Stochastic linear multistep methods for the simulation of chemical kinetics

In this paper, we introduce the Stochastic Adams-Bashforth (SAB) and Stochastic Adams-Moulton (SAM) methods as an extension of the tau-leaping framework to past information. Using the theta-trapezoidal tau-leap method of weak order two as a starting procedure, we show that the k-step SAB method with k >= 3 is order three in the mean and correlation, while a predictor-corrector implementation of the SAM method is weak order three in the mean but only order one in the correlation. These convergence results have been derived analytically for linear problems and successfully tested numerically for both linear and non-linear systems. A series of additional examples have been implemented in order to demonstrate the efficacy of this approach.

Efficient simulation of stochastic chemical kinetics with the Stochastic Bulirsch-Stoer extrapolation method

Background Biochemical systems with relatively low numbers of components must be simulated stochastically in order to capture their inherent noise. Although there has recently been considerable work on discrete stochastic solvers, there is still a need for numerical methods that are both fast and accurate. The Bulirsch-Stoer method is an established method for solving ordinary differential equations that possesses both of these qualities. Results In this paper, we present the Stochastic Bulirsch-Stoer method, a new numerical method for simulating discrete chemical reaction systems, inspired by its deterministic counterpart. It is able to achieve an excellent efficiency due to the fact that it is based on an approach with high deterministic order, allowing for larger stepsizes and leading to fast simulations. We compare it to the Euler τ-leap, as well as two more recent τ-leap methods, on a number of example problems, and find that as well as being very accurate, our method is the most robust, in terms of efficiency, of all the methods considered in this paper. The problems it is most suited for are those with increased populations that would be too slow to simulate using Gillespie’s stochastic simulation algorithm. For such problems, it is likely to achieve higher weak order in the moments. Conclusions The Stochastic Bulirsch-Stoer method is a novel stochastic solver that can be used for fast and accurate simulations. Crucially, compared to other similar methods, it better retains its high accuracy when the timesteps are increased. Thus the Stochastic Bulirsch-Stoer method is both computationally efficient and robust. These are key properties for any stochastic numerical method, as they must typically run many thousands of simulations.

Multifractal analyses of daily rainfall time series in Pearl River basin of China

The multifractal properties of daily rainfall time series at the stations in Pearl River basin of China over periods of up to 45 years are examined using the universal multifractal approach based on the multiplicative cascade model and the multifractal detrended fluctuation analysis (MF-DFA). The results from these two kinds of multifractal analyses show that the daily rainfall time series in this basin have multifractal behavior in two different time scale ranges. It is found that the empirical multifractal moment function K(q)K(q) of the daily rainfall time series can be fitted very well by the universal multifractal model (UMM). The estimated values of the conservation parameter HH from UMM for these daily rainfall data are close to zero indicating that they correspond to conserved fields. After removing the seasonal trend in the rainfall data, the estimated values of the exponent h(2)h(2) from MF-DFA indicate that the daily rainfall time series in Pearl River basin exhibit no long-term correlations. It is also found that K(2)K(2) and elevation series are negatively correlated. It shows a relationship between topography and rainfall variability.

Microscopic cooperative traffic flow: Calibration and simulation based on a next generation simulation dataset

The deployment of new emerging technologies, such as cooperative systems, allows the traffic community to foresee relevant improvements in terms of traffic safety and efficiency. Autonomous vehicles are able to share information about the local traffic state in real time, which could result in a better reaction to the mechanism of traffic jam formation. An upstream single-hop radio broadcast network can improve the perception of each cooperative driver within a specific radio range and hence the traffic stability. The impact of vehicle to vehicle cooperation on the onset of traffic congestion is investigated analytically and through simulation. A next generation simulation field dataset is used to calibrate the full velocity difference car-following model, and the MOBIL lane-changing model is implemented. The robustness of the calibration as well as the heterogeneity of the drivers is discussed. Assuming that congestion can be triggered either by the heterogeneity of drivers' behaviours or abnormal lane-changing behaviours, the calibrated car-following model is used to assess the impact of a microscopic cooperative law on egoistic lane-changing behaviours. The cooperative law can help reduce and delay traffic congestion and can have a positive effect on safety indicators.

