Existence of the atmosphere attractor

The global asymptotic behavior of solutions for the equations of large scale atmospheric motion with the non-stationary external forcing is studied in the infinite dimensional Hilbert space. Based on the properties of operators of the equations, some energy inequalities and the uniqueness theorem of solutions are obtained. On the assumption that external forces are bounded, the exsitence of the global absorbing set and the atmosphere attractor is proved, and the characteristics of the decay of effect of initial field and the adjustment to the external forcing are revealed. The physical sense of the results is discussed and some ideas about climatic numerical forecast are elucidated Work supported by the State Key Research Project on Dynamics and Predictive Theory of the Climate.     

On the existence of atmospheric attractors

In this paper, we consider the long-time dynamics for the primitive equations of large-scale dry at- mosphere. First, by energy methods, we obtain the existence and uniqueness of global strong solu- tions of the problem. Second, by studying the long-time behavior of strong solutions, we construct a global attractor which captures all the trajectories.     

Ground-motion prediction equations (GMPEs) for inelastic response and structural behaviour factors

The objective of this paper is to present ground-motion prediction equations describing constant-ductility inelastic spectral ordinates and structural behaviour factors. These equations are intended for application within the framework of Eurocode 8. Most of the strong-motion data used in the present work is obtained from the ISESD (Internet Site for European Strong-motion Data) databank. Present analysis includes ground motion records from significant Icelandic earthquakes, which are augmented by records obtained from continental Europe and the Middle East. In all cases the selected ground motion records are generated during shallow earthquakes within a distance of 100 km from the recording station. The classification of site conditions in the present work is based on the Eurocode 8 definition.     

Mathematical Modeling of Diffusion and Transport of Pollutants in the Atmospheric Boundary Layer

— The process of dispersion of air pollutants, in a broad sense, can be considered as the net outcome of various mechanisms involved in the transport of air pollutants from the source to the receptor. The major mechanisms are: (1) advection of pollutants by mean air motion, (2) mixing of pollutants by atmospheric turbulence and (3) mass diffusion due to concentration gradients. In addition, the physical and chemical nature of the effluent, the location of the stack and the nature of the terrain downwind from the stack, effect the dispersion of the pollutants. Various physical and mathematical aspects related to the transport and diffusion of air pollutants in the atmospheric boundary layer are discussed here. Further, some aspects of dispersion in a weak wind stable boundary layer are described. Finally, the current issues in the modeling of weak wind boundary layer are illustrated.     

Apparent translational component for rotational ground motions

Even though the rotational ground motion may contribute significantly to the response of certain structures, their effects are generally ignored in seismic design, because of non-availability of appropriate instruments for direct recording of the rotational components. Like many others, a simplified framework was proposed by the authors elsewhere (Rodda and Basu in Int J Earthq Impact Eng 1(3):253–288, 2016) to extract the rotational motion as a temporal derivative of an apparent translational component (ATC) followed by scaling with an apparent velocity. ATC was defined such that its time derivative is closely correlated with the respective rotational motion. But the a priori knowledge of rotational motion is required in estimating the ATC for rocking component. An empirical procedure has been proposed here to bypass the requirement of rotational motion a priori. This paper also assesses the definition of ATC through examining the similitude between the time derivative of ATC and the respective rotational motion (benchmark) quantitatively. Similitude is assessed on smoothened response spectra (by Hamming window) of the time derivative of ATC and that of rotational motion. A new definition of spectral contrast angle (SCA) based on distance correlation has been proposed to assess the spectral similitude. To differentiate the similar from non-similar spectra, SCA corresponding to an acceptable degree of similarity is proposed by studying a large ensemble of ground motions from the PEER database. This similitude study is further extended using relative energy build up and energy spectra.     

