Narrow Results

We first perform a complete Lie symmetry classification of the generalized convective Cahn–Hilliard equation. Then using the obtained symmetries, we mainly study the convective Cahn–Hilliard equation, of which a new power series solution is constructed. In particular for the crystal surface growth processes, the truncated series solution shows that the surface structures include peaks and valleys, and can exhibit different evolution trends with the driving force varying from compressive force to tensile force. Moreover, there exist several critical points for the driving force, where the surface configurations take the jump changes and show different features on the both sides of such critical points. According to the effects of driving forces, we analyze the dynamical features of crystal growth.

Transport and efficiency of over-damped Brownian particles moving in a confined narrow channel is investigated in the presence of an oscillating force and a static load force. It is found that the average velocity increases monotonously with the unbiased external driving force, while the efficiency can be a peaked function of unbiased external force, which indicates that the unbiased external force can facilitate the efficiency of energy transformation. Moreover, the average velocity and the efficiency demonstrate complex behaviors due to the consideration of Stokes efficiency.

This paper is concerned with the circumstances under which the dissipative character of a one-dimensional scalar conservation law may be described by a formalism strictly analogous to that arising naturally in the dynamics of nonlinearly elastic materials. It is shown that this occurs if and only if the entropy density, entropy flux pair associated with the conservation law takes a particular form. We compare the admissibility condition associated with this special entropy with other admissibility criteria such as those of Lax, Oleinik and regularization theory. Using the special entropy, we consider the Riemann problem for an example in which genuine nonlinearity fails and a kinetic relation is needed to determine a unique solution.

Rural tourism plays an important role in rural revitalization. Revealing the driving force of rural tourism development is the key to realizing the sustainable development of rural tourism and the hot spot of tourism and rural revitalization research. Using principal component analysis (PCA) and grey relational analysis (GRA), this paper takes 33 national key rural tourism villages in Qinghai as the research object to explore the driving forces and influencing factors of the sustainable development of rural tourism in Qinghai Tibet Plateau. The results show that: (1) The driving forces for the sustainable development of rural tourism in Qinghai Province mainly include rural service quality, ecological environment, and economy. (2) Rural service quality is driven by water, electricity, heating, and communication facilities, the ecological environment is driven by the improvement of village appearance and environment, and economic driving is driven by the per capita disposable income of towns and villages. (3) In the future, we must continue to strengthen rural infrastructure building, enhance the appearance and environment of villages, and raise the per capita disposable income level of rural cities. We will focus on developing villagers’ skills, improving lodging and catering operation standards, increasing the number of tourist reception points and urbanization rate, and raising villagers’ awareness of environmental and ecological protection, water conservation, grassland conservation, and other issues. We hope that this will promote the sustainable development of rural tourism in Qinghai Province.

In this chapter, the origin of the Earth’s motion, the characteristics of global sea–land changes, the lack of Paleozoic regional metamorphism in the Earth and the major global tectonic movements are introduced. The important driving forces of the formation of tectonic systems include changes in the Earth’s rotation speed, the effects of celestial bodies on the Earth, radioactive elements in the crust, the heterogeneity of the crust thickness, differences in the crust density, etc. Under the combined effect of these factors, multidirectional ground stresses were generated in different regions and different eras, resulting in the formation of different tectonic systems. Eight major tectonic system types on Earth are systematically proposed for the first time.

This chapter discusses the origin of the earth’s motion. Changes in the earth’s rotation speed are an important driving force for its movement. This chapter analyzes the influence of the earth’s rotation and impacts of celestial bodies on this rotation in terms of internal causes from the earth itself, geostress caused by the difference in thickness and density of the crust, and the earth’s layer structure.