Characteristic Correlation Time Research Articles

Time-frequency analysis of seismic excitation and estimates of attenuation parameters for the Friuli (Italy) local earthquakes

Stochastic modelling is applied to the analysis of local earthquake recordings, which are usually extremely rich in random incident-wave trains that are chaotically superimposed because of scattering effects in the Earth's crust. The presence in the seismic signal of effects connected with the scale of inhomogeneity in the lithosphere cannot be deterministically described in detail. The application of a stochastic second-order autoregressive model to accelerometric records for the higher magnitude ( M L ≳ 6) Friuli earthquakes and to short-period seismometric records for the aftershocks of the strong earthquake of 6 May 1976 has allowed inferences to be drawn about the spectral properties of seismic signals and the propagation mechanisms of seismic waves. These inferences are based on an extremely small number of parameters of a mathematical model suitable for simultaneously describing the random sequence of scattered wave trains in the time and frequency domains. Useful physical information has been obtained about the dynamic characteristic correlation times and the predominant frequency of the seismic signals; moreover, the strength, σ 2 e( t), of the innovation of the stochastic process fitting the real digital data set has been estimated. From the envelopes of σ 2 e( t), the quantity heuristically used in the stochastic approach to describe seismic excitation, the·mean free-path between successive scatterings ( l), or the equivalent diffusivity coefficient ( d) and turbidity ( g), and their dependence on seismic wave frequency have been investigated. For Friuli, using seismometric data at an epicentral distance of ∼ 20 km and earthquakes with a magnitude just under 2, mean free-path estimates obtained by means of autoregressive parameters vary from ∼ 5 km for the strong interaction model to ∼ 30 km for the single scattering model. Furthermore, by means of accelerometric records for the strongest earthquakes in Friuli during May and September 1976, the dependence for the maximum of the seismic excitation on the epicentral distance R was estimated as ( σ 2 e) max ∼ R − ν (with ν 1.94 ± 0.13), which is in good agreement with results obtained for the same region using standard methods by means of acceleration peaks versus R. Lastly, stochastic modelling provides a method of estimating change versus time for the predominant frequency and characteristic correlation time of narrow band digital recordings. These two parameters were computed by means of autoregressive parameters in different physical situations and were found to be functions of the earthquake source, the instrumentation frequency response, and the Earth's filtering effects.

Characteristic correlation time as estimate of optimum filter length in Maximum Entropy Spectral Analysis

Summary. An original conceptually simple criterion for the choice of filter length M for Maximum Entropy Spectral Analysis based on the correlation time-scale of data set is proposed. The following formula is obtained from the autocovariance estimates @t The application of the proposed criterion to various digital geophysical records has provided satisfactory results. The method is well suited to geophysical signals because they often have a remarkable Markovian character in the broader sense, i.e. the autocovariances have values decreasing roughly exponentially as the time lags increase. Computer simulations on mathematically defined time series confirm the reliability of this criterion.

Two purified fractions of alamethicin have different conductance properties

The properties of two purified alamethicin fractions, Fraction 4 and Fraction 6, have been studied in phosphatidylethanolamine (PE) membranes and phosphatidylserine (PS) membranes. Membranes doped with Fraction 4 show well-defined single channel conductance (mean lifetime about 20 ms). The autocorrelation function of the current fluctuations has one relaxation time of the same order as the mean lifetime of the single channels, and the current response to a voltage pulse follows an exponential with only one time constant. The conductance of a membrane doped with Fraction 6 has a voltage-independent part and a current-voltage curve with a slope that is half the slope of the Fraction 4 current-voltage curve. In the presence of Fraction 6, PS membranes and PE membranes both have symmetrical current-voltage curves even with Fraction 6 added to only one side. We did not detect any well-defined single channel levels in the presence of Fraction 6, and autocorrelation analysis of the current due to Fraction 6 gave two characteristic correlation times: a fast time (about 5 ms) and a slow time (about 50 ms). High current level kinetics of Fraction 6 also show two time constants. A possible explanation for the differences between the two fractions is that Fraction 6 monomers have a lower dipole moment than those of Fraction 4. The difference in channel stability can be explained by a lowered tendency of the monomers to line up parallel to the field. The negative branch and voltage-independent conductance can be explained by lowered energy of insertion of monomers into the membrane, and lowered energy of interaction between the monomers and the electric field.

