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This work presents a numerical investigation of the self-steepening(SS) effect on the soliton spectral tunneling(SST) effect in a photonic crystal fiber(PCF) with three zero dispersion wavelengths. Interestingly, the spectral range and flatness can be flexibly tuned by adjusting the SS value. When the SS coefficient increases, the energy between solitons and dispersion waves is redistributed, and the red-shifted soliton forms earlier in the region of long wavelength anomalous dispersion. As a consequence, the SST becomes more obvious. The findings of this work provide interesting insights in regard to the impact of the SST effect on tailored supercontinuum generation. 相似文献
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The aim of this paper is to study the Herglotz variational principle of the fractional Birkhoffian system and its Noether symmetry and conserved quantities. First, the fractional Pfaff-Herglotz action and the fractional PfaffHerglotz principle are presented. Second, based on different definitions of fractional derivatives, four kinds of fractional Birkhoff’s equations in terms of the Herglotz variational principle are established. Further, the definition and criterion of Noether symmetry of the fractional Birkhoffian system in terms of the Herglotz variational problem are given. According to the relationship between the symmetry and the conserved quantities, the Noether’s theorems within four different fractional derivatives are derived, which can reduce to the Noether’s theorem of the Birkhoffian system in terms of the Herglotz variational principle under the classical conditions. As applications of the Noether’s t heorems of the fractional Birkhoffian system in terms of the Herglotz variational principle, an example is given at the end of this paper. 相似文献
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Herglotz变分原理的作用量是由微分方程定义的,不仅可以描述所有经典变分原理能够描述的动力学过程,还可以对经典变分原理不能适用的非保守系统或耗散系统进行变分描述.时间尺度上微积分理论提供了一种可同时研究离散系统和连续系统的有效方法.本文结合Herglotz变分原理和时间尺度微积分理论来研究时间尺度上的Herglotz变分原理及其Noether定理.首先,给出时间尺度上Lagrange系统的Herglotz变分原理.其次,根据Herglotz变分原理和Dubois-Reymond引理,推导出时间尺度上Lagrange系统的Herglotz变分问题的运动微分方程.再次,基于时间尺度上Hamilton-Herglotz作用量在群的无限小变换下的不变性,给出Noether对称性的定义并导出其Noether等式.最后,建立了时间尺度上Lagrange系统的Herglotz变分问题的Noether定理,给出了连续和离散两种情况下基于Herglotz变分问题的Noether守恒量.文末举例说明结果的应用. 相似文献
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钨合金中钾的掺杂会引入大量的缺陷,如尺寸几十纳米的钾泡、高密度的位错以及微米量级的晶粒带来的晶界等,这些缺陷的浓度和分布直接影响合金的服役性能.本文运用正电子湮没谱学方法研究钾掺杂钨合金中的缺陷信息,首先模拟计算了合金中各种缺陷的正电子湮没寿命,发现钾的嵌入对空位团、位错、晶界等缺陷的寿命影响很小;然后测量了不同钾含量掺杂钨合金样品的正电子湮没寿命谱,建立三态捕获模型,发现样品中有高的位错密度和低的空位团簇浓度,验证了钾对位错的钉扎作用,阐述了在钾泡形成初期是钾元素与空位团簇结合并逐渐长大的过程;最后使用慢正电子多普勒展宽谱技术表征了样品中缺陷随深度的均匀分布和大量存在,通过扩散长度的比较肯定了钾泡、晶界等缺陷的存在. 相似文献
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货物吞吐量是衡量港口发展水平的硬性指标,进行港口吞吐量预测可以更好的指导港口基础设施的规划与发展方向.通过对曹妃甸港主要货物在"十二五"规划时期的吞吐量情况进行分析,采用灰色预测的方法并分别对主要货物建立相应的预测模型并进行检验;同时分析货物吞吐量的预测数据,为曹妃甸港口的未来发展策略提出具体建议. 相似文献
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Conservation laws for the Birkhoffian system and the constrained Birkhoffian system of Herglotz type are studied. We propose a new differential variational principle, called the Pfaff-Birkhoff-d'Alembert principle of Herglotz type. Birkhoff's equations for both the Birkhoffian system and the constrained Birkhoffian system of Herglotz type are obtained. According to the relationship between the isochronal variation and the nonisochronal variation, the conditions of the invariance for the Pfaff-Birkhoff-d'Alembert principle of Herglotz type are given. Then, the conserved quantities for the Birkhoffian system and the constrained Birkhoffian system of Herglotz type are deduced. Furthermore, the inverse theorems of the conservation theorems are also established. 相似文献
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利用对称性和守恒律, 可以简化动力学问题甚至求解力学系统的精确解, 更好地理解其动力学行为. 时间尺度分析将连续和离散动力学模型统一并拓展到时间尺度框架, 既避免了重复研究又可揭示两者之区别和联系. 因此, 通过对称性来探寻在时间尺度的框架下新的守恒定律很有必要. 本文首先建立了时间尺度上Lagrange方程, 利用时间尺度微积分性质导出了时间尺度上Lagrange系统的两个重要关系式; 其次, 依据微分方程在单参数Lie变换群下的不变性, 建立了时间尺度上Lie对称性的定义和确定方程; 最后, 建立了时间尺度上Lie对称性定理并利用上述关系式给出了证明, 得到了时间尺度上Lagrange系统的新守恒量. 当时间尺度取为实数集时, 该守恒量退化为著名的Hojman守恒量. 文末考察了一个两自由度时间尺度Lagrange系统, 在3种不同时间尺度情形下得到了该系统的Hojman守恒量, 数值计算结果验证了定理的正确性. 相似文献