THEORY OF THE PHONON BRANCHES IN THE INFRARED SPECTRUM OF SOLID HYDROGEN

1962 ◽  
Vol 40 (2) ◽  
pp. 163-178 ◽  
Author(s):  
J. D. Poll ◽  
J. Van Kranendonk
Keyword(s):  
Experimental Data ◽  
Absorption Spectrum ◽  
Infrared Absorption Spectrum ◽  
Solid Hydrogen ◽  
General Criterion ◽  
Lattice Vibrations ◽  
Mean Square ◽  
The Mean ◽  
Integrated Intensities ◽  
Absorption Features

The effect of the lattice vibrations on the infrared absorption spectrum of solid hydrogen is investigated theoretically. General expressions are derived for the integrated intensities of the phonon branches in the rotational and vibrational spectrum of solid parahydrogen. It is shown that the intensities of the pure rotational and vibrational absorption features are not appreciably affected by the lattice vibrations. A general criterion is derived for the vanishing of the contribution of instantaneous phonon processes to the integrated intensities of the phonon branches. The integrated intensities are expressed in terms of the mean square displacements of the molecules from their equilibrium positions. Explicit calculations are presented, based on the Einstein and Debye models for the lattice vibrations, and the results are compared with the available experimental data.

scholarly journals Mean Square Vibration Amplitudes in Zinc

1977 ◽  
Vol 30 (1) ◽  
pp. 105 ◽  
Author(s):  
DW Field
Keyword(s):  
Single Crystal ◽  
Debye Temperature ◽  
Mean Square ◽  
X Ray Diffraction ◽  
Zinc Single Crystal ◽  
X Ray ◽  
Structure Factors ◽  
Principal Directions ◽  
The Mean ◽  
Integrated Intensities

The structure factors of 98 independent reflections have been determined by measurement of the integrated intensities for X-ray diffraction from a zinc single crystal at 295 K. The mean square vibration amplitudes found for the two principal directions are' compared with 'other recent measurements. The X-ray Debye temperature determined from the data' is 207 � 3 K at 295 K.

Dynamic and Static Displacements of Atoms in B2-Phase of TiNi Alloy

2008 ◽  
Vol 59 ◽  
pp. 108-112
Author(s):  
Vyacheslav M. Gundyrev ◽  
Vitaly I. Zel'dovich
Keyword(s):  
Single Crystal ◽  
Crystal Lattice ◽  
Titanium Nickelide ◽  
Tini Alloy ◽  
Mean Square ◽  
Atomic Displacements ◽  
Structure Factors ◽  
The Mean ◽  
B2 Phase ◽  
Integrated Intensities

We measured integrated intensities of 26 reflections of the B2-phase of titanium nickelide single crystal and determined structure factors for these reflections. Based on the structure factors, mean squares of displacements of Ni and Ti atoms with respect to the crystal-lattice sites have been determined. After that we determined the mean squares of atomic displacements <u2>Ni and <u2>Ti in temperature range of existence of the B2-pase, at temperatures Т1=328 K and T2=376 K. We separated the mean squares of atomic displacements <u2>Ni and <u2>Ti into static and dynamic ones. The mean squares of dynamic displacements of Ni and Ti atoms are identical, but the mean square of static displacements is greater by a factor of 4.7 for Ni atoms than for Ti atoms. The Debye temperature calculated from the mean squares of displacements of Ni atoms is 360 K; that calculated for Ti atoms in a similar way is 390 K. The large value of complete atomic displacements in TiNi is due to static rather than dynamic displacements of atoms, mainly due to static displacements of nickel atoms.

scholarly journals Coding of Time-Varying Signals in Spike Trains of Integrate-and-Fire Neurons with Random Threshold

1996 ◽  
Vol 8 (1) ◽  
pp. 44-66 ◽  
Author(s):  
Fabrizio Gabbiani ◽  
Christof Koch
Keyword(s):  
Experimental Data ◽  
Information Transmission ◽  
Firing Rate ◽  
Mean Square Error ◽  
Model Neuron ◽  
Correlation Technique ◽  
Time Varying ◽  
Mean Square ◽  
Closed Expression ◽  
The Mean

