Values Of Correlation Length Research Articles

The influence of depolarization field on dielectric and pyroelectric properties of ferroelectric films

Calculations of the spontaneous polarization (Ps), dielectric susceptibility (χ) and pyroelectric coefficient (Π) of the ferroelectric films have been performed in the thermody- namic phenomenological theory framework. The Euler-Lagrange equation determining po- larization dependence on the film parameters and the external electric field was solved ana- lytically under the boundary conditions with different extrapolation lengths at two surfaces, respectively. The depolarization field contribution was taken into account in the model of short-circuited mono-domain ferroelectric film, treated as perfect insulator. The detailed analy- sis of the aforementioned quantities, space distribution and their average values in two cases with and without depolarization field was carried out. It was shown that the depolarization field shifts critical temperature to smaller values and the critical thickness to bigger value in comparison to those obtained without accounting the depolarization field. Meanwhile aver- age values of Ps, χ and Π dependences on the film parameters and temperature are similar to the corresponding dependences obtained without accounting the depolarization field. The depolarization field was shown to flatten Ps, χ and Π space distributions, which have the peculiarities otherwise (e.g. small maxima in χ and Π coordinate profiles near the film sur- faces). It was shown that depolarization field influence in short-circuited film could be ne- glected when the film thickness or the extrapolation lengths in the boundary conditions are larger than the correlation length value.

Scattering potential for interface roughness scattering

Interface roughness scattering potential is computed for the AlAs/GaAs and Ga 0.5In 0.5P/GaAs systems by using the two models proposed in the literature: the so-called eigenvalue model and the wave function model. Potentials are found to differ by large factors for the AlAs/GaAs system, while for the Ga 0.5In 0.5P/GaAs system the difference is not very significant. Values of asperity height, Δ, and correlation length, Λ, of the roughness are also calculated for the two systems, which give agreement between theory and experiment for the wave function model. It is found that the results for the AlAs/GaAs system cannot be explained by the wave function model if the roughness protrudes into the barrier; the required values of Δ and Λ for protrusion into the well also differ from those for the eigenvalue model by large factors. For the Ga 0.5In 0.5P/GaAs wells, on the other hand, the difference in the values lies between 10 and 20%.

Small angle neutron scattering study on the salt-induced phase separation of 1-propanol aqueous solution

Small angle neutron scattering (SANS) measurements have been carried out over a wide range of Q from 0.003 to 7 Å−1 on the 1-propanol-water solution with KCl and that without KCl in relation to the salt-induced reentrant phase-separation phenomena. The Q dependence of the SANS intensity for both solutions is characterized by the same fractal structure with the fractal dimension df of 1.9. The only difference between the two solutions is the value of correlation length ξ. In the solution without KCl the value of ξ is rather small, ranging from 7.4 to 6.2 Å depending on temperature, while in the solution with KCl it becomes very large, from 48 to 355 Å or more depending on temperature, and diverges toward the phase-separation temperatures in a similar way for both the upper and lower one-phase regions. No significant differences have been found on the growing structure of fluctuation in the upper and lower one-phase regions.

Two-dimensional variability in porosity, density, and electrical resistivity of Eckernförde Bay sediment

Image-based analysis techniques are employed to compare sediment density heterogeneity as interpreted from X-radiography and electrical resistivity measurements. Assessments of sediment heterogeneity in two dimensions through the use of the two methods, with some exceptions, yield similar results. Autocorrelation functions estimated from density fluctuations reveal an anisotropy between vertical and horizontal sediment structure indicated by horizontal correlation lengths being greater than vertical correlation lengths. In addition to the anisotropy, discrepancies between values of correlation lengths calculated from two statistical methods are indicative of the scale-dependent nature of the sediment structure. This scale dependence is also exemplified by the differences between the images of X-radiography and electrical resistivity. The unequal volume of sediment over which the respective methods are integrated produces results differing by the amount and type of information included in each image. Electrical microresistivity is more sensitive than X-radiography to many smaller-scale variations in sediment density. Combining the results from X-radiography and microresistivity imaging allows the calculation of Archie’s m parameter, an extremely sensitive indicator of sediment microstructure. In addition, electrical microresistivity gives a measurement of sediment tortuosity coincident with sediment porosity and density.

Surface roughness of bismuth, antimony and cadmium electrodes

Electric double layer properties of variously treated Bi, Sb and Cd electrodes were studied in terms of the Debye length dependent roughness theory, recently developed by Daikhin et al. The geometrical roughness factor, root mean square departure of the surface from flatness, height of surface roughness and the medium lateral correlation length values have been obtained. According to the experimental data and results of theoretical simulation the surface roughness rises in the order of Bi electrodes: electrochemically polished single crystal Bi(111) plane<cut at the temperature of liquid nitrogen Bi(111) plane<Bi solid drop electrode with additionally remelted surface<cut at the room temperature Bi(111) plane<electrochemically etched Bi(111) plane<chemically etched Bi(111) plane. This order of the electrode surface roughness was in agreement with the ex situ AFM data. At small electrolyte concentrations ( c el≤0.01 M) the deviation of experimental roughness function–inverse Debye length curves from the theoretically simulated ones has been observed, explained by the influence of energetic inhomogeneity of polycrystalline surfaces on the non-equal surface charge density at various homogeneous regions, exposed at the macro-polycrystalline electrode surface.

