Spectrum Of Relaxation Frequencies Research Articles

Mud as a porous medium

Since marine mud supports shear waves, it must have an elastic, though fragile, frame. It is also saturated with seawater, therefore it could be modeled as a porous medium. It is an unusual porous medium for a number of reasons. The boundary between the skeletal frame and the pore fluid is difficult to define. The effective porosity of the skeletal frame is not the same as the bulk fluid fraction. The chemistry of mud suggests that a fraction of the water is an integral part of the skeletal frame. Similarly, a fraction of the solid particles may be suspended in the pore fluid. The structure of the skeletal frame is a function of several factors, including salinity of the water and mineralogy of the clay particles. Porous media have two main loss mechanisms: losses in the skeletal frame and viscous losses due to relative motion between the frame and the pore fluid. In the case of marine mud, the frame losses may be modeled as a relaxation process. The measurements from the Seabed Characterization Experiment show it has a spectrum of relaxation frequencies, consistent with a stationary creep process. [Work supported by ONR, Ocean Acoustics Program.]

Adaptive Prefiltering for Nonnegative Discrete Spectrum of Relaxations

Recent developments in the estimation of the discrete spectrum of relaxation frequencies (DSRFs) has opened doors to more robust subsurface target discrimination using electromagnetic induction measurements. In particular, a nonnegative least squares DSRF (NNLSQ-DSRF) estimation method has been shown to be robust and free from parameter tuning. In this letter, we propose an adaptive prefiltering process to complement the NNLSQ-DSRF where we attempt to linearly combine measurements and produce a filtered signal that is very likely to have a nonnegative DSRF, as well as an enhanced signal-to-noise ratio. Using synthetic and field data, we demonstrate that the proposed adaptive prefilter can effectively produce signals with nonnegative DSRFs.

Target Classification and Identification Using Sparse Model Representations of Frequency-Domain Electromagnetic Induction Sensor Data

Frequency-domain electromagnetic induction (EMI) sensors can measure object-specific signatures that can be used to discriminate landmines from harmless clutter. In a model-based signal processing paradigm, the object signatures can often be decomposed into a weighted sum of parameterized basis functions, such as the discrete spectrum of relaxation frequencies (DSRF), where the basis functions are intrinsic to the object under consideration and the associated weights are a function of the target-sensor orientation. The basis function parameters can then be used as features for classifying the target. One of the challenges associated with effectively utilizing a model-based signal processing paradigm such as this is determining the correct model order for the measured data, as the number of basis functions containing fundamental information regarding the target under consideration is not known a priori. In this paper, sparse Bayesian relevance vector machine (RVM) regression is applied to simultaneously determine both the number of parameterized basis functions and their relative contributions to the measured signal assuming a DSRF signal model. The target is then classified utilizing the basis function parameters as features within a statistical classifier. Results for data measured with a prototype frequency-domain EMI sensor at a standardized test site are presented, and indicate that RVM regression followed by distance-based statistical classifiers utilizing the resulting model-based features provides an effective approach for classifying and identifying landmine targets.

Viscoelastic relaxation spectra of lubricating oils and their component fractions

The early work of Barlow & Lamb (1959) on linear viscoelastic relaxation at high frequencies showed that the behaviour of mineral oils could be represented by a spectrum of relaxation frequencies. It also gave an interpretation of the spectrum in terms of the hydrocarbon type analysis of the oil. We have made the first test of this interpretation by making measurements on other samples of oil and on a suitably fractionated oil. It is concluded that the relaxation spectrum cannot be interpreted solely in terms of the hydrocarbon type analysis and that other unknown characteristics of the oil have at least as great an influence. A new mechanical model for the representation of viscoelasticity, proposed by Barlow, Erginsav & Lamb (1967), fits the experimental results for HVI 330 oil and its saturate and monoaromatic fractions over a wide range of the results. Results for these oils obtained at low temperatures and all results for MVI (N) 170 and LVI 260 oils fit less well. Evidence is presented which supports a conclusion drawn by Miles (1962) that the relaxa­tion spectrum of an oil broadens as the temperature is lowered.

Relaxation of dislocations in copper

Frequency and attenuation of standing waves have been measured in polyerystalline-copper in the frequency range between 1.8 kHz and 6.5 MHz as a function of temperature from 60°K to 300°K. Owing to the wide frequency range, the activation energyW and the limiting frequencyω A associated with the attenuation peak due to dislocations have been evaluated with considerable accuracy. The values obtained (W=0.122 eV (molecule)−1,ω A =23.9·1011 s−1) agree satisfactorily with those computed according to the theories given bySeeger, Donth andPfaff. The shape of the attenuationvs. temperature curves shows that the spectrum of relaxation frequencies is a bell-shaped line with its maximum atω=ωm; each frequency of the spectrum is associated with the value ofW given above. The height of the attenuation peaks has been compared with the total relaxation exhibited by the frequencyvs. temperature curves. Below 100 kHz the results agree with the theory of relaxation effects with a continuous spectrum. At higher frequencies the polycrystalline structure gives rise to an attenuation larger than the values that could be expected from the frequency relaxation measurements. The effects of heat treatments have also been investigated, showing that the attenuation and the frequency relaxation are both reduced by treatments whose temperature does not exceed 500 °K, whilstωAis slightly increased. Treatments at higher temperatures give rise to comparatively large changes in attenuation and frequency, which do not seem directly related to the pre-existing dislocations. These changes are reversible and can be cancelled by a suitable amount of cold work.

Acoustical Techniques for the Study of Electrochemical Processes

At relatively low frequencies, sound waves produce an alternating component in the potential of a reversible electrode in accord with the thermodynamic dependence of the potential on pressure and temperature. With increasing frequency, the ac response of the electrode decreases until at sufficiently high frequencies only the alternating components associated with the variation of the electrode-solution interface capacity and the ionic vibration potentials remain. The departure of the response from thermodynamic expectations occurs because the electrode processes responsible for the establishment of the potential are too slow for instantaneous equilibrium to be maintained in the sound field. The situation is analogous to the relaxation effects associated with the excess sound absorption in polyvalent electrolytes such as magnesium sulfate. From the frequency dependence of the alternating potentials at various electrolyte concentrations and temperature, information can be obtained as to the orders, rate constants, and energy barriers for various electrode processes, e.g., electron transfer from a metallic electrode to an ion. Since most electrochemical systems involve several consecutive steps, a spectrum of relaxation frequencies is anticipated. The measurement of these acoustically produced alternating potentials offers considerable promise for the study of electrode processes which are too rapid for conventional electrochemical techniques. (This paper is based on research sponsored by the Office of Naval Research.)