Narrow Results

We study the ${\varphi }^4$ field theory in d = 4. Using bold diagrammatic Monte Carlo method, we solve the Schwinger–Dyson equations and find the spectral density function of the theory beyond the weak coupling regime. We then compare our result with the one obtained from the perturbation theory. At the end, we utilize our Monte Carlo result to find the vertex function as the basis for the computation of the physical scattering amplitudes.

In this paper we study the problem of electromagnetic wave propagation in a 3-D optical fiber. The goal is to obtain a solution for the time-harmonic field caused by a source in a cylindrically symmetric waveguide. The geometry of the problem, corresponding to an open waveguide, makes the problem challenging. To solve it, we construct a transform theory which is a nontrivial generalization of a method for solving a 2-D version of this problem given by Magnanini and Santosa.³

The extension to 3-D is made complicated by the fact that the resulting eigenvalue problem defining the transform kernel is singular both at the origin and at infinity. The singularities require the investigation of the behavior of the solutions of the eigenvalue problem. Moreover, the derivation of the transform formulas needed to solve the wave propagation problem involves nontrivial calculations.

The paper provides a complete description on how to construct the solution to the wave propagation problem in a 3-D optical waveguide with cylindrical symmetry. A follow-up article will study the particular cases of a step-index fiber and of a coaxial waveguide. In those cases we will obtain concrete formulas for the field and numerical examples.

As a relatively new means of transportation, the subway has become an important tool for the sustainable development of many cities. Being buried deep in soil under the weight of vital infrastructure, subway stations can be vulnerable to seismic excitations. Considering the high randomness of ground motions, it is important to research the failure probability and seismic performance of the subway station based on stochastic dynamic analysis. In this paper, a probability density evolution method (PDEM) coupled with a spectral representation random function is used to analyze the stochastic dynamic response and seismic probability of a subway station. First, according to the improved power spectral density model and the seismic design code of urban rail transit structures in China (GB 50909-2014), a set of nonstationary ground motions consistent with the code spectrum are obtained. Then, a great deal of deterministic dynamic calculations for Daikai subway station considering soil–structure interaction based on elastic–plastic methods are performed. In addition, the nonlinear stochastic response analysis and the dynamic probability analysis are obtained for the subway station by solving the PDEM equation. Finally, the probability density function (PDF) and cumulative distribution function (CDF) of the subway station under stochastic earthquake excitations are obtained based on three performance indices, including drift angle in the middle column, relative vertical displacement between floor and roof, and damage area ratio (DAR). The results show that the stochastic dynamic analysis and the probability density evolution method can analyze seismic response and evaluate seismic performance of subway stations effectively. The proposed method will serve as an effective tool for the seismic design of underground structures.