A stochastic exponential Euler scheme for simulation of stiff biochemical reaction systems

In order to simulate stiff biochemical reaction systems, an explicit exponential Euler scheme is derived for multidimensional, non-commutative stochastic differential equations with a semilinear drift term. The scheme is of strong order one half and A-stable in mean square. The combination with this and the projection method shows good performance in numerical experiments dealing with an alternative formulation of the chemical Langevin equation for a human ether a-go-go related gene ion channel mode

Predicting tours and probabilistic simulation for BKZ lattice reduction algorithm

We investigate the terminating concept of BKZ reduction first introduced by Hanrot et al. [Crypto'11] and make extensive experiments to predict the number of tours necessary to obtain the best possible trade off between reduction time and quality. Then, we improve Buchmann and Lindner's result [Indocrypt'09] to find sub-lattice collision in SWIFFT. We illustrate that further improvement in time is possible through special setting of SWIFFT parameters and also through the combination of different reduction parameters adaptively. Our contribution also include a probabilistic simulation approach top-up deterministic simulation described by Chen and Nguyen [Asiacrypt'11] that can able to predict the Gram-Schmidt norms more accurately for large block sizes.

Export of radioactive cesium from agricultural fields under simulated rainfall in Fukushima

In this study, we investigated the impact of rainfall on runoff, soil erosion and consequently on the discharge of radioactive cesium in agricultural fields in Fukushima prefecture using a rainfall simulator. Simulated heavy rainfalls (50 mm h-1) generated significant runoff and soil erosion. The average concentration of radioactive cesium (the sum of 134Cs and 137Cs) in the runoff sediments was [similar]3500 Bq kg-1 dry soil, more than double the concentrations measured in the field soils which should be considered in studies using the 137Cs loss to estimate long-term soil erosion. However, the estimated mass of cesium discharged through one runoff event was less than 2% of the cesium inventory in the field. This suggested that cesium discharge via soil erosion is not a significant factor in reducing the radioactivity of contaminated soils in Fukushima prefecture. However, the eroded sediment carrying radioactive cesium will deposit into the river systems and potentially pose a radioactivity risk for aquatic living organisms.

Probabilistic assessment of herbicide runoff from Japanese rice paddies: The effects of local meteorological conditions and site-specific water management

Uncertainty assessments of herbicide losses from rice paddies in Japan associated with local meteorological conditions and water management practices were performed using a pesticide fate and transport model, PCPF-1, under the Monte Carlo (MC) simulation scheme. First, MC simulations were conducted for five different cities with a prescribed water management scenario and a 10-year meteorological dataset of each city. The effectiveness of water management was observed regarding the reduction of pesticide runoff. However, a greater potential of pesticide runoff remained in Western Japan. Secondly, an extended analysis was attempted to evaluate the effects of local water management and meteorological conditions between the Chikugo River basin and the Sakura River basin using uncertainty inputs processed from observed water management data. The results showed that because of more severe rainfall events, significant pesticide runoff occurred in the Chikugo River basin even when appropriate irrigation practices were implemented. © Pesticide Science Society of Japan.

Simulation of pesticide behavior in a paddy block by a pesticide fate and transport model

A simulation model (PCPF-B) was developed based on the PCPF-1 model to predict the runoff of pesticides from paddy plots to a drainage canal in a paddy block. The block-scale model now comprises three modules: (1) a module for pesticide application, (2) a module for pesticide behavior in paddy fields, and (3) a module for pesticide concentration in the drainage canal. The PCPF-B model was first evaluated by published data in a single plot and then was applied to predict the concentration of bensulfuron-methyl in one paddy block in the Sakura river basin, Ibaraki, Japan, where a detailed field survey was conducted. The PCPF-B model simulated well the behavior of bensulfuron-methyl in individual paddy plots. It also reflected the runoff pattern of bensulfuron-methyl at the block outlet, although overestimation of bensulfuronmethyl concentrations occurred due to uncertainty in water balance estimation. Application of water management practice such as water-holding period and seepage control also affected the performance of the model. A probabilistic approach may be necessary for a comprehensive risk assessment in large-scale paddy areas.

