Gaussian Cutoff Research Articles

Comparison between Upward Continuation and Gaussian Techniques, and their Relation to the Source Depth, Case Study in Eastern Central Iraq

The IGMAS+ forward program is used to compare upward continuation and Gaussian wavelength techniques in separating residual from regional anomalies of gravity data of a synthetic model and case study area, in eastern central Iraq. The comparison indicate a certain relation between the upward continuation and the Gaussian wavelength cutoff, so it is possible to produce the same regional and residual anomaly maps using each one of them. For the study area, the Gaussian cutoff 115000 maps coincide with the upward 12km regional and residuals maps, also the Gaussian cutoff 455000 maps coincide the upward 54km.The relation between the parameters of the two techniques, in case of produce coincide maps, it may be used to obtain the depth of gravity anomaly causative sources. It is found that ratio of Gaussian wavelength cutoff parameter to the upward parameter multiplied by 1.25 equal to the average level depth below the deeper source causing the residual anomalies. The average depth of residual anomalies in the case study area found equal to 10.5 km. The basement depth in the study area were coincide with the depth values from previous studies and geologically is very acceptabile.

Fano-Hopfield model and photonic band gaps for an arbitrary atomic lattice

We study the light dispersion relation in a periodic ensemble of atoms at fixed positions in the Fano-Hopfield model (the atomic dipole being modeled with harmonic oscillators). Compared to earlier works, we do not restrict to cubic lattices, and we do not regularize the theory by hand but we renormalize it in a systematic way using a Gaussian cutoff in momentum space. Whereas no omnidirectional spectral gap is known for light in a Bravais atomic lattice, we find that, for a wide range of parameters, an omnidirectional gap occurs in a diamond atomic lattice, which may be realized in an experiment with ultracold atoms. The long-wavelength limit of the theory also provides a Lorentz-Lorenz (or Clausius-Mossotti) relation for an arbitrary lattice.

Using the Zeldovich dynamics to test expansion schemes

We apply various expansion schemes that may be used to study gravitational clustering to the simple case of the Zeldovich dynamics. Using the well-known exact solution of the Zeldovich dynamics we can compare the predictions of these various perturbative methods with the exact nonlinear result and study their convergence properties. We find that most systematic expansions fail to recover the decay of the response function in the highly nonlinear regime. ``Linear methods'' lead to increasingly fast growth in the nonlinear regime for higher orders, except for Pade approximants that give a bounded response at any order. ``Nonlinear methods'' manage to obtain some damping at one-loop order but they fail at higher orders. Although it recovers the exact Gaussian damping, a resummation in the high-k limit is not justified very well as the generation of nonlinear power does not originate from a finite range of wavenumbers (hence there is no simple separation of scales). No method is able to recover the relaxation of the matter power spectrum on highly nonlinear scales. It is possible to impose a Gaussian cutoff in a somewhat ad-hoc fashion to reproduce the behavior of the exact two-point functions for two different times. However, this cutoff is not directly related to the clustering of matter and disappears in exact equal-time statistics such as the matter power spectrum. On a quantitative level, the usual perturbation theory, and the nonlinear scheme to which one adds an ansatz for the response function with such a Gaussian cutoff, are the two most efficient methods. These results should hold for the gravitational dynamics as well (this has been checked at one-loop order), since the structure of the equations of motion is identical for both dynamics.

Determination of penumbral widths from ion chamber measurements

We have investigated methods of reconstructing beam profiles in the penumbral region using a set of axially symmetric chambers, differing only in the detector radius. In principal, the transfer functions, or kernels, of such chambers should be functions of radius only. Three chambers of radii 0.297, 0.556, and 0.714 cm have been used. The transfer functions of the chambers can be determined by deconvolving the profiles measured with each detector with the PPMC profile. The results indicate that the transfer functions can be parametrized accurately as a Gaussian cutoff at 1.75(r), with (r) the average radius of the chamber. Deconvolution of the measured profiles with the transfer functions yields a profile that agrees with the PPMC profile to +/- 0.5 mm over the 20-80% penumbra.

