non-Gaussian Properties Research Articles

Non-linear effects in rotational dynamics in the liquid state

Through general theoretical considerations, based only on the Markoffian assumption, it is shown that equilibrium non-gaussian properties can be used to predict how the decay of excited states deviates from a linear response theory behaviour. To check this prediction, a computer experiment on a ‘two-dimensional liquid’ of discs interacting via a Lennard-Jones plus electric dipole potential is carried out. The results obtained for both equilibrium and excited correlation functions confirm completely the intimate relation between equilibrium non-gaussian properties and excitation behaviour. Via approximate analytical expressions and exact solutions, it is also shown that a non-linear version of the popular itinerant oscillator provides the same equilibrium non-gaussian properties and, in consequence of that, the same kind of deviation from linear response as the two-dimensional system.

N-state Markov jump process

A certain N-state Markov jump process is studied in connection with laser mode hopping and phase switching. We show that the Chapman-Kolmogorov-Smoluchowski equations can be solved exactly to yield a simple expression for the transition probability function. Some properties of such a process and its connection with the related pre-gaussian process are examined. We also study the atomic response to excitation by a laser whose phase or frequency exhibits such jumps, and the non-gaussian property of the line shape is discussed.

Effect of a local non-linear vibration on the space-time behaviour of the neutron field in nuclear reactors

The effect of a non-linear local vibration of a reactor's structural components upon the neutron field is studied with the use of a single-mass model. We clarify first what is influential in causing pattern changes of the vibrational spectrum. It is also clarified how the non-Gaussian properties of the neutron noise arise from the non-linear vibration. A non-Gaussian property measured in the Palisades is discussed from both mathematical and physical viewpoints. These considerations will provide fundamental information in detecting incidents, malfunctions and anomalies of the structural components in nuclear reactors.

Non-Gaussian imaging properties of GRIN fiber lens arrays

The best focus for a GRIN fiber array is shown to occur when the object and image plane vertex distances are equal, even when neither plane is the proper Gaussian unit magnification plane. This analytical result agrees with previous experimental data. With non-Gaussian imaging, the image plane of best focus for the GRIN array is not coincident with the plane of best focus for the individual gradient-index fibers.

Model networks of end-linked polydimethylsiloxane chains. IX. Gaussian, non-Gaussian, and ultimate properties of the trifunctional networks

Model elastomeric networks were prepared by end-linking hydroxyl-terminated polydimethylsiloxane chains with a trialkoxy silane. Mixtures of various proportions of relatively long and very short chains were employed, since the resulting ’’bimodal’’ networks are of unique importance in characterizing non-Gaussian effects related to limited chain extensibility. Stress–strain isotherms of these trifunctional networks gave values of the elongation at which the modulus begins to increase anomalously, and values of the elongation and modulus at the point of rupture. These results were interpreted in terms of calculated values of the maximum extensibilities of the chains, and were compared with previously reported results on the corresponding tetrafunctional networks in order to characterize the effects of crosslink functionality on these properties. In addition, the elasticity constants characterizing the Gaussian regions of the isotherms, and values of the degree of equilibrium swelling were used to evaluate the most recent molecular theories of rubberlike elasticity, particularly with regard to how the elastic effectiveness of the network chains depends on chain length and extent of deformation.

Bispectral holography

In conventional holography, information at a hologram plane is obtained by taking the cross correlation between the signals at the points on the plane and a reference signal. In this paper we show that this information can also be obtained by using bispectral analyses of random signals detected at two points on the hologram plane, that is, the signal detected at a fixed point and the signal detected at scanning points on the same plane. The method, which uses this hologram and a conventional reconstrucion process and is named bispectral holography, has two special features: (i) it is completely free from additive Gaussian noises of any power spectra, and (ii) random signals, which have non-Gaussian properties, can be used as the object illuminating signals. These properties may extend the application of holographic techniques. The theoretical aspects and some discussion of the method are presented.

Anomalous transit-time dispersion in amorphous solids

Measurements of the transient photocurrent $I(t)$ in an increasing number of inorganic and organic amorphous materials display anomalous transport properties. The long tail of $I(t)$ indicates a dispersion of carrier transit times. However, the shape invariance of $I(t)$ to electric field and sample thickness (designated as universality for the classes of materials here considered) is incompatible with traditional concepts of statistical spreading, i.e., a Gaussian carrier packet. We have developed a stochastic transport model for $I(t)$ which describes the dynamics of a carrier packet executing a time-dependent random walk in the presence of a field-dependent spatial bias and an absorbing barrier at the sample surface. The time dependence of the random walk is governed by hopping time distribution $\ensuremath{\Psi}(t)$. A packet, generated with a $\ensuremath{\Psi}(t)$ characteristic of hopping in a disordered system [e.g., $\ensuremath{\Psi}(t)\ensuremath{\sim}{t}^{\ensuremath{-}(1+\ensuremath{\alpha})}$, $0l\ensuremath{\alpha}l1$], is shown to propagate with a number of anomalous non-Gaussian properties. The calculated $I(t)$ associated with this packet not only obeys the property of universality but can account quantitatively for a large variety of experiments. The new method of data analysis advanced by the theory allows one to directly extract the transit time even for a featureless current trace. In particular, we shall analyze both an inorganic ($a\ensuremath{-}{\mathrm{As}}_{2}{\mathrm{Se}}_{3}$) and an organic (trinitrofluorenone-polyvinylcarbazole) system. Our function $\ensuremath{\Psi}(t)$ is related to a first-principles calculation. It is to be emphasized that these $\ensuremath{\Psi}(t)$'s characterize a realization of a non-Markoffian transport process. Moreover, the theory shows the limitations of the concept of a mobility in this dispersive type of transport.

The effect of capillarity and resonant interactions on the second-order Doppler spectrum of radar sea echo

Previous work on the second-order contributions of radar sea echo by Hasselmann and Barrick is generalized to include the effect of capillarity (i.e., surface tension) in the hydrodynamic part of the transfer coefficient, the lossy dielectric properties of the sea, and the angle of incidence and the polarization of the electromagnetic radiation. The present theoretical results apply to the backscattering of electromagnetic radiation from water waves that are gravity or gravity capillary waves. The introduction of surface tension in the analysis allows for second-order resonant interactions of the gravity capillary wave components. To include resonant interactions of gravity waves, the analysis must be extended to higher order. In general, resonant interactions produce higher-order contributions in the Doppler spectrum at the frequency of the first-order Bragg line that represent the nonstationary and non-Gaussian properties of the water surface. Furthermore, because of the different dispersion relation of gravity capillary water waves, the secondary lines of the second-order Doppler spectrum now are shifted toward the Bragg frequency and 2½ times the Bragg frequency. Numerical results are presented from our generalized theory for various radar and sea (water surface) parameters.

Non-Gaussian properties of the EEG during sleep

A spectral and amplitude distribution analysis was made using an EEG sample taken during sleep. The analysis showed that low frequency activity (slow wave sleep) was significantly and positively correlated in time with non-Gaussian behavior of the EEG. During non-slow wave sleep, the amount of non-Gaussian activity was reduced.

Non-gaussian properties of cyclolinear poly-3-methylbutene-1-silsesquioxane molecules over a wide range of molecular wights

Non-gaussian properties of cyclolinear poly-3-methylbutene-1-silsesquioxane molecules over a wide range of molecular wights