On the 485-day Mode in the Atmospheric Angular Momentum: Spectral Analysis of IERS Data

The modification of spectral analysis especially intended for studying the disturbing functions of the atmosphere and ocean, as well as the observed polar motion (Wiener–Liouville spectrum), is used. The time series of the atmospheric disturbing functions obtained by the U.S. National Centers for Environmental Prediction (NCEP) of the International Earth Rotation and Reference Systems Service (IERS) for the period from January 1, 1980 to June 20, 2014 (http://www.iers.org/.cs1?pid=43-1100116) are analyzed. It is shown that the baric disturbing function contains a regular mode with a period of ~16 months; the contribution of this mode in the polar motion is estimated.     

Analysis of a numerical solution to the one-dimensional stochastic convection equation

Under certain conditions the concentration and flux of a substance moving in a stochastic flow field are described by the stochastic convection equation. A numerical method for solving the one-dimensional problem is studied here. The differential operator is replaced by a discrete linear operator based on finite differences. The resulting system of stochastic equations is then replaced by a system of equations whose solution is the mean concentration or mean flux. This final system is analysed and conditions for a stable numerical solution are obtained. Finally, numerical examples are given and are compared to an approximate analytical solution to the stochastic convection equation.     

Studies on finite amplitude waves in bounded water bodies

The problem treated here is the dynamics of a bay where water is driven through its opening periodically in time. The basic equations are expressed in the two horizontal coordinates and time and they are obtained by an integration of the Navier-Stokes equations in the vertical coordinate. The equations are nonlinear because of the convective terms in the acceleration. The problem of harbor dynamics provides a natural parameter as the ratio of mass of water entering the bay through the waves to the total mass of water in the bay. This small parameter multiplies the nonlinear terms and thus the problem is ideally suited for a perturbation analysis. The nonlinear terms are responsible for the generation of secondary flows and are particularly important near resonant frequences. The analysis further indicates the existence of a time independent flow analogous to acoustic streaming, known from solutions of the Navier-Stokes equations. The question of vorticity is studied and is seen that: a constant dissipation coefficient precludes the generation of vorticity even for the nonlinear case: and that only a weak (second order) vorticity can exist in the case of a variable dissipation term expressed through the Chezy coefficient. The study suggests also a semi analytic-numerical scheme with savings of 0(10²) for irregular geometries through the separation of the various order harmonics as opposed to the usual integration in time.     

Scattering of plane SH waves by a circular- arc hill with a circular tunnel

IntroductionEarthquakedamageinvestigationsandtheoreticalanalysesshowthatahillamplifiesincidentwavestremendouslyduetomulti-reflectionofthewaveswithinthehill;notabledynamicstressconcentrationisobservedonwallofatunnel(Pao,Mow,1973;Lee,Trifunac,1979).Therefore,itmaybeassumedthattheexistenceofatunnelinahillmighthavegreateramplificationeffectonthegroundmotionnearby,andthedynamicstressconcentrationofthetunnelinthehillmightbemorenotable.Itiscommonthattherailwaysorhighwaysarethroughahilloramountainwi…     

A microslip model for the seismic response analysis of drained cohesionless soil deposits

Constitutive equations for drained cohesionless soils under triaxial stress states, based on a microslip model with internal friction, are proposed and applied to the analysis of the seismic response of soil deposits. The microslips, assumed localized in the discontinuity surfaces passing through the particle-to-particle contacts, describe the effects of the sliding and rolling between grains of sand. Once the response of the model under cyclic shearing stresses and strains superimposed on the geostatic stress state has been analysed, the constitutive equations are applied to a one-dimensional shear model for the dynamic analysis of the layered deposits. An application to an instrumented soil deposit is then developed, the experimental results of which refer to both strong and weak motion earthquakes; the comparisons between the experimental and theoretical results point out the peculiarities and validity limits of the model. The model here developed may be applied also to the analysis of two- and three-dimensional sites.     

