Showing papers on "Randomness published in 1972"

Modal Analysis of Random Structural Systems

Abstract: This paper presents a method for computing the statistical variance of a structural system's eigenvalues and eigenvectors by component mode synthesis. The method relies on a modal summation to obtain engenvector derivatives where the contributions of individual modes are shown to diminish in importance as their natural frequencies become further separated from that of the eigenvector being differentiated. The convergence of mean eigenvalues and eigenvectors and their standard deviations is evaluated as the number of component modes used in the syntheses is increased. It is found that convergence proceeds in that order, with the standard deviations of eigenvectors requiring the largest number of modes for convergence. Numerical investigations show that the standard deviations of eigenvectors tend to converge for the first several modes when only a small fraction of the total number of component modes are taken into account. The dependence of convergence on the distribution of randomness and its spatial correlation is considered.

Tests for randomness of directions against equatorial and bimodal alternatives

Abstract: SUMMARY Tests of randomness of directions in three-dimensional space or equivalently tests of uniform distribution of points on the unit sphere are treated. One test is against alternatives which concentrate probability density near an equator, and the other is against alternatives which concentrate probability density near opposite poles; in each case the poles are unspecified. The tests are based on the latent roots of the matrix of sums of squares and cross-products of the co-ordinates of the observed points on the unit sphere. Against equatorial alternatives the null hypothesis is rejected if the smallest root is less than the appropriate significance point, and against bimodal alternatives the null hypothesis is rejected if the largest root is greater than the appropriate significance point. Tables of significance points are given, based on Monte-Carlo studies and the asymptotic distributions which are derived. The two-dimensional problem is also discussed.

Time and Frequency Domain Representations of Futures Prices as a Stochastic Process

Abstract: Speculative markets have often been characterized as exhibiting random price behavior where prices tend to move in a series of unconnected steps. The hypothesis of random behavior in commodity markets is investigated by three tests of randomness for a total of 167 futures contracts representing a variety of commodities. The autocorrelation function, spectral density function, and integrated period-ogram are estimated for each futures contract. The empirical results indicate that futures price behavior cannot generally be characterized by a simple random walk model, though several commodities appear to yield random behavior.

Configurational Entropy and Solute Correlation in Disordered Alloys

Abstract: which sets the excess entropy proportional to the mean value of the logarithm of the intensity. As an example of application, a concise analysis for pair correlations and thermodynamic properties at equilibrium is carried out. The result coincides with the spherical model for alloys, a variant of the Ising model resembling the Gaussian model of Clapp and Moss but far exceeding it in accuracy. In this manner the merit of the proposed entropy formulation is established, THE concern of the present investigation is with the thermodynamics of disordered binary alloy crystals as affected by deviations of the solute distribution from randomness. The Warren-Cowley short-range order coefficients 1 provide a way of characterizing the statistical arrangement of solute in such a material. A principle attribute of the short-range order coefficients is the direct relation between their Fourier transform and the diffuse intensity of X-rays or thermal neutrons scattered by an alloy crystal. With the short-range order coefficients one can also formulate the dependence of alloy properties such as the energy of mixing 2'3 upon the state of aggregation of the solute. Likewise Cowley has used the shortrange order coefficients to formulate the configurational entropy of mixing. 1'2 By suitable manipulation the expression for the energy of mixing can be converted to an equivalent form employing the diffuse intensity in place of the short-range order coefficients. Certain practical and conceptual advantages accrue by this procedure, including the fact that the elastic free energy, arising when the component atoms differ in size, is readily expressed in terms of the same intensity function. 4 The aim of the present investigation is to show that advantage is also gained by utilizing the intensity to formulate the configurational entropy of mixing. Using Cowley's result as a guide, we propose a more compact function in terms of the diffuse intensity. The merit of the proposed entropy function is tested by combining it with the parallel expression for the energy of mixing to form the free energy of mixing. Minimizing the result yields formulas for the thermodynamic functions and pair correlations at equilibrium, which are then evaluated by comparison with known formulas obtained by other means. While the emphasis here is on the entropy, auxiliary findings are noted having to do with an improved for

Localization Lengths of Electronic States in One-Dimensional Disordered Potential Chains

Abstract: We present a simple approach to the calculation of localization lengths of electronic states in a one-dimensional tight-binding model with nearest-neighbor interactions only. Monte Carlo calculations for a binary alloy with diagonal randomness only show longer-ranged states at energies which are allowed for both constituents and shorter-ranged states in the tails. The length of the longest-ranged states decreases continuously with increasing randomness, without any sharp transition. These results are compared with transmission calculations, and a simple physical interpretation is obtained thereby.

