An Quantum Kinetic Monte Carlo Method For Lindblad Equation

In this paper, we generalize the Quantum Kinetic Monte Carlo (QKMC) method of the Schrodinger equation, which was first proposed by [Z. Cai and J. Lu. SIAM J. Sci. Comput., 40(3):B706-B722, 2018] to the Lindblad equation. This algorithm makes full use of the tensor product structure of the matrices in the Lindblad equation, thus significantly reducing the storage cost, and can calculate a more extensive system than the existing methods. We demonstrate the method in the framework of the dissipative Ising model, and numerical experiments verify the validity of the method and the error analysis

Development of molecular approaches in the study of lettuce downy mildew (Bremia lactucae) population biology

Downy mildew of lettuce caused by Bremia lactucae is a serious disease resulting in yield loss. The population structure of the pathogen in the UK is poorly understood. This PhD project concentrated on developing molecular markers to differentiate the genotypic variation of B. lactucae populations, with the aim of improving methods to investigate lettuce - Bremia interactions. Thirty-seven B. lactucae isolates (including single-spore and new field isolates) were collected and characterized for virulence using the conventional International Bremia Evaluation Board (IBEB) differential set. Microsatellite markers (SSR, ISSR) were investigated for Bremia race specific marker development. Three isolates of B. lactucae were characterized by ISSR (inter simple sequence repeat) primers, although the polymorphic DNA could not be cloned in this project due to the highly variable results of the ISSR process. Some microsatellite repeats were found in B. lactucae isolates sequences that amplified by Plasmopara viticola (grape downy mildew) SSR markers. The development of Simple Sequence Repeat (SSR) markers from Bremia genomic DNA was not successful, which might result from the primers used being unsuitable for Bremia microsatellite enrichment. Bremia specific ITS primers were used for quantitative PCR. RxLR primers obtained from UC Davis (USA) were tested using the collection of B. lactucae isolates. RxLR1 primers distinguished between isolates BL801 and BL806. Eight SNPs were identified in three isolates amplified by RxLR5. No polymorphism was observed on the gel for the remaining RxLR primers on single spore races. Unrefined field isolates showed more polymorphisms on the gel than single spore isolates. The phenotypic differences between these two isolates have been identified by the IBEB differential set. Microscopy and qPCR quantification were used to investigate the compatible and incompatible interactions. The results suggest that BL801 is more virulent than BL806, as more infection structures were observed in IBEB resistant cultivars. Results of qPCR and spore count/unit weight of cotyledons showed that BL801 and BL806 were significantly different. The qPCR quantification results from 4 and 5 dpi were correlated with the spore count/unit weight of cotyledons. Although further work is required to develop race specific markers, the methods used in this project demonstrate the potential use of molecular markers to investigate lettuce - Bremia interactions

Assessment of Levee Breaching Risks to the Pearl River Delta

Flood Defenc

Efficient Frozen Gaussian Sampling Algorithms for Nonadiabatic Quantum Dynamics at Metal Surfaces

In this article, we propose a Frozen Gaussian Sampling (FGS) algorithm for simulating nonadiabatic quantum dynamics at metal surfaces with a continuous spectrum. This method consists of a Monte-Carlo algorithm for sampling the initial wave packets on the phase space and a surface-hopping type stochastic time propagation scheme for the wave packets. We prove that to reach a certain accuracy threshold, the sample size required is independent of both the semiclassical parameter $\varepsilon$ and the number of metal orbitals $N$, which makes it one of the most promising methods to study the nonadiabatic dynamics. The algorithm and its convergence properties are also validated numerically. Furthermore, we carry out numerical experiments including exploring the nuclei dynamics, electron transfer and finite-temperature effects, and demonstrate that our method captures the physics which can not be captured by classical surface hopping trajectories.Comment: 41 pages, 10 figure

An efficient iterative method for dynamical Ginzburg-Landau equations

In this paper, we propose a new finite element approach to simulate the time-dependent Ginzburg-Landau equations under the temporal gauge, and design an efficient preconditioner for the Newton iteration of the resulting discrete system. The new approach solves the magnetic potential in H(curl) space by the lowest order of the second kind Nedelec element. This approach offers a simple way to deal with the boundary condition, and leads to a stable and reliable performance when dealing with the superconductor with reentrant corners. The comparison in numerical simulations verifies the efficiency of the proposed preconditioner, which can significantly speed up the simulation in large-scale computations

Theoretical and experimental evidence on stock market volatilities: a two-phase flow model

The volume–volatility relationship usually ignores possible effects of stock shares. This article proposes a two-phase flow model assuming that capital and stock flows determine stock price and return volatility. Computational simulations suggest that monodirectional capital or stock flows and collective flows exert different effects on stock return volatilities. Considering the impact of stock flows, the positive relationship between capital and return volatility is no longer guaranteed. The inflow of capital and the outflow of stock increase stock price similarly; but exhibit completely different effects on stock return volatilities. A persistent stock inflow (outflow) reduces (intensifies) return volatilities, whereas a monodirectional persistent capital outflow has no such effect. When capital and stock flows’ velocities satisfy critical values determined by the initial state of the market, the market enlargement accompanied with increasing stock and capital shows no impact on market stability because of stable return volatilities. Otherwise, stock flows drive return volatilities with stronger effects than capital flows. Further experimental studies that simulate the real stock market through a trading system provide strong evidence supporting the two-phase flow model. Given similar driving forces of capital and stock flows, the interaction of them should be considered in constructing investment strategies and setting polici

Short-term Traffic Flow Prediction Based on Genetic Artificial Neural Network and Exponential Smoothing

In order to improve the accuracy of short-term traffic flow prediction, a combined model composed of artificial neural network optimized by using Genetic Algorithm (GA) and Exponential Smoothing (ES) has been proposed. By using the metaheuristic optimal search ability of GA, the connection weight and threshold of the feedforward neural network trained by a backpropagation algorithm are optimized to avoid the feedforward neural network falling into local optimum, and the prediction model of Genetic Artificial Neural Network (GANN) is established. An ES prediction model is presented then. In order to take the advantages of the two models, the combined model is composed of a weighted average, while the weight of the combined model is determined according to the prediction mean square error of the single model. The road traffic flow data of Xuancheng, Anhui Province with an observation interval of 5 min are used for experimental verification. Additionally, the feedforward neural network model, GANN model, ES model and combined model are compared and analysed, respectively. The results show that the prediction accuracy of the optimized feedforward neural network is much higher than that before the optimization. The prediction accuracy of the combined model is higher than that of the two single models, which verifies the feasibility and effectiveness of the combined model