The Random Batch Method proposed in our previous work(Jin et al.J Comput Phys,2020)is not only a numerical method for interacting particle systems and its mean-field limit,but also can be viewed as a model of the part...The Random Batch Method proposed in our previous work(Jin et al.J Comput Phys,2020)is not only a numerical method for interacting particle systems and its mean-field limit,but also can be viewed as a model of the particle system in which particles interact,at discrete time,with randomly selected mini-batch of particles.In this paper,we investigate the mean-field limit of this model as the number of particles N→∞.Unlike the classical mean field limit for interacting particle systems where the law of large numbers plays the role and the chaos is propagated to later times,the mean field limit now does not rely on the law of large numbers and the chaos is imposed at every discrete time.Despite this,we will not only justify this mean-field limit(discrete in time)but will also show that the limit,as the discrete time intervalτ→0,approaches to the solution of a nonlinear Fokker-Planck equation arising as the mean-field limit of the original interacting particle system in the Wasserstein distance.展开更多
This paper discusses a numerical method for computing the evolution of large interacting system of quantum particles.The idea of the random batch method is to replace the total interaction of each particle with the N−...This paper discusses a numerical method for computing the evolution of large interacting system of quantum particles.The idea of the random batch method is to replace the total interaction of each particle with the N−1 other particles by the interaction with p≪N particles chosen at random at each time step,multiplied by(N−1)/p.This reduces the computational cost of computing the interaction potential per time step from O(N^(2))to O(N).For simplicity,we consider only in this work the case p=1—in other words,we assume that N is even,and that at each time step,the N particles are organized in N/2 pairs,with a random reshuffling of the pairs at the beginning of each time step.We obtain a convergence estimate for the Wigner transform of the single-particle reduced density matrix of the particle system at time t that is both uniform in N>1 and independent of the Planck constant h̵.The key idea is to use a new type of distance on the set of quantum states that is reminiscent of the Wasserstein distance of exponent 1(or Monge-Kantorovich-Rubinstein distance)on the set of Borel probability measures on Rd used in the context of optimal transport.展开更多
The population balance modeling is regarded as a universally accepted mathematical framework for dynamic simulation of various particulate processes, such as crystallization, granulation and polymerization. This artic...The population balance modeling is regarded as a universally accepted mathematical framework for dynamic simulation of various particulate processes, such as crystallization, granulation and polymerization. This article is concerned with the application of the method of characteristics (MOC) for solving population balance models describing batch crystallization process. The growth and nucleation are considered as dominant phenomena, while the breakage and aggregation are neglected. The numerical solutions of such PBEs require high order accuracy due to the occurrence of steep moving fronts and narrow peaks in the solutions. The MOC has been found to be a very effective technique for resolving sharp discontinuities. Different case studies are carried out to analyze the accuracy of proposed algorithm. For validation, the results of MOC are compared with the available analytical solutions and the results of finite volume schemes. The results of MOC were found to be in good agreement with analytical solutions and superior than those obtained by finite volume schemes.展开更多
The present study describes the production optimization of recombinant L-asparaginase II of Pectobacterium carotovorum MTCC 1428 in Escherichia coli BL21 (DE3) at batch and fed batch bioreactor level. Production of re...The present study describes the production optimization of recombinant L-asparaginase II of Pectobacterium carotovorum MTCC 1428 in Escherichia coli BL21 (DE3) at batch and fed batch bioreactor level. Production of recombinant L-asparaginase II in batch and fed batch mode was found to be 1.34 and 5.38 folds higher, respectively as compared to shake flask culture. SDS-PAGE and native PAGE of the purified enzyme revealed that molecular mass of the subunits and native enzyme are ~37.5 kDa and ~150 kDa, respectively. Optimum range of pH and temperature for hydrolysis of L-asparagine were found to be 7.5 - 8.5 and 47°C - 52°C, respectively. The recombinant enzyme is very specific for its natural substrate, L-asparagine. The activity of recombinant L-asparaginase II is improved by mono cations and diverse effectors including Na+, K+, L-cystine, L-histidine, glutathione and 2-mercaptoethanol whereas, it is moderately inhibited by different divalent cations and thiol group blocking reagent. The kinetic parameters Km, Vmax, kcat and Km/Kcat of purified recombinant L-asparaginase II were determined. The purified L-asparaginase II possesses no partial glutaminase activity, which is prerequisite to reduce the possibility of side effects during the course of anti-cancer therapy.展开更多
This paper discusses a queueing system with a retrial orbit and batch service, in which the quantity of customers’ rooms in the queue is finite and the space of retrial orbit is infinite. When the server starts servi...This paper discusses a queueing system with a retrial orbit and batch service, in which the quantity of customers’ rooms in the queue is finite and the space of retrial orbit is infinite. When the server starts serving, it serves all customers in the queue in a single batch, which is the so-called batch service. If a new customer or a retrial customer finds all the customers’ rooms are occupied, he will decide whether or not to join the retrial orbit. By using the censoring technique and the matrix analysis method, we first obtain the decay function of the stationary distribution for the quantity of customers in the retrial orbit and the quantity of customers in the queue. Then based on the form of decay rate function and the Karamata Tauberian theorem, we finally get the exact tail asymptotics of the stationary distribution.展开更多
基金supported by National Natural Science Foundation of China(Grant No.31571071)supported by National Natural Science Foundation of China(Grant Nos.11901389 and 11971314)Shanghai Sailing Program(Grant No.19YF1421300)。
文摘The Random Batch Method proposed in our previous work(Jin et al.J Comput Phys,2020)is not only a numerical method for interacting particle systems and its mean-field limit,but also can be viewed as a model of the particle system in which particles interact,at discrete time,with randomly selected mini-batch of particles.In this paper,we investigate the mean-field limit of this model as the number of particles N→∞.Unlike the classical mean field limit for interacting particle systems where the law of large numbers plays the role and the chaos is propagated to later times,the mean field limit now does not rely on the law of large numbers and the chaos is imposed at every discrete time.Despite this,we will not only justify this mean-field limit(discrete in time)but will also show that the limit,as the discrete time intervalτ→0,approaches to the solution of a nonlinear Fokker-Planck equation arising as the mean-field limit of the original interacting particle system in the Wasserstein distance.
