Structural-dynamical model spectral function

To calculate L(Z) in terms of the structural-dynamical model of water, we introduce the longitudinal and transverse dimensionless projections, q = py /p and = p /p, of a dipole-moment vector p. These projections are directed, respectively, along and across to the local symmetry axis. In our case (see Fig. 56b), the latter coincides with an equilibrium direction of the H-bond. Next, we introduce the longitudinal and transverse spectral functions as... 

Chapter 3 presented the Bayesian spectral density approach for the parametric identification of the multi-degree-of-freedom dynamical model using the measured response time history. The methodology is applicable for linear models and can also be utilized for weakly nonlinear models by obtaining the mean spectrum with equivalent linearization or strongly nonlinear models by obtaining the mean spectrum with simulations. The stationarity assumption in modal/model identification for an ambient vibration survey is common but there are many cases where the response measurements are better modeled as nonstationary, e.g., the structural response due to a series of wind gusts or seismic responses. In the literature, there are very few approaches which consider explicitly nonstationary response data, for example, [226,229]. Meanwhile, extension of the Bayesian spectral density approach for nonstationary response measurement is difficult since construction of the likelihood function is nontrivial in the frequency domain. Estimation of the time-dependent spectrum requires a number of data sets, which are associated with the same statistical time-frequency properties but this is impossible to achieve in practice. 

In liquids and solutions a chemical shift model should ideally account for the dynamical disordering of the solvent structures. This calls for models that are based on a decomposition of the intermolecular contributions to the shift and a parameterization of these contributions in terms of solvent stmcture, for example, atom-atom distribution functions. Such models should ideally account for the dependence of shift on temperature and pressure. From the distribution functions the shifts can be derived as well as the full photoelectron spectral function, including shift, width, and asymmetry, upon condensation. A basic assumption is that photoionization is vertical, meaning that both initial and final states can be associated with the same nuclear conformation. This approximation is well grounded considering the time scales between the photoelectron process and the rearrangement of the solvent molecules, which means that the solvent is not in equilibrium with respect to the final state. A common assumption behind such models is also that the internal solute nuclear motion is decoupled from external forces. This means that the spectral function/ can be written as a convolution of internal and external parts,/ and/ / respectively,... 

The most important aspect of the study of Co(II) metalloenzymes is the possibility of using the metal ion as a functional, built-in reporter of the dynamics of the active site. The spectral and magnetic properties of Co (II) carbonic anhydrase have given valuable clues to the catalytic function of this enzyme. The recent studies of Co(II) alkaline phosphatase and Co (II) carboxypeptidase A indicate the general applicability of this approach to enzymes where the probe properties of the constitutive metal ion are poor. The comparison of the absorption spectra of these enzymes and low-molecular weight models have shown that the proteins provide irregular, and in some cases nearly tetrahedral environments. It is obvious, however, that a knowledge of the crystal structures of the enzymes is necessary before the full potential of this method can be exploited. 

The above experimental developments represent powerful tools for the exploration of molecular structure and dynamics complementary to other techniques. However, as is often the case for spectroscopic techniques, only interactions with effective and reliable computational models allow interpretation in structural and dynamical terms. The tools needed by EPR spectroscopists are from the world of quantum mechanics (QM), as far as the parameters of the spin Hamiltonian are concerned, and from the world of molecular dynamics (MD) and statistical thermodynamics for the simulation of spectral line shapes. The introduction of methods rooted into the Density Functional Theory (DFT) represents a turning point for the calculations of spin-dependent properties [7],... 

Computer simulation of molecular dynamics is concerned with solving numerically the simultaneous equations of motion for a few hundred atoms or molecules that interact via specified potentials. One thus obtains the coordinates and velocities of the ensemble as a function of time that describe the structure and correlations of the sample. If a model of the induced polarizabilities is adopted, the spectral lineshapes can be obtained, often with certain quantum corrections [425,426]. One primary concern is, of course, to account as accurately as possible for the pairwise interactions so that by carefully comparing the calculated with the measured band shapes, new information concerning the effects of irreducible contributions of inter-molecular potential and cluster polarizabilities can be identified eventually. Pioneering work has pointed out significant effects of irreducible long-range forces of the Axilrod-Teller triple-dipole type [10]. Very recently, on the basis of combined computer simulation and experimental CILS studies, claims have been made that irreducible three-body contributions are observable, for example, in dense krypton [221]. 

ABSTRACT This work proposes a robust optimization criterion of mechanical parameters in the design of linear Tuned Mass Dampers (TMD) located at the top of a main structural system subject to random base accelerations. The dynamic input is modelled as a stationary filtered white noise random process. The aim is to properly consider non-uniform spectral contents that happen in many real physical vibration phenomena. The main structural system is described as a single linear degree of freedom, and it is assumed that uncertainty affects the system model. The problem parameters treated are described as random uncorrelated variables known only by the estimation of their means and variances. Robustness is formulated as a multi-objective optimization problem in which both the mean and variance of a conventional objective function (OF) are minimized simultaneously. Optimal Pareto fronts are obtained and results show a significant improvement in performance stability compared to a standard conventional solution. 

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