Continuous prediction technique for fast determination of cyclic steady state in simulated moving bed process

In the simulation of cyclic processes, such as simulated moving bed (SMB), the system should be equilibrated to reach a cyclic steady state (CSS) before evaluating the process performance. However, the conventional method of successive substitution is quite time-consuming. In this work, a continuous predicting method (CPM) is developed for fast determination of CSS in SMB. In CPM, the direct prediction of state variable at CSS and solving model equation are conducted alternately until CSS is reached. In order to give a guideline for the selection of the acceleration factor, CPM is applied on SMB process for enantio separation of 1,1'-bi-2-naphtol racemate and with the optimized acceleration factor, 59% of computation time saved compared with successive substitution. In addition, this method is further successfully used in a sugar separation process. Given its efficiency and simplicity, this method could provide a useful tool for SMB simulations

Performance of various correlation measures in quantum renormalization-group method: A case study of quantum phase transition

We have investigated quantum phase transition employing the quantum renormalization group (QRG) method while in most previous literature barely entanglement (concurrence) has been demonstrated. However, it is now well known that entanglement is not the only signature of quantum correlations and a variety of computable measures have been developed to characterize quantum correlations in the composite systems. As an illustration, two cases are elaborated: one dimensional anisotropic (i) XXZ model and (ii) XY model, with various measures of quantum correlations, including quantum discord (QD), geometric discord (GD), measure-induced disturbance (MID), measure-induced nonlocality (MIN) and violation of Bell inequalities (eg. CHSH inequality). We have proved that all these correlation measures can effectively detect the quantum critical points associated with quantum phase transitions (QPT) after several iterations of the renormalization in both cases. Nonetheless, it is shown that some of their dynamical behaviors are not totally similar with entanglement and even when concurrence vanishes there still exists some kind of quantum correlations which is not captured by entanglement. Intriguingly, CHSH inequality can never be violated in the whole iteration procedure, which indicates block-block entanglement can not revealed by the CHSH inequality. Moreover, the nonanalytic and scaling behaviors of Bell violation have also been discussed in detail. As a byproduct, we verify that measure-induced disturbance is exactly equal to the quantum discord measured by \sigma_z for general X-structured states.Comment: Published version. 10 pages, 8 figure