Earthquake interaction forces between two structures of different rigidities

A combined structure is assumed to be composed of a rigid part and a flexible part. Each component structure would have a different period of natural vibration if it were built independently. When they are combined in one structure and subjected to an earthquake, there must be generated some interaction forces so that the component structures will have a common vibration. In this paper is an analytical method described to evaluate such interaction forces The general principle is as follows. For each of the component structures, equations of motion taking account of the unknown interaction forces are derived first. Then by eliminating the interaction forces, equations of motion of the combined structure are obtained. After solving these equations and substituting the solution into the equations of motion of the component structures, the unknown interaction forces are obtained directly In the present paper, two structures corresponding to two-degree elastic systems are considered; numerical examples also are included.     

长型大截面地下结构的横向自由振动方程

文中综合考虑了内阻尼、外阻尼、剪切变形、横截面转动惯性、轴力和地基模型参数的影响,推得了弹性地基梁的一般自由振动方程。由这一方程可以得到一系列特殊情况下地下结构的自由振动方程。这一方程不仅能从理论上扩展了Timoshenko粱理论,而且在后续的研究中,为研究上述因素对于地下结构的自由振动和强迫振动的影响奠定了理论基础。     

Quasi-Rayleigh Waves in Transversely Isotropic Half-Space with Inclined Axis of Symmetry

A method for determination of characteristics of quasi-Rayleigh (qR) wave in a transversely isotropic homogeneous half-space with inclined axis of symmetry is outlined. The solution is obtained as a superposition of qP, qSV and qSH waves, and surface wave velocity is determined from the boundary conditions at the free surface and at infinity, as in case of Rayleigh wave in an isotropic half-space. Though the theory is simple enough, a numerical procedure for calculation of surface wave velocity presents some difficulties. The difficulty is caused by necessity to calculate complex roots of a non-linear equation, which in turn contains functions determined as roots of non-linear equations with complex coefficients. Numerical analysis shows that roots of the equation corresponding to the boundary conditions do not exist in the whole domain of azimuths and inclinations of the symmetry axis. The domain of existence of qR wave depends on the ratio of the elastic parameters: for some strongly anisotropic models the wave cannot exist at all. For some angles of inclination qR-wave velocities deviate from those calculated on the basis of the perturbation method valid for weak anisotropy, though they have the same tendency of variation with azimuth. The phase of qR wave varies with depth unlike Rayleigh wave in an isotropic half-space. Unlike Rayleigh wave in an isotropic half-space, qR wave has three components - vertical, radial and transverse. Particle motion in horizontal plane is elliptic. Direction of the major axis of the ellipsis coincides with the direction of propagation only in azimuths 0° (180°) and 90° (270°).     

Scattering of plane SH waves by a cylindrical alluvial valley of circular-arc cross-section

A closed-form solution of two-dimensional scattering of plane SH waves by a cylindrical alluvial valley of circular-arc cross-section in a half-space is presented using the wave functions expansion. The solution is reduced to solving a set of infinite linear algebraic equations using the exterior region form of Graf's addition theorem. Numerical solutions are obtained by truncation of the infinite equations and their accuracies are demonstrated by convergence of the numerical results to the exact boundary condition with the increasing of the truncation order. The present solution is compared with the existing one presented by Todorovska and Lee for the same problem and their differences are analysed. Complicated effects of the depth-to-width ratio of the alluvial valley on surface ground motion are finally illustrated.     

任意圆弧形凸起地形中隧洞对入射平面SH波的影响

借助辅助函数的思想， 采用波函数展开法给出了圆弧形凸起地形中隧洞对入射平面SH波影响问题的一个解析解．数值结果表明，凸起地形中隧洞的存在以及隧洞大小，对凸起地形表面运动，以及凸起地形中的隧洞的动应力集中均具有显著影响．      

Discrete models for vertical vibrations of surface and embedded foundations

A five-parameter discrete model that approximates the dynamic force4isplacement relationship for rigid foundations undergoing vertical vibrations on a uniform elastic half-space is presented. The model involves a combination of two springs, two viscous dampers and a mass. Values of the parameters for circular, square and rectangular foundations placed on the surface or embedded in an elastic half-space are listed. The parameters are obtained by minimizing the discrepancy between the force4isplacement relation for the model and that obtained by solution of the mixed boundary-value problem of the rigid foundation on an elastic half-space. The definition of an appropriate input motion to represent wave excitation is also discussed. The input motion to the discrete model differs from the input motion that should be used in a continuum model.     

