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It is known that under resonance conditions, a group of strongly interacting bosonic atoms, trapped in a double-well potential, mimics a single particle, performing Rabi oscillations between the wells. By implication, all atoms need to tunnel at roughly the same time, even though the Bose–Hubbard Hamiltonian accounts only for one-atom-at-a-time transfers. The mechanism of this collective behavior is analyzed, the Rabi frequencies in the process are evaluated, and the limitation of this simple picture is discussed. In particular, it is shown that the small rapid oscillations superimposed on the slow Rabi cycle result from splitting the transferred cluster at the sudden onset of tunnelling, and disappear if tunnelling is turned on gradually. 相似文献
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Detailed gas-phase chemical kinetic models are widely used in combustion research, and many new mechanisms for different fuels and reacting conditions are developed each year. Recent works have highlighted the need for error checking when preparing such models, but a useful community tool to perform such analysis is missing. In this work, we present a simple online tool to screen chemical kinetic mechanisms for bimolecular reactions exceeding collision limits. The tool is implemented on a user-friendly website, cloudflame.kaust.edu.sa, and checks three different classes of bimolecular reactions; (ie, pressure independent, pressure-dependent falloff, and pressure-dependent PLOG). In addition, two other online modules are provided to check thermodynamic properties and transport parameters to help kinetic model developers determine the sources of errors for reactions that are not collision limit compliant. Furthermore, issues related to unphysically fast timescales can remain an issue even if all bimolecular reactions are within collision limits. Therefore, we also present a procedure to screen ultrafast reaction timescales using computational singular perturbation. For demonstration purposes only, three versions of the rigorously developed AramcoMech are screened for collision limit compliance and ultrafast timescales, and recommendations are made for improving the models. Larger models for biodiesel surrogates, tetrahydropyran, and gasoline surrogates are also analyzed for exemplary purposes. Numerical simulations with updated kinetic parameters are presented to show improvements in wall-clock time when resolving ultrafast timescales. 相似文献
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Jamil Chaker 《Mathematische Nachrichten》2019,292(11):2316-2337
We consider systems of stochastic differential equations of the form for with continuous, bounded and non‐degenerate coefficients. Here are independent one‐dimensional stable processes with . In this article we research on uniqueness of weak solutions to such systems by studying the corresponding martingale problem. We prove the uniqueness of weak solutions in the case of diagonal coefficient matrices. 相似文献
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In this paper, we prove the existence and uniqueness of relaxation oscillation cycle of a slow–fast modified Leslie–Gower model via the entry–exit function and geometric singular perturbation theory. Numerical simulations are also carried out to illustrate our theoretical result. 相似文献
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Zvi Artstein 《Optimization》2019,68(1):81-98
ABSTRACTAn optimization problem of maximizing an integral of a function over a family of probability measures is considered. The problem is a generalization of a well-studied variational problem in mathematical economics, concerning optimal allocations. The specific generalization that we examine arises also in the limit of singularly perturbed optimal control problems. We examine the mathematical problem and allude to the singular perturbation motivation. 相似文献
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Cai and Zhang establish separate perturbation bounds for distances with spectral and Frobenius norms (Cai T, Zhang A. Rate‐optimal perturbation bounds for singular subspaces with applications to high‐dimensional statistics. The Annals of Statistics. 2018; Vol. 46, No. 1: 60?89). We extend their theorem to each unitarily invariant norm. It turns out that our estimation is optimal as well. 相似文献