Instabilities of quantum critical metals in the limit $N_f\rightarrow0$

We study a model in 2+1 dimensions composed of a Fermi surface of N_fNf flavors of fermions coupled to scalar fluctuations near quantum critical points (QCPs). The N_f\rightarrow0Nf→0 limit allows us to non-perturbatively calculate the long-range behavior of fermion correlation functions. We use this to calculate charge, spin and pair susceptibilities near different QCPs at zero and finite temperatures, with zero and finite order parameter gaps. While fluctuations smear out the fermionic quasiparticles, we find QCPs where the overall effect of fluctuations leads to enhanced pairing. We also find QCPs where the fluctuations induce spin and charge density wave instabilities for a finite interval of order parameter fluctuation gaps at T=0T=0. We restore a subset of the diagrams suppressed in the N_f\rightarrow0Nf→0 limit, all diagrams with internal fermion loops with at most 2 vertices, and find that this does not change the long-range behavior of correlators except right at the QCPs.

Robust Optimization of Industrial Process Operation Parameters Based on Data-Driven Model and Parameter Fluctuation Analysis

The fluctuation of industrial process operation parameters will severely influence the production process. How to find the robust optimal process operation parameters is an effective method to address this problem. In this paper, a scheme based on data-driven model and variable fluctuation analysis is proposed to obtain the robust optimal operation parameters of industrial process. The data-driven modelling method: multivariate Gaussian process regression (MGPR) based on Bayesian statistical learning theory can map the process operation parameters to objective performance with the flexibility in nonparameter inferring and the self-adaptiveness to determinate hyperparameters. According to the minimum variance criterion, the parameter fluctuation analysis can be performed through multiobjective evolutionary algorithm based on the MGPR model. To analyze the robustness influence of a single parameter, cross validation is applied to evaluate the model output with 2% fluctuation. After that, the robust optimal process operation parameters can be obtained and applied to guide the production. The effectiveness and reliability of the proposed method have been verified with the hydrogen cyanide production process and compared with other model methods and single objective optimization method.

Introducing Undergraduate Students to Nonlinear Dynamics through A Numerical Approach

This paper describes a numerical method that used to solve the nonlinear Schr\"{o}dinger equation. The methods are an exponential time differencing method and a spectral method. The result indicates that at a certain parameter, fluctuation of wave function has contained chaotic dynamics. This case is expected to be used as an example for introducing numerical methods to undergraduate students on nonlinear dynamics. This introduction is deemed necessary, referring to the curriculum and syllabus used in several educational institutions in various countries that have included the topic of nonlinearity.