A lattice determination of QCD field strength correlators

We study field strength correlators in presence of a static quark-antiquark pair by use of lattice methods. The lattice data have been acquired recently in the context of a determination of relativistic corrections to the static interquark potential. We extract independent estimates of the form factors of two point correlation functions and investigate the effect of higher order correlators. Our results confirm the dominance of the two point correlators in the regions of intermediate and large quark separations, and are compatible with correlation length values obtained from different approaches.

Field-cycling nuclear magnetic resonance relaxometry of molecular dynamics at biological interfaces in eye lenses: The Lévy walk mechanism

We have studied the water dynamics in whole rabbit lens and fragments using H1-field-cycling nuclear magnetic resonance relaxometry. We have measured the proton spin–lattice relaxation time T1 as a function of the Larmor frequency. The data can be interpreted well using the reorientation mediated by translational displacement model in combination with the mechanism of bulk-mediated surface diffusion, where individual water molecules perform Lévy walks with a Cauchy diffusion propagator. This gives evidence of anomalous water surface diffusion on proteins in the rabbit lens. We assume that the lens protein surface topology can be modeled by a polyhedral structure of randomly oriented faces with individual correlation lengths s0. For the whole lens we obtained the most frequent s0 value of 2.5 nm whereas for fragments from the rabbit cortex and the nucleus we obtained values of 3 and 0.3 nm, respectively. The correlation length values obtained for the lens can be attributed to the short-range order of the lens proteins necessary for maintaining lens transparency.

Production of statistically nonstationary stochastic structure realizations for infrared background scene simulations

We describe the development of a 3-D statistically nonstationary earthlimb stochastic structure representation and its application to earthlimb infrared (IR) background structure simulations. An earthlimb viewing geometry is defined by the location of both observer and source in space. The line-of-sight tangent altitude is the minimum altitude of the trajectory, defined at the earth-centered perpendicular to the line of sight. The stochastic structure overlay is constructed from a 2-D diagonal cut through a 3-D matrix of correlated Gaussian deviates; each plane of the matrix represents a statistically constant representation of the 2-D correlation lengths at a given altitude above the earth. Each matrix plane is generated using successive 2-D fast Fourier transform routines that have empirical values of vertical and horizontal correlation lengths as input. The total deviate variance versus altitude is then scaled from empirical measurements of fluctuations in atmospheric density, temperature, and/or emissivity. These structure generators are used both as perturbations on input atmospheric data to IR radiance codes and as high-resolution overlays to earthlimb lR mean-radiance 2-D scenes. An IR structured scene realization and scene validation analysis is presented.

Inverting the Dirac matrix for SU(2) lattice gauge theory by means of parallel transported multigrid

We compare the convergence rates for inverting the Dirac matrix of a non-abelian gauge theory by the parallel transported multigrid algorithm (PTMG) and by the conjugate gradient (CG) approach. The test is carried out for SU(2) lattice gauge theory in two dimensions. The gauge field configurations are generated in the quenched approximation for various values of the gauge field correlation length ξ(β). We have performed runs for three different lattice sizes with the ratio ξ/ L kept fixed; L denotes the linear dimension of the square lattices used. As L increases, the PTMG becomes more and more efficient. On a 256×256 lattice with the bare quark mass m bare = 0.0005 and ξ = 20, the PTMG is at least ten times faster than the CG. It seems reasonable to expect similar results also in four dimensions.

Microtopographical roughness of oscillatory ripple fields.

Large-scale bottom topography measurements are being made with a number of sonar mapping systems, yet little is known of the small-scale relief of the seafloor. High-resolution roughness height measurements of the seafloor have been made using stereo photogrammetry. Roughness power spectra are generated from closely spaced height measurements in order to develop a valid stochastic model for fine-scale seafloor topography and, ultimately, to predict high-frequency acoustic scattering from the seafloor. The anisotropy inherent in an oscillatory ripple field gives a peculiar signature to the power-law decay of the roughness spectrum. Roughness power spectra are presented for the crest to crest and along-strike directions at four shallow-water sites. Comparisons of periodograms derived from storm-generated ripples off the Pacific, Atlantic, and Gulf of Mexico coasts show a strong dependence on grain size. Grain size constrains the possible ripple morphologies through grain-to-grain interactions characteristic of silt, fine sand, or coarse sand. Predictably, values of correlation length estimated from the spectra for the two orientations examined in the ripple fields are indicative of sediment type.

