Phase transition in the EM scheme of an SDE driven by α\alpha-stable noises with α∈(0,2]\alpha \in (0,2]

We study in this paper the EM scheme for a family of well-posed critical SDEs with the drift $-x\log(1+|x|)$ and $\alpha$-stable noises. Specifically, we find that when the SDE is driven by a rotationally symmetric $\alpha$-stable processes with $\alpha=2$ (i.e. Brownian motion), the EM scheme is bounded in the $L^2$ sense uniformly w.r.t. the time. In contrast, if the SDE is driven by a rotationally symmetric $\alpha$-stable process with $\alpha \in (0,2)$, all the $\beta$-th moments, with $\beta \in (0,\alpha)$, of the EM scheme blow up. This demonstrates a phase transition phenomenon as $\alpha \uparrow 2$. We verify our results by simulations

Electromagnetic Force in Dispersive and Transparent Media

A hydrodynamic-type, macroscopic theory was set up recently to simultaneously account for dissipation and dispersion of electromagnetic field, in nonstationary condensed systems of nonlinear constitutive relations~\cite{JL}. Since it was published in the letter format, some algebra and the more subtle reasonings had to be left out. Two of the missing parts are presented in this paper: How algebraically the new results reduce to the known old ones; and more thoughts on the range of validity of the new theory, especially concerning the treatment of dissipation.Comment: 10 pages, 0 figur

An empirical study of the time-varying spillover effects between China’s crude oil futures market and new energy markets

The time-varying spillover effect of China’s crude oil futures market and new energy market has an important impact on promoting the green development of China’s economy. This study uses the dynamic connectedness method based on DCC-GARCH model to analyze the time-varying spillover effects between Shanghai crude oil futures and various industries in new energy markets. The results show that there was a stable volatility correlation and high degree of connectedness between Shanghai crude oil futures and the new energy stock market. The new energy vehicle and energy storage industries were driving the market, while Shanghai crude oil futures and both wind power and photovoltaic industries were driven by the market.With the analysis results, the study provides scientific policy recommendations for the development of China’s crude oil futures market and new energy market, which are expected to contribute to the sustainable development of the energy market

Research on Passenger Flow Control Plans for a Metro Station Based on Social Force Model

To better utilise the service capacity of the limited facilities of a metro station, as well as ensure safety and transport efficiency during peak hours, a large passenger flow control plan is studied through theoretical analysis and numerical simulation. Firstly, by passenger data collection and data analysis, the characteristics of the inbound and outbound passenger flow of a T metro station are analysed. Secondly, AnyLogic evacuation simulation models for the T Station during peak hours, peak hours without/with passenger flow control are established based on real passenger flow data as well as the station structures and layouts by using the AnyLogic software. The results show that there are no obvious congestions in the station hall, and the travel delay is significantly reduced when effective passenger flow control measures are taken. By controlling the speed, direction and movement path of passengers, as well as adjusting the operation of escalators, entrances and automatic ticket-checking machines, passenger flow can become more orderly, transport efficiency can also be improved, and congestion in the station can be well mitigated

Modelling of cavity optomechanical magnetometers

Cavity optomechanical magnetic field sensors, constructed by coupling a magnetostrictive material to a micro-toroidal optical cavity, act as ultra-sensitive room temperature magnetometers with tens of micrometre size and broad bandwidth, combined with a simple operating scheme. Here, we develop a general recipe for predicting the field sensitivity of these devices. Several geometries are analysed, with a highest predicted sensitivity of 180~p$\textrm{T}/\sqrt{\textrm{Hz}}$ at 28~$\mu$m resolution limited by thermal noise in good agreement with previous experimental observations. Furthermore, by adjusting the composition of the magnetostrictive material and its annealing process, a sensitivity as good as 20~p$\textrm{T}/\sqrt{\textrm{Hz}}$ may be possible at the same resolution. This method paves a way for future design of magnetostrictive material based optomechanical magnetometers, possibly allowing both scalar and vectorial magnetometers.Comment: 13 pages, 7 figures; manuscript contributed to the Special Issue Sensors Based on Quantum Phenomen