Estimation Formula of Modal Frequency of High-Rise Buildings under Different Wind Speeds during Typhoons

On 18 October 2016, the wind-induced effects of a high-rise building with square section was measured by the monitoring system in Haikou of China during Typhoon Sarika. The wind characteristics atop the building and the time-history responses of the translational and rotational accelerations on different floors were measured by the monitoring system; the first three modal parameters were identified according to the measured acceleration. The results show that the combinations of the cross spectral density function, phase spectrum, and coherence function can clearly judge the phase of the measured floors in the frequency resonance area as well as its modal frequencies at the first three orders. The modal frequencies at the first three orders decrease linearly with the growth of mean wind speed within the range of 0~20m/s. The estimation formula of the modal frequencies of high-rise buildings considering the influences of different wind speeds is put forward, which is expected to fill the gap in the existing specification for the quantitative analysis of the influences of wind-loads on the fundamental frequencies of high-rise buildings.

Influence of a Turbulent Jet Engine Exhaust on Laguerre-Gaussian Correlated Shell-Model Beams

In this paper, we investigated the influence of a turbulence jet engine exhaust on Laguerre-Gaussian correlated shell-model beams (LGSMBs). The analytical formulae of the cross-spectral density function as well as the beam width are derived based on the Huygens-Fresnel diffraction principle and the second-order moments of the Wigner distribution function, respectively. From our main results, the spectral density, the degree of coherence and beam width of a LGSMB are analyzed numerically. It is found that for high source coherence width, the spectral density changes gradually its profiles from circular to elliptical shape at short propagation distance, then the beam transforms into a well like Gaussian at long propagation distance. Although, at very short propagation distance, the beam becomes an elliptical dark hollow if the source coherence is very lower. Also, the numerical results show that the LGSMB spreads more rapidly than the GSMB in the same conditions.

Simulation of Spatially Correlated Multipoint Ground Motions in a Saturated Alluvial Valley

Based on Biot’s theory, the boundary element method, and spectral representation method, an effective simulation method for multiple-station spatially correlated ground motions on both bedrock and surface is developed, incorporating the spectral density function, coherence function, and site transfer function that consider both the wave scattering effect and the medium saturation. The accuracy and feasibility of the present method are validated by a typical numerical example. Our results indicate that the local site conditions and the saturation property of the medium significantly affect the multipoint spatially correlated earthquake ground motions, especially in the long-period range. It is necessary to use spatially varying ground motions with the rational consideration of local site effects and medium saturation as input during the seismic analysis of large-span structures.

Limiting Spectral Distribution of Large-Dimensional Sample Covariance Matrices Generated by the Periodic Autoregressive Model

The explicit representation for the limiting spectral moments of sample covariance matrices generated by the periodic autoregressive model (PAR) is established. We propose to use the moment-constrained maximum entropy method to estimate the spectral density function. The experiments show that the maximum entropy spectral density function curve obtained based on the fourth-order limiting spectral moment can match histograms of the eigenvalues of the covariance matrices very well.

Correlations obtained from optical spectra of Fe-pnictides using an extended Drude-Lorentz model

We introduce an analysis model, an extended Drude–Lorentz model, and apply it to Fe-pnictide systems to extract their electron–boson spectral density functions (or correlation spectra). The extended Drude–Lorentz model consists of an extended Drude mode for describing correlated charge carriers and Lorentz modes for interband transitions. The extended Drude mode can be obtained by a reverse process starting from the electron–boson spectral density function and extending to the optical self-energy, and eventually, to the optical conductivity. Using the extended Drude–Lorentz model, we obtained the electron–boson spectral density functions of K-doped BaFe 2 As 2 (Ba-122) at four different doping levels. We discuss the doping-dependent properties of the electron–boson spectral density function of K-doped Ba-122. We also can include pseudogap effects in the model using this new approach. Therefore, this new approach is very helpful for understanding and analyzing measured optical spectra of strongly correlation electron systems, including high-temperature superconductors (cuprates and Fe-pnictides).

