Numerical Verification

In this section, a single-degree-of-freedom linear system is considered to verify the approximations used in the method. The actual parameters are = 4 rad/s, f = 1%, S/o = 1 cm s and response time histories are generated using the MATLAB function Isim [171] for T = 1000 s with the time step At = 0.005 s. However, the measurements are assumed to be observed with a sampling time interval At = 0.05 ssoN = 20000. This is done on purpose to simulate the reality that there is inevitably a frequency content in the signal higher than the Nyquist frequency. Furthermore, measurements are assumed to be noise-free in this example, i.e., 5g0 0  

Another reason for the difference from the theoretical spectral density is leakage. The effect of leakage comes from the fact that the measurement does not contain an exact integer-multiple of the periods of the Fourier components. Instead of showing a single spike in the spectrum, the spectral value is being leaked out to the nearby frequencies. Therefore, it can be observed primarily at frequencies around the natural frequency, causing the expected values of the spectral density estimator to be smaller than the theoretical spectral density. 

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By analyzing the diagrams expansions of both bridge functions Bwhole numbers, this means that the values of m are degenerated values. In passing, it is noticeable that the Kiselyov and Martynov approximation [95] is recovered with the possible couple of values (n = 1 m 2), namely, // (r) = B r) for any thermodynamic state. 

Itoh, N., and H. Takahashi. 1990. A handwritten numeral verification method using distribution maps of structural features. Proc. SPIE Image Communications and Workstations, p. 1258. 

Numerical Verifications for Quantization A DetaUed Study of the H-tH2 System... 

The prediction based on the perturbation theory should open to numerical verifications. The modified FPU model, in which identical particles in the original FPU model are replaced by those with alternating masses, has been studied to check the validity of perturbative estimate, although detailed conditions of the modified FPU model are not exactly the same as those given as Eq. (1). The Hamiltonian of the modified FPU model is given as... 

The existing concept of mobility control is that the displacing fluid mobility should be equal to or less than the (minimum) total mobility of displaced multiphase fluids. This chapter first uses a simulation approach to demonstrate that the existing concept is invalid the simulation results suggest that the displacing fluid mobility should be related to the displaced oil phase mobility, rather than the total mobility of the displaced fluids. From a stability point of view, a new criterion regarding the mobility control requirement is derived when one fluid displaces two mobile oil and water fluids. The chapter presents numerical verification and analyzes some published experimental data to justify the proposed criterion. 

Finally, numerical verification investigates an elliptical structure. Specifically, a 3-D domain in the presence of an elliptical-cylindrical lossy scatterer with a height of 0.75 m and... 

As a result of numerical verification analogous to those of Section 3.1, we have established that the integral over the interval of normalized frequencies [0,2] of the quantity in (4) equals 2 for any binary multilayer structure ... 

THE EXTENDED JENCKEL EQUATION, AN EFFICIENT VISCOSITY TEMPERATURE FORMULA. I. PROPERTIES AND APPLICABILITY OF THE EQUATION ON THE NUMERICAL INTERPOLATION. II. PHYSICAL STATEMENTS FROM THE NUMERICAL VERIFICATION. 

Another important electronic structure principle is the maximum hardness principle " (MHP) which may be stated as, There seems to be a rule of nature that molecules arrange themselves to be as hard as possible . Numerical verification of this principle has been made in several physico-chemical problems such as molecular vibrations , internal rotations , chemical reactions" , isomer stability , pericyclic reactions and Woodward-Hoffmann rules , stability of magic clusters , stability of super atoms ", atomic shell structure" , aromaticity , electronic excitations , chaotic ionization, time-dependent problems like ion-atom collision and atom-field interaction " etc. 

Gudmundson P. and Ostlund S. (1992) Numerical verification of a procedure for calculation of elastic constants in microcracking composite laminates. Journal of Composite Materials, 26(17), 2480-2492. 

However, Eqs. (D.39) and (D.41) must be used with some caution for large a values due to the lack of numerical verification. 

Stoll E., Kolb M., Courtens E. Numerical verification of scaling for scattering from fractons. Phys. Rev. Lett. 1992 16 2472-2475... 

Experimental and Numerical Verification 19.3.1 Ni Films at the Ambient Temperature... 

Gantes CJ, Fragkopoulos Kq (2010) Strategy for numerical verification of steel structures at the ultimate limit state. Struct Infi astruct Eng 6(l-2) 225-255... 

The effective MTC is the group of terms within the braces in Equation 13.11. The concentration differences across the mixed surface layer of thickness h (m), is the interface vapor-phase concentration, Cai(mg/m ), minus the vapor-phase concentration at z = h, Cah (mg/m ). In addition to the kinetic transport parameter Dbs/h, the MTC contains the thermodynamic parameter ratio Kd/H, which imparts the sorbed-phase chemical loading fraction characteristic of the solid particles. When mobilized by the macrofauna this fraction significantly enhances the magnitude of the MTC. For certain strongly sorbed chemicals the coefficient can be very large so that this mechanism dominates the rate of chemical movement from within the soil layers to the soil-air interface. See Example 13.6.1 below for numerical verification of this behavior. 

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