基金The work of Shi Jin was partly supported by NSFC grants No.11871297 and No.31571071We thank E.Moulines for kindly indicating several references on stochastic approximation.
文摘This paper discusses a numerical method for computing the evolution of large interacting system of quantum particles.The idea of the random batch method is to replace the total interaction of each particle with the N−1 other particles by the interaction with p≪N particles chosen at random at each time step,multiplied by(N−1)/p.This reduces the computational cost of computing the interaction potential per time step from O(N^(2))to O(N).For simplicity,we consider only in this work the case p=1—in other words,we assume that N is even,and that at each time step,the N particles are organized in N/2 pairs,with a random reshuffling of the pairs at the beginning of each time step.We obtain a convergence estimate for the Wigner transform of the single-particle reduced density matrix of the particle system at time t that is both uniform in N>1 and independent of the Planck constant h̵.The key idea is to use a new type of distance on the set of quantum states that is reminiscent of the Wasserstein distance of exponent 1(or Monge-Kantorovich-Rubinstein distance)on the set of Borel probability measures on Rd used in the context of optimal transport.
文摘The population balance modeling is regarded as a universally accepted mathematical framework for dynamic simulation of various particulate processes, such as crystallization, granulation and polymerization. This article is concerned with the application of the method of characteristics (MOC) for solving population balance models describing batch crystallization process. The growth and nucleation are considered as dominant phenomena, while the breakage and aggregation are neglected. The numerical solutions of such PBEs require high order accuracy due to the occurrence of steep moving fronts and narrow peaks in the solutions. The MOC has been found to be a very effective technique for resolving sharp discontinuities. Different case studies are carried out to analyze the accuracy of proposed algorithm. For validation, the results of MOC are compared with the available analytical solutions and the results of finite volume schemes. The results of MOC were found to be in good agreement with analytical solutions and superior than those obtained by finite volume schemes.
文摘The present study describes the production optimization of recombinant L-asparaginase II of Pectobacterium carotovorum MTCC 1428 in Escherichia coli BL21 (DE3) at batch and fed batch bioreactor level. Production of recombinant L-asparaginase II in batch and fed batch mode was found to be 1.34 and 5.38 folds higher, respectively as compared to shake flask culture. SDS-PAGE and native PAGE of the purified enzyme revealed that molecular mass of the subunits and native enzyme are ~37.5 kDa and ~150 kDa, respectively. Optimum range of pH and temperature for hydrolysis of L-asparagine were found to be 7.5 - 8.5 and 47°C - 52°C, respectively. The recombinant enzyme is very specific for its natural substrate, L-asparagine. The activity of recombinant L-asparaginase II is improved by mono cations and diverse effectors including Na+, K+, L-cystine, L-histidine, glutathione and 2-mercaptoethanol whereas, it is moderately inhibited by different divalent cations and thiol group blocking reagent. The kinetic parameters Km, Vmax, kcat and Km/Kcat of purified recombinant L-asparaginase II were determined. The purified L-asparaginase II possesses no partial glutaminase activity, which is prerequisite to reduce the possibility of side effects during the course of anti-cancer therapy.
文摘This paper discusses a queueing system with a retrial orbit and batch service, in which the quantity of customers’ rooms in the queue is finite and the space of retrial orbit is infinite. When the server starts serving, it serves all customers in the queue in a single batch, which is the so-called batch service. If a new customer or a retrial customer finds all the customers’ rooms are occupied, he will decide whether or not to join the retrial orbit. By using the censoring technique and the matrix analysis method, we first obtain the decay function of the stationary distribution for the quantity of customers in the retrial orbit and the quantity of customers in the queue. Then based on the form of decay rate function and the Karamata Tauberian theorem, we finally get the exact tail asymptotics of the stationary distribution.