Recently, methods of statistical estimation theory have been applied by Bialek and collaborators (1991) to reconstruct time-varying velocity signals and to investigate the processing of visual information by a directionally selective motion detector in the fly's visual system, the H1 cell. We summarize here our theoretical results obtained by studying these reconstructions starting from a simple model of H1 based on experimental data. Under additional technical assumptions, we derive a closed expression for the Fourier transform of the optimal reconstruction filter in terms of the statistics of the stimulus and the characteristics of the model neuron, such as its firing rate. It is shown that linear reconstruction filters will change in a nontrivial way if the statistics of the signal or the mean firing rate of the cell changes. Analytical expressions are then derived for the mean square error in the reconstructions and the lower bound on the rate of information transmission that was estimated experimentally by Bialek et al. (1991). For plausible values of the parameters, the model is in qualitative agreement with experimental data. We show that the rate of information transmission and mean square error represent different measures of the reconstructions: in particular, satisfactory reconstructions in terms of the mean square error can be achieved only using stimuli that are matched to the properties of the recorded cell. Finally, it is shown that at least for the class of models presented here, reconstruction methods can be understood as a generalization of the more familiar reverse-correlation technique.

scholarly journals Neutron Diffraction Determination of Mean-square Atomic Displacements in InAs and GaSb

1981 ◽  
Vol 34 (6) ◽  
pp. 689 ◽  
Author(s):  
JE Tibballs ◽  
SM Feteris ◽  
Z Barnea
Keyword(s):  
Bragg Reflection ◽  
Perturbation Approach ◽  
Mean Square ◽  
Thermal Diffuse Scattering ◽  
Atomic Displacements ◽  
Diffraction Determination ◽  
Potential Perturbation ◽  
The Mean ◽  
The One ◽  
Integrated Intensities

Integrated intensities for Bragg reflection of neutrons from single crystals of the III-V compounds InAs and GaSb have been measured at room temperature. The data were collected at two wavelengths, 0'947 and 1�241 A, in order' to establish the adequacy of a correction for moderate to severe anisotropic extinction. Data were also obtained for InAs at four temperatures from 408 to 933 K. Corrections for thermal diffuse scattering were applied. The results were analysed in the one-particle potential perturbation approximation with terms to fourth order in the atomic displacements u == (ut, U2, U3)' At 296 K, the mean-square components <u;) determined were: In, 0'0116(2) A2; As, 0'0102(1) A2; and Ga, 0,0120(3) A2; Sb, 0,0107(3) A2. The third-order coefficients for InAs are comparable with those for Si and Ge, while those for GaSb are comparable with those for zinc cha1cogenides. Below 400 K, the mean-square displacements in InAs decrease faster than predicted by the present perturbation approach.

scholarly journals Asymptotic Properties of MSE Estimate for the False Discovery Rate Controlling Procedures in Multiple Hypothesis Testing

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1913
Author(s):  
Sofia Palionnaya ◽  
Oleg Shestakov
Keyword(s):  
Experimental Data ◽  
False Discovery Rate ◽  
Mean Square Error ◽  
Asymptotic Properties ◽  
Multiple Hypothesis Testing ◽  
Mean Square ◽  
Practical Applications ◽  
False Discovery ◽  
Wide Range ◽  
The Mean

Problems with analyzing and processing high-dimensional random vectors arise in a wide variety of areas. Important practical tasks are economical representation, searching for significant features, and removal of insignificant (noise) features. These tasks are fundamentally important for a wide class of practical applications, such as genetic chain analysis, encephalography, spectrography, video and audio processing, and a number of others. Current research in this area includes a wide range of papers devoted to various filtering methods based on the sparse representation of the obtained experimental data and statistical procedures for their processing. One of the most popular approaches to constructing statistical estimates of regularities in experimental data is the procedure of multiple testing of hypotheses about the significance of observations. In this paper, we consider a procedure based on the false discovery rate (FDR) measure that controls the expected percentage of false rejections of the null hypothesis. We analyze the asymptotic properties of the mean-square error estimate for this procedure and prove the statements about the asymptotic normality of this estimate. The obtained results make it possible to construct asymptotic confidence intervals for the mean-square error of the FDR method using only the observed data.