Prediction of the fate of oxytetracycline and oxolinic acid in a fish pond using simulation model: A preliminary study

The fate of two popular antibiotics, oxytetracycline and oxolinic acid, in a fish pond were simulated using a computational model. The VDC model, which is designed based on a model for predicting pesticide fate and transport in paddy fields, was modified to take into account the differences between the pond and the paddies as well as those between the fish and the rice plant behaviors. The pond conditions were set following the typical practice in South East Asia aquaculture. The two antibiotics were administered to the animal in the pond through medicated feed during a period of 5 days as in actual practice. Concentrations of oxytetracycline in pond water were higher than those of oxolinic acid at the beginning of the simulation. Dissipation rate of oxytetracycline is also higher as it is more readily available for degradation in the water. For the long term, oxolinic acid was present at higher concentration than oxytetracycline in pond water as well as pond sediment. The simulated results were expected to be conservative and can be useful for the lower tier assessment of exposure risk of veterinary medicine in aquaculture industry but more data are needed for the complete validation of the model.

Fate and transport of bensulfuron-methyl and imazosulfuron in paddy fields: Experiments and model simulation

Experiments were conducted to determine the fate of bensulfuron-methyl (BSM) and imazosulfuron (IMS) under paddy conditions. Initially, laboratory experiments were conducted and the photolysis half-lives of the two herbicides were found to be much shorter than their hydrolysis half-lives in aqueous solutions. In the aerobic water–soil system, dissipation followed first-order kinetics with water half-lives of 9.1 and 11.0 days and soil half-lives of 12.4 and 18.5 days (first phase) and 35.0 and 44.1 days (second phase) for bensulfuron-methyl and imazosulfuron, respectively. However, the anaerobic soil half-lives were only 12.7 and 9.8 days for BSM and IMS, respectively. The values of K d were determined to be 16.0 and 13.8 for BSM and IMS, respectively. Subsequent field measurements for the two herbicides revealed that dissipation of both herbicides in paddy water involved biphasic first-order kinetics, with the dissipation rates in the first phase being much faster than those in the second phase. The dissipation of bensulfuron-methyl and imazosulfuron in the paddy surface soil were also followed biphasic first-order kinetics. These results were then used as input parameters for the PCPF-1 model to simulate the fate and transport of BSM and IMS in the paddy environment (water and 1-cm surface soil layer). The measured and simulated values agreed well and the mass balance error during the simulation period was −1.2 and 2.8% of applied pesticide, respectively, for BSM and IMS.

Influence of friction during forming processes-a study using a numerical simulation technique

Friction has an important influence in metal forming operations, as it contributes to the success or otherwise of the process. In the present investigation, the effect of friction on metal forming was studied by simulating compression tests on cylindrical Al-Mg alloy using the finite element method (FEM) technique. Three kinds of compression tests were considered wherein a constant coefficient of friction was employed at the upper die-work-piece interface. However, the coefficient of friction between the lower die-work-piece interfaces was varied in the tests. The simulation results showed that a difference in metal flow occurs near the interfaces owing to the differences in the coefficient of friction. It was concluded that the variations in the coefficient of friction between the dies and the work-piece directly affect the stress distribution and shape of the work-piece, having implications on the microstructure of the material being processed.

Reliable estimation via simulation

Let a and s denote the inter arrival times and service times in a GI/GI/1 queue. Let a (n), s (n) be the r.v.s, with distributions as the estimated distributions of a and s from iid samples of a and s of sizes n. Let w be a r.v. with the stationary distribution lr of the waiting times of the queue with input (a, s). We consider the problem of estimating E [w~], tx > 0 and 7r via simulations when (a (n), s (n)) are used as input. Conditions for the accuracy of the asymptotic estimate, continuity of the asymptotic variance and uniformity in the rate of convergence to the estimate are obtained. We also obtain rates of convergence for sample moments, the empirical process and the quantile process for the regenerative processes. Robust estimates are also obtained when an outlier contaminated sample of a and s is provided. In the process we obtain consistency, continuity and asymptotic normality of M-estimators for stationary sequences. Some robustness results for Markov processes are included.

Dynamic analysis and simulation of a VSC based Back-to-Back HVDC link

This paper presents the modeling and analysis of a voltage source converter (VSC) based back-to-back (BTB) HVDC link. The case study considers the response to changes in the active and reactive power and disturbance caused by single line to ground (SLG) fault. The controllers at each terminal are designed to inject a variable (magnitude and phase angle) sinusoidal, balanced set of voltages to regulate/control the active and reactive power. It is also possible to regulate the converter bus (AC) voltage by controlling the injected reactive power. The analysis is carried out using both d-q model (neglecting the harmonics in the output voltages of VSC) and three phase detailed model of VSC. While the eigenvalue analysis and controller design is based on the d-q model, the transient simulation considers both models.