Static and dynamic behavior of semidilute polymer solutions

Reported results of dynamic light scattering experiments on semidilute solutions of linear non-charged polymers are reviewed. It is shown that, while for many systems the nature of the so-called slow modes may have a wide range of different causes, for a linear polymer in poor and moderately good solvents, the slow modes are mainly due to the effect of topological constraints. Values of static and dynamic correlation length reported by different research groups are compared with each other and with theory

Antiferromagnetic phase transition in Cd1-xMnxSe epilayers.

Neutron-diffraction spectra of molecular-beam-epitaxy-grown single-crystal zinc-blende films of ${\mathrm{Cd}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Mn}}_{\mathit{x}}$Se reveals the onset of type-III antiferromagnetic ordering (AFM-III) for x=0.70 and 0.75 at a sharp N\'eel temperature. The AFM-III order is long range, with correlation lengths of around 400 \AA{}, and the transition is of second order. This contrasts sharply with earlier studies of bulk ${\mathit{A}}_{1\mathrm{\ensuremath{-}}\mathit{x}}^{\mathrm{II}}$${\mathrm{Mn}}_{\mathit{x}}$${\mathit{B}}^{\mathrm{VI}}$ diluted magnetic semiconductors, where only short-range AFM-III correlations are observed, evolving gradually with decreasing temperature, and saturating at correlation length values less than 70 \AA{}.

The supermolecular structure of poly(vinyl chloride)–poly(methyl methacrylate) blends

AbstractInvestigations of the supermolecular structure of PVC/PMMA blends, covering a wide range of composition, are presented. It was found that a transition layer exists between PVC and PMMA phases. The thickness of the transition layer is independent of blend composition. The scattering intensity distribution function for blends is characteristic of isotropic, amorphous systems with a completely random distribution of phases. It was shown that scattering intensity distribution function may be used for calculation of a distribution, which corresponds a two‐phase system with sharp phase boundaries. Values of correlation lengths, inhomogeneity lengths, and specific surfaces were then calculated. A model of the supermolecular structure of PVC/PMMA blend was finally proposed.

Optimal Gaussian solutions of nonlinear stochastic partial differential equations

We present a linearization procedure of a stochastic partial differential equation for a vector field (X i (t,x)) (t∈[0, ∞),x∈R d ,i=l,...,n): ∂ t X i (t,x)=b i (X(t, x)) +D, ΔX i (t, x) + σ i f i (t, x). HereΔ is the Laplace-Beltrami operator inR d , and (f i (t,x)) is a Gaussian random field with 〈f i (t,x)f j (t′,x′)〉 = δ ij δ(t − t′)δ(x − x′). The procedure is a natural extension of the equivalent linearization for stochastic ordinary differential equations. The linearized solution is optimal in the sense that the distance between true and approximate solutions is minimal when it is measured by the Kullback-Leibler entropy. The procedure is applied to the scalar-valued Ginzburg-Landau model in R1 withb 1(z) =μz - vz 3. Stationary values of mean, variance, and correlation length are calculated. They almost agree with exact ones ifμ ≲ 1.24 (ν 2θ 1 4 /D 1 1/3:=μ c . Whenμ⩾μ c , there appear quasistationary states fluctuating around one of the bottoms of the potentialU(z) = ∫b 1(z)dz. The second moment at the quasistationary states almost agrees with the exact one. Transient phenomena are also discussed. Half-width at half-maximum of a structure function decays liket −1/2 for small t. The diffusion term∂ 2 X accelerates the relaxation from the neighborhood of an unstable initial stateX(0,x) ∼ 0.

Supercritical Correlation Length of Carbon Dioxide Along the Critical Isochore

Values of the total correlation length have been calculated in the hydrodynamical region by equating the critical part of measured values of the thermal diffusivity to the Kawasaki expression for the diffusivity. These new values of the correlation length are found to agree rather closely in the range $0.1l~\ensuremath{\Delta}Tl~10\ifmmode^\circ\else\textdegree\fi{}$ C with values calculated from (a) angular anisotropy data and (b) static compressibility data, the latter interpreted according to Ornstein-Zernike theory, with a constant direct correlation length ${R}_{0}=4.2$ \AA{}.

X-Ray Study of Critical Opalescence in Argon

The small-angle x-ray scattering from argon has been investigated at the critical pressure and at four other pressures over a range of temperatures above and below the liquid—vapor transition temperature for each pressure. For three of these pressures the angular distribution of the scattering was analyzed in terms of the Ornstein—Zernike theory of critical opalescence and found to be in good agreement with this theory. Values of the short-range correlation length and relative values of the isothermal compressibility were determined for each condition of pressure and temperature. For the conditions for which compressibilities can be found by numerical differentiation of the isotherms of Michels, Levelt, and De Graff, the compressibility values calculated by numerical differentiation are in good agreement with those obtained from the scattering curves.