Discussion: “Three-Dimensional Vortex Method for Gas-Particle Two-Phase Compound Round Jet” (Uchiyama, T., and Fukase, A., 2005, ASME J. Fluids Eng., 127, pp. 32–40)

Discussion: “Three-Dimensional Vortex Method for Gas-Particle Two-Phase Compound Round Jet” (Uchiyama, T., and Fukase, A., 2005, ASME J. Fluids Eng., 127, pp. 32–40)

An SU(3) Symmetric One-Boson-Exchange Potential between Two Octet Baryons

The SU(3) symmetric one-boson-exchange potential (OBEP) with a Gaussian soft core is proposed for interactions between two octet baryons. In this potential model, the breaking of the SU(3) symmetry is introduced by using the physical masses for the baryons and mesons. In the outer region (r ≥ 1fm), the OBEP works very well. In the core region (r ≤ 1fm), SU(3) symmetric Gaussian cores are introduced to guarantee the coexistence of the mechanisms of the meson exchange and the core, and the Gaussian cutoff function is multiplied to the OBEP. There are 22 free parameters, which consist of 11 SU(3) parameters for nonet mesons (g1, g8, gF/(gF+gD)= α,θ : each mesons) and 11 core parameters (core strength, core range). These parameters are determined via SU(3) relations by the method of χ2-fitting to reproduce the NN phase shifts and YN data. The fitting is quite satisfactory on the whole. Therefore, this OBEP is applicable to the calculation of nuclear and hyper-nuclear structures.

Flocculation of Hematite with Polyacrylic Acid: Fractal Structures in the Reaction- and Diffusion-Limited Aggregation Regimes

The structure of hematite aggregates in the presence of fairly monodisperse polyacrylic acid (PAA) with two different molecular weights (Mw= 1.36 × 106,Mw/Mn= 1.53;Mw= 3.69 × 104,Mw/Mn= 1.60) was studied using static light scattering (SLS). The fractal dimensions were calculated from the scattering exponents, after taking into account the finite size of aggregates, using exponential and Gaussian cutoff functions. Three flocculation regimes, namely, pre-DLA, DLA (diffusion-limited aggregation), and post-DLA, were defined based on the polymer concentration. In the DLA regime, fractal dimension values,Df= 1.84 ± 0.02 and 1.73 ± 0.02, were obtained using exponential and Gaussian cutoff functions, respectively. A fractal dimension of approximately 2.0 was found, as expected, in the pre-DLA regime (at PAA concentrations lower than the optimal dosage for a DLA regime) where the flocculation rate was reaction limited. In contrast, in the post-DLA regime, the flocculation was slow but the structure of aggregates was as tenuous as in the DLA regime with a fractal dimensionDf≈ 1.8. Moreover, for all three regimes, theDfvalues were independent of the molecular weights of PAA. The lower fractal dimension in post-DLA was probably due to the increased concentration of polymer chains between adjacent particles in aggregates. The steric hindrance favored tip-to-tip aggregation, leading to a more tenuous structure.

Spectroturbidimetry of fractal clusters: test of density correlation function cutoff

I have measured the relative increase in turbidity τ/τ(t = 0) as a function of wavelength exponent w = -∂(log τ)/∂(log λ) in the process of the reaction-limited cluster-cluster aggregation of polystyrene latex with a particle diameter of 90 nm. It is shown that this dependence is not sensitive to particular details of sample preparation and is described for independent measurements by one master curve. Theoretical calculations made in the single-scattering and Berry-Percival mean-field theory approximations considering small-angle light-scattering effects and cluster polydispersity also demonstrate that this dependence is sufficiently universal and its shape can be practically determined solely by the choice of the density correlation function cutoff model. Comparing the experimental τ/τ(0) = ƒ(w) curves with calculated theoretical plots I conclude that the Gaussian cutoff model is the best among all the models of the exponential family. This is in accord with a previous finding [Langmuir 8, 2964-2069 (1992)] that was obtained by using angular scattering from diffusion-limited cluster-cluster aggregation soot aggregates.

Test of static structure factors for describing light scattering from fractal soot aggregates

The authors compare several static structure factors for light scattering from fractal aggregates. The variation between these structure factors is a result of different cutoff functions for the cluster density correlation function. Light scattering data obtained from soot aggregates in a premixed CH{sub 4}/O{sub 2} flame are fit with three respresentative structure factors. Fractal dimensions determined from these fits under the assumptions of a monodisperse size distribution are all unsatisfactory. Inclusion of a scaling cluster size distribution yields good fits to structure factors derived from correlation functions with cutoffs faster than exponential, the exponential structure factor yielding a poor fit. A Gaussian cutoff was found to work the best. 18 refs., 7 figs., 1 tab.

Achievable information rates on digital subscriber loops: limiting information rates with crosstalk noise

The capacity and cutoff rates for channels with linear intersymbol interference, power dependent crosstalk noise, and additive white noise are examined, focusing on high speed digital subscriber line data transmission. The effects of varying the level of additive white noise, crosstalk coupling gain, sampling rate, and input power levels are studied in detail for a set of simulated two-wire local loops. A closed-form expression for the shell constrained Gaussian cutoff rate on the crosstalk limited channel is developed and related to the capacity, showing that the relationship between these two rates is the same as on a channel without crosstalk noise. The study also projects achievable rates on a digital subscriber line, inside and outside of a carrier serving area, with a sophisticated but realizable receiver. >

Regular effective action of gauge field theory and quantum gravity.