Effect of Mg 2+ on membrane fluidity and K + transport in rat liver mitochondria

1. 1. The effects of Mg 2+ on the fluidity and on the transport properties of mitochondrial inner membrane were compared in parallel experiments. The fluidity was measured by intercalated fatty acid spin probes. Valinomycin-induced K + uptake was followed using an ion-selective electrode. 2. 2. The rotational diffusion rate of lipids was very slightly affected by Mg 2+, whereas the ordering of the probed region of the inner membrane increased considerably above 30°C in the presence of Mg 2+ . Mg 2+ strongly inhibited K + transport, particularly above 30°C. 3. 3. In the presence of different concentration of MgCl 2 (0–30 mM) the order parameter showed no significant variation, whereas the rotational correlation time had essentially biphasic character with a minimum (i.e., faster diffusion rate) at 10 mM MgCl 2. 4. 4. We conclude that Mg 2+ induces structural changes in the mitochondrial inner membrane and concomitant changes in its functional properties. The term ‘fluidity’ is inadequate for the interpretation of the data, since changes in the order parameter and in the characteristic correlation time of the inner membrane upon addition of Mg 2+ did not show parallel tendencies.

Rotational diffusion of Escherichia coli ribosomes : I. - Free 70 S, 50 S and 30 S particles

The rotational brownian diffusion of Escherichia coli ribosomes has been studied by following the transient dichroism generated by optical excitation of a covalent probe into its triplet state. The induced absorption anisotropy decays exponentially with characteristic correlation times: 2.5 microseconds, 1.6 microseconds and 1.1 microseconds for the 70S ribosome and the 50S and 30S subparticles respectively. The corresponding Stokes radii are in the same order, 133 A, 115 A and 103 A. The hydrodynamic properties are discussed in terms of an ellipsoidal shape of the ribosome particles.

Analysis of the 5 min oscillatory photospheric motion

A more objective statistical technique is applied directly to the four time series used in Paper I. The empirical probability density functions indicate that the measurements are realizations of a narrow-band random process with Gaussian statistics. This result allows quantitative statistical use of the mean autocorrelation function. For example, a characteristic correlation time is 23 min, and the motion becomes statistically uncorrelated over intervals greater than 40 min. The mean autocorrelation function is found to be free of secondary maxima that have been so troublesome in other analyses. The question raised in this paper is whether our statistical model of the motion as a Gaussian random process is also applicable to smaller regions on the order of 1'' to 2'' in size. (auth)

Analysis of the 5 min oscillatory photospheric motion

Four Mt. Wilson measurements (T>4 h) of the photospheric motion at one point on the Sun are shown to have the characteristics of a narrow-band random process. The motion is shown to have a characteristic correlation time of 23 min and a mean power spectrum that is a smooth, single-peaked function centered at 3.4 mHz. In order to make this classification we use the analytic signal to estimate the amplitude, phase, and frequency as functions of time. The power spectrum analysis differs from the common approaches in that it uses the theoretical expression for the mean spectrum for a sequence of random pulses. Because of the random nature of the motion, we doubt the existence of more than one eigenfrequency characteristic of the photosphere as a whole. Likewise, any description of the observed motion in terms of simple deterministic functions will be inadequate for the data used here.

Frequency Dependence of Proton Spin Relaxation in Aqueous Solutions of Paramagnetic Ions

Magnetic resonance relaxation times T1 and T2 were measured for protons in aqueous solutions of Cr(H2O)6+++, Mn(H2O)x++, Co(H2O)x++, and Nd(H2O)x++ in the frequency range 2.7 to 28.7 Mc/sec. T1 was observed to decrease with decreasing frequency for the first two ions, but not the last two, while T2 was essentially constant for each ion. The abnormally large values of T1/T2 which have been previously reported appear as a result of the effect at high frequencies. Those observations are interpreted in terms of a theoretical model of the magnetic interaction between ion and proton in which a random thermal process is presumed to occur with a characteristic correlation time, τe, of 10—8 to 10—11 sec.