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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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下载免费PDF全文 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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本文介绍了以有机玻璃废弃物为原料制备高黏合强度的水基黏合剂的实验方法、黏合剂组成分析及黏合性能研究等内容.本实验可以锻炼学生的合成技能,拓宽学生的化学视野,培养学生的创新思想.同时,教师还可以针对本实验涉及的能源和环境问题对学生进行思政教育,激发学生努力学习,用专业知识为国效力的决心和使命感. 相似文献
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介绍了一个研究型大学化学综合实验——一种超分子弹性体的制备及其自修复性能的研究.主要包括聚合物复合物的制备、表征及修复性能研究.通过本实验的实践,学生可以掌握超分子作用力的特点及其在制备可修复材料领域的应用.本实验有助于拓宽学生的化学视野,对培养学生的创新能力和对知识的综合运用能力具有重要作用. 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