Conservation-Dissipation Formalism for Soft Matter Physics: II. Application to Non-isothermal Nematic Liquid Crystals

To most existing non-equilibrium theories, the modeling of non-isothermal processes was a hard task. Intrinsic difficulties involved the non-equilibrium temperature, the coexistence of conserved energy and dissipative entropy, etc. In this paper, by taking the non-isothermal flow of nematic liquid crystals as a typical example, we illustrated that thermodynamically consistent models in either vectorial or tensorial forms could be constructed within the framework of Conservation-Dissipation Formalism (CDF). And the classical isothermal Ericksen-Leslie model and Qian-Sheng model were shown to be special cases of our new vectorial and tensorial models in the isothermal, incompressible and stationary limit. Most importantly, from above examples, it was learnt that mathematical modeling based on CDF could easily solve the issues relating with non-isothermal situations in a systematic way. The first and second laws of thermodynamics were satisfied simultaneously. The non-equilibrium temperature was defined self-consistently through the partial derivative of entropy function. Relaxation-type constitutive relations were constructed, which gave rise to the classical linear constitutive relations, like Newton's law and Fourier's law, in stationary limits. Therefore, CDF was expected to have a broad scope of applications in soft matter physics, especially under the complicated situations, such as non-isothermal, compressible and nanoscale systems.Comment: 29 page

Continuous-time weakly self-avoiding walk on Z\mathbb{Z} has strictly monotone escape speed

Weakly self-avoiding walk (WSAW) is a model of simple random walk paths that penalizes self-intersections. On $\mathbb{Z}$, Greven and den Hollander proved in 1993 that the discrete-time weakly self-avoiding walk has an asymptotically deterministic escape speed, and they conjectured that this speed should be strictly increasing in the repelling strength parameter. We study a continuous-time version of the model, give a different existence proof for the speed, and prove the speed to be strictly increasing. The proof uses a supersymmetric version of BFS--Dynkin isomorphism theorem, spectral theory, Tauberian theory, and stochastic dominance.Comment: 37 pages, 1 figur

Chinese information processing

A survey of the field of Chinese information processing is provided. It covers the following areas: the Chinese writing system, several popular Chinese encoding schemes and code conversions, Chinese keyboard entry methods, Chinese fonts, Chinese operating systems, basic Chinese computing techniques and applications

A general approach to massive upper bound for two-point function with application to self-avoiding walk torus plateau

We prove a sufficient condition for the two-point function of a statistical mechanical model on $\mathbb{Z}^d$, $d > 2$, to be bounded uniformly near a critical point by $|x|^{-(d-2)} \exp [ -c|x| / \xi ]$, where $\xi$ is the correlation length. The condition is given in terms of a convolution equation satisfied by the two-point function, and we verify the condition for strictly self-avoiding walk in dimensions $d > 4$ using the lace expansion. As an example application, we use the uniform bound to study the self-avoiding walk on a $d$-dimensional discrete torus with $d > 4$, proving a ``plateau'' of the torus two-point function, a result previously obtained for weakly self-avoiding walk in dimensions $d > 4$ by Slade. Our method has the potential to be applied to other statistical mechanical models on $\mathbb{Z}^d$ or on the torus.Comment: 23 page

Development of simplified models for crashworthiness analysis.

Simplified modeling generates a great deal of interest in the area of crashworthiness analysis. Modeling methods used to create simplified computer models for crashworthiness have been well developed. In advanced simplified models, researchers develop simplified elements that can correctly predict structure\u27s crash behavior based on the existing collapse theories. These developed simplified elements then are applied to develop the simplified models. Nevertheless, most of the exiting collapse theories are regarding the thin-walled box section beams. However, in addition to the box section member, the channel section member is another popular member and is widely used in engineering for architectural structures, vehicles, and etc. Therefore, to simplify the thin-walled channel section beams, new collapse theory is required to predict the crash behavior for such beams. This topic is the focus of this dissertation. This dissertation develops a mathematical model to predict the crash behavior of the thin-walled channel section beams based on their real collapse mechanisms. The derived math formulae are verified through several basic applications. After that, both the existing collapse theories and the developed collapse theory regarding the thin-walled channel section beams are applied to simplify the detailed truck chassis model. The developed simplified model is used for crashworthiness analysis and the results are compared to those from the detailed model. The developed theory and the modeling method are then validated through the comparison. Additionally, in developing the simplified truck chassis model, the cross members that were modeled using coarse shell elements in previous simplified models are remodeled using simple elements. Two of the simplified modeling methods, the superelement method and the equivalent beam method, are utilized to generate the simplified models for the cross members of the truck chassis model. The principle of both methods is to use simple elements to transfer the original members\u27 mass and stiffness matrices. The equivalent beam method is recommended after comparison of the results of the crashworthiness analyses of each method. The primary contributions of this work are first, the derivation of crash theory that can predict the crash behavior of thin-walled channel section beams. The second is the use of equivalent beams to simplify the cross members within truck chassis models. Finally, a simplified modeling methodology is presented and evaluated. All the theory and modeling method developed in this work are applied for creating simplified models. Both the simplified and detailed models are used for crashworthiness analyses, results show that the errors caused by the simplified models are fewer than 10% and the simplified models only take less than 10% of the computer time of the corresponding detailed models

Tai Ji Quan: An overview of its history, health benefits, and cultural value

AbstractTai Ji Quan is considered to be a part of traditional Chinese Wushu (a martial art) and comprises various styles that have evolved historically from the Chen, Yang, Wǔ, Wú, and Sun families (schools). Recent simplification of the original classic styles has made Tai Ji Quan easier to adopt in practice. Thus, the traditional legacy of using Tai Ji Quan for self-defense, mindful nurturing of well-being, and fitness enhancement has been expanded to more contemporary applications that focus on promoting physical and mental health, enhancing general well-being, preventing chronic diseases, and being an effective clinical intervention for diverse medical conditions. As the impact of Tai Ji Quan on physical performance and health continues to grow, there is a need to better understand its historical impact and current status. This paper provides an overview of the evolution of Tai Ji Quan in China, its functional utility, and the scientific evidence of its health benefits, as well as how it has been a vehicle for enhancing cultural understanding and exchanging between East and West