Method high-frequency

Conductometry. This rather unspecific method is used most frequently in the control of industrial chemical processes the output controls of particular technological processes are important in the pollution control, mainly of flowing waters and the atmosphere. The very low conductivity of pure water permits this method to be used to track the total content of pollutants, which is frequently sufficient. A typical example of the use of conductometric methods for environmental protection are analyzers of detergents in waste waters, of concentration of synthetic fertilizers in irrigation waters, of the quality of potable waters, etc. In addition to classical conductometric methods, high frequency methods (oscillometry) are also used, in which the electrode system is not in direct contact with the sample. 

The detection of residual austenite in fact requires average frequency, however for comparison reasons (reference) with a different recognized method, it is recommended to use high frequency, as with high frequency of eddy currents the penetration depth is comparable in the diffraction method and eddy current method. 

A novel optimization approach based on the Newton-Kantorovich iterative scheme applied to the Riccati equation describing the reflection from the inhomogeneous half-space was proposed recently [7]. The method works well with complicated highly contrasted dielectric profiles and retains stability with respect to the noise in the input data. However, this algorithm like others needs the measurement data to be given in a broad frequency band. In this work, the method is improved to be valid for the input data obtained in an essentially restricted frequency band, i.e. when both low and high frequency data are not available. This... 

The result is an imagery with the same quality as that given by a more high frequency method. VIII. REFERENCES... 

The LIN method (described below) was constructed on the premise of filtering out the high-frequency motion by NM analysis and using a large-timestep implicit method to resolve the remaining motion components. This technique turned out to work when properly implemented for up to moderate timesteps (e.g., 15 Is) [73] (each timestep interval is associated with a new linearization model). However, the CPU gain for biomolecules is modest even when substantial work is expanded on sparse matrix techniques, adaptive timestep selection, and fast minimization [73]. Still, LIN can be considered a true long-timestep method. 

In this paper, we discuss semi-implicit/implicit integration methods for highly oscillatory Hamiltonian systems. Such systems arise, for example, in molecular dynamics [1] and in the finite dimensional truncation of Hamiltonian partial differential equations. Classical discretization methods, such as the Verlet method [19], require step-sizes k smaller than the period e of the fast oscillations. Then these methods find pointwise accurate approximate solutions. But the time-step restriction implies an enormous computational burden. Furthermore, in many cases the high-frequency responses are of little or no interest. Consequently, various researchers have considered the use of scini-implicit/implicit methods, e.g. [6, 11, 9, 16, 18, 12, 13, 8, 17, 3]. 

The analytical treatment of high frequency terms in the Hamiltonian proposed here allows to use SISM significantly longer integration time step than can be used by other methods of the same order and complexity. 

Abstract. The overall Hamiltonian structure of the Quantum-Classical Molecular Dynamics model makes - analogously to classical molecular dynamics - symplectic integration schemes the methods of choice for long-term simulations. This has already been demonstrated by the symplectic PICKABACK method [19]. However, this method requires a relatively small step-size due to the high-frequency quantum modes. Therefore, following related ideas from classical molecular dynamics, we investigate symplectic multiple-time-stepping methods and indicate various possibilities to overcome the step-size limitation of PICKABACK. 

Molecular Dynamics and Monte Carlo Simulations. At the heart of the method of molecular dynamics is a simulation model consisting of potential energy functions, or force fields. Molecular dynamics calculations represent a deterministic method, ie, one based on the assumption that atoms move according to laws of Newtonian mechanics. Molecular dynamics simulations can be performed for short time-periods, eg, 50—100 picoseconds, to examine localized very high frequency motions, such as bond length distortions, or, over much longer periods of time, eg, 500—2000 ps, in order to derive equiUbrium properties. It is worthwhile to summarize what properties researchers can expect to evaluate by performing molecular simulations ... 

J)Other analytical methods which include, among many, a thermometric method (104), a high frequency titration (105), and a colored indicator method (106). 

Special drying methods, such as superheated steam, solvent, vacuum, infrared radiation, and high frequency dielectric and microwave heating, are occasionally employed when accelerated drying is desired and the species being dried can withstand severe conditions without damage. None of these methods is of significant commercial importance. 

Commercial dryers differ fundamentally by the methods of heat transfer employed (see classification of diyers, Fig. 12-45). These industrial-diyer operations may utihze heat transfer by convection, conduction, radiation, or a combination of these. In each case, however, heat must flow to the outer surface and then into the interior of the solid. The single exception is dielectric and microwave diying, in which high-frequency electricity generates heat internally and produces a high temperature within the material and on its surface. 

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