Edgeworth Expansion for the Whittle Maximum Likelihood Estimator of Linear Regression Processes with Long Memory Residuals

We establish an Edgeworth expansion for the distribution of the Whittle maximum likelihood estimator of the parameter of a time series generated by a linear regression model with Gaussian, stationary, and long-memory residuals. This is done by imposing an extra condition on coefficients of the regression model in addition to the standard conditions imposed on the the spectral density function and the parameter values and making use of the results of Andrews et al. (2005), who provided an Edgeworth expansion for the residual component.

An algorithm to simulate nonstationary and non-Gaussian stochastic processes

We proposed a new iterative power and amplitude correction (IPAC) algorithm to simulate nonstationary and non-Gaussian processes. The proposed algorithm is rooted in the concept of defining the stochastic processes in the transform domain, which is elaborated and extend. The algorithm extends the iterative amplitude adjusted Fourier transform algorithm for generating surrogate and the spectral correction algorithm for simulating stationary non-Gaussian process. The IPAC algorithm can be used with different popular transforms, such as the Fourier transform, S-transform, and continuous wavelet transforms. The targets for the simulation are the marginal probability distribution function of the process and the power spectral density function of the process that is defined based on the variables in the transform domain for the adopted transform. The algorithm is versatile and efficient. Its application is illustrated using several numerical examples.

Topological Atomic Chains on 2D Hybrid Structure

Mid-gap 1D topological states and their electronic properties on different 2D hybrid structures are investigated using the tight binding Hamiltonian and the Green’s function technique. There are considered straight armchair-edge and zig-zag Su–Schrieffer–Heeger (SSH) chains coupled with real 2D electrodes which density of states (DOS) are characterized by the van Hove singularities. In this work, it is shown that such 2D substrates substantially influence topological states end evoke strong asymmetry in their on-site energetic structures, as well as essential modifications of the spectral density function (local DOS) along the chain. In the presence of the surface singularities the SSH topological state is split, or it is strongly localized and becomes dispersionless (tends to the atomic limit). Additionally, in the vicinity of the surface DOS edges this state is asymmetrical and consists of a wide bulk part together with a sharp localized peak in its local DOS structure. Different zig-zag and armachair-edge configurations of the chain show the spatial asymmetry in the chain local DOS; thus, topological edge states at both chain ends can appear for different energies. These new effects cannot be observed for ideal wide band limit electrodes but they concern 1D topological states coupled with real 2D hybrid structures.

A stochastic model explains the periodicity phenomenon of influenza on network

Influenza is an infectious disease with obvious periodic changes over time. It is of great practical significance to explore the non-environment-related factors that cause this regularity for influenza control and individual protection. In this paper, based on the randomness of population number and the heterogeneity of population contact, we have established a stochastic infectious disease model about influenza based on the degree of the network, and obtained the power spectral density function by using the van Kampen expansion method of the master equation. The relevant parameters are obtained by fitting the influenza data of sentinel hospitals. The results of the numerical analysis show that: (1) for the infected, the infection period of patients who go to the sentinel hospitals is particularly different from the others who do not; (2) for all the infected, there is an obvious nonlinear relationship between their infection period and the visiting rate of the influenza sentinel hospitals, the infection rate and the degree. Among them, only the infection period of patients who do not go to the sentinel hospitals decreased monotonously with the infection rate (increased monotonously with the visiting rate), while the rest had a non-monotonic relationship.

Correlated dipolar and dihedral fluctuations in a protein

Correlation between dihedral fluctuations is a possible way to understand coordination between various amino acid residues of the protein. The nanosecond timescales of correlated fluctuations of dihedral angle do not allow direct probing by experimental methods. However, NMR experiments probe dipolar fluctuations given in terms of cross correlated relaxation (CCR) rates, expressed as zero frequency spectral density function (J) of the fluctuations of the mutual orientation of two spatially separated dipole vectors. Here we illustrate the correlation of protein dipolar and dihedral angle using molecular dynamics simulation of protein Ubiquitin (Ub) and GB3. We calculate CCR rates between protein bond vector from simulation and compare with CCR data obtained from NMR experiments. A good correlation between theoretical and experimental values is found. We further show that the zero frequency spectral functions of backbone dihedral ψ auto-correlation function and dipole orientation fluctuations show strong correlations. These correlations are not sensitive to protein and forcefield parameters. Hence, CCR may act as a marker for protein backbone dihedral fluctuations.