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1.
We address the problem of telegraphic transport in several dimensions. We review the derivation of two and three dimensional telegrapher’s equations—as well as their fractional generalizations—from microscopic random walk models for transport (normal and anomalous). We also present new results on solutions of the higher dimensional fractional equations.  相似文献   
2.
A mean-field type model with random growth and reset terms is considered. The stationary distributions resulting from the corresponding master equation are relatively easy to obtain; however, for practical applications one also needs to know the convergence to stationarity. The present work contributes to this direction, studying the transient dynamics in the discrete version of the model by two different approaches. The first method is based on mathematical induction by the recursive integration of the coupled differential equations for the discrete states. The second method transforms the coupled ordinary differential equation system into a partial differential equation for the generating function. We derive analytical results for some important, practically interesting cases and discuss the obtained results for the transient dynamics.  相似文献   
3.
离心压缩机是压缩空气储能系统中关键设备之一,需具备在较宽流量、压力范围内高负荷高效率运行的能力。作为一种变工况调节技术,可调扩压器可以扩大压缩机工作流量范围,改善气动性能。因此,本文以某压缩空气储能系统用离心压缩机为研究对象,通过数值计算方法研究了可调扩压器调节时压缩机性能变化规律。结果表明采用可调扩压器可以有效拓宽压缩机运行特性,工作流量范围扩大44%,压比范围扩大25%.此后,本文采用Kriging模型获得了压缩机综合性能曲线图和不同储能工况需求下扩压器的调节方案及规律,为压缩空气储能系统离心压缩机变工况主动控制提供了依据。  相似文献   
4.
遵循“学生主体、教师主导”的教育教学理念,借助信息化教学工具,合理有效地设计好每一个教学环节.采用演示、体验、探究、问题导向和分组讨论等教学手段和方法,让学生在课堂中自主发现问题、分析问题并解决问题,实现“学生做中学、教师做中教”,大大提升教学效果.  相似文献   
5.
利用孤立子方程KdV-mKdV的朗斯基解的形式和结构,我们提出了朗斯基形式展开法,运用这一方法获得了KdV-mKdV方程的丰富的新的复合函数解,并且朗斯基行列式中的元素不满足任何线性偏微分方程组.所得到的复合函数解是使用其它的方法得不到的.  相似文献   
6.
李军  陈勇 《理论物理通讯》2021,73(1):15001-5
Despite some empirical successes for solving nonlinear evolution equations using deep learning,there are several unresolved issues.First,it could not uncover the dynamical behaviors of some equations where highly nonlinear source terms are included very well.Second,the gradient exploding and vanishing problems often occur for the traditional feedforward neural networks.In this paper,we propose a new architecture that combines the deep residual neural network with some underlying physical laws.Using the sine-Gordon equation as an example,we show that the numerical result is in good agreement with the exact soliton solution.In addition,a lot of numerical experiments show that the model is robust under small perturbations to a certain extent.  相似文献   
7.
Ying Yang 《中国物理 B》2021,30(11):110202-110202
The research of rogue waves is an advanced field which has important practical and theoretical significances in mathematics, physics, biological fluid mechanics, oceanography, etc. Using the reductive perturbation theory and long wave approximation, the equations governing the movement of blood vessel walls and the flow of blood are transformed into high-order nonlinear Schrödinger (NLS) equations with variable coefficients. The third-order nonlinear Schrödinger equation is degenerated into a completely integrable Sasa-Satsuma equation (SSE) whose solutions can be used to approximately simulate the real rogue waves in the vessels. For the first time, we discuss the conditions for generating rogue waves in the blood vessels and effects of some physiological parameters on the rogue waves. Based on the traveling wave solutions of the fourth-order nonlinear Schrödinger equation, we analyze the effects of the higher order terms and the initial deformations of the blood vessel on the wave propagation and the displacement of the tube wall. Our results reveal that the amplitude of the rogue waves are proportional to the initial stretching ratio of the tube. The high-order nonlinear and dispersion terms lead to the distortion of the wave, while the initial deformation of the tube wall will influence the wave amplitude and wave steepness.  相似文献   
8.
使用Galerkin方法,结合Sobolev空间理论和不等式技巧,给出了广义神经传播方程解的存在唯一性定理,然后利用吸引子存在性定理,采用半群方法证明了方程整体吸引子的存在性.  相似文献   
9.
We have performed numerical analysis of the one-dimensional dynamics of the cylindrical/spherical dust ion acoustic shock waves in unmagnetized dusty plasma consisting of positive ions, immobile dust particles, and nonextensive distributed cold and hot electrons. A multiple-scale expansion method is used to derive Burgers Equation (BE) and modified Burgers equation (MBE) by including higher order nonlinearity. The basic characteristics of the shock waves have been analysed numerically and graphically for different physical parameters relevant to Saturn' E ring through 2D figures. The parametric dependence of dust ion acoustic shock waves on some plasma parameters nonextensive index, density, and temperature of cold and hot electrons, concentration of dust particles, thermal effects and kinematic viscosity of ions is explored. Furthermore, it is found that the nonplanar geometry effects have an important impact on the establishment of shock waves. The amplitude of the wave decreases faster as one departs away from the axis of the cylinder or centre of the sphere. Such decaying behaviour continues as time progresses. It is also found that an increasing dust concentration decreases the amplitude of the dust ion acoustic shock waves.  相似文献   
10.
通过引入参数,构造了一个全平面上的、含双曲函数的非齐次核函数。利用正切函数的有理分式展开,建立了最佳常数因子与正切函数高阶导数相关联的Hilbert型积分不等式。 作为应用,通过赋予参数不同的值,建立了一些有意义的特殊结果。  相似文献   
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