Density Modelling by Monte Carlo Inversion—I Methodology

Abstract: Summary Monte Carlo inversion of geophysical data provides a method of specifying the Earth's density distribution within the uncertainties present in the data. It is possible to estimate the reliability of non-uniqueness bounds defined by a family of randomly generated models by means of a statistical procedure proposed by Anderssen & Seneta. We have devised a technique by which physically realistic models are generated without violating the condition of randomness, to counter the criticism that the method is inherently biased towards complex models. We have also examined a further criticism that the use of variational parameters to calculate theoretical eigenperiods favours the acceptance of -near (as opposed to -far) solutions. The objection is valid in principle, but may be circumvented by the adoption of suitably conservative acceptability criteria for the eigenperiod residuals. Our Monte Carlo technique was used to invert the seismic data from which the model HB2 is derived. The suite of models thus obtained provide a measure of the non-uniqueness inherent in the HB2 data, whilst confirming that the parametric constraints imposed on the density gradient by Bullen & Haddon are entirely compatible with their data. We conclude that major discrepancies between the density models of Bullen & Haddon and those of Press cannot be attributed to methodological differences in the derivation of these models.

Total reflection of a plane wave by a semi-infinite random medium †

Abstract: An exact result in the theory of wave propagation in random media is presented. Using the ergodic theory of dynamical systems, it is shown that a semi-infinite, one-dimensional random medium is totally reflecting. A direct numerical study shows that the mean reflection coefficient converges exponentially to one.

Random Thoughts about Randomness

Abstract: In this paper I shall bring together some philosophical and logical ideas about randomness many of which have been said before in scattered places. For less philosophical aspects see, for example [27].

Concepts of randomness

Abstract: The notion of randomness has always been rather perplexing. Although it is frequently used in natural and social science, both technically and informally, it seems to have been somewhat neglected by philosophers of science ever since the discussion of the foundations of the so-called frequency theory of probability, in which it was assigned a basic role, has faded. Yet this discussion is of such significance that any attempt at clarifying the notion of randomness will have to relate to it. After a few preliminary remarks on some of the problems and puzzles of randomness, I shall, therefore, expound and discuss a concept of random distribution of a property in classes and sequences, defined in terms of relative frequencies and their limits. Because of certain shortcomings of this concept it appears advisable to turn to probabilities, in terms of which a quite different concept, viz., that of random conjunction of properties, can readily be defined as stochastic independence. This concept still has features clashing with the ordinary sense of ‘randomness’ which become manifest in cases where certain probabilities assume extreme values. However, when we take measures defined in information theory as measuring the degree of randomness, to which purpose they lend themselves particularly well, we find that these seemingly troublesome cases are rather harmless. A by-product of the discussion of measures of randomness is the concept of primitive randomness. The conclusion points out some further problems.

Coherent potential theory of off-diagonal randommess: Binary alloy

Abstract: The single-site coherent potential approximation (SS-CPA) for a disordered binary alloy is extended in a self-consistent manner to the case of off-diagonal randomness. The density of states for a bcc lattice is calculated in the split band limit for no correlation between diagonal and off-diagonal randomness and compared with the ordered and SS-CPA density of states.

Electronic density of states in disordered alloys

Abstract: The electronic densities of states are calculated for a two-sublattice alloy in single-site coherent potential approximation (CPA) and for an alloy with off-diagonal randomness in two-site CPA. In the first part of this paper, we study the compositional dependent energy gap and bound states for a Hubbard-like model. In the second part, we investigate the effect of the off-diagonal randomness on the impurity states.

Qualitative consequences of randomness in a linear kinetic system.

Abstract: SUMMARY Biological data, either by convenience or necessity, are often characterized by large spread, small sample size, non-stationarity, and other qualities that make it difficult or impossible to apply conventional statistical methods of analysis. This paper presents a qualitative modeling approach to the analysis of such data. The technique is illustrated by the analysis of data representing the uptake of acetylcholine by synaptic vesicles, and it is demonstrated that a number of properties of that biological process can be determined from what would normally be considered rather poor data. In particular, it is shown that a deterministic model in this case appears to be insufficient to represent the system and that at least two types of randomness are involved.

Random Chords of a Sphere

Abstract: : Eight models of randomness for chords of a unit sphere are considered, and the distribution, mean, and variance of the chord length are obtained for each model.

Neutron diffusion as a random walk problem.

Abstract: The one-dimensional random walk problem has been generalized to allow for absorption at lattice sites, and then this technique has been used to study one velocity neutron diffusion. We show that most of the results that are normally obtained by solving the diffusion equation under appropriate boundary conditions, can be obtained directly. Various special cases have been considered, including leakage from a finite lattice and neutron-wave propagation in an infinite lattice.

Some properties of quadratic similarity judgements between four-dimensional stimuli

Abstract: A model for quadratic similarity judgements developed previously (Gregson, 1969, 1970) is extended to deal with a form of bias, and to assess the information taken up by the parameters in the model. It is shown that judgements collapse, in terms of the model, into near randomness under restricted information conditions, but that this collapse is generally explicable in form, although it exhibits marked inter-individual differences. Implications for similarity scaling models are noted.

Performance of antennas in random fields

Abstract: The behavior of some typical antennas or antenna systems when subjected to random fields is investigated with the purpose of determining their performance. Some relevant parameters, which are directly obtainable from a correlation matrix, are considered. Numerical results, regarding the dependence of the matrix elements and some of the antenna parameters on the illumination of circular apertures, are reported for fluctuating incident fields of variable randomness.