Predicting some Effects of Lattice Vibrations on Proton Scattering Patterns

1970 ◽  
Vol 14 ◽  
pp. 1-10
Author(s):  
C. S. Barrett
Keyword(s):  
Temperature Factor ◽  
Lattice Vibrations ◽  
Proton Scattering ◽  
Mean Square ◽  
X Ray Diffraction ◽  
X Ray ◽  
Structure Factors ◽  
Integrated Intensity ◽  
The Mean ◽  
Thermal Vibrations

AbstractA method of predicting the approximate relative intensities of lines in proton blocking patterns recently proposed, which is based on summing the squares of structure factors for the various orders of reflection of a plane, is found to predict certain effects of lattice vibrations on the lines in some recently reported patterns. The mean square amplitude of vibration enters the calculations through a Debye-Waller temperature factor like that used in X-ray diffraction. When patterns are compared for groups of crystals that are nearly identical except for this temperature factor, the qualitative predictions by this method agree with the observations. If it is also arbitrarily assumed that the integrated intensity dip at a spot where lines intersect is approximated by summing the calculated Integrated intensity dips for all of the lines crossing at the spot, one has a simple and convenient method of predicting relative spot intensities. Such calculations have been successful in establishing the order of decreasing intensity for most of the spots along a given line, with several different kinds of crystals. This method also serves to predict qualitatively how prominent the spots appear relative to the lines, in general, in patterns of crystals that differ appreciably only in the amplitude of the thermal vibrations.

THEORY OF THE Q BRANCH OF THE INFRARED SPECTRUM OF SOLID HYDROGEN

1964 ◽  
Vol 42 (5) ◽  
pp. 980-1003 ◽  
Author(s):  
V. F. Sears ◽  
J. Van Kranendonk
Keyword(s):  
Experimental Data ◽  
Infrared Spectrum ◽  
Absorption Line ◽  
Line Profile ◽  
Solid Hydrogen ◽  
Total Width ◽  
Percolation Problem ◽  
Integrated Intensity ◽  
Integrated Intensities ◽  
Theoretical Results

The theory of the zero-phonon Q branch of the infrared spectrum of solid hydrogen is developed. At low ortho-concentrations the spectrum can be analyzed in terms of transitions due to single and pairs of neighboring ortho-molecules. The Q1(1) transitions due to single ortho-molecules give rise to a sharp absorption line, the Q2(0) transitions to a band with a total width of about 3 cm−1 and a line profile following approximately a Δν3/2 law. The integrated intensities of these lines are calculated and compared with the experimental data. The Q1(1) and Q1(0) transitions due to pairs of ortho-molecules give rise to a number of components resulting from the removal of the ninefold degeneracy of the orientational state of the pair of ortho-molecules by the quadrupole–quadrupole interaction. The intensities and frequency separations of these components are calculated. Finally, a calculation is presented of the total integrated intensity of the zero-phonon Q branch at arbitrary ortho-concentrations. These theoretical results are of importance for the study of the percolation problem in solid hydrogen, and of the order-disorder transition taking place at high ortho-concentrations.

Lattice Dynamics of Molybdenum and Chromium

1980 ◽  
Vol 35 (2) ◽  
pp. 230-235
Author(s):  
B. P. Singh ◽  
L. P. Pathak ◽  
M. P. Hemkar
Keyword(s):  
Experimental Data ◽  
Temperature Dependence ◽  
Lattice Dynamics ◽  
Waller Factor ◽  
Mean Square ◽  
Frequency Wave ◽  
Debye Waller Factor ◽  
Nearest Neighbours ◽  
The Mean ◽  
First Time

Abstract The frequency-wave vector dispersion relations, the frequency spectrum, the Debye temperature, the temperature dependence of the Debye-Waller factor and the mean square displacements of the atoms molybdenum and chromium, the metals for which long range forces are also important, have been computed on the basis of the extended improved Fielek model for BCC transition metals. The model considers, for the first time the d shell-d shell central interactions upto next-nearest-neighbours. The calculated results show a satisfactory agreement with the available experimental data.

The Bordeaux Automatic Meridian Circle

1978 ◽  
Vol 48 ◽  
pp. 227-228
Author(s):  
Y. Requième
Keyword(s):  
Mean Square Error ◽  
Mean Square ◽  
Meridian Circle ◽  
The Mean ◽  
Full Automation

In spite of important delays in the initial planning, the full automation of the Bordeaux meridian circle is progressing well and will be ready for regular observations by the middle of the next year. It is expected that the mean square error for one observation will be about ±0.”10 in the two coordinates for declinations up to 87°.

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