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We investigate the linearization of systems of n-component nonlinear diffusion equations; such systems have physical applications in soil science, mathematical biology and invariant curve flows. Equivalence transformations of their auxiliary systems are used to identify the systems that can be linearized. We also provide several examples of systems with two-component equations, and show how to linearize them by nonlocal mappings. 相似文献
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The relationship between symmetries and Gauss kernels for the Schrödinger equation iut=uxx+f(x)u is established. It is shown that if the Lie point symmetries of the equation are nontrivial, a classical integral transformations of the Gauss kernels can be obtained. Then the Gauss kernels of Schrödinger equations are derived by inverting the integral transformations. Furthermore, the relationship between Gauss kernels for two equations related by an equivalence transformation is identified. 相似文献
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We study the dynamical energy equipartition properties in the integrable Toda model with additional uniform or disordered on-site energies by extensive numerical simulations. The total energy is initially equidistributed among some of the lowest frequency linear modes. For the Toda model with uniform on-site potentials, the energy spectrum keeps its profile nearly unchanged in a relatively short time scale. On a much longer time scale, the energies of tail modes increase slowly with time. Energy equipartition is far away from being attached in our studied time scale. For the Toda model with disordered on-site potentials, the energy transfers continuously to the high frequency modes and eventually towards energy equipartition. We further perform a systematic study of the equipartition time teq depending on the energy density εand the nonlinear parameter α in the thermodynamic limit for the Toda model with disordered on-site potentials. We find teq∝(1/ε)~a(1/α)~b, where b ≈ 2 a. The values of a and b are increased when increasing the strengths of disordered on-site potentials or decreasing the number of initially excited modes. 相似文献
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Distinct edge states and optical conductivities in the zigzag and armchair silicene nanoribbons under exchange and electric fields
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Based on the tight binding model, we investigate the low energy bandstructures, edge states, and optical absorptions for the silicene nanoribbons(SiNRs) with different terminations under an in-plane exchange field and/or a perpendicular electric field. We find that the zigzag SiNRs are gapped by the exchange field, but they could reenter the metallic state after the application of the electric field. Contrarily, a certain kind of armchair SiNRs remain gapless even if a weak exchange field is present. Furthermore, the combination of the exchange and electric fields could effectively modulate the penetration length and the components of the edge states in the SiNRs. The corresponding optical conductivities for the SiNRs are also calculated, which show remarkable dependence on the edge types of the SiNRs and the two external fields. 相似文献
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采用再生水进行河流补给,对河流生态系统健康产生直接或潜在的危害.探讨河流水环境系统的不确定性,基于忽略弥散的一维河流水质模型,建立了再生水补给影响下的河流水质模型,选用三角模糊数来描述和处理水环境风险评价.应用结果表明,所建模型对于河流水质模拟与风险评价具有很好的适用性和稳定性. 相似文献
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通过精选教材典例,进行一题多变,深度的加工设计,旨在培养学生对数学问题也能守正创新的意识,减负提质,更好地发展学生几何直观,空间观念等核心素养. 相似文献
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The relationship between symmetries and Gauss kernels for the Schrdinger equation iut=uxx+f(x)u is established.It is shown that if the Lie point symmetries of the equation are nontrivial,a classical integral transformations of the Gauss kernels can be obtained.Then the Gauss kernels of Schrdinger equations are derived by inverting the integral transformations.Furthermore,the relationship between Gauss kernels for two equations related by an equivalence transformation is identified. 相似文献
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使用密度泛函理论中的广义梯度近似对内掺Sc原子的graphene-Sc-graphene扩展三明治结构的几何结构、电子结构和储氢性能进行计算研究. 计算发现: Sc原子位于单层石墨烯中六元环上方的结构具有较大的结合能, 但小于固体Sc的内聚能实验值(3.90 eV), 然而, 当单个Sc原子或者多个Sc原子在双层石墨烯中间与底层相距2 Å时, Sc原子与基底的结合能增加到5 eV以上, 远远大于固体Sc的内聚能实验值(3.90 eV), 因此相邻的Sc原子可以有效避免成簇. 由此可见, 三明治结构的形成明显增加了Sc原子与基底的结合强度, 该结构可以进一步储氢来满足18电子规则而更加稳定, 从而成为理想的新型储氢纳米材料. 扩展三明治结构graphene-Sc-graphene的(2×3)单元中每个Sc原子最多可以吸附2个H2分子, 对H2的平均吸附能分别为0.67 eV和0.54 eV, 介于物理吸附和化学吸附(0.1~0.8 eV)之间, 因此该体系可以实现常温常压下对H2的可逆吸附. 由储氢机制分析可知: 扩展三明治结构graphene-Sc-graphene主要通过Dewar-Kubas作用进行储氢, 形成了π-δ-π型的电子结构. 相似文献