Gaussian Effective Potential and the Coleman's normal-ordering Prescription : the Functional Integral Formalism

For a class of system, the potential of whose Bosonic Hamiltonian has a Fourier representation in the sense of tempered distributions, we calculate the Gaussian effective potential within the framework of functional integral formalism. We show that the Coleman's normal-ordering prescription can be formally generalized to the functional integral formalism.Comment: 6 pages, revtex; With derivation details and an example added. To appear in J. Phys.

Flat lens without optical axis: Theory of imaging

We derive a general theory for imaging by a flat lens without optical axis. We show that the condition for imaging requires a material having elliptic dispersion relations with negative group refraction, equivalent to an effective anisotropic refractive index n(theta). Imaging can be achieved with both negative (n0) refractive indices. The Veselago-Pendry lens is a special case with isotropic negative refractive index of n(theta)=-1. Realizations of the imaging conditions using anisotropic media and inhomogeneous media, particularly photonic crystals, are discussed. Numerical examples of imaging and requirements for sub-wavelength imaging are also presented.Comment: 5 pages, 4 figure

A novel improved model for building energy consumption prediction based on model integration

Building energy consumption prediction plays an irreplaceable role in energy planning, management, and conservation. Constantly improving the performance of prediction models is the key to ensuring the efficient operation of energy systems. Moreover, accuracy is no longer the only factor in revealing model performance, it is more important to evaluate the model from multiple perspectives, considering the characteristics of engineering applications. Based on the idea of model integration, this paper proposes a novel improved integration model (stacking model) that can be used to forecast building energy consumption. The stacking model combines advantages of various base prediction algorithms and forms them into “meta-features” to ensure that the final model can observe datasets from different spatial and structural angles. Two cases are used to demonstrate practical engineering applications of the stacking model. A comparative analysis is performed to evaluate the prediction performance of the stacking model in contrast with existing well-known prediction models including Random Forest, Gradient Boosted Decision Tree, Extreme Gradient Boosting, Support Vector Machine, and K-Nearest Neighbor. The results indicate that the stacking method achieves better performance than other models, regarding accuracy (improvement of 9.5%–31.6% for Case A and 16.2%–49.4% for Case B), generalization (improvement of 6.7%–29.5% for Case A and 7.1%-34.6% for Case B), and robustness (improvement of 1.5%–34.1% for Case A and 1.8%–19.3% for Case B). The proposed model enriches the diversity of algorithm libraries of empirical models

Coupled thermo-mechanical damage modelling for structural steel in fire conditions

This paper aims at developing a coupled thermo-mechanical damage model for structural 6 steel at elevated temperatures. The need for adequate modelling of steel deterioration behaviour 7 remains a challenging task in structural fire engineering because of the complexity inherent in 8 the damage states of steel under combined actions of mechanical and fire loading. A fully three9 dimensional damage-coupled constitutive model is developed in this work based on the hypothesis 10 of effective stress space and isotropic damage theory. The new coupling model, adapted from 11 an enhanced Lemaitre’s ductile damage equation and taking into account temperature-dependent 12 thermal degradation, is a phenomenological approach where the underlying mechanisms that govern 13 the damage processes have been retained. The proposed damage model comprises a limited number 14 of parameters that could be identified using unloading slopes of stress-strain relationships through 15 tensile coupon tests. The proposed damage model is successfully implemented in the finite element 16 software ABAQUS and validated against a comprehensive range of experimental results. The 17 damage-affected structural response is accurately reproduced under various loading conditions and 18 a wide temperature range, demonstrating that the proposed damage model is a useful tool in giving a 19 realistic representation of steel deterioration behaviour for structural fire engineering applications