We examine the effectiveness and accuracy of this technique first using a model problem with variable stiffness. We assess the effect of using an approximation of the CSP-slow-manifold by either reusing the CSP vectors calculated in previous steps or from a pre-built tabulation. We find that while accuracy is preserved, the associated CPU cost was reduced substantially by this method. We used two ignition simulations – hydrogen–air and heptane–air mixtures – to demonstrate the feasibility of using the new method to handle realistic kinetic mechanisms. We test the effect of utilizing an approximation of the CSP-slow-manifold and find that its use preserves the order of the explicit integrator, produces no degradation in accuracy, and results in a scheme that is competitive with traditional implicit integration. Further analysis on the performance data demonstrates that the tabulation of the CSP-slow-manifold provides an increasing level of efficiency as the size of the mechanism increases. From the software engineering perspective, all the machinery developed is Common Component Architecture compliant, giving the software a distinct advantage in the ease of maintainability and flexibility in its utilization. Extension of this algorithm is underway to implement an automated tabulation of the CSP-slow-manifold for a detailed chemical kinetic system either off-line, or on-line with a reactive flow simulation code.     

The Singularity of Kontsevich’s Solution for QH<Superscript>*</Superscript>(CP<Superscript>2</Superscript>)

In this paper we study the nature of the singularity of the Kontsevichs solution of the WDVV equations of associativity. We prove that it corresponds to a singularity in the change of two coordinates systems of the Frobenius manifold given by the quantum cohomology of CP². Mathematics Subject Classifications (2000) 53C99, 32D99, 14N35, 88A99.     

On warped product manifolds satisfying some curvature conditions

We determine curvature properties of pseudosymmetric type of certain warped product manifolds, and in particular of generalized Robertson–Walker spacetimes, with Einsteinian or quasi-Einsteinian fibre.     

Intersubband transitions in InxAl（l-x）N/InyGa（l-y）N quantum well operating at 1.55 μm

In this paper, we theoretically study the effects of doping concentration ND and an external electric field on the intersubband transitions in InxAl（l-x）N/InyGa（l-y）N single quantum well by solving the Schrodinger and Poisson equations self-consistently. Obtained results including transition energies, the band structure, and the optical absorption have been discussed. The lowest three intersubband transitions （E2 -El）, （E3 -El）, and （E3 -E2） are calculated as functions of doping concentration ND. By increasing the doping concentration ND, the depletion effect can be reduced, and the ionized electrons will compensate the internal electric field which results from the spontaneous polarization. Our results show that an optimum concentration ND exists for which the transition 0.8 eV （1.55 μm） is carried out. Finally, the dependence of the optical absorption α13（ω） on the external electric field and doping concentration is studied. The maximum of the optical absorption can be red-shifted or blue-shifted through varying the doping concentration and the external electric field. The obtained results can be used for designing optical fiber telecommunications operating at 1.55 μm.     

Intersubband transitions in In_xAl_(1-x)N/In_yGa_(1-y)N quantum well operating at 1.55 μm

In this paper, we theoretically study the effects of doping concentration NDand an external electric field on the intersubband transitions in InxAl(1-x)N/InyGa(1-y)N single quantum well by solving the Schr¨odinger and Poisson equations self-consistently. Obtained results including transition energies, the band structure, and the optical absorption have been discussed. The lowest three intersubband transitions(E2- E1),(E3- E1), and(E3- E2) are calculated as functions of doping concentration ND. By increasing the doping concentration ND, the depletion effect can be reduced, and the ionized electrons will compensate the internal electric field which results from the spontaneous polarization. Our results show that an optimum concentration NDexists for which the transition 0.8 eV(1.55 μm) is carried out. Finally, the dependence of the optical absorption α13(ω) on the external electric field and doping concentration is studied. The maximum of the optical absorption can be red-shifted or blue-shifted through varying the doping concentration and the external electric field. The obtained results can be used for designing optical fiber telecommunications operating at 1.55 μm.     

On nondegenerate coupling forms

The aim of the present paper is to investigate new classes of symplectically fat fibre bundles. We prove a general existence theorem for fat vectors with respect to the canonical invariant connections. Based on this result we give new proofs of some constructions of symplectic structures. This includes twistor bundles and locally homogeneous complex manifolds. The proofs are conceptually simpler and allow for obtaining more general results.     

Two Classes of New Exact Solutions to (2+1)-Dimensional Breaking Soliton Equation

The singular manifold method is used to obtain two general solutions to a (2 1)-dimensional breaking soliton equation, each of which contains two arbitrary functions. Then the new periodic wave solutions in terms of the Jacobi elliptic functions are generated from the general solutions. The long wave limit yields the new types of dromion and solitary structures.     

调和映射在线性非平衡热力学中的应用

本文将一类线性非平衡热力学系统归结为调和映射问题.文中将昂塞格系数从常数推广成状态变量的函数,并应用调和映射讨论了系统的定态及其稳定性问题,给出了判定系统定态稳定性的判据.最后讨论了这些结果与原有的最小熵产生定理间的关系.     

Computational singular perturbation with non-parametric tabulation of slow manifolds for time integration of stiff chemical kinetics

This paper presents a novel tabulation strategy for the adaptive numerical integration of chemical kinetics using the computational singular perturbation (CSP) method. The strategy stores and reuses CSP quantities required to filter out fast dissipative processes, resulting in a non-stiff chemical source term. In particular, non-parametric regression on low-dimensional slow invariant manifolds (SIMs) in the chemical state space is used to approximate the CSP vectors spanning the fast chemical subspace and the associated fast chemical time-scales. The relevant manifold and its dimension varies depending on the local number of exhausted modes at every location in the chemical state space. Multiple manifolds are therefore tabulated, corresponding to different numbers of exhausted modes (dimensions) and associated radical species. Non-parametric representations are inherently adaptive, and rely on efficient approximate-nearest-neighbor queries. As the CSP information is only a function of the non-radical species in the system and has relatively small gradients in the chemical state space, tabulation occurs in a lower-dimensional state space and at a relatively coarse level, thereby improving scalability to larger chemical mechanisms. The approach is demonstrated on the simulation of homogeneous constant pressure H₂–air and CH₄–air ignition, over a range of initial conditions. For CH₄–air, results are shown that outperform direct implicit integration of the stiff chemical kinetics while maintaining good accuracy.