On the electron dynamics in the field of a whistler wave propagating along a magnetic field in a weakly inhomogeneous plasma

The relativistic motion of electrons in the field of a finite amplitude circularly polarized whistler propagating along a constant magnetic field in a plasma with longitudinal inhomogeneity is considered. It is shown that the equations of the particle motion exhibit a constant of the motion despite the spatial dependence of the wave parameters. The existence of the constant allows one to reduce the equations of motion to a canonical form describing one-dimensional oscillations of a particle with the Hamiltonian slowly varying in the process of the oscillations.     

Mass rig system for shaking table tests of slender columns

A new mass rig system is proposed to minimize the deficiencies in current shaking table testing setups. This is accomplished by placing the inertial mass on a convex path designed to impose P‐Delta demands on slender cantilever columns. The design and performance of the mass rig system, and the principles used in deriving the equations of motion and their analytical validation against results obtained from shaking table tests, are presented. Formulation of the governing equations of motion was based on Lagrangian mechanics and solved using an implicit linear acceleration method with an adaptive time step formulation. Friction developed in the sliding system was also incorporated in the equations of motion. Experimental results validated the accuracy in the derivation and solution of the equations of motion. Validated by analytical and experimental results, P‐Delta effects were found to increase the displacement demands on slender columns in the low‐frequency range of acceleration input, while in the high‐frequency range P‐Delta effects led to no increase and in some cases even a reduction in displacement demands. Copyright © 2015 John Wiley & Sons, Ltd.     

Characterization of Stress Drops on Asperities Estimated from the Heterogeneous Kinematic Slip Model for Strong Motion Prediction for Inland Crustal Earthquakes in Japan

Dense strong motion observation networks provided us with valuable data for studying strong motion generation from large earthquakes. From kinematic waveform inversion of seismic data, the slip distribution on the fault surface of large earthquakes is known to be spatially heterogeneous. Because heterogeneities in the slip and stress drop distributions control the generation of near-source ground motion, it is important to characterize these heterogeneities for past earthquakes in constructing a source model for reliable prediction of strong ground motion. The stress changes during large earthquakes on the faults recently occurring in Japan are estimated from the detailed slip models obtained by the kinematic waveform inversion. The stress drops on and off asperities are summarized on the basis of the stress change distributions obtained here. In this paper, we define the asperity to be a rectangular area whose slip is 1.5 or more times larger than the average slip over the fault according to the previous study for inland crustal earthquakes. The average static stress drops on the asperities of the earthquakes studied here are in the range 6?C23?MPa, whereas those off the asperities are below 3?MPa. We compiled the stress drop on the asperities together with a data set from previous studies of other inland earthquakes in Japan and elsewhere. The static stress drop on the asperity depends on its depth, and we obtained an empirical relationship between the static stress drop and the asperity??s depth. Moreover, surface-breaking asperities seemed to have smaller stress drops than buried asperities. Simple ground motion simulations using the characterized asperity source models reveal that deep asperities generate larger ground motion than shallow asperities, because of the different stress drops of the asperities. These characteristics can be used for advanced source modeling in strong ground motion prediction for inland crustal earthquakes.     

Scattering of plane SH waves by a cylindrical canyon of circular-arc cross-section

A closed-form solution of two-dimensional scattering of plane SH waves by a cylindrical canyon of circular-arc cross-section in a half-space is studied using the wave functions expansion method. The solution is reduced to solving infinite linear algebraic equations using the Graf's addition theorem in an appropriate form. Numerical results of the solution are obtained by truncation of the infinite equations and accuracies of the truncation are checked by the extent to which the numerical results fit the boundary condition and by convergence of the numerical results with the truncation order. Complicated effects of the depth-to-width ratio of the canyon on surface ground motion are shown by the numerical results for typical cases.