We present a perturbative formalism for the effective quantum action of a general Fermi-Bose field theory. We propose a unitary alternative to the conventional virtual ghost prescription for handling the functional integral of gauge fields, based on the functional space metric that is determined by the Dirac brackets of the canonical theory. A gauge-invariant Gaussian cutoff is introduced by extending the functional space metric into a regular counterpart. The regular one-loop contributions of a scalar field to the photon and the graviton self-energies are computed. The otherwise logarithmically divergent contributions are found, in our scheme, to be independent of cutoff.

Small-Scale Structure of a Scalar Field Convected by Turbulence

Batchelor's theory of the turbulent straining of small-spatial-scale amplitude variations of a convected scalar field is re-examined to see the effects of fluctuation of the rates of strain in space and time. The k−1 viscous-convective-range spectrum is unaltered, except for the constant of proportionality, but spectrum level in the viscous-diffusive range displays a sensitivity to fluctuations which increases with wavenumber. The Gaussian cutoff found by Batchelor is replaced by more gently decreasing dependences of spectrum level on wavenumber. The scalar spectrum is also treated by the Lagrangian-history direct-interaction approximation. The k−5/3 inertial-convective range of Obukhov and Corrsin, the k−1 viscous-convective range, and the k−17/3 inertial-diffusive range of Batchelor, Howells, and Townsend all are recovered. For a given rate of spectral transport of scalar variance, the predicted spectrum levels in the k−5/3 and k−1 ranges are too small, in comparison with experiment, by numerical factors in the neighborhood of one to three. The largest error is for the k−1 range at large Reynolds number.

Two-Nucleon L·S Potential in Pseudoscalar Meson Theory

Nonstatic corrections to the two-nucleon potential of Brueckner and Watson and of Gartenhaus are computed within the framework of the γ5 theory. These terms appear as spin-orbit corrections of order μ/M to the static potentials. The S matrix is calculated in second and fourth order for a reduced form of the relativistic theory. The potential is then chosen so as to duplicate this S matrix to the required order in the coupling constant and μ/M. We consider to what extent our reduction of the γ5 theory changes its character. The resulting potentials are given in analytic form for no cutoff in momentum space and in numerical form for the Gaussian cutoff employed by Gartenhaus. We give also some additional static corrections to previous potentials. A qualitative comparison is made with the experimental observations in nucleon-nucleon scattering, the fine structure in the splitting of the He5 nucleus, and the contribution of the nonstatic potential to the magnetic moment of the deuteron.

Solutions of the Static Theory Integral Equations for Pion-Nucleon Scattering in the One-Meson Approximation

Numerical solutions of the one-meson approximation of the Low equations for elastic pion-nucleon scattering in the fixed-nucleon, extended-source theory are obtained with a Gaussian cutoff function. The validity of the method requires that the scattering amplitudes have no zeros in the complex plane other than at z = plus or minus 1. The functions obtained for the (3,3) and (1,1) states satisfy the Low equations within the accuracy of the method, but the (1,3) and (3,1) states are only approximately given. This difficulty with the (1,3) and (3,1) states is correlated with the development of a zero in the corresponding scattering amplitude well before physically interesting values of the parameters (coupling constant and cutoff) are reached. A best fit to the (3,3)-state data up to 170-Mev pion laboratory energy requires a coupling constant, f/sup 2/, less than 0.08. The solution is consistent with the (3,1)- state data, but gives a (1,1)-state phase shift of larger magnitude than experiment appears to permit. It is found that the cutoff function does not prevent strong interactions at very high energies. Their occurrence appears to be a property of the static model. The contributions of such interactions to various static-theory calculations is briefiy discussed.more » It is shown that in the p-wave part of the relativistic dispersion relations, where there is no cutoff function, if use is made of the low-energy data, then the very high-energy contributions of the static theory are replaced by recoil terms of order mu /M. (auth)« less

CXI. Two dimensional diffusion phenomena in crystal growth from solution

Abstract Multiple-beam white light fringes of equal chromatic order are used for the study of the growth from solution of sodium chlorate. They are sharper and much more informative than monochromatic Fizeau fringes, and have proved to be very sensitive for the measurement of variation of concentration. The experimental results are found to be in agreement with the assumption of the existence of the quasi-stationary state theory introduced by Rieck and further developed recently by Frank. According to this theory, the radial gradient of concentration is analogous to a static potential field multiplied by a Gaussian cut off factor. The law relating the concentration to the radius is found to be of logarithmic form near the crystal and exponential at larger distances.