Diffusion Models for Double-ended Queues with Renewal Arrival Processes

We study a double-ended queue where buyers and sellers arrive to conduct trades. When there is a pair of buyer and seller in the system, they immediately transact a trade and leave. Thus there cannot be non-zero number of buyers and sellers simultaneously in the system. We assume that sellers and buyers arrive at the system according to independent renewal processes, and they would leave the system after independent exponential patience times. We establish fluid and diffusion approximations for the queue length process under a suitable asymptotic regime. The fluid limit is the solution of an ordinary differential equation, and the diffusion limit is a time-inhomogeneous asymmetric Ornstein-Uhlenbeck process (O-U process). A heavy traffic analysis is also developed, and the diffusion limit in the stronger heavy traffic regime is a time-homogeneous asymmetric O-U process. The limiting distributions of both diffusion limits are obtained. We also show the interchange of the heavy traffic and steady state limits

Number-resolved master equation approach to quantum transport under the self-consistent Born approximation

We construct a particle-number(n)-resolved master equation (ME) approach under the self-consistent Born approximation (SCBA) for quantum transport through mesoscopic systems. The formulation is essentially non-Markovian and incorporates the interlay of the multi-tunneling processes and many-body correlations. The proposed n-SCBA-ME goes completely beyond the scope of the Born-Markov master equation, being applicable to transport under small bias voltage, in non-Markovian regime and with strong Coulomb correlations. For steady state, it can recover not only the exact result of noninteracting transport under arbitrary voltages, but also the challenging nonequilibrium Kondo effect. Moreover, the n-SCBA-ME approach is efficient for the study of shot noise.We demonstrate the application by a couple of representative examples, including particularly the nonequilibrium Kondo system.Comment: arXiv admin note: substantial text overlap with arXiv:1302.638

Heating And Air-conditioning Technology For Radiant Heat Recovery In Kiln Wall Of Cement Plant

There is a large amount of energy waste in the cement production process, in which the waste of rotary kiln heat and the waste of high temperature exhaust gas at the kiln tail are the most serious. Therefore, the full and reasonable utilization of this waste heat resource is an important measure to improve the utilization degree and energy efficiency of waste heat, effectively reduce the heat pollution caused by waste heat emission to the environment, and protect the ecological environment. It is of great significance to realize energy conservation and emission reduction and regional sustainable development. The strategic goals are extremely important. At present, the waste heat mainly used by cement plants is the high-temperature flue gas at the kiln head and kiln tail, and there are few cases of recycling the radiant heat of the kiln tube wall. Therefore, based on the data provided by a cement plant in Shandong Province, China, a set of waste heat recovery equipment for the rotary kiln of a cement plant is designed. According to actual needs, a suitable lithium bromide absorption refrigeration unit and heat exchanger are selected to determine the waste heat utilization plan in winter, summer and transition season and make economic analysis

Rectified Pessimistic-Optimistic Learning for Stochastic Continuum-armed Bandit with Constraints

This paper studies the problem of stochastic continuum-armed bandit with constraints (SCBwC), where we optimize a black-box reward function $f(x)$ subject to a black-box constraint function $g(x)\leq 0$ over a continuous space $\mathcal X$. We model reward and constraint functions via Gaussian processes (GPs) and propose a Rectified Pessimistic-Optimistic Learning framework (RPOL), a penalty-based method incorporating optimistic and pessimistic GP bandit learning for reward and constraint functions, respectively. We consider the metric of cumulative constraint violation $\sum_{t=1}^T(g(x_t))^{+},$ which is strictly stronger than the traditional long-term constraint violation $\sum_{t=1}^Tg(x_t).$ The rectified design for the penalty update and the pessimistic learning for the constraint function in RPOL guarantee the cumulative constraint violation is minimal. RPOL can achieve sublinear regret and cumulative constraint violation for SCBwC and its variants (e.g., under delayed feedback and non-stationary environment). These theoretical results match their unconstrained counterparts. Our experiments justify RPOL outperforms several existing baseline algorithms

Accurate Estimation of Transport Coefficients Using Model-free Time Correlation Functions in Equilibrium Simulations

Transport coefficients, such as the diffusion coefficient and shear viscosity, are important material properties that are calculated in computer simulations. In this study, the criterion for the best estimation of viscosity, as an example of transport coefficients, is determined by using the Green-Kubo formula without any artificial models. The related algorithm is given by the estimation of the viscosities of polyethylene oxide solutions by using a molecular dynamics simulation for testing. The algorithm can be used in the simulations of complex systems with a long tail of correlations typically found in macromolecular and biological simulation systems.Comment: 8 pages, 5 figures, 1 tabl