The cost of calculating nuclear hessians, either analytically or by finite difference methods, during the course of quantum chemical analyses can be prohibitive for systems containing hundreds of atoms. In many applications, though, only a few eigenvalues and eigenvectors, and not the full hessian, are required. For instance, the lowest one or two eigenvalues of the full hessian are sufficient to characterize a stationary point as a minimum or a transition state (TS), respectively. We describe here a method that can eliminate the need for hessian calculations for both the characterization of stationary points as well as searches for saddle points. A finite differences implementation of the Davidson method that uses only first derivatives of the energy to calculate the lowest eigenvalues and eigenvectors of the hessian is discussed. This method can be implemented in conjunction with geometry optimization methods such as partitioned-rational function optimization (P-RFO) to characterize stationary points on the potential energy surface. With equal ease, it can be combined with interpolation methods that determine TS guess structures, such as the freezing string method, to generate approximate hessian matrices in lieu of full hessians as input to P-RFO for TS optimization. This approach is shown to achieve significant cost savings relative to exact hessian calculation when applied to both stationary point characterization as well as TS optimization. The basic reason is that the present approach scales one power of system size lower since the rate of convergence is approximately independent of the size of the system. Therefore, the finite-difference Davidson method is a viable alternative to full hessian calculation for stationary point characterization and TS search particularly when analytical hessians are not available or require substantial computational effort.
Abstract The response of two arch dams to spatially varying ground motions recorded during earthquakes is computed by a recently developed linear analysis procedure, which includes dam–water–foundation rock interaction effects and recognizes the semi‐unbounded extent of the rock and impounded water domains. By comparing the computed and recorded responses, several issues that arise in analysis of arch dams are investigated. It is also demonstrated that spatial variations in ground motion, typically ignored in engineering practice, can have profound influence on the earthquake‐induced stresses in the dam. This influence obviously depends on the degree to which ground motion varies spatially along the dam–rock interface. Thus, for the same dam, this influence could differ from one earthquake to the next, depending on the epicenter location and the focal depth of the earthquake relative to the dam site. Copyright © 2009 John Wiley & Sons, Ltd.
An improved capacity-demand-diagram method that uses the well-known constant-ductility design spectrum for the demand diagram is developed and illustrated by examples. This method estimates the deformation of inelastic SDF systems consistent with the selected inelastic design spectrum, while retaining the attraction of graphical implementation of the ATC-40 Nonlinear Static Procedure. One version of the improved method is graphically similar to ATC-40 Procedure A whereas the second version is graphically similar to ATC-40 Procedure B. However, the improved procedures differ from ATC-40 procedures in one important sense. The demand diagram used is different: the constant-ductility demand diagram for inelastic systems in the improved procedure versus the elastic demand diagram in ATC-40 for equivalent linear systems. The improved method can be conveniently implemented numerically if its graphical features are not important to the user. Such a procedure, based on equations relating the yield strength reduction factor, R y , and ductility factor, μ, for different period, T n , ranges, has been presented, and illustrated by examples using three different R y - μ - T n relations.
The signal recovered from the first reported experimental secure communication system via chaotic synchronization contains some inevitable noise which degrades the fidelity of the original message. In this letter we show by computer experiments that this noise can be significantly reduced by cascading the output of the receiver in the original system into an identical copy of this receiver.
Although bulk silicon is not known to exhibit susceptibility to cyclic fatigue, micron-scale structures made from silicon films are known to be vulnerable to degradation by fatigue in ambient air environments, a phenomenon that has been recently modeled in terms of a mechanism of sequential oxidation and stress-corrosion cracking of the native oxide layer.
An entry from the Cambridge Structural Database, the world’s repository for small molecule crystal structures. The entry contains experimental data from a crystal diffraction study. The deposited dataset for this entry is freely available from the CCDC and typically includes 3D coordinates, cell parameters, space group, experimental conditions and quality measures.
